Methodology for distinguishing between
man's influence and climatic effects
on the hydrological cycle
J.C. Refsgaard,
W.M. Alley and
V.S. Vuglinsky
IHP-III Project 6.3
Unesco, Pans, 1989
s c -89/."3- 22
The designations cmployed and the presentation o f material throq$i;out
the publication do not imply the expression o f any opinion
whatsoever on the parr o f Unesco concerning the legal-status
of any country, territory, city or o f its authorities, or
concerning the delimitation of its frontiers or boundaries.
PREFACE
A l t h o u g h t h e t o t a l amount o f w a t e r on E a r t h i s g e n e r a l l y assumed t o have r e mained v i r t u a l l y c o n s t a n t during r e c o r d e d h i s t o r y ,
p e r i o d s o f f l o o d and
d r o u g h t have c h a l l e n g e d t h e i n t e l l e c t o f man t o have t h e c a p a c i t y t o c o n t r o l
t h e w a t e r r e s o u r c e s a v a i l a b l e t o h i m . C u r r e n t l y , t h e r a p i d g r o w t h o f popul a t i o n , t o g e t h e r w i t h t h e e x t e n s i o n o f i r r i g a t e d a g r i c u l t u r e and i n d u s t r i a l
development, a r e s t r e s s i n g t h e q u a n t i t y and q u a l i t y a s p e c t s o f t h e n a t u r a l
system. Because o f t h e i n c r e a s i n g problems, man has begun t o r e a l i z e t h a t he
can no l o n g e r f o l l o w a "use and d i s c a r d " p h i l o s o p h y
e i t h e r w i t h water resources o r any o t h e r n a t u r a l r e s o u r c e . As a r e s u l t , t h e need f o r a c o n s i s t e n t
p o l i c y o f r a t i o n a l management o f w a t e r r e s o u r c e s has become e v i d e n t .
--
R a t i o n a l w a t e r management, however, s h o u l d b e founded upon a t h o r o u g h
u n d e r s t a n d i n g o f w a t e r a v a i l a b i l i t y and movement. Thus, as a c o n t r i b u t i o n t o
t h e s o l u t i o n o f t h e w o r l d ' s w a t e r problems, Unesco, i n 1985, began t h e f i r s t
w o r l d w i d e programme o f s t u d i e s o f t h e h y d r o l o g i c a l c y c l e -- t h e I n t e r n a t i o n a l
H y d r o l o g i c a l Decade ( I H D ) . The r e s e a r c h programme was complemented by a m a j o r
e f f o r t i n t h e f i e l d o f h y d r o l o g i c a l e d u c a t i o n and t r a i n i n g . The a c t i v i t i e s
u n d e r t a k e n during t h e Decade p r o v e d t o b e o f g r e a t i n t e r e s t and v a l u e t o
Member S t a t e s . B y t h e end o f t h a t p e r i o d , a m a j o r i t y o f Unesco's Member S t a t e s
h a d formed I H D N a t i o n a l Committees t o c a r r y o u t t h e r e l e v a n t n a t i o n a l a c t i v i t i e s and t o p a r t i c i p a t e i n r e g i o n a l and i n t e r n a t i o n a l c o - o p e r a t i o n w i t h i n t h e
I H D programme. The knowledge o f t h e w o r l d ' s w a t e r r e s o u r c e s as an i n d e p e n d e n t
p r o f e s s i o n a l o p t i o n and f a c i l i t i e s f o r t h e t r a i n i n g o f h y d r o l o g i s t s h a d been
developed.
Conscious o f t h e need t o expand upon t h e e f f o r t s i n i t i a t e d d u r i n g t h e
I n t e r n a t i o n a l H y d r o l o g i c a l Decade,
and,
f o l l o w i n g t h e recommendations o f
Member S t a t e s , Unesco, i n 1975, l a u n c h e d a new l o n g - t e r m i n t e r g o v e r n m e n t a l
programme , t h e I n t e r n a t i o n a l H y d r o l o g i c a l Programme (IHP) , t o f o l l o w t h e Decade.
A l t h o u g h t h e I H P i s b a s i c a l l y a s c i e n t i f i c and e d u c a t i o n a l programme,
Unesco has been aware f r o m t h e b e g i n n i n g o f a need t o d i r e c t i t s a c t i v i t i e s
towards t h e p r a c t i c a l s o l u t i o n s o f t h e w o r l d ' s v e r y r e a l w a t e r r e s o u r c e s p r o b lems. A c c o r d i n g l y , and i n l i n e w i t h t h e recommendations o f t h e 1977 U n i t e d
N a t i o n s Water Conference, t h e o b j e c t i v e s o f t h e I n t e r n a t i o n a l H y d r o l o g i c a l
Programme have been g r a d u a l l y expanded i n o r d e r t o c o v e r n o t o n l y h y d r o l o g i c a l
p r o c e s s e s c o n s i d e r e d i n i n t e r r e l a t i o n s h i p w i t h t h e environment and human act i v i t i e s , but a l s o t h e s c i e n t i f i c a s p e c t s o f m u l t i - p u r p o s e u t i l i z a t i o n and
c o n s e r v a t i o n of w a t e r r e s o u r c e s t o meet t h e needs o f economic and s o c i a l development. Thus, w h i l e m a i n t a i n i n g I H P ' s s c i e n t i f i c concept, t h e o b j e c t i v e s
have s h i f t e d p e r c e p t i b l y towards a m u l t i d i s c i p l i n a r y approach t o t h e assessm e n t , p l a n n i n g and r a t i o n a l management o f w a t e r r e s o u r c e s .
As p a r t o f IJnesco's c o n t r i b u t i o n t o t h e o b j e c t i v e s o f t h e I H P , t w o publ i c a t i o n s e r i e s a r e i s s u e d : " S t u d i e s and R e p o r t s i n H y d r o l o g y " and " T e c h n i c a l
Papers i n H y d r o l o g y " . I n a d d i t i o n t o t h e s e p u b l i c a t i o n s , and i n o r d e r t o exp e d i t e exchange o f i n f o r m a t i o n , some works a r e i s s u e d i n t h e f o r m o f T e c h n i c a l
Documents.
ABSTRACT
The h y d r o l o g i c a l c y c l e i s i n f l u e n c e d b o t h b y t h e c l i m a t e and by catchment
c h a r a c t e r i s t i c s such as topography,
geology,
soil,
vegetation,
and w a t e r
development. A methodology i s p r e s e n t e d f o r d i s t i n g u i s h i n g between t h e e f f e c t s
o f man's a c t i v i t y and c l i m a t e on t h e h y d r o l o g i c a l c y c l e , i n p a r t i c u l a r streamf l o w and groundwater. The methodology i s based on j o i n t a p p l i c a t i o n o f s t a t i s t i c a l t r e n d t e s t i n g methods and h y d r o l o g i c a l ( o r s t a t i s t i c a l r e g r e s s i o n )
models o f s t r e a m f l o w o r groundwater. The methodology i s i l l u s t r a t e d b y two
case s t u d i e s .
TAIjLE OF CONTENTS
Page
FOREWORD
1.
2.
3.
INTRODUCTION
1-1
1.1
1.2
1.3
1-1
1-2
1-4
SUMMARY AND RECOMMENDATIONS
2-1
2.1
2.2
2.3
2-1
2-3
2-3
3.3
5.
Methodology
State of the A r t
Recommendations
HYDROLOGICAL TOOLS
3.1
3.2
4.
Background
Factors A f f e c t i n g the H y d r o l o g i c a l C y c l e
Contents o f the Report
Introduction
D e t e r m i n i s t i c Models
3.2.1
E m p i r i c a l models
3.2.2
Lumped, c o n c e p t u a l m o d e l s
3.2.3
D i s t r i b u t e d , p h y s i c a l l y based m o d e l s
3.2.4
S e l e c t i o n o f appropriate m o d e l type
3.2.5
V a l i d a t i o n o f hydrological models
S t a t i s t i c a l Models
3-1
3-1
3-1
3-2
3-3
3-4
3-5
3-7
3-8
STATISTICAL METHODS
4-1
4.1
4.2
4.3
4.4
4-1
4-3
4-3
4-5
Introduction
S t e p Trends
Monotonic Trends
Complications
METHODOLOGY FOR DISTINGUISHING BETWEEN MAN'S
INFLUENCE AND CLIMATE V A R I A B I L I T Y
5.1
5.2
5.3
5.4
5.5
5.6
Introduction
STEP 1: D e t e r m i n a t i o n o f S t e p o r M o n o t o n i c
Trend Analysis
STEP 2 :
S e l e c t i o n of M o d e l Type
STEP 3:
Model C a l i b r a t i o n , V a l i d a t i o n
and A p p l i c a t i o n
5.4.1
Lumped, c o n c e p t u a l m o d e l s
5.4.2
D i s t r i b u t e d , p h y s i c a l l y based m o d e l s
5.4.3
S t a t i s t i c a l regression m o d e l s
Trend T e s t
STEP 4:
5.5.1
No m o d e l
5.5.2
Lumped, conceptual m o d e l s
5.5.3
D i s t r i b u t e d , p h y s i c a l l y based m o d e l s
5.5.4
S t a t i s t i c a l regression models
STEP 5:
Further H y d r o l o g i c a l A n a l y s i s
5.6.1
No m o d e l
5.6.2
Lumped, conceptual m o d e l
5.6.3
D i s t r i b u t e d , p h y s i c a l l y based m o d e l
5.6.4
S t a t i s t i c a l r e g r e s s i o n models
5-1
5-1
5-1
5-3
5-4
5-4
5-5
5-8
5-8
5-8
5-8
5-9
5-9
5-11
5-11
5-11
5-11
5-12
Page
G.
REFERENCES
6- 1
7.
CASE STUDIES
7-1
7.1
7.2
7- 1
7- 2
7.3
Introduction
Groundwater Development i n t h e Kqge A and
Suss Catchments, Denmark
7.2.1
D e s c r i p t i o n o f catchments and
h y d r o l o g i c a l models
7.2.2
Example 1 : Kqge A
7.2.3
Example 2 : Sus; a t V e t t e r s l e v
7.2.4
References
The B l u e R i v e r B a s i n , Nebraska, USA
APPENDIX A :
I n f l u e n c e o f G l o b a l C l i m a t e Changes on Water Resources.
(M.1. Budyko and K.Y. V i n n i k o v )
7- 2
7-5
7-8
7-11
7-12
FOREWORD
T h i s r e p o r t o n "Methodology f o r D i s t i n g u i s h i n g between Man's I n f l u e n c e and
C l i m a t i c E f f e c t s on t h e H y d r o l o g i c a l C y c l e " emanates f r o m t h e I n t e r n a t i o n a l
H y d r o l o g i c a l Programme
(IHP)
Intergovernmental
C o u n c i l which,
i n 1984,
appointed t h e f o l l o w i n g f o u r r a p p o r t e u r s f o r t h e I H P - I 1 1 P r o j e c t 6.3
Mr.
,
Mr.
J.C.
Refsgaard
( D a n i s h H y d r a u l i c I n s t i t u t e , Denmark)
Rapporteur
Mr.
W.M.
Alley
(U.S.
Mr.
D.A.
Kraijenhoff
( A g r i c u l t u r a l U n i v e r s i t y Wageningen, N e t h e r l a n d s )
CO-rapporteur
Mr.
V.S.
Vuglinsky
( S t a t e H y d r o l o g i c a l I n s t i t u t e Leningrad,
CO-rapporteur
D.A.
G e o l o g i c a l Survey, U S A ) ,
Principal
CO-rapporteur
USSR)
,
,
K r a i j e n h o f f w i t h d r e w f r o m t h e group i n August 1988.
The Terms o f Reference drawn b y t h e IHP C o u n c i l f o r t h e p r o j e c t a r e :
o
E s t a b l i s h m e n t o f a methodology f o r d i s t i n g u i s h i n g between man's i n f l u e n c e
and c l i m a t e v a r i a b i l i t y i n t h e h y d r o l o g i c a l c y c l e , i n p a r t i c u l a r streamf l o w and groundwater.
o
Preparation o f a state-of-the-art
r e p o r t on m e t h o d o l o g i e s f o r d i s t i n g u i s h i n g between man's i n f l u e n c e and c l i m a t e v a r i a b i l i t y i n t h e h y d r o l o g i c a l cycle.
The p r i n c i p a l r a p p o r t e u r p a r t i c i p a t e d i n t h e t h i r d p l a n n i n g m e e t i n g o n
t h e W o r l d C l i m a t e Programme-Water Geneva 1 8 - 2 2 November, 1985, f o r c o o r d i n a t i o n o f t h i s p r o j e c t w i t h o t h e r r e l a t e d o n g o i n g a c t i v i t i e s . The r a p p o r t e u r s
m e t f o r a w o r k i n g s e s s i o n i n P a r i s , 18-22 May, 1987. The f i n a l p r o j e c t coo r d i n a t i o n was c a r r i e d o u t i n c o n n e c t i o n w i t h t h e f o u r t h p l a n n i n g m e e t i n g on
t h e World C l i m a t e Programme - Water, i n P a r i s September 12-16,
1988, where
t h r e e of t h e rapporteurs p a r t i c i p a t e d .
The work h a s b e e n s u p p o r t e d by a s s i s t a n c e f r o m t h e D i v i s i o n o f Water
Science o f t h e U n i t e d N a t i o n s E d u c a t i o n a l , S c i e n t i f i c and C u l t u r a l O r g a n i z a t i o n (UNESCO) r e p r e s e n t e d by M r . M . I .
Rusinov up t o August 1988 and M r . W.H.
G i l b r i c h f o r t h e remaining p e r i o d .
1-1
1.
INTRODUCTION
1.1 Backsround
Man's development o f w a t e r r e s o u r c e s h a s r e s u l t e d i n g r e a t economic and s o c i a l
b e n e f i t s b y p r o v i d i n g f a v o u r a b l e environments f o r a g r i c u l t u r e , i n d u s t r y and
l i v i n g c o n d i t i o n s . However, i f n o t c a r e f u l l y planned, a d v e r s e e f f e c t s may a l s o
occur. The assessment o f t h e i n f l u e n c e o f man's management a c t i v i t i e s o n t h e
h y d r o l o g i c a l c y c l e and o n t h e W o r l d ' s c l i m a t e i s t h e r e f o r e becoming a p r o b l e m
o f i n c r e a s i n g concern.
The e f f e c t o f human a c t i v i t y on t h e l a n d and w a t e r r e s o u r c e s o f t h e e a r t h
has been v i s i b l e s i n c e man s t a r t e d a g r i c u l t u r a l p r o d u c t i o n . However, w i t h t h e
r a p i d i n c r e a s e i n p o p u l a t i o n , a g r i c u l t u r a l p r o d u c t i o n and i n d u s t r i a l i z a t i o n
man's i n f l u e n c e on t h e h y d r o l o g i c a l c y c l e has i n c r e a s e d g r e a t l y i n r e c e n t decades. The p r e d i c t i o n o f t h e h y d r o l o g i c a l e f f e c t s o f man's a c t i v i t y h a s t h e r e f o r e become i n c r e a s i n g l y i m p o r t a n t .
The e f f e c t o f human a c t i v i t y on t h e g l o b a l c l i m a t e h a s been n e g l i g i b l e o r
n o t r e c o g n i z e d u n t i l r e c e n t l y . However, t h e r e i s i n c r e a s i n g c o n c e r n a b o u t mani n d u c e d g l o b a l c l i m a t e changes i n t h e n e x t few decades r e s u l t i n g f r o m i n c r e a s i n g c o n c e n t r a t i o n s o f carbon d i o x i d e and o t h e r t r a c e gases. One o f t h e most
i m p o r t a n t i m p a c t s t o s o c i e t y o f such f u t u r e c l i m a t e changes w i l l be changes i n
t h e water resources a v a i l a b i l i t y .
I n t h e p r e s e n t r e p o r t t h e t e r m c l i m a t e v a r i a b i l i t y i s d e f i n e d as t h e var i a t i o n f r o m y e a r t o y e a r , w h i l e t h e t e r m c l i m a t e change i s d e f i n e d as a s i g n i f i c a n t change i n c l i m a t e v a r i a b l e s f r o m one p e r i o d t o a n o t h e r p e r i o d . C l i mate v a r i a b i l i t y i s g e n e r a l l y an e f f e c t o f n a t u r a l c o n d i t i o n s , w h i l e c l i m a t e
change can be caused b o t h by n a t u r a l c o n d i t i o n s and by man's a c t i v i t y .
Long h y d r o l o g i c a l and m e t e o r o l o g i c a l t i m e s e r i e s may b e a n a l y s e d w i t h t h e
o b j e c t i v e o f making i n f e r e n c e s r e g a r d i n g c l i m a t e v a r i a b i l i t y and i t s e f f e c t on
t h e h y d r o l o g i c a l regime. Such r e s e a r c h s t u d i e s a r e p r e s e n t l y b e i n g c a r r i e d o u t
w i t h i n t h e framework o f t h e W o r l d C l i m a t e Programme. I n t h i s c o n n e c t i o n , i t i s
necessary t o be a b l e t o i d e n t i f y and t o e l i m i n a t e t h e e f f e c t s o f man's a c t i v i t y from t h e h y d r o l o g i c a l t i m e s e r i e s .
S i m i l a r l y , l o n g h y d r o l o g i c a l and m e t e o r o l o g i c a l t i m e s e r i e s can b e anal y s e d f o r i n v e s t i g a t i n g t h e e f f e c t s o f man's a c t i v i t y . However, o f t e n t h e mani n d u c e d changes a r e s m a l l compared t o t h e e f f e c t s o f c l i m a t e v a r i a b i l i t y . F u r thermore, t h e changes a r e o f t e n masked b y measurement e r r o r s . D e t e c t i o n o f
such changes i s t h e r e f o r e d i f f i c u l t , e s p e c i a l l y f o r s h o r t o b s e r v a t i o n p e r i o d s .
Thus i t i s i m p o r t a n t t o e s t a b l i s h a methodology f o r d i s t i n g u i s h i n g between t h e e f f e c t s o f man's i n f l u e n c e and c l i m a t e on t h e h y d r o l o g i c a l c y c l e .
1-2
Factors A f f e c t i n g t h e Hydrological Cycle
1.2
T h e i n t e r a c t i o n s between man's a c t i v i t y , t h e c l i m a t e , t h e catchment
t e r i s t i c s and t h e h y d r o l o g i c a l c y c l e a r e i l l u s t r a t e d i n F i g . 1 . 2 . 1 .
charac-
Man's a c t i v i t i e s a r e i n f l u e n c e d b y t h e c l i m a t i c and t h e catchment c o n d i t i o n s . T h i s i s o f t e n most obvious f o r man's a g r i c u l t u r a l a c t i v i t i e s , but i s
generally valid.
I n t h e p r e s e n t t e x t t h e t e r m catchment c h a r a c t e r i s t i c s i n a d d i t i o n t o
n a t u r a l c h a r a c t e r i s t i c s such as geology, s o i l s , and topography a l s o i n c l u d e s
man-made s t r u c t u r e s such as w a t e r d i v e r s i o n and groundwater pumpage schemes.
ACTIVITY
MAN'S
o
forestry
o
agriculture
o
urbanization
o
industrialization
o
water
r e s o u r c e s management
CATCHMENT C H A R A C T E R L S T I C S
CLIMATE
(either natural or
i n f l u e n c e d b y man)
o
topography
o
precipitation
o
radiation
o
temperature
o
l a k e s a n d swamps
o
wind
o
d r a i n a g e system
o
h u m i d i t y
o
vegetation,
o
hydraulic
geology,
soils,
l a n d use
structures
HYDROLOGICAL CYCLE
Fig. 1.2.1
o
precipitation
o
s o i l moisture
o
evapotranspiration
o
groundwater
o
streamflow
The p r i n c i p a l i n t e r a c t i o n s among man's a c t i v i t y , t h e c l i m a t e ,
catchment c h a r a c t e r i s t i c s and t h e h y d r o l o g i c a l c y c l e .
the
1-3
Man's a c t i v i t y can have a c o n s i d e r a b l e i m p a c t on t h e catchment c h a r a c t e r i s t i c s and hence on t h e h y d r o l o g i c a l regime. Depending o n t h e n a t u r e o f t h i s
i m p a c t , man's a c t i v i t y may b e c l a s s i f i e d i n t o t h e f o l l o w i n g c a t e g o r i e s .
o
A c t i v i t i e s l e a d i n g t o changes i n t h e v e g e t a t i o n and l a n d u s e ( d e f o r e s t a t i o n and a f f o r e s t a t i o n , a g r i c u l t u r e , d r a i n a g e o f swamps and m a r s h - r i d d e n
areas, u r b a n i z a t i o n , e t c . )
o
A c t i v i t i e s l e a d i n g t o changes i n t h e topography and d r a i n a g e system (cons t r u c t i o n o f v a r i o u s h y d r a u l i c s t r u c t u r e s such as dams, b a r r a g e s , embankments , p o l d e r s , t e r r a c e s , and c o n t o u r p l o w i n g )
.
o
A c t i v i t i e s l e a d i n g t o d i r e c t and i n d i r e c t w a t e r d i v e r s i o n s f r o m o r t o t h e
r i v e r o r t h e groundwater system ( s u r f a c e and groundwater a b s t r a c t i o n f o r
use o u t s i d e t h e a r e a , e f f l u e n t d i s c h a r g e , a r t i f i c i a l groundwater r e charge, d r a i n a g e , i r r i g a t i o n , e t c . )
The e x t e n t of man's i n f l u e n c e on t h e catchment c h a r a c t e r i s t i c s c a n v a r y ,
r a n g i n g from n e a r zero i n f l u e n c e i n t h e cases o f n a t u r a l f o r e s t s and o t h e r
n o n - c u l t i v a t e d areas w i t h o u t any w a t e r development t o c l o s e t o 1 0 0 % i n f l u e n c e
i n t h e case of a p o l d e r area, where t h e topography, d r a i n a g e system and
v e g e t a t i o n a r e man-made and where t h e h y d r o l o g i c a l system i s more o r l e s s comp l e t e l y regulated.
Man's a c t i v i t i e s can have some i n f l u e n c e on t h e l o c a l c l i m a t e (hundreds
t o thousands of square k i l o m e t r e s ) . F o r example, i t h a s been documented t h a t
u r b a n i z a t i o n i n some cases can cause a s i g n i f i c a n t i n c r e a s e i n t h e h i g h i n t e n s i t y r a i n f a l l . W i t h r e s p e c t t o t h e r e g i o n a l and g l o b a l c l i m a t e , man's a c t i v i t i e s have i n t h e p a s t a p p a r e n t l y o n l y h a d n e g l i g i b l e e f f e c t s on t h e h y d r o l o g i c a l c y c l e . The r e s e a r c h r e s u l t s o b t a i n e d b y S o v i e t s c i e n t i s t s show, f o r
example, t h a t i n case o f l y g e - s c a l e i r r i g a t i o n p r o j e c t s , c o v e r i n g an a r e a i n
t h e o r d e r o f 400-500,000 k m , t h e change i n t h e a n n u a l p r e c i p i t a t i o n does n o t
exceed 1 - 2 % ( G r i g o r i e v a e t a l . 1 9 8 3 ) .
However, man's a c t i v i t y may cause a s i g n i f i c a n t change i n t h e g l o b a l c l i mate i n t h e f u t u r e . Thus, many s c i e n t i s t s s u p p o r t t h e h y p o t h e s i s t h a t t h e i n c r e a s e o f c a r b o n d i o x i d e c o n c e n t r a t i o n i n t h e atmosphere due t o t h e burning o f
f o s s i l f u e l s w i l l cause a g l o b a l t e m p e r a t u r e i n c r e a s e i n t h e coming decades,
(see Appendix A o f t h i s r e p o r t ) . T h i s i n c r e a s e o f t h e mean g l o b a l a i r temperat u r e may have s i g n i f i c a n t e f f e c t s on t h e h y d r o l o g i c a l regime i n v a r i o u s r e gions o f t h e Earth.
The h y d r o l o g i c a l c y c l e i s a f f e c t e d by b o t h t h e c l i m a t e and t h e catchment
c h a r a c t e r i s t i c s . B o t h catchment c h a r a c t e r i s t i c s and c l i m a t e a r e i n turn a f f e c t e d b y t h e h y d r o l o g i c a l c y c l e . F o r example, t h e w a t e r a v a i l a b i l i t y i n t h e
h y d r o l o g i c a l c y c l e may a f f e c t catchment c h a r a c t e r i s t i c s such as t h e t y p e and
t h e e x t e n t of vegetation. S i m i l a r l y , t h e h y d r o l o g i c a l c y c l e , i n c l u d i n g t h e
exchange o f w a t e r and energy a c r o s s t h e s o i l s u r f a c e t h r o u g h e v a p o r a t i o n , has
l a r g e e f f e c t s on t h e c l i m a t e .
Man's i n f l u e n c e on t h e c l i m a t e i s b e i n g s t u d i e d under t h e W o r l d C l i m a t e
Programme. The i m p a c t o f c l i m a t e v a r i a b i l i t y on t h e h y d r o l o g i c a l c y c l e i s a l s o
b e i n g s t u d i e d u n d e r t h e w o r l d C l i m a t e Programme, e.g.
Klemes ( 1 9 8 5 ) . Man's
i n f l u e n c e on t h e h y d r o l o g i c a l c y c l e by a f f e c t i n g t h e catchment c h a r a c t e r i s t i c s
has been documented by v a r i o u s s c i e n t i s t s , e.g. UNESCO (1980).
1-4
The c o m p l e x i t y o f t h e s e i n t e r r e l a t i o n s may be i l l u s t r a t e d b y an example.
I f t h e c l i m a t e , e i t h e r a s a consequence o f a change o r as t h e r e s u l t o f l o n g t e r m v a r i a b i l i t y , becomes d r y e r ( l e s s p r e c i p i t a t i o n ) € o r a p e r i o d o f some decades man may change t h e a g r i c u l t u r a l p r a c t i c e s from i r r i g a t e d f a r m i n g t o d r y
l a n d f a r m i n g . T h i s change i n l a n d use w i l l reduce t h e e v a p o t r a n s p i r a t i o n l o s s es and t h u s t o some e x t e n t compensate f o r t h e r e d u c t i o n i n p r e c i p i t a t i o n . I f
s t r e a m f l o w r e c o r d s f r o m two p e r i o d s , b e f o r e and a f t e r t h e c l i m a t e change, r e s p e c t i v e l y , w e r e a n a l y s e d assuming no change i n e v a p o t r a n s p i r a t i o n l o s s e s , t h e
c o n c l u s i o n s would u n d e r e s t i m a t e t h e s t r e a m f l o w r e d u c t i o n caused b y t h e c l i m a t e
change.
I n o t h e r cases, man's a c t i o n s a f t e r a c l i m a t e change may a c c e l e r a t e t h e
c l i m a t e e f f e c t s and c r e a t e a d d i t i o n a l adverse e f f e c t s . T h e r e f o r e , i t i s v e r y
i m p o r t a n t t o account f o r c l i m a t e v a r i a b i l i t y and man-induced catchment changes
i n s e p a r a t e ways.
Man's i m p a c t o n t h e h y d r o l o g i c a l c y c l e can b e a r e s u l t o f b o t h mani n d u c e d c l i m a t e changes o r man-induced changes i n catchment c h a r a c t e r i s t i c s .
I n t h e p r e s e n t r e p o r t , however, t h e t e r m man's i n f l u e n c e on t h e h y d r o l o g i c a l
c y c l e , w i l l o n l y r e f e r t o t h e e f f e c t s i n d u c e d b y catchment changes. F u r t h e r more , when c o n s i d e r i n g t h e c l i m a t e ' s i n f l u e n c e on t h e h y d r o l o g i c a l c y c l e t.he
p r e s e n t r e p o r t does n o t d i s t i n g u i s h between t h e e f f e c t s o f c l i m a t e v a r i a b i l i t y
and c l i m a t e changes. Thus, t h i s r e p o r t i s r e s t r i c t e d i n scope t o d i s t i n g u i s h i R g t h e i n f l u e n c e o f a r r o w A i n F i g . 1.2.1 f r o m arrow B.
1.3
Contents o f t h e Report
I n a d d i t i o n t o t h i s i n t r o d u c t o r y , chapter,
t e r s and one appendix.
t h e r e p o r t c o n t a i n s f o u r main chap-
C h a p t e r 2 c o n t a i n s a b r i e f summary o f t h e proposed methodology, a b r i e f
summary o f t h e s t a t e o f t h e a r t , and some recommendations r e g a r d i n g t h e need
for future activities w i t h i n t h i s field.
C h a p t e r 3 g i v e s an i n t r o d u c t i o n t o t h e v a r i o u s h y d r o l o g i c a l t o o l s which
can be used f o r a s s e s s i n g t h e h y d r o l o g i c a l i m p a c t o f c l i m a t e and man's a c t i v i t y . I n Chapter 4 a p r e s e n t a t i o n i s g i v e n o f t h e a p p r o p r i a t e s t a t i s t i c a l t e s t
p r o c e d u r e s f o r t r e n d t e s t s . These c h a p t e r s do n o t p r e s e n t any new methods, and
t h e y can b e seen as a necessary background f o r Chapter 5,
I n Chapter 5 t h e e s t a b l i s h e d methodology f o r d i s t i n g u i s h i n g between man's
i n f l u e n c e and c l i m a t e i s d e s c r i b e d and d i s c u s s e d . Subsequently, t h e a p p l i c a t i o n cjf t h i s methodology i s i l l u s t r a t e d i n t h e case s t u d i e s g i v e n i n Chapter
7.
Thus, i n accordance w i t h t h e t e r m s o f r e f e r e n c e f o r t h e p r o j e c t t h e main
r e p o r t i s p r i m a r i l y c o n f i n e d t o t h e e s t a b l i s h m e n t o f t h e methodology f o r d i s t i n g u i s h i n g between t h e e f f e c t s G € man's i n f l u e n c e and c l i m a t e on t h e hydrol o g i c a l cycle.
The methodology d e a l s w i t h t h e a n a l y s i s o f h i s t o r i c a l e f f e c t s as opposed
t o t h e p r e d i c t i o n o f f u t u r e e f f e c t s . However, as t h e g l o b a l c l i m a t e changes
become v e r y l i k e l y , t h e p r a c t i c a l i m p o r t a n c e o f b e i n g a b l e t o p r e d i c t t h e
1-5
changes i n w a t e r r e s o u r c e s a v a i l a b i l i t y as a consequence o f t h e c l i m a t e
changes becomes c r u c i a l . T h e r e f o r e , an i n t r o d u c t i o n t o t h i s t o p i c i s g i v e n i n
Appendix A, w h i c h c o n t a i n s a b r i e f i n t r o d u c t i o n t o knowledge r e g a r d i n g t h e
i n f l u e n c e o f g l o b a l c l i m a t e changes on w a t e r r e s o u r c e s . The r a p p o r t e u r s exp r e s s t h e i r a p p r e c i a t i o n t o D r . ' s Budyko and V i n n i k o v € o r p r e p a r i n g t h i s
appendix.
2-1
2.
SUMMARY AND RECOMMENDATIONS
B o t h man's a c t i v i t y and c l i m a t e can have a v e r y s i g n i f i c a n t e f f e c t on t h e hyd r o i o g i c a l c y c l e . These e f f e c t s a r e i n c r e a s i n g g r e a t l y as a consequence o f t h e
r a p i d i n c r e a s e i n p o p u l a t i o n , a g r i c u l t u r a l p r o d u c t i o n , and i n d u s t r i a l i z a t i o n .
I n connection w i t h t h e ongoing research a c t i v i t i e s on t h e i n f l u e n c e o f
g l o b a l c l i m a t e changes on w a t e r r e s o u r c e s , l o n g h i s t o r i c a l t i m e s e r i e s can b e
a n a l y s e d and i n f e r e n c e s can be made r e g a r d i n g c l i m a t e and i t s e f f e c t s on t h e
h y d r o l o g i c a l regime. F o r t h i s purpose i t i s n e c e s s a r y t o be a b l e t o d i s t i n g u i s h between t h e e f f e c t s o f man's a c t i v i t y and o f c l i m a t e and hence t o
i d e n t i f y and e l i m i n a t e t h e e f f e c t s o f man's a c t i v i t y .
2.1
Methodology
A methodology has been e s t a b l i s h e d f o r d i s t i n g u i s h i n g between t h e e f f e c t s o f
man's a c t i v i t y and c l i m a t e on t h e h y d r o l o g i c a l c y c l e , i n p a r t i c u l a r s t r e a m f l o w
and groundwater. The methodology i s based o n j o i n t a p p l i c a t i o n o f s t a t i s t i c a l
t e s t methods and r e g r e s s i o n o r d e t e r m i n i s t i c h y d r o l o g i c a l models. The methodol o g y i s i l l u s t r a t e d s c h e m a t i c a l l y i n F i g . 2 . 1 . 1 and e x p l a i n e d s t e p b y s t e p i n
C h a p t e r 5.
A k e y element i n t h e methodology i s t h e performance o f a s t a t i s t i c a l
t r e n d t e s t u s i n g c l a s s i c a l h y p o t h e s i s - t e s t i n g procedures. T y p i c a l l y , t h e n u l l
hypothesis, H
i s t h a t t h e r e i s no t r e n d i n t h e p o p u l a t i o n f r o m w h i c h t h e
0'
d a t a were d r a w n . A s t e p t r e n d t e s t c a n be used i n case o f a sudden change. F o r
t h i s case, t h e n o n - p a r a m e t r i c W i l c o x o n Rank-Sum t e s t i s recommended. A l t e r n a t i v e l y , i n t h e case o f a g r a d u a l change, a m o n o t o n i c t r e n d t e s t can be c a r r i e d
o u t by use o f t h e n o n - p a r a m e t r i c Mann-Kendall t e s t .
The t e s t s can be c a r r i e d o u t d i r e c t l y on t h e h y d r o l o g i c a l t i m e s e r i e s .
However, t h i s approach does n o t d e a l w i t h t h e c o m p l i c a t i o n s a r i s i n g f r o m c l i mate e f f e c t s on t h e h y d r o l o g i c a l t i m e s e r i e s . T h i s n a t u r a l v a r i a b i l i t y w i l l
decrease t h e power o f t h e s t a t i s t i c a l method t o d e t e c t t r e n d s , when t h e y do
e x i s t , and when t r e n d s do n o t e x i s t , may r e s u l t i n f a l s e d e t e c t i o n o f t r e n d s
t h a t are a r t i f a c t s o f the h i s t o r y o f climatic conditions during the period.
T h e r e f o r e , t h e recommended approach i n v o l v e s j o i n t use o f models and a
s t a t i s t i c a l t r e n d t e s t i n g p r o c e d u r e . The model i s used t o e x p l a i n t h e n a t u r a l
f l u c t u a t i o n s i n t h e h y d r o l o g i c a l v a r i a b l e caused by t h e c l i m a t i c c o n d i t i o n s ,
and t h e s t a t i s t i c a l t r e n d t e s t i s a p p l i e d t o t h e r e m a i n i n g u n e x p l a i n e d v a r i a b i l i t y . Three d i f f e r e n t model t y p e s may be used f o r t h i s purpose, namely a
s t a t i s t i c a l r e g r e s s i o n model, a lumped c o n c e p t u a l h y d r o l o g i c a l model, o r a
d i s t r i b u t e d p h y s i c a l l y based h y d r o l o g i c a l model.
I f a h y d r o l o g i c a l model i s a p p l i e d i t m u s t be a d e q u a t e l y v a l i d a t e d . The
t r a d i t i o n a l l y a p p l i e d s p l i t - s a m p l e t e s t i s n o t s u f f i c i e n t f o r t h i s purpose. A
' h i e r a r c h i c a l scheme € o r s y s t e m a t i c t e s t i n g o f h y d r o l o g i c a l s i m u l a t i o n m o d e l s '
proposed b y Klemes (1985) i s recommended.
Determination o f
s t e p o r monotonic
trend analysis
STEP1
I
Data a v a i l a b l e b o t h
b e f o r e and a f t e r
disturbance data?
STEP 2
1 'r'
STEP3
i
:
STEP4
STEP5
Fig. 2.1.1
S e l e c t i o n of
model t y p e
N o model
Distributed
Distributed
physically
based model
c
S t a t i s t i c a l trend t e s t
step trend
- monotonic t r e n d
-
-
step trend
monotonic t r e n d
-
effects o f climate
e f f e c t s o f man's a c t i v i t y
q u a l i t a t i v e consistency
q u a n t i t a t i v e consistency
S c h e m a t i z a t i o n o f t h e methodology.
I n t h e case o f a s t e p t r e n d t e s t two p e r i o d s a r e s e l e c t e d f o r t h e a n a l y ses, namely a p e r i o d b e f o r e t h e e v e n t c a u s i n g t h e p o s s i b l e t r e n d o c c u r r e d
( r e f e r e n c e p e r i o d ) and a p e r i o d a f t e r t h i s e v e n t ( t e s t p e r i o d ) . The two
samples a r e t h e n t e s t e d as t o whether o r n o t t h e y can be assumed t o b e l o n g t o
t h e same p o p u l a t i o n , i . e .
t h a t no s i g n i f i c a n t change h a s o c c u r r e d . When a
model i s used, i t i s c a l i b r a t e d and v a l i d a t e d on d a t a f r o m t h e t e s t p e r i o d and
t h e s t a t i s t i c a l t e s t i s t h e n c a r r i e d o u t on t h e r e s i d u a l s ( o b s e r v e d v a l u e s
minus simul.ated v a l u e s ) f r o m t h e model a p p l i e d t o b o t h t h e t e s t and r e f e r e n c e
periods.
I n t h e case o f a m o n o t o n i c t r e n d t e s t , o n l y one p e r i o d i s s e l e c t e d f o r
t h e a n a l y s e s , and i t i s t h e n t e s t e d as t o w h e t h e r o r n o t a s t a t i s t i c a l l y s i g n i f i c a n t t r e n d h a s o c c u r r e d . When a model i s used, t h e c a l i b r a t i o n and v a l i d a t i o n m u s t n o t b e c a r r i e d o u t on t h e p e r i o d s e l e c t e d f o r t h e s t a t i s t i c a l t e s t .
Hence c a l i b r a t i - o n an?. v a l i d a t i o n have t o be c a r r i e d o u t o n a n o t h e r p e r i o d o r
a l t e r n a t i v e l y u s i n g d a t a f r o m o t h e r b a s i n s and o b s e r v i n g t h e recommended v a l i clation procedures.
2-3
A f t e r t h e s t a t i s t i c a l t r e n d t e s t f u r t h e r h y d r o l o g i c a l a n a l y s i s may i n
some cases be c a r r i e d o u t . The e x t e n t o f p o s s i b l e h y d r o l o g i c a l a n a l y s i s depends upon t h e s e l e c t e d m o d e l l i n g approach. I n t h e cases o f no model and r e g r e s s i o n model no f u r t h e r a n a l y s i s i s p o s s i b l e . I n t h e case o f a lumped conc e p t u a l model i t may be p o s s i b l e t o e x p l a i n t h e d e t e c t e d changes q u a l i t a t i v e l y
w i t h i n t h e framework o f t h e known human a c t i v i t i e s . I n t h e case o f a d i s t r i b u t e d p h y s i c a l l y based model t h e e f f e c t s o f c l i m a t e and man's a c t i v i t y c a n be
e s t i m a t e d s e p a r a t e l y and t h e q u a n t i t a t i v e c o n s i s t e n c y o f t h e t e s t r e s u l t s may
be checked i n some cases, b y u t i l i z i n g t h e model t o p r e d i c t t h e e f f e c t s o f
human a c t i v i t y and comparing t h i s w i t h t h e r e c o r d e d d a t a . As an i n t e g r a t e d
p a r t o f such f u r t h e r a n a l y s i s , s t a t i s t i c a l t r e n d t e s t s may i n some cases b e
c a r r i e d o u t . A s p e c i a l case a r i s e s when a s t e p t r e n d t e s t h a s been s e l e c t e d
but d a t a a r e o n l y a v a i l a b l e f o r t h e t e s t p e r i o d . I n t h i s case, a s t e p t r e n d
t e s t i s s t r i c t l y n o t v a l i d . However, i n some cases, i t i s p o s s i b l e t o e s t i m a t e
t h e e f f e c t s o f c l i m a t e and man's a c t i v i t y and t o a n a l y z e whether a s i g n i f i c a n t
t r e n d (caused by man's a c t i v i t y ) between t h e r e f e r e n c e and t h e t e s t p e r i o d s
would have been d e t e c t e d , i f d a t a h a d e x i s t e d a l s o f o r t h e r e f e r e n c e p e r i o d .
The methodology i s i l l u s t r a t e d by t w o case s t u d i e s .
2.2
State o f the A r t
O n l y v e r y few s t u d i e s f o c u s s i n g e x p l i c i t l y o n t h e d i s t i n g u i s h i n g between man's
i n f l u e n c e and c l i m a t e e f f e c t s have been r e p o r t e d . However, i n a g r e a t number
o f a n a l y s e s man-induced changes as w e l l as c l i m a t e v a r i a b i l i t y have been
i n c l u d e d , Hence, a c o n s i d e r a b l e e x p e r i e n c e e x i s t s o n t h e s u b j e c t .
As t h e methodology i s new and appears as an i n t e g r a t i o n o f s t a t i s t i c a l
methods and h y d r o l o g i c a l m o d e l l i n g , w h i c h t r a d i t i o n a l l y a r e a p p l i e d s e p a r a t e l y , n o s t u d i e s , t o t h e a u t h o r s ' knowledge, e x i s t , w h i c h f o l l o w s t r i c t l y t h e
e s t a b l i s h e d methodology.
However, t h e d i f f e r e n t elements i n t h e methodology a r e g e n e r a l l y s c i e n t i f i c a l l y w e l l p r o v e n and w i d e s p r e a d f o r p r a c t i c a l a p p l i c a t i o n s . The o n l y except i o n i s t h a t v a l i d a t i o n o f h y d r o l o g i c a l models a r e n o t always c a r r i e d o u t o n a
s c i e n t i f i c a l l y sound b a s i s . T h i s i s becoming i n c r e a s i n g l y i m p o r t a n t e s p e c i a l l y
w i t h r e g a r d t o t h e advanced d i s t r i b u t e d p h y s i c a l l y based models, w h i c h a r e
o f t e n claimed t o be able t o p r e d i c t almost anything. I n t e r n a t i o n a l l y accepted
p r o c e d u r e s f o r model v a l i d a t i o n a r e r e q u i r e d .
2.3
Recommendations
(a)
The methodology e s t a b l i s h e d i n t h i s r e p o r t h a s been t e s t e d o n t w o case
s t u d i e s by u s i n g e x i s t i n g r e s u l t s from o t h e r p r e v i o u s s t u d i e s a v a i l a b l e
t o t h e a u t h o r s . However, t h e s e p r e v i o u s s t u d i e s d i d n o t c o m p l e t e l y a l l o w
f o r a s t r i c t a p p l i c a t i o n o f t h e methodology, and an e x t e n s i o n o f t h e s e
s t u d i e s was o u t s i d e t h e scope o f t h e p r e s e n t p r o j e c t . T h e r e f o r e , i t i s
recommended t h a t t h e methodology be f u r t h e r a p p l i e d and d e v e l o p e d i n t e r n a t i o n a l l y d u r i n g t h e coming y e a r s . Research p r o j e c t s s h o u l d b e e s t a b l i s h e d w i t h t h i s purpose i n c o n n e c t i o n w i t h comprehensive case s t u d i e s
where t h e e f f e c t s o f man's a c t i v i t y and c l i m a t e a r e n o t g e n e r a l l y a g r e e d
upon beforehand.
2-4
(b)
The p r e s e n t methodology i s l i m i t e d i n scope t o d i s t i n g u i s h between t h e
e f f e c t s o f c l i m a t e and t h o s e o f changes i n catchment c h a r a c t e r i s t i c s .
Thus no d i s t i n g u i s h m e n t i s made between man-induced c1imat.e changes and
n a t u r a l l y caused c l i m a t e changes. I t i s recommended t h a t t h e methodology
be extended s o t h a t t h e d i s t i n g u i s h i n g , c a l l e d f o r i n t h e terms o f r e f e r e n c e , between t h e e f f e c t s o f man's a c t i v i t y and " c l i m a t e v a r i a b i l i t y "
a l s o i n c l u d e t h e e f f e c t o f man's a c t i v i t y t h r o u g h c l i m a t e changes and
i n t e r p r e t t h e t e r m " c l i m a t e v a r i a b i l i t y " as t h e n a t u r a l c l i m a t e .
(c)
The d i s t r i b u t e d , p h y s i c a l l y based models s h o u l d be t e s t e d i n t e r n a t i o n a l l y
on t h e b a s i s o f comprehensive v a l i d a t i o n procedures. Thus, an intercompar i s o n o f s e v e r a l o f t h e s e models on t h e i r a b i l i t y t o p r e d i c t r u n o f f f r o m
unqauged catchments, t o p r e d i c t t h e e f f e c t s o f changed c l i m a t i c c o n d i t i o n s and t o p r e d i c t t h e e f f e c t s o f v a r i o u s k i n d s o f man's a c t i v i t y ( e . g .
l a n d u s e change and groundwater development) s h o u l d be c a r r i e d o u t under
t h e management o f an i n t e r n a t i o n a l o r g a n i z a t i o n .
(d)
F u r t h e r i n s i g h t on t h e e f f e c t s o f catchment changes on t h e h y d r o l o g i c a l
c y c l e v e r s u s t h e e f f e c t s o f c l i m a t e may be g a i n e d by a n a l y z i n g t h e r e s u l t s o f t r e n d a n a l y s e s a p p l i e d t o s e v e r a l catchments w i t h i n a p a r t i c u l a r
r e g i o n . I t i s recommended t h a t t h i s b e done f o r s e l e c t e d r e g i o n s . F o r
example, i n many cases, one may e x p e c t t h a t t r e n d s due t o c l i m a t e e f f e c t s
would b e d i s p l a y e d more c o n s i s t e n t l y o v e r a r e g i o n t h a n t h o s e due t o
catchment changes.
3-1
3.
HYDROLOGICAL TOOLS
3.1
Introduction
I n t h i s c h a p t e r an i n t r o d u c t i o n i s g i v e n t o t h e h y d r o l o g i c a l t o o l s w h i c h can
be a p p l i e d t o assess t h e i m p a c t o f c l i m a t e and t h e i m p a c t o f man's a c t i v i t y o n
t h e h y d r o l o g i c a l c y c l e , i n p a r t i c u l a r s t r e a m f l o w and groundwater. I t i s n o t
i n t e n d e d t o g i v e v e r y d e t a i l e d d e s c r i p t i o n s of t h e v a r i o u s t o o l s o r methods
but t o g i v e more fundamental d e s c r i p t i o n s t o g e t h e r w i t h a d i s c u s s i o n o f t h e
a p p l i c a b i l i t y and l i m i t a t i o n s o f t h e d i f f e r e n t methods p r e s e n t l y a v a i l a b l e .
F o r more d e t a i l e d d e s c r i p t i o n , r e f e r e n c e s a r e g i v e n t o t h e l i t e r a t u r e .
The a v a i l a b l e h y d r o l o g i c a l methods a p p l i c a b l e f o r t h e p r e s e n t purpose c a n
b a s i c a l l y b e c l a s s i f i e d i n t w o groups, namely t h e d e t e r m i n i s t i c methods and
t h e s t a t i s t i c a l methods.
3.2
D e t e r m i n i s t i c Models
D e t e r m i n i s t i c methods i n h y d r o l o g y i n p r a c t i c e r e f e r t o m a t h e m a t i c a l d e t e r m i n i s t i c models, o f t e n s i m p l y denoted as h y d r o l o g i c a l models.
I n p r i n c i p l e , a h y d r o l o g i c a l model i s a s i m p l i f i e d q u a n t i t a t i v e d e s c r i p t i o n o f ( p a r t s o f ) t h e h y d r o l o g i c a l c y c l e . A h y d r o l o g i c a l model may b e a v e r y
s i m p l e f o r m u l a , o r i t may be a v e r y comprehensive and c o m p l i c a t e d computerbased m a t h e m a t i c a l model.
The fundamental b a s i s f o r t h e d e t e r m i n i s t i c d e s c r i p t i o n o f t h e h y d r o l o g i c a l p r o c e s s e s i s a c o n t i n u i t y e q u a t i o n ( c o n s e r v a t i o n o f mass) and a f l o w equat i o n ( c o n s e r v a t i o n of momentum). These e q u a t i o n s t a k e d i f f e r e n t forms € o r t h e
d i f f e r e n t processes. The c o n t i n u i t y e q u a t i o n i s o f t e n f o r m u l a t e d as a w a t e r
balance equation:
P = E
+
Q
+
A
+
AS
where
= precipitation
= evaporation
= runoff
= w a t e r a b s t r a c t i o n f r o m t h e catchment minus a d d i t i o n a l w a t e r
i n f l o w t o t h e catchment due t o man's a c t i v i t y
AS = w a t e r s t o r a g e a t t h e end minus s t o r a g e a t t h e b e g i n n i n g o f t h e
time step
P
E
Q
A
The w a t e r balance e q u a t i o n i s v a l i d f o r catchments u n d e r t h e assumption
t h a t t h e t o p o g r a p h i c a l and groundwater d i v i d e s c o i n c i d e .
3-2
The input P-E t o t h e catchment e q u a l s t h e o u t p u t Q+A p l u s t h e i n c r e a s e o f
s t o r a g e AS. T h i s A S , w h i c h expresses t h e non-steady c h a r a c t e r o f t h e f l o w p r o cess, can sometimes be n e g l e c t e d w h e n t h e w a t e r balance e q u a t i o n i s a p p l i e d t o
long time i n t e r v a l s .
T h e w a t e r b a l a n c e method has been used e x t e n s i v e l y d u r i n g t h e p a s t decades f o r v a r i o u s purposes i n c l u d i n g some a p p l i c a t i o n s f o r s t u d y i n g t h e i m p a c t
o f man's a c t i v i t y on t h e h y d r o l o g i c a l c y c l e . As t h e method i s v e r y easy t o use
and o n l y r e q u i r e s few d a t a , i t can be used f o r an i n i t i a l s c r e e n i n g o f t h e
data.
I n a d d i t i o n t o t h e w a t e r b a l a n c e methods, t h e d e t e r m i n i s t i c models o f
p a r t i c u l a r i n t e r e s t a r e those which are a b l e t o simulate ( p a r t o f ) t h e l a n d
phase o f t h e h y d r o l o g i c a l c y c l e o v e r a l o n g p e r i o d o f t i m e ( s e v e r a l y e a r s ) .
I n t h e s e models, t h e catchment c h a r a c t e r i s t i c s i n c l u d i n g t h e man-induced
changes o f l a n d use and w a t e r development a r e r e p r e s e n t e d somehow i n t h e model
p a r a m e t e r s , w h i l e t h e c l i m a t i c v a r i a b l e s a r e t h e main input d a t a (e.g. meteor o l o g i c a l t i m e s e r i e s ) . I n t h i s way, a change i n t h e catchment c h a r a c t e r i s t i c s
and a change o r v a r i a b i l i t y i n t h e c l i m a t e a r e r e p r e s e n t e d i n s e p a r a t e ways i n
t h e s i m u l a t i o n o f t h e h y d r o l o g i c a l c y c l e . As d i s c u s s e d b e l o w , t h i s f a c t i s
v e r y i m p o r t a n t f o r a p p l i c a t i o n o f t h e h y d r o l o g i c a l models f o r t h e p r e s e n t purpose.
D e t e r m i n i s t i c models can be c l a s s i f i e d a c c o r d i n g t o whether t h e model
g i v e s a lumped o r a d i s t r i b u t e d d e s c r i p t i o n o f t h e c o n s i d e r e d area, and
whether t h e d e s c r i p t i o n o f t h e h y d r o l o g i c a l processes i s e m p i r i c a l , concept u a l , o r more p h y s i c a l l y based. A s most c o n c e p t u a l models a r e a l s o lumped and
as most p h y s i c a l l y based models a r e a l s o d i s t r i b u t e d , t h e f o l l o w i n g t h r e e main
groups o f d e t e r m i n i s t i c models emerge:
o
o
0
E m p i r i c a l models ( b l a c k b o x )
Lumped, c o n c e p t u a l models ( g r e y b o x )
D i s t r i b u t e d , p h y s i c a l l y based models
( w h i t e box)
B l a c k b o x models a r e e m p i r i c a l , i n v o l v i n g a m a t h e m a t i c a l e q u a t i o n t h a t has
been assessed, n o t f r o m t h e p h y s i c a l p r o c e s s e s i n t h e catchment, but from anal y s e s of c o n c u r r e n t input and o u t p u t t i m e s e r i e s .
P r o b a b l y , t h e h e s t known b l a c k box models i n h y d r o l o g y a r e t h e u n i t hyd r o g r a p h model and models a p p l y i n g t h e u n i t h y d r o g r a p h p r i n c i p l e s , c f . Sherman
( 1 9 3 2 ) and Nash ( 1 9 5 9 ) .
The b l a c k box models have been d e v e l o p e d and e x t e n s i v e l y a p p l i e d b e f o r e
t h e computer t e c h n o l o g y made i t p o s s i b l e t o use more p h y s i c a l l y c o r r e c t (and
t h u s more complex) models. Today, b l a c k box p r i n c i p l e s a r e o f t e n u s e d i n some
components o f a l a r g e r model, e.g.
t h e u n i t h y d r o g r a p h i s o f t e n used f o r
strearnf 1.0w r o u t i r ~ qi n c o n c e p t u a l r a i n f a l l - r u n o f f models.
The s t a t i s t i c a l r e g r e s s i o n models w h i c h may b e u t i l i z e d as d e t e r m i n i s t i c
t r a n s f e r f u n c t i o n models can a l s o h e c a t e g o r i z e d as e m p i r i c a l models, c f . Sect i o n 3.3.
3-3
Lumped, c o n c e p t u a l models o p e r a t e w i t h d i f f e r e n t and m u t u a l l y i n t e r r e l a t e d
s t o r a g e s r e p r e s e n t i n g p h y s i c a l elements i n t h e catchment. The mode o f operat i o n may b e c h a r a c t e r i z e d as a bookkeeping system c o n t i n u o u s l y a c c o u n t i n g € o r
the moisture contents i n t h e storages.
w:
cl
1-1
Meteoroloqical
Input
Input-Output
Storage
/7P r o c e s s
Evapotrans
piration
7""
-
-
- - --- -
I n t e r c e p t i o n Storage
Overland F l o w
Infiltration
I
I
I upper
Zone Storage
- 1
I
Channel
Simulated
Streamf l o w
Fig.
3.2.1
S t r u c t u r e o f t h e S t a n f o r d Watershed Model,
C r a w f o r d and L i n s l e y ( 1 9 6 6 ) .
simplified after
Due t o t h e lumped d e s c r i p t i o n , where a l l p a r a m e t e r s and v a r i a b l e s r e p r e s e n t average v a l u e s o v e r t h e e n t i r e catchment, t h e d e s c r i p t i o n o f t h e h y d r o l o g i c a l processes cannot be based d i r e c t l y on t h e e q u a t i o n s v a l i d f o r i n d i v i d u a l
s o i l columns. Hence, t h e e q u a t i o n s a r e s e m i - e m p i r i c a l ,
but w i t h a p h y s i c a l
b a s i s . T h e r e f o r e , t h e model p a r a m e t e r s cannot u s u a l l y b e assessed f r o m f i e l d
data, but have t o b e o b t a i n e d t h r o u g h c a l i b r a t i o n .
The S t a n f o r d Model ( C r a w f o r d and L i n s l e y (1966) , t h e s t r u c t u r e o f w h i c h
i s s c h e m a t i c a l l y shown i n F i g . 3 . 2 . 1 ,
i s c e r t a i n l y t h e b e s t known w a t e r s h e d
model o f t h e lumped, c o n c e p t u a l t y p e .
3-4
D u r i n g t h e decade f o l . l o w i n g t h e development o f t h e S t a n f o r d Model s e v e r a l
o t h e r models o f t h e same t y p e w e r e developed, c f . F l e m i n g ( 1 9 7 5 ) a n d Kuchment
(1980) f o r r e v i e w s . B e i n g g e n e r a l purpose r a i n f a l l - r u n o f f
models, many o f
t h e s e models a r e t o d a y a p p l i e d on an o p e r a t i o n a l b a s i s f o r a v a r i e t y o f purposes.
I t s h o u l d b e emphasized t h a t n o t a l l models s t r i c t l y f i t i n t o t h e above
t h r e e groups o f models. Many models f a l l i n between a c o n c e p t u a l and a phys i c a l l y based approach. Some o f t h e c o n c e p t u a l models a r e s e m i - d i s t r i b u t e d i n
t h e sense t h a t subareas w i t h t h e same h y d r o l o g i c a l c h a r a c t e r i s t i c s (e.g. p r e c i p i t a t i o n , t e m p e r a t u r e , s o i l , v e g e t a t i o n , and s l o p e ) a r e grouped t o g e t h e r t o
form h y d r o l o g i c a l response u n i t s . The G G I - 8 5 model (Vinogradov, 1 9 8 5 ; and
V u g l i n s k y , 1987) i s an example o f such a model t y p e .
The p r i n c i p a l mode o f o p e r a t i o n o f
i l l u s t r a t e d i n F i g . 3.2.2.
a distributed,
p h y s i c a l l y based model i s
Contrary t o t h e lumped,
c o n c e p t u a l models, a d i s t r i b u t e d , p h y s i c a l l y
based model does n o t c o n s i d e r t h e w a t e r f l o w s i n a catchment t o t a k e p l a c e
between a f e w s t o r a g e s . I n s t e a d , t h e f l o w s o f water and energy a r e d i r e c t l y
c a l c u l a t e d from t h e governing d i f f e r e n t i a l equations , f o r i n s t a n c e t h e S a i n t
Venant e q u a t i o n s f o r o v e r l a n d f l o w , R i c h a r d s ’ e q u a t i o n f o r u n s a t u r a t e d zone
f l o w , and B o u s s i n e s q ’ s e q u a t i o n f o r groundwater f l o w .
The d i s t r i b u t e d , p h y s i c a l l y based models g i v e a d e t a i l e d and p o t e n t i a l l y
more c o r r e c t d e s c r i p t i o n o f t h e h y d r o l o g i c a l processes i n t h e catchment t h a n
do t h e o t h e r model t y p e s . T h e r e f o r e , t h e y have p o t e n t i a l l y more f i e l d s o f
a p p l i c a t i o n as d i s c u s s e d below. O f course, due t o t h e c o m p l e x i t y o f t h e c a t c h ment i t w i l l never i n p r a c t i c e b e p o s s i b l e t o o b t a i n s u f f i c i e n t d a t a t o g i v e a
ful-ly correct simulation i n a l l d e t a i l s .
A f i r s t a t t e m p t t o o u t l i n e t h e p o t e n t i a l s and some o f t h e elements i n a
d i s t r i b u t e d , p h y s i c a l l y based model was made b y Freeze and H a r l a n ( 1 9 6 9 ) .
Today, s e v e r a l p h y s i c a l l y based models t r e a t i n g o n l y s i n g l e h y d r o l o g i c a l p r o cesses have been d e v e l o p e d and e x t e n s i v e l y a p p l i e d . Almost a l l groundwater
models € o r i n s t a n c e a r e o f t h e d i s t r i b u t e d , p h y s i c a l l y based t y p e . Examples o f
models c o v e r i n g t h e e n t i r e l a n d phase o f t h e h y d r o l o g i c a l c y c l e a r e r e p o r t e d
b y Weeks e t a l . ( 1 9 7 4 ) , Wardlaw ( 1 9 7 8 ) , R e f s g a a r d and Hansen ( 1 9 8 2 ) . These mod e l s a r e g e n e r a l l y s p e c i f i c purpose models w i t h a lumped, c o n c e p t u a l d e s c r i p t i o n o f those processes t h a t a r e l e s s i m p o r t a n t f o r t h e i r p a r t i c u l a r applicat i o n . The SHE model ( A b b o t t e t a l . 1986; Storm, 1 9 8 6 ) , t h e IHDM model ( M o r r i s ,
1980, Rogers e t a l . 1985) and t h e model d e s c r i b e d by Kuchment e t a l . (1983)
a r e some o f t h e few more g e n e r a l purpose m o d e l l i n g systems w h i c h a r e a p p l i c a b l e under a wide v a r i e t y o f h y d r o l o g i c a l and h y d r o g e o l o g i c a l c o n d i t i o n s .
3- 5
EVAPOTRANSPIRATION
MODEL
I
1
1
I
Evaporation from
Transpiration
Evaporation Irom
Soil Surlaces
Sublimation I r o m
Snow P a c k
Rain
and Snow
Intercepted
f
I
lrom ground
t
I(
Rain.
Snow,
Vapour
n
KEY.
Fig.
3.2.2
Schematic diagram o f a w a t e r s h e d and a q u a s i t h r e e d i m e n s i o n a l d i s t r i b u t e d p h y s i c a l l y based model o f t h e
watershed ( t h e SHE model, c f . S t o r m ( 1 9 8 6 ) ) .
3.2.4
S e l e c t i o n o f a p p r o p r i a t e model t y p e
...........................................
l a r g e number o f h y d r o l o g i c a l models e x i s t s o f w h i c h many a r e f u n c t i o n i n g
f u n d a m e n t a l l y i n t h e same way. F o r i n s t a n c e , a t l e a s t 2 0 d i f f e r e n t r a i n f a l l r u n o f f models o f t h e lumped, c o n c e p t u a l t y p e e x i s t . A l t h o u g h t h e s e models a t a
f i r s t g l a n c e may l o o k v e r y d i f f e r e n t , f u n d a m e n t a l l y t h e y have t h e same s t r u c t u r e and a r e b a s i c a l l y f u n c t i o n i n g a l o n g t h e same p r i n c i p l e s .
A
Thus, t h e q u e s t i o n " w h i c h model i s most a p p r o p r i a t e f o r a p a r t i c u l a r
h y d r o l o g i c a l problem?" c a n n o t be answered s t r i c t l y b y g i v i n g t h e name o f one
model. I n s t e a d , a g e n e r a l d i s c u s s i o n w i l l b e g i v e n on t h e a p p r o p r i a t e n e s s o f
t h e above m e n t i o n e d model t y p e s f o r t h e d i f f e r e n t k i n d s o f h y d r o l o g i c a l p r o blems.
The e m p i r i c a l models a r e g e n e r a l l y o f i n t e r e s t as s i n g l e e v e n t models o r
as subcomponents o f more c o m p l i c a t e d models. The e m p i r i c a l models d i r e c t l y
a p p l i c a b l e f o r t h e p r e s e n t purpose a r e t h e s t a t i s t i c a l r e g r e s s i o n models, (see
Section 3.3).
The lumped, c o n c e p t u a l models a r e e s p e c i a l l y w e l l s u i t e d f o r s i m u l a t i o n
o f t h e r a i n f a l l - r u n o f f p r o c e s s when h y d r o l o g i c a l t i m e s e r i e s e x i s t t h a t a r e
s u f f i c i e n t l y l o n g f o r a model c a l i b r a t i o n o r d a t a e x i s t f o r r e g i o n a l i z a t i o n o f
model p a r a m e t e r s . Thus, t y p i c a l f i e l d s o f a p p l i c a t i o n a r e :
3-6
o
E x t e n s i o n o f s h o r t s t r e a m f l o w r e c o r d s based o n l o n g r a i n f a l l r e c o r d s .
o
Real-time r a i n f a l l - r u n o f f
s i m u l a t i o n e.g.
f o r flood forecasting.
The lumped, c o n c e p t u a l models a r e o f i n t e r e s t i n t h e p r e s e n t c o n t e x t f o r
t h e i r a b i l i t y t o s i m u l a t e t h e e f f e c t s o f c l i m a t e on s t r e a m f l o w .
The d i s t r i b u t e d , p h y s i c a l l y based models can i n p r i n c i p l e b e a p p l i e d t o
a l m o s t any k i n d o f h y d r o l o g i c a l p r o b l e m . Some examples o f t y p i c a l a p p l i c a t i o n s
are :
o
P r e d i c t i o n o f t h e e f f e c t s o f catchment changes due t o human i n t e r f e r e n c e
i n t h e h y d r o l o g i c a l c y c l e , such as changes i n l a n d use, u r b a n i z a t i o n ,
groundwater development, o r i r r i g a t i o n . S i n c e parameters o f t h e model
t e n d t o b e more p h y s i c a l l y based, t h e change i n parameter v a l u e s c o r r e s p o n d i n g t o t h e catchment changes can sometimes b e e s t i m a t e d d i r e c t l y .
0
P r e d i c t i o n of r u n o f f f r o m ungauged catchments and f r o m catchments w i t h
r e l a t i v e l y s h o r t r e c o r d s . A s opposed t o t h e lumped, c o n c e p t u a l models,
w h i c h r e q u i r e l o n g h i s t o r i c a l t i m e s e r i e s o f r a i n f a l l , r u n o f f , and evap o r a t i o n d a t a f o r t h e p a r a m e t e r assessment, t h e p a r a m e t e r s o f t h e d i s t r i b u t e d , p h y s i c a l l y based models may be assessed d i r e c t l y f r o m i n t e n s i v e ,
short-term f i e l d i n v e s t i g a t i o n s .
0
K a t e r q u a l i t y and s o i l e r o s i o n m o d e l l i n g f o r w h i c h a more d e t a i l e d and
p h y s i c a i l y c o r r e c t s i m u l a t i o n o f water flows i s important.
The main problems u s u a l l y m e n t i o n e d i n c o n n e c t i o n w i t h t h e a p p l i c a t i o n o f
d i s t r i b u t e d , p h y s i c a l l y based models a r e :
a)
L a r g e reyui.rements o f d a t a ,
I.ogy, s o i l , and v e g e t a t i o n .
e s p e c i a l l y t h o s e d e s c r i b i n g m e t e o r o l o g y , geo-
b)
I n s u f f i c i e n t knowledge o f t h e p h y s i c s o f t h e h y d r o l o g i c a l p r o c e s s e s w h i c h
a r e modelled i n q r e a t d e t a i l .
c)
S c a l e problems when e x t e n d i n g t h e p r o c e s s d e s c r i p t i o n f r o m a s i n g l e p o i n t
t o an e n t i r e catchment.
d)
L a r g e computer r e q u i r e m e n t s .
The d i s t r i b u t e d , p h y s i c a l l y based models a r e a b l e d i r e c t l y t o u t i l i z e t h e
d i s t r i b u t e d i n f o r m a t i o n u s u a l l y a v a i l a b l e i n t o p o g r a p h i c a l , g e o l o g i c a l , and
s o i l maps and o t h e r r e m o t e l y sensed i n f o r m a t i o n , i n c l u d i n g c o n t i n u o u s u p d a t i n g
o f catchment. c o n d i t i o n s (e.g. snow c o v e r ) . Thus, t h e d a t a r e q u i r e m e n t s U - s u a l l y
l i s t e d f o r t h e s e models a r e huge, b u t t h i s m e r e l y r e f l e c t s t h a t t h e models can
u t i l i z e a l l . o f t h e s e d a t a , i f t h e y a r e made a v a i l - a b l e . O n t h e o t h e r hand, t h e
models can b e o p e r a t e d with l e s s d a t a a v a i l a b l - e , i n w h i c h case t h e p r e d i c t e d
r e s u l t s w i . 1 1 I3e more u n c e r t a i n u n l e s s a c a l i b r a t i o n i s p o s s i b l e .
S i m i l a r l y , w i t h r e s p e c t t o t h e argument t h a t t h e r e s t i l l i s an i n s u f f i c i e n t knowledge o f t h e h y d r o l o g i c a l p r o c e s s , proponents o f p h y s i c a l l y based
models m t e t h a t a c o m p a r a t i v e l y l a r g e r p a r t o f t h e e x i s t i n g knowledge can h e
b u i l t i n t o t h e s e m o d e l s , t h a n i n t o t-he lumped, c o n c e p t u a l models.
3-7
The s c a l e problems a r e o f a m e t h o d o l o g i c a l n a t u r e r e s u l t i n g f r o m t h e spat i a l v a r i a b i l i t y o f t h e p h y s i c a l p a r a m e t e r s , as w e l l as t h e h y d r o m e t e o r o l o g i c a l input. D e t a i l e d f i e l d measurements i n d i c a t e t h a t f o r i n s t a n c e t h e h y d r a u l i c c o n d u c t i v i t y may v a r y s e v e r a l o r d e r s o f magnitude w i t h i n a s m a l l f i e l d
p l o t w h i c h i s t r a d i t i o n a l l y c h a r a c t e r i z e d as "homogeneous" and b e l o n g i n g t o
t h e same s o i l t y p e ( N i e l s e n e t a 1 1 9 7 3 ) . I t c a n t h e r e f o r e b e e x p e c t e d t h a t t h e
f i e l d d a t a depend on t h e measurement s c a l e . I n p a r t i c u l a r , t h e v a r i a n c e o f
l a r g e - s c a l e measurements w i l l b e l e s s t h a n t h a t o f s m a l l c o r e samples. Thus,
t h e r e i s some i n t e r d e p e n d e n c e between t h e measurement s c a l e , t h e model s t r u c t u r e and t h e a p p r o p r i a t e p a r a m e t e r v a l u e a t t h e model g r i d s c a l e . The s c a l e
problems a r e known t o be i m p o r t a n t i n s o l u t e t r a n s p o r t and w a t e r q u a l i t y
m o d e l l i n g , b u t a r e a l s o i m p o r t a n t i n some cases o f w a t e r f l o w m o d e l l i n g . Many
research a c t i v i t i e s are c u r r e n t l y b e i n g c a r r i e d out i n t e r n a t i o n a l l y on t h i s
s u b j e c t (e.g. Freeze, 1980; Jensen and R e f s g a a r d , 1 9 8 8 ) .
F i n a l l y , w i t h r e s p e c t t o p o i n t d) above, t h e computer r e q u i r e m e n t s no
l o n g e r p r o h i b i t p r a c t i c a l a p p l i c a t i o n o f l a r g e complex models l i k e t h e d i s t r i b u t e d , p h y s i c a l l y based models. A n i n c r e a s i n g number o f t h e s e models c a n now
be o p e r a t e d even on m i c r o - o r p e r s o n a l computers.
The d i s t r i b u t e d , p h y s i c a l l y based models a r e o f i n t e r e s t i n t h e p r e s e n t
c o n t e x t f o r t h e i r a b i l i t y t o s i m u l a t e t h e e f f e c t s o f c l i m a t e as w e l l as man's
a c t i v i t y on b o t h groundwater and s t r e a m f l o w .
H y d r o l o g i c a l s i m u l a t i o n models o f t h e t y p e s d e s c r i b e d above a r e o n l y u s e f u l ,
as l o n g as t h e y a r e a b l e t o p r o v i d e r e s u l t s o f s u f f i c i e n t l y good a c c u r a c y .
T h e r e f o r e , t h o r o u g h and p r o p e r t e s t i n g s o f such models a r e r e q u i r e d , b e f o r e
they are applied i n practice.
The t e s t i n g p r o c e d u r e t r a d i t i o n a l l y used, t h e s o - c a l l e d s p l i t - s a m p l e
t e s t , i s n o t always s u f f i c i e n t . T h e r e f o r e , a more comprehensive p r o c e d u r e i s
r e q u i r e d . I n g e n e r a l , t h e ' h i e r a r c h i c a l scheme f o r s y s t e m a t i c t e s t i n g o f
h y d r o l o g i c a l s i m u l a t i o n models' p r o p o s e d b y Klemes (1985) i s recommended. The
scheme i s c a l l e d h i e r a r c h i c a l , because t h e m o d e l l i n g t a s k s a r e o r d e r e d a c c o r d i n g t o t h e i r i n c r e a s i n g c o m p l e x i t y , and t h e demands o f t h e t e s t i n c r e a s e i n
t h e same d i r e c t i o n . The scheme i s b r i e f l y summarized as f o l l o w s .
The scheme comprises f o u r c a t e g o r i e s o f t e s t s :
(1) A s p l i t - s a m p l e t e s t i s used, when t h e r e a r e s u f f i c i e n t d a t a f o r a model
c a l i b r a t i o n i n t h e a c t u a l b a s i n , and when t h e model i s n o t u s e d f o r
e x t r a p o l a t i o n s t o d r y e r o r w e t t e r c l i m a t e segments. The a v a i l a b l e r e c o r d
i s s p l i t i n t o two segments one o f w h i c h i s used € o r c a l i b r a t i o n and t h e
other f o r validation.
(2)
A proxy-basin
t e s t i s used, when a model i s t o b e a p p l i e d o n an ungauged
b a s i n i n a r e g i o n , where gaugings a r e a v a i l a b l e f r o m o t h e r b a s i n s . Two
such gauged b a s i n s a r e s e l e c t e d and t h e model i s c a l i b r a t e d on one o f t h e
b a s i n s and v a l i d a t e d on t h e o t h e r and v i c e v e r s a .
3-8
(3)
A d i f f e r e n t i a l s p l i t - s a m p l e t e s t i s used, when a model i s t o b e used t o
s i m u l a t e v a r i . a b l e s i n a p a r t i c u l a r b a s i n under c o n d i t i o n s w h i c h a r e d i f f e r e n t f r o m t h o s e e x i s t i n g i n t h e c a l i b r a t i o n p e r i o d . T h i s case i s r e l e v a n t b o t h f o r changes i n catchment c h a r a c t e r i s t i c s due t o man's a c t i v i t i e s and f o r changes i n c l i m a t e c o n d i t i o n s . The t e s t p r o c e d u r e may i n
t h i s case have s e v e r a l v a r i a n t s depending on t h e s p e c i f i c n a t u r e o f t h e
changes. I f t e s t d a t a a r e n o t a v a i l a b l e f o r t h e b a s i n , t e s t s have t o be
c a r r i e d o u t o n s u b s t i t u t e b a s i n s , where s i m i l a r changes have t a k e n p l a c e .
(4)
A p r o x y - b a s i n d i f f e r e n t i a l s p l i t - s a m p l e t e s t i s used when a model i s supposed t o be a p p l i c a b l e t o ungauged catchments under c o n d i t i o n s d i f f e r e n t
f r o m t h o s e u n d e r w h i c h i t was p r e v i o u s l y t e s t e d . T h i s t e s t , w h i c h can b e
seen as a c o m b i n a t i o n o f ( 2 ) and ( 3 ) i s v e r y comprehensive i n v o l v i n g
t e s t s o n s e v e r a l s u b s t i t u t e catchments.
F o r a more d e t a i l e d d e s c r i p t i o n o f
Klemes ( 1 9 8 5 ) o r Klemes ( 1 9 8 6 ) .
3.3
these
tests
reference
i s
made
to
S t a t i s t i c a l Models
The s t a t i s t i c a l methods o f p a r t i c u l a r i n t e r e s t f o r t h e p r e s e n t p u r p o s e a r e t h e
s t a t i s t i c a l r e g r e s s i o n models. These models may be u t i l i z e d t o p r e d i c t t h e
e f f e c t o f c l i m a t e v a r i a b i l i t y on h y d r o l o g i c a l v a r i a b l e s , e.g.,
by r e g r e s s i n g
streamflow o r groundwater l e v e l t i m e s e r i e s on m e t e o r o l o g i c a l t i m e s e r i e s .
4-1
4
STATISTICAL METHODS
4.1
Introduction
T e s t i n g f o r t r e n d s i n a h y d r o l o g i c t i m e s e r i e s may b e t r e a t e d as a c l a s s i c a l
h y p o t h e s i s - t e s t i n g problem. T y p i c a l l y , t h e n u l l h y p o t h e s i s , H
i s t h a t there
0'
i s no t r e n d i n t h e p o p u l a t i o n f r o m w h i c h t h e d a t a were drawn. Consequently,
t h e a l t e r n a t i v e h y p o t h e s i s , H , may b e e i t h e r t h a t a t r e n d e x i s t s i n t h e d a t a
i n e i t h e r d i r e c t i o n (two-sided t e s t ) o r t h a t a p o s i t i v e ( o r a n e g a t i v e ) t r e n d
e x i s t s i n t h e d a t a (one-sided t e s t ) . A o n e - s i d e d t e s t s h o u l d be used o n l y i f
i t i s known i n advance t h a t t h e change i n t h e u n d e r l y i n g p r o c e s s w o u l d b e pos i t i v e o r n e g a t i v e . T h i s d e c i s i o n s h o u l d b e made b e f o r e l o o k i n g a t t h e d a t a .
The f a c t t h a t t h e d a t a appear t o d i s p l a y e i t h e r a p o s i t i v e o r n e g a t i v e t r e n d
s h o u l d e x e r t n o i n f l u e n c e on t h i s d e c i s i o n .
Within t h i s framework, t h e n u l l h y p o t h e s i s w i l l have some p r e c i s e mathem a t i c a l d e f i n i t i o n and w i l l i n c o r p o r a t e c e r t a i n c r i t i c a l assumptions a b o u t t h e
u n d e r l y i n g process b e i n g t e s t e d f o r trends. Therefore, i t i s i m p o r t a n t t h a t
t h e d e f i n i t i o n o f H and i t s u n d e r l y i n g assumptions b e u n d e r s t o o d and r e s u l t s
0
c a r e f u l l y reported.
The f o u r p o s s i b l e outcomes o f a t r e n d t e s t a r e shown i n T a b l e 4.1.1.
True S i t u a t i o n
No t r e n d
( HO t r u e )
Trend
(Ho f a l s e )
Deci s i on
Decide no t r e n d
(do not r e j e c t Ho)
Decide t r e n d
( r e j e c t Ho)
Table 4.1.1
1-a
6
(type I 1 error)
a
(type I e r r o r )
1-6
(power)
P o s s i b l e outcomes o f a t r e n d t e s t .
There a r e two p o s s i b i l i t i e s f o r d r a w i n g e r r o n e o u s c o n c l u s i o n s . F i r s t , i t
i s p o s s i b l e t o d e c i d e t h e r e i s a t r e n d when no t r e n d e x i s t s ( t y p e I e r r o r ) .
The p r o b a b i l i t y of t h i s o c c u r r i n g i s a , g i v e n t h a t t h e assumptions b e h i n d t h e
t r e n d t e s t a r e c o r r e c t . Second, i t i s ' p o s s i b l e t o d e c i d e t h e r e i s n o t r e n d
when i n f a c t a t r e n d e x i s t s ( t y p e I 1 e r r o r ) . The p r o b a b i l i t y o f t h i s o c c u r r i n g
i s B , g i v e n t h a t t h e assumptions b e h i n d t h e t r e n d t e s t a r e c o r r e c t . The p r o b a b i l i t y of d e t e c t i n g a t r e n d when i n f a c t a t r e n d e x i s t s i s e q u a l t o 1 - 6 and
i s r e f e r r e d t o as t h e power o f a t r e n d t e s t .
4-2
T y p i c a l l y , one o f two approaches a r e used i n r e p o r t i n g t h e r e s u l t s o f a
t r e n d t e s t . One approach i s t o p r e - s e l e c t
( e . g . , Q = 0 . 0 5 ) based o n t h e r i s k
o f t y p e Ie r r o r t h a t one i s w i l l i n g t o b e a r . T h i s d e f i n e s a c r i t i c a l r e g i o n ( a
r a n g e o f v a l u e s of t h e t e s t s t a t i s t i c Z f o r w h i c h one w i l l r e j e c t H ) such
t h a t t h e p r o b a b i l i t y o f f a l l i n g w i t h i n the c r i t i c a l r e g i o n i s a i f H ?s t r u e
0
(see F i g u r e 4 . 1 . 1 ) .
The r e s u l t s o f t h e t r e n d t e s t a r e t h e n r e p o r t e d as e i t h e r
a r e j e c t i o n o r acceptance o f t h e n u l l h y p o t h e s i s a t t h e s p e c i f i e d a l p h a l e v e l
o f s i g n i f i c a n c e . A n a l t e r n a t i v e method i s t o r e p o r t t h e r e s u l t s i n terms o f
t h e s i z e o f t h e c r i t i c a l r e g i o n (p l e v e l ) . I n t h a t case, t h e r e a d e r can i n t e r p r e t whether t h e s i z e o f t h e c r i t i c a l r e g i o n exceeds t h a t v a l u e f o r w h i c h
h e j s h e would r e j e c t H
A n example o f t h e l a t t e r approach i s g i v e n i n t h e case
0'
study i n S e c t i o n 7.3.
PROBABILITY
DENSITY
A R E A U N D E R CURVE
AREA
F i g . 4.1.1
SHADED
=
1.0
= a
D i s t r i b u t i o n o f t e s t s t a t i s t i c Z and c r i t i c a l r e g i o n f o r
two-sided t r e n d t e s t .
There a r e a number o f d i f f e r e n t s t a t i s t i c a l t e s t s f o r t r e n d s i n a v a r i a b l e o v e r t i m e . G e n e r a l l y , t h e s e t e s t s a r e f o r e i t h e r s t e p t r e n d s o r f o r monot o n i c t r e n d s . A s t e p t r e n d ( a l s o c a l l e d a s t e p change) i s a d i s t i n c t change i n
t h e " l o c a t i o n " (mean, median, e t c . ) o f t h e v a r i a b l e a t a p o i n t i n t i m e . WhereES,
a s e r i e s e x h i b i t s monotonic t r e n d i f t h e r e i s a c o n t i n u i n g i n c r e a s e o r
decrease i n t h e mean o r median w i t h t i m e .
The two g e n e r a l t y p e s o f t e s t s a r e d e s c r i b e d below. F i r s t , t h e S t u d e n t ' s
t - t e s t and i t s n o n p a r a m e t r i c e q u i v a l e n t , t h e Wilcoxon Rank-Sum t e s t , a r e des c r i b e d f o r t e s t i n g f o r s t e p t r e n d s . Second, t h e use o f r e g r e s s i o n and t h e
Mann-Kendall t e s t a r e d e s c r i b e d f o r t e s t i n g f o r monotonic t r e n d s . I n each
case, one can t e s t f o r a s i g n i f i c a n t t r e n d and t h e magnitude o f t h a t t r e n d can
be e s t i m a t e d . F i n a l l y , some c o m p l i c a t i o n s i n t e s t i n g f o r t r e n d s a r e d i s c u s s e d .
The s t a t i s t i c a l t e s t s d e s c r i b e d i n t h e r e m a i n i n g p a r t o f t h i s Chapter a r e
o n l y a s u b s e t o f t h o s e avai1ahl.e. O t h e r a p p r o p r i a t e t e s t s c o u l d be used, but
i t 1:; beyond t h e scope o f t h i s document t o t r e a t more t h a n a few o f t h e poss i b l e t e s t s . Some o t h e r t e c h n i q u e s a r e i n c l u d e d 111 r e p o r t s by t h e S t a t e tIydrol o g i c a l I n s t i t u t e o f t h e USSR ( 1 9 8 4 , 1 9 8 6 ) .
4- 3
4.2
S t e p Trends
T e s t i n g f o r a s t e p t r e n d may be a c c o m p l i s h e d b y a two-sample comparison o f
means. A s i m p l e p r o c e d u r e f o r comparing two means i s t h e S t u d e n t ' s t - t e s t . The
computed s t a t i s t i c i s compared t o t a b u l a t e d ( o r computer g e n e r a t e d ) v a l u e s o f
t h e t - d i s t r i b u t i o n . Tables and background t h e o r y f o r t h i s t e s t a r e i n c l u d e d i n
most s t a t i s t i c s t e x t s and v i r t u a l l y a l l s t a t i s t i c a l s o f t w a r e packages a r e capable o f performing the t e s t . I f s i g n i f i c a n t differences are detected b y t h e
t-test,
t h e n a n e s t i m a t e o f t h e change i n means i s s i m p l y t h e mean f o r t h e
f i r s t p e r i o d s u b t r a c t e d f r o m t h e mean f o r t h e second p e r i o d .
The t - t e s t assumes t h e d a t a a r e i n d e p e n d e n t and come f r o m n o r m a l l y d i s t r i b u t e d p o p u l a t i o n s w i t h e q u a l v a r i a n c e s . The assumption o f e q u a l v a r i a n c e s
s h o u l d be checked u s i n g an F - t e s t . I f t h e v a r i a n c e s p r o v e t o b e s i g n i f i c a n t l y
d i f f e r e n t , one c a n use t h e W i l c o x o n Rank-Sum t e s t d e s c r i b e d below.
A s i g n i f i c a n t l i m i t a t i o n o f t h e t - t e s t i s t h e assumption o f n o r m a l i t y .
Most h y d r o l o g i c v a r i a b l e s do n o t appear t o be n o r m a l l y d i s t r i b u t e d ; i n f a c t
t h e b e s t d i s t r i b u t i o n t o f i t t o t h e d a t a may be q u i t e u n c l e a r . F o r t h i s r e a son, a d i s t r i b u t i o n - f r e e t e s t such as t h e Wilcoxon Rank-Sum t e s t may be used
i n s t e a d o f t h e t - t e s t . The t e s t s t a t i s t i c f o r t h i s t e s t i s based on t h e sums
o f r a n k s o f t h e two samples; t h e a c t u a l d a t a v a l u e s a r e n o t used. The t h e o r y
and p r o c e d u r e o f t h e t e s t a r e d e s c r i b e d i n B r a d l e y (1968). S i m p l i f i e d d i s c u s s i o n s o f t h e Wilcoxon Rank-Sum t e s t a r e p r o v i d e d i n b a s i c s t a t i s t i c s t e x t s ,
and t h e t e s t i s i n c l u d e d i n most s t a t i s t i c a l s o f t w a r e packages. I t i s a l s o
c a l l e d t h e Mann-Whitney t e s t . The m i n i m u m r e l a t i v e e f f i c i e n c y o f t h e W i l c o x o n
Rank-Sum t e s t i s 86.4% r e l a t i v e t o t h e t - t e s t when t h e assumptions o f t h e
t - t e s t a r e met ( B r a d l e y , 1 9 6 8 ) . When t h e assumptions a r e n o t met, t h e n t h e
power o f t h e t - t e s t can be s t r o n g l y d i m i n i s h e d i n comparison t o o t h e r t e s t s
such as t h e W i l c o x o n Rank-Sum t e s t ( K e n d a l l and S t u a r t , 1 9 7 9 , p. 5 2 3 - 5 2 5 ) .
I f t h e Wilcoxon Rank-Sum t e s t i n d i c a t e s t h a t a s i g n i f i c a n t d i f f e r e n c e
e x i s t s between t h e two t i m e p e r i o d s , t h e n a r e a s o n a b l e e s t i m a t e o f t h e magn i t u d e o f t h i s d i f f e r e n c e can b e o b t a i n e d u s i n g t h e Hodges-Lehmann e s t i m a t o r
(Hodges and Lehmann, 1963; H o l l a n d e r and Wolfe, 1973, p. 7 5 - 7 7 ) .
This e s t i m a t o r i s computed as t h e median o f a l l p o s s i b l e p a i r w i s e d i f f e r e n c e s between
t h e v a l u e s o f t h e v a r i a b l e a f t e r t h e presumed s t e p change and b e f o r e t h e p r e sumed s t e p change. The Hodges-Lehmann e s t i m a t o r A i s r e l a t e d t o t h e Rank-Sum
t e s t i n t h a t a s h i f t o f s i z e A w o u l d make t h e d a t a appear d e v o i d o f any e v i dence o f d i f f e r e n c e between t h e b e f o r e and a f t e r t i m e s e r i e s when t e s t e d by
t h e Rank-Sum t e s t .
4.3
Monotonic Trends
T e s t i n g f o r monotonic t r e n d s may be done b y p e r f o r m i n g a s i m p l e l i n e a r r e g r e s sion o f the hydrological variable against time (Y. = a + b * T . + e . i = l ,
,
n) A t - t e s t on t h e c o e f f i c i e n t b t h e n can b e use% t o t e s t wheth2r t h e t r u e
slope i s s i g n i f i c a n t l y d i f f e r e n t from zero. I f a s i g n i f i c a n t l i n e a r t r e n d i s
i n d i c a t e d , t h e n t h e t r u e s l o p e (change p e r u n i t t i m e ) may b e e s t i m a t e d b y t h e
c o e f f i c i e n t b.
. ..
The a p p l i c a b i l i t y o f t h e r e g r e s s i o n model must be checked f o r adequacy;
t h a t i s t h e r e s i d u a l s s h o u l d appear homoscedastic and n o r m a l . I n o r d e r t o meet
these assumptions i t i s o f t e n d e s i r a b l e t o l o g t r a n s f o r m t h e Y v a r i a b l e . I n
4- 4
t h i s case, i f b i s t h e t r e n d s l o p e computed f r o m t h e l o g d a t a (assume n a t u r a l
l o g s a r e used)
t h e n t h e p e r c e n t a g e change i n t h e v a r i a b l e p e r t i m e s t e p i s
'b
e s t i m a t e d as ( e - 1 ) * 1 0 0 . N o t e t h a t t h i s i m p l i e s t h a t t h e t r e n d i s exponent i a l r a t h e r than l i n e a r w i t h r e s p e c t t o time.
N o t e t h a t a r e g r e s s i o n model c o u l d be used t o t e s t f o r
s u b s t i t u t i n g f o r T a n " i n d i c a t o r v a r i a b l e " denoted I where
i
step trends by
i
I . = 0 i f i i s b e f o r e t h e p o s s i b l e s t e p change
1
= 1 i f i i s a f t e r t h e p o s s i b l e s t e p change
A n a l t e r n a t i v e t e s t f o r monotonic t r e n d i s t h e Mann-Kendall t e s t (Mann,
1945; K e n d a l l , 1 9 7 5 ) . L i k e t h e Wilcoxon Rank-Sum t e s t , t h i s p r o c e d u r e does n o t
r e q u i r e t h e assumption t h a t t h e d a t a a r i s e f r o m any p a r t i c u l a r d i s t r i b u t i o n .
The Mann-Kendall t e s t i s d e s c r i b e d by G i l b e r t (1987) and t h e World Meteorolog i c a l O r g a n i z a t i o n p r o v i d e s a computer program f o r t h e t e s t (WMO, 1 9 8 8 ) . The
WMO r e f e r s t o t h e t e s t as t h e Mann t e s t o f t r e n d .
I n p e r f o r m i n g t h e Mann-Kendall t e s t t h e f i r s t s t e p i s t o l i s t t h e d a t a i n
t h e o r d e r i n w h i c h t h e y were c o l l e c t e d o v e r t i m e : Y
Y ,
Y
Then d e t e r n
where j>k. The t e s t
mine t h e s i g n o f a l l n ( n - 1 ) / 2 p o s s i b l e d i f f e r e n c e s
s t a t i s t i c , S I i s computed as t h e number o f p o s i t i v e d i f k k n c e s minus t h e numb e r o f negative differences. This i s ,
ly'.-+
.
n
n-1
s =
...,
c
c
k=l
j=k+l
s g n ( Y -Yk)
j
where s g n ( Y -Yk)
j
1 i f Y . - Y >O
3 k
= 0 i f Y . - Y =O
l
k
= -1 i f Y .-Yk<O
I
=
I f S i s a l a r g e p o s i t i v e number, measurements t a k e n l a t e r i n t i m e t e n d t o
be l a r g e r t h a n t h o s e t a k e n e a r l i e r . S i m i l a r l y , i f S i s a l a r g e n e g a t i v e numb e r , measurements t a k e n l a t e r i n t i m e t e n d t o b e s m a l l e r .
P r o b a b i l i t y v a l u e s f o r t h e Mann-Kendall t e s t f o r nS10 a r e g i v e n i n
K e n d a l l ( 1 9 7 5 ) . A n e x t e n s i o n o f t h i s t a b l e up t o n=40 i s g i v e n i n T a b l e A.21
i n H o l l a n d e r and Wolfe ( 1 9 7 3 ) . However, K e n d a l l ( 1 9 7 5 , p. 55) i n d i c a t e s t h a t a
n o r m a l a p p r o x i m a t i o n may b e u s e d f o r n as small. as 1 0 u n l e s s t h e r e a r e many
t i e d d a t a v a l u e s . The t e s t p r o c e d u r e i s t o compute S as d e s c r i b e d b e f o r e . Then
compute t h e v a r i a n c e o f S by t h e f o l l o w i n g e q u a t i o n , w h i c h t a k e s i n t o account
t h a t t i e s may b e p r e s e n t :
-
VAR(S)
= 1/18
[
n(n-1) (2n+5)
-
q
c t ( t -1) ( 2 t
p=l P P
P
+
1
5)
where q i s number o f t i e d groups and t i s number of Y ' s i n t h e p t h t i e group.
F o r example, g i v e n t h e sequence c11, '12,
3, 1 2 , 1 2 , 11) , t h e n t =2 f o r t h e
1
t i e d v a l u e 11, t =3 f o r t h e t i e d v a l u e 1 2 , and q=2.
2
Finally,
lows:
S
and V A R ( S )
a r e used t o compute t h e t e s t s t a t i s t i c
Z
as
fol-
4 -5
Then Z i s checked a g a i n s t t h e s t a n d a r d n o r m a l d i s t r i b u t i o n t o d e t e r m i n e
i f i t i s i n t h e c r i t i c a l r e g i o n . N o t e t h a t f o r l a r g e sample s i z e s , n, t h e t e r m
( S - 1 ) o r ( S + 1 ) can b e a p p r o x i m a t e d as s i m p l y S . T h i s s i m p l i f i c a t i o n i s done i n
t h e WMO program (WMO, 1 9 8 8 ) . N o t e a l s o t h a t t h e WMO program assumes s u f f i c i e n t
d a t a f o r t h e above normal a p p r o x i m a t i o n t o be v a l i d .
I n a s s o c i a t i o n w i t h t h e Mann-Kendall t e s t , one can e s t i m a t e t h e magnitude
o f a t r e n d s l o p e u s i n g an e s t i m a t o r proposed by T h i e l (1950) and Sen ( 1 9 6 8 ) .
Here, t h e e s t i m a t o r B f o r t h e t r e n d s l o p e i s t h e median v a l u e o f
among a l l ( Y . , Y ) p a i r s where l S k < j S n . By u s i n g t h e median o f t h e i n d i v i d u a l
k
d
v a l u e s , &he e s t i m a t o r i s q u i t e r e s i s t a n t t o t h e e f f e c t o f extreme v a l u e s
i i k t h e data.
4.4
Complications
A number o f c h a r a c t e r i s t i c s o f h y d r o l o g i c a l t i m e s e r i e s can c o m p l i c a t e t h e use
o f t h e above-mentioned s i m p l e t r e n d t e s t s . These c o m p l i c a t i o n s i n c l u d e season a l i t y , s e r i a l dependence , and t h e presence o f " l e s s - t h a n " o r " g r e a t e r - t h a n "
v a l u e s ( c e n s o r e d samples).
-
Seasonality
The v a r i a t i o n added b y seasonal o r o t h e r c y c l e s can g r e a t l y
c o m p l i c a t e d e t e c t i o n o f l o n g - t e r m t r e n d s . F o r example,
suppose t h e MannK e n d a l l t e s t i s a p p l i e d t o m o n t h l y s t r e a m f l o w d a t a i n w h i c h t h e r e i s an o v e r a l l upward t r e n d . I n t h i s case, many downtrends c o u l d be c o u n t e d i n making t h e
month-to-month comparisons s i m p l y because f l o w s i n some months a r e n a t u r a l l y
l e s s than those i n others.
Techniques f o r d e a l i n g w i t h s e a s o n a l i t y i n t r e n d t e s t s a r e d i s c u s s e d by
H i r s c h and o t h e r s (1982), van B e l l e and Hughes ( 1 9 8 4 ) , and G i l b e r t ( 1 9 8 7 ) .
G r a p h i c a l t e c h n i q u e s such as t h o s e d e v e l o p e d b y C l e v e l a n d e t a l . (1979) a l s o
may b e u s e f u l i n examining s e a s o n a l i t y (e.g.,
see L i n s , 1987).
There a r e two g e n e r a l p r o c e d u r e s t h a t can be used t o i n c o r p o r a t e a cons i d e r a t i o n o f s e a s o n a l i t y i n t o a t r e n d t e s t . The f i r s t p r o c e d u r e i s t h e u s e o f
p e r i o d i c f u n c t i o n s t o d e s c r i b e t h e s e a s o n a l v a r i a t i o n s . T h i s approach i s easy
t o a p p l y i n c o n j u n c t i o n w i t h a r e g r e s s i o n a n a l y s i s f o r e i t h e r monotonic o r
s t e p t r e n d s . The s i m p l e s t case i s :
Y = B
0
+
B
1
+
sin(2nt)
B
2
cos (21'rt)
+
t r e n d term
+
e
where t i s t i m e i n years.
I f t h e r e s i d u a l s s t i l l show s e a s o n a l i t y ( f o r example as seen by b o x p l o t s
o f t h e r e s i d u a l s ) , a d d i t i o n a l p e r i o d i c f u n c t i o n s can be added w i t h p e r i o d s o f
1 / 2 o r 1 / 3 o r o t h e r f r a c t i o n s o f a y e a r . F o r example
Y = B
+
0
+
+
B sin(2nt)
1
B5 s i n (61'rt)
+
B
6
B
2
cos(21'rt)
cos(61'rt)
+
'+
B
3
sin(4I'rt)
t r e n d term
+
e
+
B cos(41'rt)
4
4-6
One a p p r o p r i a t e way t o d e t e r m i n e how many terms t o u s e i s t o add t h e m ,
two a t a t i m e , t o t h e r e g r e s s i o n and a t each s t e p do an F t e s t f o r t h e s i g n i f i c a n c e o f t h e p a i r o f t e r m s . A s a r e s u l t one may s e t t l e o n a model i n w h i c h
t h e t - s t a t i - s t i c s f o r one o r two o f t h e c o e f f i c i e n t s a r e n o t s i g n i f i c a n t , b u t
as a p a i r t h e y a r e s i g n i f i c a n t . L e a v i n g o u t j u s t t h e s i n e o r just. t h e cosine
s h o u l d n o t be done, because i t f o r c e s t h e p e r i o d i c t e r m t o have a c o m p l e t e l y
a r b i t r a r y phase s h i f t . S c h e r t z and H i r s c h (1985) p r o v i d e a n example o f t h i s
approach.
A d i f f e r e n t approach f o r d e a l i n g w i t h s e a s o n a l i t y can be used w i t h nonp a r a m e t r i c t r e n d t e s t s ( s u c h as t h e Mann-Kendall o r Wilcoxon Rank-Sum t e s t ) .
F o r t h e s e t e s t s , f i r s t compute t h e t e s t s t a t i s t i c and compute i t s e x p e c t a t i o n
and v a r i a n c e under t h e n u l l hypotheses f o r each season. Then, sum t h e t e s t
s t a t i s t i c s t o f o r m t h e new o v e r a l l t e s t s t a t i s t i c . A l s o , sum t h e e x p e c t a t i o n s
a n d sum t h e v a r i a n c e s . G e n e r a l l y , when t h e p r o d u c t o f number o f seasons and
number o f y e a r s i s more t h a n a b o u t 25, t h e d i s t r i b u t i o n o f t h e o v e r a l l t e s t
s t a t i s t i c can b e approximated q u i t e w e l l by a n o r m a l d i s t r i b u t i o n w i t h exp e c t a t i o n e q u a l t o t h e sum o f t h e e x p e c t a t i o n s and v a r i a n c e e q u a l t o t h e sum
o f t h e v a r i a n c e s . The o v e r a l l t e s t s t a t i s t i c can be s t a n d a r d i z e d and compared
t o t h e s t a n d a r d n o r m a l . Parameters l i k e s l o p e s o r s t e p s i z e s can b e computed
i?s medians o f a l l e s t i m a t e s based o n a l l p o s s i b l e p a i r s f r o m each o f t h e seasons. See H i r s c h , e t a l . (1982) and WMO (1988) f o r an example u s i n g t h e MannK e n d a l l t e s t and B r a d l e y (1966) € o r an example o f a p p l y i n g t h e W i l c o x o n RankSum t e s t t o grouped d a t a .
I n t h e l a t t e r case,
t h e groups r e f e r r e d t o by
B r a d l e y c o u l d be seasons.
The approaches d e s c r i b e d above a r e a l l ways o f o b t a i n i n g a s i . n g l e r e s u l t
f o r a g i v e n d a t a s e t i n t e r m s o f an o v e r a l l upward o r downward t r e n d . These
f a i l t o r e v e a l d i f f e r e n c e s i n b e h a v i o r i n d i f f e r e n t seasons. F o r example, i t
i s p o s s i b l e t h a t t h e v a r i a b l e e x h i b i t s a s t r o n g t r e n d i n i t s summer v a l u e s and
n o t r e n d i n t h e o t h e r seasons. Van B e l l e and Hughes (1984) p r o v i d e a s i n g l e
s t a t i s t i c w h i c h c a n b e u s e d t o i n d i c a t e whether seasons a r e b e h a v i n g i n a s i m i l a r f a s h i o n (homogeneous) o r b e h a v i n g d i f f e r e n t l y f r o m each o t h e r ( h e t e r o geneous)
.
S e r i a l Dependence - A l l o f t h e above t e s t s assume independence o f observ a t i o n s . T h i s may b e a s a t i s f a c t o r y assumption f o r some a n n u a l t i m e s e r i e s b u t
becomes l e s s s o as d a t a o f g r e a t e r f r e q u e n c y a r e used. h%en s e r i a l dependence
e x i s t s , t r e n d s w i l l be i n d i c a t e d when none e x i s t s ( t y p e I e r r o r ) more o f t e n
t h a n s p e c i f i e d by t h e n o m i n a l s i g n i f i c a n c e l e v e l , a . There a r e s e v e r a l methods
f o r d e a l i n g w i t h s e r i a l dependence. H i r s c h and S l a c k (1984) d e s c r i b e m o d i f i c a t i o n s t o t h e Mann-Kendall t e s t t o a c c o u n t f o r s e r i a l dependence, and t h e s e a r e
i n c l u d e d i n t K e WMO (1982) computer program f o r a n a l y s i n g h y d r o l o g i c a l d a t a .
L e t t e n m a i e r (1976) uses t h e concept o f e f f e c t i v e independent sample s i z e t o
c h t a i n a d j u s t e d c r i t i c a l . v a l u e s f o r t h e W i l c o x o n Rank-Sum t e s t and Spearman's
r h o c o r r e i a t i o n t e s t ( a t e s t s i m i l a r t o t h e Mann-Kendall t e s t ) . Montgomery and
Reckhow (1984) i l l u s t r a t e L e t t e n m a i e r ' s p r o c e d u r e and p r o v i d e t a b l e s o f c o r rection factors.
I f a l o n g t i m e sequence o f e q u a l l y spaced d a t a i s a v a i l a b l e , i n t e r v e n t i o n
a n a l y s i s (Box and T i a o , 1 9 7 5 ) may h e u s e d t o d e t e c t s t e p t r e n d s i n s e r i a l l y
dependent d a t a . T h i s approach i s a g e n e r a l i z a t i o n o f t h e a u t o - r e g r e s s i v e i n t e c j r a t e d m o v i n g average ( A R I M A ) t i m e s e r i e s models d e s c r i b e d by Box and J e n k i n s
(1976) . A p p l i c a t i o n o f t h e s e models, however, i s n o n t r i v i a l . A l i m i t a t i o n o f
t r a d i t i o n a l i n t e r v e n t i o ~a n a l y s i s i s t h e r e q u i r e m e n t f o r e q u a l l y spaced d a t a ;
m i s s i r i q d a t a o r d a t a r e p o r t e d ds l e s s - t h a n v a l u e s can p r e v e n t i t s use.
I
4- 7
Censored samples - Censored samples a r e r e c o r d s i n w h i c h some o f t h e d a t a
a r e known o n l y t o b e ' ' l e s s t h a n " o r " g r e a t e r t h a n " some t h r e s h o l d . Two common
examples i n h y d r o l o g y a r e c o n s t i t u e n t c o n c e n t r a t i o n s l e s s t h a n t h e d e t e c t i o n
l i m i t and f l o o d s which a r e known t o b e l e s s t h a n some t h r e s h o l d o f p e r c e p t i o n
(e.g. , t h e a n n u a l f l o o d o f 1887 was n o t s u f f i c i e n t l y l a r g e t h a t l o c a l r e c o r d
k e e p e r s b o t h e r e d t o r e c o r d t h e maximum s t a g e ) . There i s no s i m p l e way t o i n c o r p o r a t e censored samples i n a r e g r e s s i o n a n a l y s i s , a l t h o u g h censored maximum
l i k e l i h o o d p r o c e d u r e s can b e used.
The Mann-Kendall t e s t can be u s e d w i t h o u t d i f f i c u l t y , p r o v i d e d t h a t o n l y
one c e n s o r i n g t h r e s h o l d e x i s t s . I n t h a t case, t h e comparisons between a l l
p a i r s o f observations a r e p o s s i b l e . A l l t h e " l e s s thans" a r e considered t o be
t i e d w i t h each o t h e r .
When more t h a n one t h r e s h o l d l i m i t e x i s t s , t h e n t h e Mann-Kendall t e s t
c a n n o t b e done i n a s t r a i g h t f o r w a r d f a s h i o n . C o n s i d e r t h e d a t a s e t : (1, (1, 3,
<5, 7 . How does one compare <1 t o ( 5 o r 3 t o < 5 ? One way t o run t h i s t e s t i s
t o r e c o d e t h e d a t a t o t h e h i g h e r t h r e s h o l d . Thus, t h e d a t a w o u l d become: (5,
( 5 , (5, <5, 7. There i s , however, a l o s s of i n f o r m a t i o n i n making t h i s change.
N o t e t h a t when any censored v a l u e s e x i s t , t h e s l o p e e s t i m a t o r o f T h e i l
and Sen i s n o t a p p r o p r i a t e u n l e s s i t c a n b e d e m o n s t r a t e d t h a t knowledge o f t h e
e x a c t v a l u e s o f t h e censored d a t a w o u l d have n o i m p a c t o n t h e median v a l u e o f
d . k . The s l o p e e s t i m a t o r r e q u i r e s c a l c u l a t i n g d i f f e r e n c e s between v a l u e s and
t i e r e i s no way t o compute a d i f f e r e n c e between say a " l e s s t h a n " and a n o t h e r
number.
5-1
5.
METHODOLOGY FOR DISTINGUISHING BETWEEN MAN'S INFLUENCE AND CLIMATE
5.1
Introduction
There a r e s e v e r a l p o s s i b l e approaches t h a t c a n be used i n an a t t e m p t t o d i s t i n g u i s h between t h e e f f e c t s o f man's a c t i v i t i e s and t h e e f f e c t s o f c l i m a t e o n
a h y d r o l o g i c a l time series.
One p o s s i b l e approach i s t o d i r e c t l y a p p l y t h e s t a t i s t i c a l t r e n d t e s t i n g
p r o c e d u r e s d e s c r i b e d i n Chapter 4 t o t h e h y d r o l o g i c a l t i m e s e r i e s . However,
t h i s approach does n o t d e a l w i t h t h e c o m p l i c a t i o n s t h a t a r i s e f r o m t h e
climate-induced v a r i a b i l i t y i n t h e h y d r o l o g i c a l time series. This n a t u r a l
v a r i a b i l i t y w i l l decrease t h e power o f s t a t i s t i c a l methods t o d e t e c t t r e n d s
when t h e y do e x i s t , and when t r e n d s do n o t e x i s t , can r e s u l t i n f a l s e d e t e c t i o n o f t r e n d s t h a t a r e a r t i f a c t s of t h e h i s t o r y o f c l i m a t i c c o n d i t i o n s d u r i n g
t h e p e r i o d . F o r example, a downtrend f o r a p a r t i c u l a r p e r i o d may b e i n d i c a t e d
s i m p l y because t h e b e g i n n i n g o f t h e p e r i o d was r e l a t i v e l y wet w h i l e t h e l a t t e r
p a r t was r e l a t i v e l y d r y .
A p r e f e r r e d approach i n v o l v e s j o i n t u s e o f models and s t a t i s t i c a l t r e n d
t e s t i n g p r o c e d u r e s . The model i s u s e d t o e x p l a i n t h e n a t u r a l f l u c t u a t i o n s i n
the hydrological variable o f interest,
and t h e s t a t i s t i c a l t r e n d t e s t i s
a p p l i e d t o t h e r e m a i n i n g u n e x p l a i n e d v a r i a b i l i t y . The model may b e e i t h e r one
o f t h e d e t e r m i n i s t i c model t y p e s d e s c r i b e d i n S e c t i o n 3.2 o r a s t a t i s t i c a l
r e g r e s s i o n model t y p e , c f . S e c t i o n 3 . 3 . The methodology i s i l l u s t r a t e d schem a t i c a l l y i n F i g . 5 . 1 . 1 and i s e x p l a i n e d s t e p b y s t e p below.
I f human i n f l u e n c e s have r e s u l t e d i n c l i m a t i c changes, t h e n t h e s e changes
o f t e n would b e r e f l e c t e d i n t h e v a l u e s o f t h e exogeneous v a r i a b l e f o r
r e g r e s s i o n o r i n t h e m e t e o r o l o g i c a l input t o t h e h y d r o l o g i c model. Thus, t h e
p r o c e d u r e s o u t l i n e d i n t h i s c h a p t e r a r e i n t e n d e d t o i s o l a t e t h e t r e n d s due t o
human i n f l u e n c e s on t h e b a s i n h y d r o l o g y f r o m t h e combined e f f e c t s o f c l i m a t i c
v a r i a b i l i t y and c l i m a t i c change.
5.2.
S t e p 1: D e t e r m i n a t i o n o f S t e p o r Monotonic T r e n d A n a l y s i s
I n a p a r t i c u l a r case i t i s n o t always o b v i o u s whether t o t e s t f o r s t e p t r e n d s
o r monotonic t r e n d s . The f o l l o w i n g c o n t a i n s some g e n e r a l r u l e s
(1) A s t e p t r e n d t e s t i s a " b e f o r e " and " a f t e r " t y p e o f t e s t , w h i c h t y p i c a l l y
i s c a r r i e d o u t i n case o f a d i s t i n c t e v e n t . Examples i n c l u d e b e f o r e and
a f t e r development o f a new w e l l f i e l d o r c o n s t r u c t i o n o f a dam. I n t h i s
case,
t i m e s e r i e s d a t a a r e r e q u i r e d f o r two p e r i o d s , w h i c h w i l l b e
d e n o t e d t h e r e f e r e n c e p e r i o d ( b e f o r e e v e n t ) and t h e t e s t . p e r i o d ( a f t e r
e v e n t ) , r e s p e c t i v e l y . The two p e r i o d s may b e some t i m e a p a r t .
5-2
ci'
Start
T
STEP 1
I
Data a v a i l a b l e b o t h
b e f o r e and a f t e r
disturbance data?
STEP 2
I
STEP3
I
STEP4
1
Statistical
regression
mode1
Lumped
conceptual
mode1
-
S t a t i s t i c a l trend t e s t
step trend
- monotonic t r e n d
-
-
-
Distributed
physically
based model
step trend
monotonic t r e n d
Distributed
physically
based model
T
1
1
Further hydrological analysis
- effects o f climate
e f f e c t s o f man's a c t i v i t y
q u a l i t a t i v e consistency
q u a n t i t a t i v e consistency
-
I
(2)
1
f
NO model
STEP5
Fig. 5.1.1
No
Consistency a c c e p t a b l e P 1
NO
r
L
S c h e m a t i z a t i o n o f t h e methodology.
I f t h e r e i s a m a j o r gap i n t h e r e c o r d ( f o r example 1 0 y e a r s o f d a t a ,
f o l l o w e d by a I O - y e a r gap, f o l l o w e d by 5 more y e a r s o f d a t a ) one may want
t o l o o k a t t h e d i f f e r e n c e between t h e " e a r l y " and t h e " l a t e " p e r i o d s by
u s i n g a s t e p t r e n d t e s t , p a r t i c u l a r l y i f t h e d i f f e r e n c e s w i t h i n t h e two
p e r i o d s seem t o b e s m a l l compared t o d i f f e r e n c e s between t h e p e r i o d s . One
can al.so t e s t f o r m o n o t o n i c t r e n d s , i f t h e r e a r e r e a s o n s t o think o f t h e
t r e n d a s a s i n g l e l o n g - t e r m " r a m p " o f c o n s t a n t slope.
5- 3
(3)
I f one l o o k s a t a d a t a s e t g r a p h i c a l l y (by p l o t t i n g t h e v a r i a b l e v e r s u s
t i m e o r by double mass a n a l y s i s ) and sees an a p p a r e n t s t e p change a t a
s p e c i f i c t i m e , but has no a p r i o r i e x p l a n a t i o n f o r t h a t change, a s t e p
t r e n d p r o c e d u r e s h o u l d n o t be u s e d f o r t h a t b r e a k p o i n t . The r e s u l t s w i l l
b e b i a s e d b y t h e p r o c e s s of v i s u a l l y s e l e c t i n g t h e b e s t t i m e t o d i v i d e
t h e d a t a i n t o b e f o r e and a f t e r s e t s . I f one were t o use t h i s p r o c e d u r e o n
t r u l y s t a t i o n a r y d a t a and s e t t h e a l p h a l e v e l t o 0 . 0 5 ,
significant
changes w o u l d be d e t e c t e d i n more t h a n 5 % o f t h e cases.
-
G e n e r a l l y , t h e p e r i o d s s h o u l d be as l o n g as p o s s i b l e i n o r d e r t o e n s u r e
as p o w e r f u l a s t a t i s t i c a l t e s t as p o s s i b l e . I n p r a c t i c e , t h e p e r i o d l e n g t h s
w i l l b e l i m i t e d by t h e d a t a a v a i l a b i l i t y and by t h e r e s o u r c e s made a v a i l a b l e
f o r a g i v e n s t u d y . I n t h e case o f a d e t e r m i n i s t i c model a p p l i c a t i o n t h e l e n g t h
o f t h e p e r i o d s s h o u l d a l l o w a p r o p e r model c a l i b r a t i o n and v a l i d a t i o n , t y p i c a l l y a t l e a s t on t h e o r d e r o f 3-10 y e a r s depending on t h e p a r t i c u l a r model
and t h e p a r t i c u l a r catchments. F u r t h e r m o r e , t h e r e f e r e n c e p e r i o d s h o u l d , i f
p o s s i b l e , comprise b o t h dry and wet c l i m a t e segments.
5.3
Step 2 :
S e l e c t i o n o f Model Type
S t e p 2 i n v o l v e s t h e s e l e c t i o n o f an a p p r o p r i a t e model t o b e used t o a c c o u n t
f o r and remove t h e h y d r o l o g i c a l e f f e c t s o f c l i m a t e v a r i a b i l i t y . I f s u f f i c i e n t
d a t a a r e a v a i l a b l e f o r t h e s e l e c t e d p e r i o d ( s ) , b a s i c a l l y f o u r a l t e r n a t i v e opt i o n s e x i s t w i t h r e s p e c t t o t h e m o d e l l i n g approach:
(1)
(2)
(3)
(4)
No model
D e t e r m i n i s t i c , lumped, c o n c e p t u a l models
D e t e r m i n i s t i c , d i s t r i b u t e d , p h y s i c a l l y based models
S t a t i s t i c a l r e g r e s s i o n models
The "no model" approach i s as m e n t i o n e d p r e v i o u s l y g e n e r a l l y n o t p r e f e r r e d , because i t i s n o t a b l e t o a c c o u n t f o r t h e c l i m a t e i n d u c e d v a r i a b i l i t y
i n t h e h y d r o l o g i c a l time series.
The t h r e e m o d e l l i n g approaches do n o t i n p r i n c i p l e have t h e above d i s advantages, because a model s h o u l d b e a b l e t o e x p l a i n some o f t h e v a r i a b i l i t y
o f t h e concerned h y d r o l o g i c a l v a r i a b l e t h a t r e s u l t s f r o m t h e c l i m a t e v a r i a b i l i t y . I t i s i m p o r t a n t t o n o t e t h a t t h e u t i l i t y o f a model as p a r t o f t h e t r e n d
t e s t i s dependent on t h e s t r e n g t h o f t h e c o r r e l a t i o n o f t h e s i m u l a t e d v a l u e s
w i t h t h o s e t h a t would have o c c u r r e d n a t u r a l l y a t t h e s i t e o f i n t e r e s t . I n h e r e n t b i a s i n an u n c a l i b r a t e d h y d r o l o g i c a l model t o u n d e r p r e d i c t o r o v e r p r e d i c t
on average i s o f l e s s concern, so l o n g as d i f f e r e n t model b i a s does n o t e x i s t
under d i f f e r e n t c l i m a t i c c o n d i t i o n s .
The q u e s t i o n r e g a r d i n g w h i c h o f t h e t h r e e model t y p e s t o s e l e c t c a n n o t b e
u n i v e r s a l l y answered. However, some f a c t o r s t o b e t a k e n i n t o a c c o u n t a r e :
(a)
Advantages o f r e g r e s s i o n models a r e t h a t t h e y a r e easy t o a p p l y , and i n
many s i t u a t i o n s , may be j u s t as e f f e c t i v e as t h e use o f h y d r o l o g i c a l
models f o r a p a r t i c u l a r t r e n d a p p x i c a t i o n . The advantage o f t h e u s e o f a
h y d r o l o g i c a l model i s t h a t i t may b e t t e r e x p l a i n t h e n a t u r a l h y d r o l o g i c a l
v a r i a b i l i t y and hence r e s u l t i n a more p o w e r f u l s t a t i s t i c a l t r e n d t e s t .
I n some cases, t h e u s e o f a h y d r o l o g i c a l model may a l l o w f o r f u r t h e r
h y d r o l o g i c a l a n a l y s i s as d e s c r i b e d i n S t e p 5 .
5-4
(b)
The lumped, c o n c e p t u a l models a r e g e n e r a l l y r a i n f a l l - r u n o f f
models and
a r e a p p l i c a b l e f o r t r e n d t e s t s r e g a r d i n g s t r e a m f l o w v a r i a h l e s . However,
i f t h e h y d r o l o g i c a l v a r i a b l e o f i n t e r e s t f o r the t r e n d t e s t deals w i t h
ground w a t e r t h i s model t y p e w i l l o f t e n n o t be a f e a s i b l e c h o i c e . B o t h
r e g r e s s i o n models and d i s t r i b u t e d , p h y s i c a l l y based models can be a p p l i e d
t o b o t h ground w a t e r and s t r e a m f l o w .
(c)
There i s t h e p o s s i b i l i t y t h a t by u s i n g a d i s t r i b u t e d , p h y s i c a l l y based
model t h e man-induced changes c a n b e accounted f o r i n t h e model p a r a m e t e r s and hence a d i s t i n c t i o n can b e made between t h e e f f e c t s o f c l i m a t e
and man's i n f l u e n c e . I n t h i s way a q u a n t i t a t i v e c o n s i s t e n c y may b e t e s t e d
i n t h e f i n a l h y d r c l o g i c a l a n a l y s i s i n S t e p 5.
(d)
I n some cases o n l y t h e d i s t r i b u t e d , p h y s i c a l l y based models a r e a p p l i c a b l e , i n p a r t i c u l a r i f d a t a f o r t h e concerned v a r i a b l e , e.g. s t r e a m f l o w ,
are e i t h e r n o t a v a i l a b l e o r o n l y a v a i l a b l e f o r t o o s h o r t a sub-period
w i t h i n one o f t h e two s e l e c t e d p e r i o d s .
(e)
The r e g r e s s i o n and h y d r o l o g i c a l m o d e l l i n g approaches can be used i n
c o m b i n a t i o n b y u s i n g t h e o u t p u t f r o m a h y d r o l o g i c a l model - c a l i b r a t e d
outside the t e s t period
as t h e exogenous v a r i a b l e i n a r e g r e s s i o n
e q u a t i o n . Furthermore b o t h r e g r e s s i o n models and h y d r o l o g i c a l models may
b e u s e d s e p a r a t e l y as somewhat independent t e s t s f o r t r e n d .
-
5.4
Step 3 : Model C a l i b r a t i o n , V a l i d a t i o n and A p p l i c a t i o n
The p r o c e d u r e s f o r model c a l i b r a t i o n , v a l i d a t i o n and a p p l i c a t i o n depend o n
w h i c h model t y p e i s used and t h e t y p e o f t r e n d t e s t .
I t i s emphasized t h a t a p r o p e r model v a l i d a t i o n i s a p r e r e q u i s i t e f o r a
subsequent model a p p l i c a t i o n f o r t h e p r e s e n t purpose. I n t h e s u b s e c t i o n s below
t h e names o f a numbex o f d i f f e r e n t t e s t s a r e g i v e n . These t e s t s a r e d e s c r i b e d
b r i e f l y i n Subsection 3.2.5
and i n more d e t a i l i n Klemes ( 1 9 8 5 ) and Klemes
(1986).
5 . 4 . 1 Lumped, c o n c e p t u a l models
---------___----___------------
- Step .trend t e s t
........................
Case 1
The f o l l o w i n g d e s c r i p t i o n a p p l i e s t o t h e s t e p t r e n d t e s t case, where two per i o d s ha.ve been s e l e c t e d , namely a t e s t p e r i o d and a r e f e r e n c e p e r i o d .
(1)
C a l i b r a t e and v a l i d a t e t h e model u s i n g h i s t o r i c a l d a t a f r o m t h e r e f e r e n c e
period. Preferably a d i f f e r e n t i a l split-sample t e s t should b e c a r r i e d o u t
a s f o l l o w s . I f t h e t e s t p e r i o d i s g e n e r a l l y more wet t h a n t h e r e f e r e n c e
p e r i o d , t h e model s h o u l d b e c a l i b r a t e d on a d r y segment and v a l i d a t e d o n
a wet segment o f t h e r e f e r e n c e p e r i o d , o r v i c e v e r s a . Ifi t i s n o t poss i b l e t o i d e n t i f y such segments w i t h s u f f i c i e n t l y d i f f e r e n t c l i m a t i c cond i t i o n s w i t h i n t h e r e f e r e n c e p e r i o d t h e model s h o u l d b e t e s t e d i n t h e
above manner i n a s u b s t i t u t e catchment, and an o r d i n a r y s p l i t - s a m p l e t e s t
s h o u l d b e c a r r i e d o u t i n t h e catchment of i n t e r e s t . O n l y by such a comp r e h e n s i v e model t e s t i n g , can i t be ensured t h a t t h e tal-ibrated model
5-5
i s a b l e t o s i m u l a t e o t h e r p e r i o d s w i t h t h e same degree o f a c c u r a c y as i n
t h e c a l i b r a t i o n p e r i o d , p r o v i d e d n o changes i n catchment c h a r a c t e r i s t i c s
take place.
(2)
Make model s i m u l a t i o n s f o r t h e t e s t p e r i o d by u s e of t h e p a r a m e t e r s
o b t a i n e d f r o m c a l i b r a t i o n o n t h e r e f e r e n c e p e r i o d and by u s e o f t h e
c l i m a t e d a t a from t h e t e s t p e r i o d .
The above procedure assumes t h a t any b i a s t h a t i s i n t r o d u c e d i n t o t h e
model parameters b y t h e c a l i b r a t i o n would a l s o have been i n t r o d u c e d , i f t h e
model c o u l d b e c a l i b r a t e d t o t h e t e s t p e r i o d under n a t u r a l c o n d i t i o n s .
- Monotonic t r e n d t e s t
__________________-----------
Case 2
when t e s t i n g f o r monotonic t r e n d s , t h e h y d r o l o g i c a l model s h o u l d n o t b e c a l i b r a t e d t o t h e b a s i n o f i n t e r e s t u s i n g any d a t a f r o m t h e t e s t p e r i o d d u r i n g
w h i c h t r e n d s a r e b e i n g examined. O t h e r w i s e , some o f t h e a d j u s t m e n t s i n model
parameters t h a t r e s u l t f r o m t h e c a l i b r a t i o n p r o c e s s may account f o r S O I ~ o f
t h e t r e n d s . T h i s can o c c u r i n comp1.e.x and u n p r e d i c t a b l e ways. Thus, t h e model
s h o u l d be e i t h e r : ( a ) u n c a l i b r a t e d and use b e s t e s t i m a t e s o f t h e model p a r a m e t e r s under n a t u r a l c o n d i t i . o n s ( t h e s e may b e r e g i o n a l i z e d e s t i m a t e s f r o m
o t h e r a p p l i c a t i o n s o f t h e model) , o r (b) c a l i b r a t e d t o a p r e v i o u s p e r i o d n o t
i n c l u d e d i n t h e t r e n d t e s t d u r i n g w h i c h t h e r e was m i n i m a l human i n f l u e n c e o n
t h e h y d r o l o g i c a l t i m e s e r i e s . I f an u n c a l i b r a t e d model i s a p p l i e d , t h e model
s h o u l d have passed a p r o x y - b a s i n d i f f e r e n t i a l split,-sample t e s t t o v e r i f y i t s
c a p a b i l i t y t o s i m u l a t e d i f f e r e n t c l i m a t e c o n d i t i o n s i n an ungauged catchment.
I f c a l i b r a t i o n i s c a r r i e d o u t on a p r e v i o u s p e r i o d , t h e t e s t r e q u i r e m e n t i s a
d i f f e r e n t i a l s p l i t - s a m p l e t e s t f o r changes i n c l i m a t e c o n d i t i o n s .
D i s t r i b u t e d , p h y s i c a l l y based models
___-_____--__----------------------------5.4.2
Three d i f f e r e n t cases a r i s e depending on d a t a a v a i l a b i l i t y and t e s t p r o c e d u r e ,
see F i g . 5 . 4 . 1 .
The p r o c e d u r e i s s i m i l a r t o t h e s t e p t r e n d t e s t case f o r lumped, c o n c e p t u a l
models, c f . Subsection 5.4.1,
Case 1, w i t h t h e e x c e p t i o n t h a t t h e e f f e c t s o f
t h e man-induced changes may a l s o b e p r e d i c t e d by u s e o f t h e model.. Hence t h e
p r o c e d u r e i s as f o l l o w s :
(1)
C a l i b r a t e and v a l i d a t e t h e model u s i n g h i s t o r i c a l d a t a f r o m t h e r e f e r e n c e
period.
The r e q u i r e m e n t s f o r
t e s t procedures a r e a s d e s c r i b e d i n
S u b s e c t i o n 5.4.1,
a d i f f e r e n t i a l s p l i t sample t e s t € o r changes i n c l i m a t e
conditions.
(2)
Make t w o model s i m u l a t i o n s f o r t h e t e s t p e r i o d :
o
One s i m u l a t i o n where t h e model parameters a r e unchanged as compared
t o t h e reference p e r i o d ( t i m e s e r i e s S I M ) . This t i m e s e r i e s w i l l be
1
used i n t h e s t a t i s t i c a l t r e n d t e s t ( S t e p 4 ) .
5-6
o
Another s i m u l a t i o n where t h e man-induced changes i n catchment char a c t e r i s t i c s a r e accounted f o r d i r e c t l y i n t h e model parameters
(time series SIM )
T h i s model s i m u l a t i o n serves as a t e s t o f t h e
2
m o d e l ' s a b i l i t y t o p r e d i c t t h e e f f e c t s o f changes i n catchment char a c t e r i s t i c s , and w i l l be u s e d i n t h e f u r t h e r h y d r o l o g i c a l a n a l y s i s
( S t e p 5 ) . Note t h a t S I M
and S I M
are i d e n t i c a l i n t h e reference,
1
2
but n o t i n the t e s t period.
.
Case
2:
S t e p t r e n d t e s t . Data a v a i l a b l e f o r o n l y one p e r i o d
_______________---------------------------------------------I n case o f a s t e p t r e n d t e s t , where d a t a a r e o n l y a v a i l a b l e f o r one p e r i o d ,
denoted t h e t e s t p e r i o d , t h e p r o c e d u r e i s as f o l l o w s :
(1) C a l i b r a t e and v a l i d a t e
period,
(differential
conditions).
t h e model u s i n g h i s t o r i c a l d a t a from t h e t e s t
split-sample
test
for
changes
in
climate
(2)
Make p r o x y - b a s i n d i f f e r e n t i a l s p l i t - s a m p l e
u s i n g d a t a f r o m o t h e r catchments.
(3)
Make two model s i m u l a t i o n s :
o
tests
for
catchment
change
One s i m u l a t i o n where t h e model p a r a m e t e r s correspond t o t h e c a t c h ment c h a r a c t e r i s t i c s v a l i d i n t h e r e f e r e n c e p e r i o d ( t i m e s e r i e s
SIM
1.
1
o
Another s i m u l a t i o n where t h e model parameters
a c t u a l catchment c h a r a c t e r i s t i c s v a l i d i n t h e
series S I M 1.
2
correspond t o t h e
t e s t p e r i o d (time
Comparison o f S I M and S I M w i l l be used t o e s t i m a t e t h e e f f e c t s o f t h e
1
changes i n catchment c h a r a c 5 e r i s t i c s ( S t e p 5 ) .
F o r t h e same reasons as d i s c u s s e d i n S u b s e c t i o n 5 . 4 . 1 n e i t h e r model c a l i b r a t i o n n o r v a l i d a t i o n s h o u l d b e c a r r i e d o u t t o any o f t h e d a t a t o b e used f o r
t h e subsequent s t a t i s t i c a l t e s t p r o c e d u r e . Thus t h e procedure i s :
C a l i b r a t e and v a l i d a t e t h e model e i t h e r o n o t h e r catchments ( p r o x y - b a s i n
d i f f e r e n t i a l s p l i t - s a m p l e t e s t f o r changes i n c l i m a t e c o n d i t i o n s ) o r on
t h e same catchment b u t u s i n g a p r e v i o u s p e r i o d ( d i f f e r e n t i a l s p l i t sample
t e s t f o r changes i n c l i m a t e c o n d i t i o n s ) .
Make d i f f e r e n t i a l
o t h e r catchments.
split-sample
tests for
catchment
change on d a t a f r o m
Make t w o model s i m u l a t i o n s f o r t h e e n t i r e p e r i o d :
0
One s i m u l a t i o n ,
where t h e model parameters a r e k e p t c o n s t a n t ,
c o r r e s p o n d i n g t o t h e catchment c h a r a c t e r i s t i c s a t a p a r t i c u l a r t i m e ,
e.g. a t t h e b e g i n n i n g o f t h e p e r i o d ( S I M 1 . T h i s t i m e s e r i e s w i l l be
1
used i n t h e s t a t i s t i c a l t r e n d t e s t ( S t e p 4 ) .
5-7
CASE1:
-
STEP TREND TEST
DATA A V A I L A B L E FOR BOTH PERIODS
Time
Reference
Test
Series
Period
Period
Explanation
1-1
SIMl
SIM2
DEVl
DEVZ
CASE2:
OB S
p7777771
I-
STEP TREND TEST
---
-4
- DATA A V A I L A B L E F O R
P a r a m e t e r va l u z s
f r o m r e f e r e n c e perj.od
Parameter v a l u e s f r o m
actual periods
OBS-SIM1
OBS-SIM2
O N L Y ONE PERIOD
Parameter
reference
S IMI
SIM2
p7777771
values from
period
parameter values
from t e s t p e r i o d
OBS-SIM1
DEV2
CASE3:
+----I
OBS-SIM2
MONOTONIC T R E N D T E S T
OBS
Fig. 5.4.1
o
SIM1
Constant parameter values
SIM2
Actual transient
parameter values
DEVl
OBS-SIM1
DEV
OBS-SIM,
..
Observed r e c o r d s ( O B S ) , s i m u l a t e d r e c o r d s ( S I M and S I M 1 ,
2
and d e r i v e d t e s t d a t a s e t (DEV and DEV ) € o r &he t h r e e cases
2
t h a t o c c u r when d i s t r i b u t e d , p k y s i c a l l y based models a r e a p p l i e d .
Another s i m u l a t i o n , where t h e model p a r a m e t e r s a r e t r a n s i e n t c o r r e s p o n d i n g t o t h e a c t u a l c h a n g i n g catchment c h a r a c t e r i s t i c s ( S I M 2 ) .
T h i s t i m e s e r i e s w i . 1 1 be used i n t h e f u r t h e r h y d r o l o g i c a l a n a l y s i s
(Step 5 ) .
5 -8
5.4.3 S t a t i s t i c a l r e g r e s s i o n models
___-_----__-_____-___-------------A s i m p l e m o d e l l i n g approach i s t o p e r f o r m r e g r e s s i o n on an "exogeneous v a r i . -
a b l e " t h a t should e x p l a i n a l a r g e p a r t o f t h e n a t u r a l v a r i a b i l i t y o f t h e v a r i a b l e b e i n g t e s t e d f o r t r e n d . The exogenous v a r i a b l e s h o u l d b e f r e e o f t r e n d
due t o human m o d i f i c a t i o n s o f t h e b a s i n h y d r o l o g y . Examples o f c a n d i d a t e exogenous v a r i a b l e s i n c l u d e p r e c i p i t a t i o n d e p t h and s t r e a m f l o w a t a n e a r b y r e l a t i v e l y u n a f f e c t e d s t a t i o n . The u s e o f s t a t i s t i c a l r e g r e s s i o n models i n conj u n c t i o n w i t h t r e n d t e s t i n g i s d i s c u s s e d i n S t e p 4.
5.5
S t e r , 4:
Trend T e s t
The n u l l h y p o t h e s i s , H , i s t h a t t h e r e i s no t r e n d i n t h e d a t a sample. The
e x a c t p r o c e d u r e used ?o p e r f o r m a t r e n d t e s t depends o n w h i c h m o d e l l i n g
approach i s used.
The d a t a w h i c h w i l l be s u b j e c t t o t h e t e s t a r e t h e t i m e s e r i e s OBS as d e f i n e d
by :
Y1,
".. ,Yi'
... , Yn,
.Y
n+m
where Y i s t h e observed v a l u e , n and m a r e t h e number o f o b s e r v a t i o n s i n t h e
i
r e f e r e n c e and t e s t p e r i o d , r e s p e c t i v e l y , i n case o f a s t e p t r e n d t e s t and n+m
i s t h e number o f o b s e r v a t i o n s f o r t h e s i n g l e t e s t p e r i o d i n t h e case o f a monotonic trend test.
The t e s t s € o r s t e p t r e n d and monotonic t r e n d t h e n f o l l o w s t h e p r o c e d u r e s
o u t l i n e d i n S e c t i o n s 4.2 and 4.3, r e s p e c t i v e l y .
I f t h e n u l l h y p o t h e s i s i s accepted, no s i g n i f i c a n t t r e n d can b e d e t e c t e d
i n t h e a n a l y s e d v a r i a b l e . I f , on t h e o t h e r hand, a s i g n i f i c a n t t r e n d e x i s t s ,
i t has n o t y e t been i d e n t i f i e d , whether t h i s t r e n d i s t h e r e s u l t o f man's i m p a c t o r due t o c l i m a t e e f f e c t s . The recommended procedure € o r t h a t purpose i s
o u t l i n e d b elow.
5.5.2 Lumped, c o n c e p t u a l models
...............................
The d a t a w h i c h w i l l be s u b j e c t t o t h e t e s t a r e t h e t i m e s e r i e s DEV as d e f i n e d
1
by :
el,...,ei,...lenlen+Ir...re
where e
i
n+m
i s t h e r e s i d u a l ( t h e observed v a l u e l e s s t h e s i m u l a t e d v a l u e ) .
Again,
t h e t e s t s f o l l o w t h e p r o c e d u r e s o u t l i n e d i n S e c t i o n s 4.2
I
and 4.3.
5- 9
I f t h e n u l l h y p o t h e s i s , i . e . no t r e n d i n t h e r e s i d u a l v a l u e s , i s a c c e p t ed, t h e n t r e n d i n t h e h y d r o l o g i c a l t i m e s e r i e s may be e x p l a i n e d by c l i m a t e e f f e c t s . If,
on t h e o t h e r hand, t h e h y p o t h e s i s i s r e j e c t e d , i t c a n be c o n c l u d e d
t h a t some s i g n i f i c a n t changes i n t h e catchment c h a r a c t e r i s t i c s h a v e o c c u r r e d .
F u r t h e r , t.he e f f e c t o f t h e s e catchment changes can b e e s t i m a t e d f r o m t h e s t a t i s t i c a l analyses.
The same p r o c e d u r e f o r s t a t i s t i c a l t r e n d t e s t i n g as d e s c r i b e d f o r t h e lumped
c o n c e p t u a l models i n S u b s e c t i o n 5 . 5 . 2
above w i t h t h e e x c e p t i o n o f t h e case
where d a t a a r e a v a i l a b l e f o r o n l y one p e r i o d ( t e s t p e r i o d ) as d e s c r i b e d i n
Case 2 o f S u b s e c t i o n 5.4.2.
Although a s t a t i s t i c a l s t e p t r e n d
f u r t h e r h y d r o l o g i c a l a n a l y s i s (Step 5)
and man's a c t i v i t y s e p a r a t e l y . As p a r t
a s t e p t r e n d t e s t may be c a r r i e d o u t ,
see S u b s e c t i o n 5.6.3.
t e s t i s s t r i c t l y n o t v a l i d i n Case 2,
may r e v e a l t h e e f f e c t s o f b o t h c l i m a t e
o f such f u r t h e r h y d r o l o g i c a l a n a l y s i s ,
a l t h o u g h i n a s l i g h t l y d i f f e r e n t way,
5
. 5 . 4 S t a t i s t i c a l r e g r e s s i o n models
-_----__----_----____--------------The p r o c e d u r e i s somewhat d i f f e r e n t when a r e g r e s s i o n model i s used t o a c c o u n t
€ o r t h e n a t u r a l v a r i a b i l i t y . The e x a c t p r o c e d u r e used t o i n c o r p o r a t e c l - i m a t i c
v a r i a b i l i t y i n t o t h e a n a l y s i s w i l l depend on whether a p a r a m e t r i c o r nonparam e t r i c t r e n d t e s t i s used i n c o n j u n c t i o n w i t h t h e r e g r e s s i o n model.
_____-__________-__
P a r a m e t r i c Approach
A method o f a c c o u n t i n g € o r c i m a t i c v a r i a b i l i t y i s most s t r a i g h t f o r w a r d i n t ne
case o f o v e r a l l use o f r e g r e s s i o n t o s i m u l t a n e o u s l y t e s t f o r monotonic t r e n d s
and t o account f o r c l i m a t i c e f f e c t s . I n t h a t case, a m u l t i p l e r e g r e s s i o n equat i o n i s f o r m u l a t e d as f o l l o w s :
'
i
= a
+
bf(X.1
1
+
cT
i
+
e
i
i=l,...,
n
+
m
(Eq.
5.4.1)
where Y denotes t h e h y d r o l o g i c a l v a r i a b l e o f i n t e r e s t , X denotes an exogenous
v a r i a b l e t o account f o r t h e e f f e c t s o f c l i m a t i c v a r i a b i l i t y , T denotes t i m e , e
i s t h e r e s i d u a l , and n + m i s t h e number o f t i m e p e r i o d s . The t e r m f ( X ) c o u l d
be X, b u t t h e r e may be reasons f o r u s i n g a s i m p l e f u n c t i o n such as R n X o r 1 / X .
E q u a t i o n 5 . 4 . 1 i s shown i n t e r m s o f a s i n g l e exogenous v a r i a b l e , however, sev e r a l c o u l d b e used s i m u l t a n e o u s l y . Terms c o u l d a l s o b e added t o a c c o u n t f o r
s e a s o n a l i t y as d i s c u s s e d i n S e c t i o n 4.3.
The p r o c e d u r e f o r t e s t i n g € o r monotonic t r e n d s u s i n g r e g r e s s i o n i s as f o l l o w s :
(a)
S e l e c t exogenous v a r i a b l e s t h a t s h o u l d b e c o r r e l a t e d with t h e h y d r o l o g i c a l v a r i a b l e o f i n t e r e s t under n a t u r a l conditions.
(b)
Determine t h e b e s t r e g r e s s i o n e q u a t i o n Y . = a -t b f ( X . ) + e . ( S e a s o n a l i t y
1
1
terms a l s o s h o u l d be added t o t h e r e g r e s s i o n model a t t h i s p o i n t , as
5-10
a p p r o p r i a t e ) . Examine t h e e r r o r s o f t h i s model t h r o u g h r e s i d u a l p l o t s and
o t h e r d i a g n o s t i c checks t o a s s u r e t h a t t h e assumptions o f t h e model a r e
met.
(c)
used.
I f a s t a t i s t i c a l l y s i g n i f i c a n t model was n o t found d u r i n g s t e p b, t h e n
s i m p l y a p p l y t h e r e g r e s s i o n model Y
= a + cT
+ e i as i n S e c t i o n 4.2.
i
i
O t h e r w i s e , a p p l y Eq. 5.4.1.
The n u l l h y p o t h e s i s o f no t r e n d i s t h a t c = 0
and t h e magnitude o f t h e t r e n d s l o p e i s e s t i m a t e d by t h e v a l u e o f c .
N o t e t h a t more e l a b o r a t e r e g r e s s i o n models o f t h e t i m e t e r m
F o r example, an i n t e r a c t i o n t e r m c o u l d be added r e s u l t i n g i n
'i
= a
+
bf(Xi)
+
CT
i
+
d f (Xi)Ti
+
c o u l d be
ei.
I n c l u d i n g t h e i n t e r a c t i o n t e r m i n t h e model a l l o w s t h e s l o p e o f t h e Y vs.
x r e l a t i o n s h i p t o change w i t h t i m e . Note, however, t h a t t h e c o e f f i c i e n t c i s
n o l o n g e r s i m p l y i n t e r p r e t e d as t h e magnitude o f t h e t r e n d s l o p e .
These more complex models s h o u l d b e examined o n l y a f t e r t h e e x i s t e n c e o f
a s i g n i f i c a n t t r e n d i s e s t a b l i s h e d u s i n g t h e s i m p l e r model (Eq. 5 . 4 . 1 ) . T r y i n g
models w i t h d i f f e r e n t t r e n d terms u n t i l a s t a t i s t i c a l l y s i g n i f i c a n t model i s
d i s c o v e r e d r e s u l t s i n s t r o n g b i a s e s t o w a r d f i n d i n g a s i g n i f i c a n t t r e n d when
none e x i s t s .
A s l i g h t m o d i f i c a t i o n o f t h e above approach can be used t o t e s t f o r s t e p
t r e n d s by s u b s t i t u t i n g an i n d i c a t o r v a r i a b l e f o r T
(see S e c t i o n 4.3, p. 4 - 4 ) .
i
F o r t h e p a r a m e t r i c approach d e s c r i b e d above, one can combine i n t o a s i n g l e
r e g r e s s i o n model an exogenous t e r m t o a c c o u n t f o r t h e e f f e c t s o f c l i m a t e and a
t i m e t e r m t o account f o r t h e t r e n d . T h i s i s n o t t h e case w h e n u s i n g a r e g r e s s i o n model t o account f o r t h e c l i m a t i c e f f e c t s and a n o n p a r a m e t r i c t e s t
for trend analysis.
One approach t h a t h a s been recommended (Guy, 1957; H i r s c h e t a l . , 1982;
and G i l b e r t , 1987) i s t o p e r f o r m t h e t r e n d t e s t i n two s t e p s . F i r s t , f i t a
r e g r e s s i o n model o f t h e v a r i a b l e o f i n t e r e s t on an exogenous v a r i a b l e . Then,
a p p l y t h e n o n p a r a m e t r i c t e s t t o t h e r e s i d u a l s f r o m t h e r e g r e s s i o n model. T h i s
approach i s s i m i l a r t o t h a t d e s c r i b e d i n S u b s e c t i o n 5.5.2
f o r use w i t h a
h y d r o l o g i c a l model. See S e c t i o n 7.3 f o r an example o f t h i s approach.
The above method i s easy t o a p p l y i n p r a c t i c e . A l i m i t a t i o n o f t h e method
i s t h a t i t w i l l t e n d t o u n d e r e s t i m a t e t h e magnitude o f t h e t r e n d and t o r e s u l t
i n some l o s s i n power as a r e s u l t o f i g n o r i n g t h e i n t e r a c t i o n between t h e exogenous v a r i a b l e and t i m e ( A l l e y , 1 9 8 7 ) . The magnitude o f t h e s e l i m i t a t i o n s and
a p o s s i b l e f i x - u p a r e d i s c u s s e d b y A l l e y ( 1 9 8 8 ) . The problems can b e avoided
by e s t i m a t i n g t h e p a r a m e t e r s o f t h e r e g r e s s i o n model u s i n g d a t a f r o m o u t s i d e
the t e s t period.
5-11
5.6
Step 5: Further Hydrological Analysis
I f i t i s concluded t h a t some s i g n i f i c a n t changes i n catchment c h a r a c t e r i s t i c s
have o c c u r r e d , f u r t h e r h y d r o l o g i c a l a n a l y s e s may b e c a r r i e d o u t . I t s h o u l d b e
p o s s i b l e t o e x p l a i n t h e changes q u a l i t a t i v e l y w i t h i n t h e framework o f t h e
known human a c t i v i t i e s .
The p r o c e d u r e s f o r t h e f u r t h e r
upon t h e s e l e c t e d model approach.
hydrological
analysis
depend v e r y much
I n t h i s case n o f u r t h e r a n a l y s i s can b e c a r r i e d o u t .
5.6.2
o n_
ce
l model
_
_ _ _Lumped,
_ _ _ _ _c _
_p_t u_a_
_____-__------A r e c a l i b r a t i o n o f t h e model s h o u l d b e c a r r i e d o u t u s i n g t h e d a t a f o r t h e t e s t
p e r i o d and a h y d r o l o g i c a l i n t e r p r e t a t i o n o f t h e changes i n model p a r a m e t e r
v a l u e s s h o u l d b e made i n o r d e r t o check q u a l i t a t i v e c o n s i s t e n c y i n t h e t e s t
r e s u l t s . I f some o b v i o u s i n c o n s i s t e n c i e s emerge during t h e h y d r o l c g i c a l anal y s i s , t h e e n t i r e a n a l y s i s s t a r t i n g f r o m S t e p l h a s t o be r e c o n s i d e r e d .
I n t h i s case, t h e a n a l y s i s may b e more q u a n t i t a t i v e because i t may be p o s s i b l e
t o p r e d i c t t h e e f f e c t s o f human a c t i v i t y and compare t h i s w i t h t h e r e c o r d e d
data.
F o r t h i s purpose t h e S I M t i m e s e r i e s d e s c r i b e d i n S u b s e c t i o n 5 . 4 . 2 a r e
2
u t i l i z e d . The approaches f o r t h e t h r e e d i f f e r e n t cases t h a t a r i s e (see S u b s e c t i o n 5 . 4 . 2 o r F i g . 5 . 4 . 1 ) a r e as f o l l o w s :
The t i m e s e r i e s DEV = OBS-SIM i s d e r i v e d as t h e observed minus t h e s i m u l a t e d
2
2
v a l u e s w i t h t h e a c t u a l catchment d a t a . By making a s t a t i s t i c a l t e s t on CEV?
€ o r - t r e n d between t h e r e f e r e n c e and t e s t p e r i o d s i t can b e v e r i f i e d whethe?
t h e model, t h r o u g h changes i n model p a r a m e t e r v a l u e s caused by t h e changes i r !
catchment c h a r a c t e r i s t i c s , i s a b l e t o e x p l a i n t h e d e t e c t e d t r e n d i n t h e obs e r v e d s e r i e s . I f a h y p o t h e s i s o f z e r o t r e n d i n DEV i s accepted, a q u a n t i t a t i v e consistency e x i s t s , w i t h i n t h e u n c e r t a i n t y 2 1 i m i t s accepted i n t h e
s t a t i s t i c a l t e s t , and a n a l y s e s can be made r e g a r d i n g t h e e f f e c t s o f t h e c l i mate and o f t h e catchment, changes, r e s p e c t i v e l y . I f on t h e o t h e r hand t h e
z e r o t r e n d h y p o t h e s i s i s r e j e c t e d , a s i g n i f i c a n t i n c o n s i s t e n c y e x i s t s and t h e
e n t i r e a n a l y s i s s t a r t i n g f r o m S t e p 1. h a s t o be r e c o n s i d e r e d .
5-12
I n t h i s case, a s t e p t r e n d t e s t as c a r r i e d o u t under S t e p 4 i s s t r i c t l y n o t
v a l i d . However, i t i s p o s s i b l e t h r o u g h t h e f o l l o w i n g p r o c e d u r e t o a n a l y z e
whether a s i g n i f i c a n t t r e n d (caused by man's a c t i v i t y ) between t h e r e f e r e n c e
and t h e t e s t p e r i o d s w o u l d have been d e t e c t e d , i f d a t a h a d e x i s t e d a l s o f o r
t h e r e f e r e n c e p e r i o d . T h i s a n a l y s i s r e q u i r e s t h e assumption t h a t t h e human
a c t i v i t i e s a r e p r o p e r l y a c c o u n t e d f o r b y t h e h y d r o l o g i c a l model. T h i s assumpt i o n i s a l s o r e q u i r e d i n Case 1 above, where d a t a a r e a v a i l a b l e f o r b o t h
p e r i o d s . However, t h e assumption i s more c r u c i a l i n t h i s case because d a t a do
n o t e x i s t f o r a r e f e r e n c e p e r i o d , and hence no q u a n t i t a t i v e c o n s i s t e n c y check,
as d e s c r i b e d i n Case 1 above, i s p o s s i b l e h e r e .
The t w o t i m e s e r i e s DEV
= OBS-SIM
and DEV = OBS-SIM
a r e d e r i v e d as
1
t h e observed s e r i e s minus t h e s i m u l a t e d s e r i e s Z u r i n g t h e ? e s t p e r i o d w i t h
p a r a m e t e r v a l u e s c o r r e s p o n d i n g t o no man a c t i v i t y and a c t u a l man a c t i v i t y ,
r e s p e c t i v e l y . A s t a t i s t i c a l t r e n d t e s t i s t h e n c a r r i e d o u t w i t h t h e n u l l hyp o t h e s i s , H , t h a t DEV and DEV can be assumed i d e n t i c a l , i . e . t h a t no t r e n d
1
2
has o c c u r r e g as t h e consequence o f man a c t i v i t y . A s a r e s u l t o f t h i s a n a l y s i s
t h e e f f e c t s o f man's a c t i v i t y a r e e s t i m a t e d . Furthermore, i f t h e H i s r e j e c t 0
e d i t may be c o n c l u d e d t h a t t h e s e e f f e c t s w o u l d have been s 1 g n i f i c a n t . i . f d a t a
h a d e x i s t e d f o r t h e r e f e r e n c e p e r i o d . I f H i s accepted i t may on t h e o t h e r
0
hand be concluded t h a t t h e s e e f f e c t s a r e so s m a l l as compared t o t h e
u n c e r t a i n t i e s i n t h e model p r e d i c t i o n s t h a t t h e y m i g h t n o t have been d e t e c t e d
as s i g n i f i c a n t i f d a t a h a d e x i s t e d f o r t h e r e f e r e n c e p e r i o d .
I n t h i s case t h e p r o c e d u r e i s i d e n t i c a l t o Case 1 above, e x c e p t t h a t a monot o n i c t r e n d t e s t i s c a r r i e d o u t on t h e DEV
time s e r i e s i n s t e a d of a s t e p
2
trend test.
5.6.4 S t a t i s t i c a l r e g r e s s i o n models
....................................
I n t h i s case, no f u r t h e r a n a l y s i s can be c a r r i e d o u t . However, a f t e r a f i r s t
q u i c k a n a l y s i s , S t e p 1-Step 4, u s i n g a s t a t i s t i c a l r e g r e s s i o n model i t may
sometimes b e u s e f u l t o c a r r y o u t more comprehensive a n a l y s i s b y u s i n g a hydrol o g i c a l model i n w h i c h case f u r t h e r h y d r o l o g i c a l a n a l y s i s c a n be made.
I
6-1
6.
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catchment. P a r t 1: Model d e s c r i p t i o n , and P a r t 2 : Simulat i o n s o f s t r e a m f l o w d e p l e t i o n s due t o groundwater a b s t r a c t i o n s . N o r d i c Hydrology, 1 3 , pp. 299-322.
Rogers, C.C.M. , Beven, K.J. , M o r r i s , E.M. , and Anderson, M.G.
(1985) : Sensit i v i t y a n a l y s i s , c a l i b r a t i o n and p r e d i c t i v e u n c e r t a i n t y o f t h e I n s t i t u t e o f
H y d r o l o g y D i s t r i b u t e d Model. J o u r n a l o f H y d r o l o g y , 81, pp. 179-191.
Rumiantsev, V.A.,
K o n d r a t i e v , S.A.,
Kapotova,
O p y t r a z r a b o t k i i primenenia mat.ematicheskikh
( E x p e r i e n c e o n development and a p p l i c a t i o n of
r i v e r basins)
L i n e n g r a d , G i d r o m e t e o i z d a t , pp.
-
N.I.,
L i v a n o v a , N.A.
(1985):
modelei basseinov malykh r e k
m a t h e m a t i c a l models o f s m a l l
94.
S c h e r t z , T.L.,
and H i r s c h , R.M.
( 1 9 8 5 ) : T r e n d a n a l y s i s o f weekly a c i d r a i n
data
1978-83. U. S. G e o l o g i c a l Survey Water Resources I n v e s t i g a t i o n s R e p o r t
85-4211.
-
Sen, P.K.
( 1 9 6 8 ) : E s t i m a t e s o f t h e r e g r e s s i o n c o e f f i c i e n t based on K e n d a l l ’ s
t a u . J o u r n a l o f t h e American S t a t i s t i c a l A s s o c i a t i o n , 63, pp. 1379-1389.
Sherman, L.K.
(1932) : Streamflow f r o m
E n g l i s h News Record, 108, pp. 501-505.
rainfall
by
the
u n i t . g r a p h method.
S t a t e H y d r o l o g i c a l I n s t i t u t e (1.984) : Recommendations on s t a t i s t i c methods f o r
t h e a n a l y s i s o f homogeneity o f space-time v a r i a t i o n s o f s t r e a m f l o w , L e n i n g r a d .
S t a t e H y d r o l o g i c a l I n s t i t u t e (1986) : M e t h o d o l o g i c a l recommendations o f t h e
e s t i m a t i o n o f man’s a c t i v i t y e f f e c t s o n r u n o f f o f m i d - s i z e d and l a r g e r i v e r s
and t h e r e c o v e r y o f r u n o f f c h a r a c t e r i s t i c s , Leningrad..
Storm, B.
( 1 9 8 6 ) : SHE. Systgme H y d r o l o g i q u e Europ6en.
Danish H y d r a u l i c I n s t i t u t e .
A
short
description.
T h i e l , H. ( 1 9 5 0 ) : A r a n k - i n v a r i a n t method o f l i n e a r and p o l y n o m i a l r e g r e s s i o n
a n a l y s i s , P a r t 3, I n : Proceedings o f K o n i n a l i j k e Nederlandse Akademie van
Wetenschatpen A, 53, pp. 1397-1412.
UNESCO (1980) : Casebook o f methods o f c o m p u t a t i o n o f q u a n t i t a t i v e changes i n
t h e h y d r o l o g i c a l regime o f r i v e r b a s i n s due t o human a c t i v i t i e s . S t u d i e s and
r e p o r t s i n Hydrology, 28, P a r i s .
( 1 9 8 4 ) : Nonparametric t e s t s f o r t r e n d i n w a t e r
Van B e l l e , G . , and Bughes, J.P.
q u a l i t y . Water Resources Research, 20, pp. 127-136.
Vinogradov, Yu.B.
(1385) : Model “Ob’em p o l o v o d i a - C G I - 8 2 “
volume - CGI-82’’ M o d e l ) . T r a n s . C G I , v o l . 304, pp. 3-42.
(“Snowmelt
(1987) : GGI-85 Model o f r u n o f f h y d r o g r a p h f o r m a t i o n
Vuglinsky, V.S.
D e s c r i p t i o n . S t a t e H y d r o l o g i c a l I n s t i t u t e , Leningrad, USSR.
flood
- Brief
6-4
Wardlaw, R.B.
( 1 9 7 8 ) : The development o f a d e t e r m i n i s t i c i n t e g r a t e d s u r f a c e / s u b s u r f a c e h y d r o l o g i c a l response model. Ph.D.
T h e s i s , U n i v . of S t r a t c h c l y d e ,
Glasgow.
Weeks, J.B.
e t a 1 ( 1 9 7 4 ) : S i m u l a t e d e f f e c t s of o i l - s h a l e development on t h e
h y d r o l o g y o f t h e Piceance b a s i n , Colorado.
U.S.
G e o l o g i c a l Survey, P r o f e s s i o n a l Paper 908.
W o r l d M e t e o r o l o g i c a l O r g a n i z a t i o n (1988) : A n a l y z i n g l o n g t i m e s e r i e s o f hydrol o g i c a l d a t a w i t h r e s p e c t t o c l i m a t e v a r i a b i l i t y - P r o j e c t d e s c r i p t i o n . World
C l i m a t e Programme A p p l i c a t i o n s WCAP-3, WMO/TD
No. 2 2 4 .
-
7-1
7.
CASE STUDIES
7.1
Introduction
A l t h o u g h many analyses o f man-induced changes as w e l l as o f c l i m a t e e f f e c t s
have been made, few s t u d i e s t h a t f o c u s e x p l i c i t l y on d i s t i n g u i s h i n g between
man's i n f l u e n c e and c l i m a t e have been r e p o r t e d .
A s t h e above methodology i s new and appears as an i n t e g r a t i o n o f s t a t i s t i c a l methods and h y d r o l o g i c a l m o d e l l i n g , w h i c h t r a d i t i o n a l l y have been a p p l i ed s e p a r a t e l y , n o case s t u d i e s , t o t h e a u t h o r s ' knowledge, e x i s t , w h i c h f o l l o w
s t r i c t l y t h e e s t a b l i s h e d methodology. T h e r e f o r e , a few case s t u d i e s have been
p r e p a r e d f o r i l l u s t r a t i v e purposes by e x t r a c t i n g r e s u l t s f r o m and e x t e n d i n g
r e l e v a n t studies.
7- 2
7.2
Groundwater Development i n t h e Kgge
Sus; Catchments, Denmark
A and
T h i s case s t u d y i l l u s t r a t e s t h e a p p l i c a t i o n o f a d i s t r i b u t e d , p h y s i c a l l y based
model.The case s t u d y h a s been d e r i v e d f r o m t h e Susd p r o j e c t , w h i c h i s d e s c r i b ed i n more d e t a i l i n Hansen and D y h r - N i e l s e n (1983) and t h e m o d e l l i n g a c t i v i t i e s i n p a r t i c u l a r i n R e f s g a a r d and Hansen ( 1 9 8 2 ) .
The Sus: p r o j e c t was c a r r i e d o u t i n 1977-81 as p a r t o f a m a j o r D a n i s h I H P
r e s e a r c h p r o j e c t i n t h e Suss Catchment. The main h y d r o l o g i c a l problem i n v e s t i g a t e d i n t h e p r o j e c t was t h e i n t e r a c t i o n between groundwater and s u r f a c e w a t e r
i n o r d e r t o be a b l e t o p r e d i c t t h e h y d r o l o g i c a l consequences on s t r e a m f l o w s
and h y d r a u l i c heads o f groundwater developments. A s p e c i f i c o b j e c t i v e was t o
d e v e l o p a m a t h e m a t i c a l model s u i t a b l e f o r l o w f l o w p r e d i c t i o n .
The s t u d y area, i n c l u d i n g t h e catchments o f Sus3 and t h e n e i g b o u r i n g
catchments K@ge A , V e d s k G l l e A and T r y g g e v e l d e A , c o v e r s a b o u t 1000 k m o f t h e
c e n t r a l and s o u t h e r n p a r t o f Zealand, a t a d i s t a n c e o f 50-70 k m south-west o f
Copenhagen. The model area, t h e t o p o g r a p h i c d i v i d e s , and t h e groundwater model
p o l y g o n a l mesh a r e shown i n F i g . 7.2.1.
9
The w a t e r s u p p l y o f m u n i c i p a l i t i e s and i n d u s t r i e s w i t h i n t h e b a s i n i s
g e n e r a l l y based on l o w - i n t e n s i t y groundwater a b s t r a c t i o n schemes. However, a
c e n t r a l i z e d h i g Q - i n t e n s i t y groundwater a b s t r a c t i o n f o r Copenhagen approximatel y 1 5 m i l l i o n m / y e a r i s l o c a t e d around Reqnemark w i t h i n and j u s t o u t s i d e t h e
n o r t h - e a s t e r n p a r t o f t h e catchment. The groundwater a b s t r a c t i o n d u r i n g t h e
1950-80 p e r i o d i s shown i n F i g . 7.2.2.
Discharge s i t e s
Fig.
7.2.1
Model area,
catchment b o u n d a r i e s and groundwater p o l y g o n a l grid,
and d i s c h a r g e s i t e s u t i l i z e d i n t h e t w o examples.
7- 3
Groundwater o brt roct ion
A (106 myytwrl
Grandvoter obstruction
lm'k)
+
F i g . 7.2.2
The gryundwater a b s t r a c t i o n during t h e 1950-80 p e r i o d w i t h i n t h e
940 k m a r e a c o v e r e d by t h e groundwater model.
F i g . 7.2.3
Schematic d e s c r i p t i o n o f groundwater movements, r e c h a r g e an6 d i s charge areas.
The landscape i s a moraine l a n d s c a p e formed b y g l a c i e r s d u r i n g t h e l a s t g l a shows a schematic c r o s s e c t i o n t h r o u g h one o f t h e m a i n
c i a l p e r i o d . F i g . 7.2.3
r i v e r v a l l e y s and an upstream c r e e k . The l o w e r c o n f i n e d a q u i f e r i s r e g i o n a l
and c o n s i s t s o f l i m e s t o n e . I t i s o v e r l a y e r e d by g l a c i a l d e p o s i t s , p r e d o m i n a n t l y c o n s i s t i n g of moraine c l a y , y e t w i t h some few a r e a s w i t h sandy s o i l . The
t h i c k n e s s o f t h e g l a c i a l d e p o s i t s ranges f r o m l e s s t h a n 1 0 m e t r e s i n a few
p l a c e s i n t h e c e n t r a l p a r t c f t h e catchment, t o more t h a n 100 m e t r e s i n t h e
n o r t h - w e s t e r n p a r t s . The p h r e a t i c w a t e r t a b l e i n t h e g l a c i a l d e p o s i t s i s obs e r v e d t o b e h i g h l y dependent on t h e topography, and i s g e n e r a l l y s i t u a t e d a
c o u p l e o f m e t r e s below t h e g r o u n d s u r f a c e .
7-4
The o v e r a l l s t r u c t u r e o f t h e model i s o u t l i n e d i n F i g . 7 . 2 . 4 .
A s may b e
observed, t h e model c o n s i s t s o f f o u r s e p a r a t e components f o r t h e c o n f i n e d r e g i o n a l a q u i f e r , t h e a q u i t a r d , t h e p h r e a t i c a q u i f e r s and t h e r o o t zone, r e s p e c t i v e l y . T h e t i m e s t e p s i n t h e c a l c u l a t i o n s a r e one day f o r a l l components
of t h e model.
The n e a r l y h o r i z o n t a l groundwater f l o w i n t h e c o n f i n e d r e g i o n a l a q u i f e r
i s accounted f o r b y a t r a d i t i o n a l ,
s p a t i a l l y d i s t r i b u t e d , two-dimensional
model o f t h e i n t e g r a t e d f i n i t e d i f f e r e n c e t y p e .
The l o c a l v e r t i c a l exchange o f w a t e r t h r o u g h t h e a q u i t a r d between t h e
p h r e a t i c and t h e c o n f i n e d a q u i f e r depends on t h e h e i g h t d i f f e r e n c e between t h e
w a t e r t a b l e and t h e p i e z o m e t r i c head. The n o n - s t a t i o n a r y a q u i t a r d f l o w s a r e
c a l c u l a t e d b y n u m e r i c a l i n t e g r a t i o n o f a n a l y t i c a l a q u i t a r d response f u n c t i o n s .
Precipitation
Evaporation
U I l
Jf
Snow storage
1.
Main area
Meadow
97%
Root
zone
Surface
flow from
meadow
areas
Model distribution
M o d e l parameters
Lumped 7 sub-areas
Degree day factor
1 Evapotranspiration
I loss
I
I
I
M a i n area
I
I
I
Meadow
Evapotransporation
parameters
I
Lumped
7 x 5 sub-areas
Phreatic
aquifer
I
I
Meadow
I
I
I
I
M a i n area
Rootdistribution
factor
'
Root depths
I
Leaf-area index
Lumped
7 sub-areas
I
I
I
Field capacity
I
Wilting point
I
Threshold values
I
Bypass constants
I
I
Storage capacities
Meadowarea
in each polygon
Evapotranspiration
loss coming from
baseflow or from
phreatic aquifer
1
I
I
Aquitard
t
--
t
Confined
aquifer
--
Subsurface
outflow,
groundwater
abstraction,
etc.
112 x 4 sub-polygons
Storage coefficient
time constants
112 x 4 sub-polygons
Hydraulic conductivity
specific storage
112 polygons
Transmissivity
storage coefficient
c
Fig.
7.2.4
The v e r t i c a l s t r u c t u r e ,
t h e h y d r o l o g i c a l model.
spatial distribution,
and p a r a m e t e r s o f
The h o r i z o n t a l w a t e r movement i n t h e p h r e a t i c a q u i f e r i s m o d e l l e d as a
d i r e c t r o u t i n g o f r u n o f f t o t h e r i v e r s , l i n e a r l y dependent on t h e h e i g h t of
t h e w a t e r t a b l e e l e v a t i o n above a b a s e f l o w and a d r a i n w a t e r o u t l e t ( e l e v a t i o n
o f t i l e drain pipes).
7-5
F o r t h e r o o t zone c a l c u l a t i o n s , t h e catchment i s d i v i d e d i n t o seven subareas denoted p r e c i p i t a t i o n areas w i t h s e p a r a t e p r e c i p i t a t i o n input and s o i l
parameters. S p a t i a l v a r i a t i o n i n v e g e t a t i o n i s accounted f o r b y s u b d i v i d i n g
each o f t h e seven p r e c i p i t a t i o n areas f u r t h e r i n t o s i x d i f f e r e n t v e g e t a t i o n
a r e a s i n accordance w i t h t h e a c t u a l v e g e t a t i o n d i s t r i b u t i o n w i t h i n each p r e c i p i t a t i o n area.
F o r t h e p r e s e n t p u r p o s e , some m o d e l l i n g r e s u l t s from two catchments have
been e x t r a c t e d and a p p l i e d a c c o r d i n g t o t h e methodology d e s c r i b e d i n C h a p t e r
5. I t i s emphasized t h a t t h e o r i g i n a l s t u d y was n o t c a r r i e d o u t w i t h t h i s
methodology i n mind. Hence t h e two cases have been p r e p a r e d i n c o n n e c t i o n w i t h
t h e p r e s e n t r e p o r t m a i n l y f o r i l l u s t r a t i v e purposes. The m a i n q u e s t i o n t o b e
a n a l y s e d was whether t h e Regnemark groundwater development, i n o p e r a t i o n s i n c e
1964/65 had any s i g n i f i c a n t i n f l u e n c e on s e l e c t e d h y d r o l o g i c a l variables;! i . e .
t h e annual mean f l o w s Q
and y n u a l m i n i m u m f l o w s Q
f o r t h e 1 3 3 k m K@ge
min
A a t L e l l i n g e and f o r thaeve256 k m Sus: a t V e t t e r s l e v .
7.2.2
Example 1: Koge
........................
fi
The m a i n p a r t o f t h e w e l l f i e l d s f o r t h e Regnemark Waterworks i s l o c a t e d w i t h -
i n t h e KGge A catchments, and hence a c o n s i d e r a b l e i n f l u e n c e i s e x p e c t e d o n
t h e r i v e r f l o w s . D i s c h a r g e d a t a was a v a i l a b l e f r o m 1350 onwards and t h u s i n c l u d e 1 4 y e a r s b e f o r e t h e s t a r t o f t h e development.
T h e methodology has been a p p l i e d s t e p by s t e p as f o l l o w s :
A s t e p t r e n d t e s t was s e l e c t e d , because t h e groundwater a b s t r a c t i o n t o t h e
Regnemark Waterworks was i n c r e a s e d f r o m z e r o t o f u l l c a p a c i t y w i t h i n a few
y e a r s . The u n d e r l y i n g monotonic t r e n d i n t h e l o c a l w a t e r s u p p l y , see F i g .
7.2.2,
i s o f m i n o r i m p o r t a n c e i n t h i s catchment and i s hence n e g l e c t e d .
The two p e r i o d s s e l e c t e d f o r a n a l y s i s were 1959-63
1974-78 ( t e s t p e r i o d ) .
( r e f e r e n c e p e r i o d ) and
STEP2: S e l e c t i o n o f model t y p e
..............................
Two a l t e r n a t i v e m o d e l l i n g approaches were c o n s i d e r e d ,
namely
(a)
No model,
(b)
The d i s t r i b u t e d p h y s i c a l l y based Sus5 model d e s c r i b e d above.
i.e.
s t a t i s t i c a l t e s t on t h e r e c o r d e d s t r e a m f l o w d a t a o n l y ,
and
STEP3: Model c a l i b r a t i o n , v a l i d a t i o n and a p p l i c a t i o n
_____-_-_--__--------------------------------------I t i s r e c a l l e d f r o m Chapter 5 t h a t t h e methodology p r e s c r i b e s a model c a l i b r a t i o n on t h e r e f e r e n c e p e r i o d , i n c l u d i n g a d i f f e r e n t i a l s p l i t sample t e s t f o r
changes i n c l i m a t e c o n d i t i o n s . T h i s p r o c e d u r e was n o t f o l l o w e d i n t h e o r i g i n a l
s t u d y and EO r e c a l i b r a t i o n / r e v a l i d a t i o n was c a r r i e d o u t f o r t h e p u r p o s e o f %he
present p r o j e c t
.
7-6
The c a l i b r a t i o n and v a l i d a t i o n p r o c e d u r e i n c l u d e d many o f t h e recommended
elements, such as c a l i b r a t i o n i n one subcatchment and v a l i d a t i o n i n a n o t h e r
( u n c a l i b r a t e d ) subcatchment, c a l i b r a t i o n i n one t i m e p e r i o d and v a l i d a t i o n i n
a n o t h e r t i m e p e r i o d w i t h d i f f e r e n t groundwater pumping r a t e s . F o r d e t a i l s r e g a r d i n g t h e c a l i b r a t i o n and v a l i d a t i o n p r o c e d u r e r e f e r e n c e s a r e made t o t h e
o r i g i n a l r e p o r t s b y S t a n g ( 1 9 8 1 ) , R e f s g a a r d ( 1 9 8 1 ) , and Refsgaard and Stang
( 1 9 8 1 ) . A l e s s d e t a i l e d d e s c r i p t i o n i s g i v e n i n Refsgaard and Hansen (1982).
I n t h e s e p u b l i c a t i o n s a l s o t h e s i m u l a t i o n r e s u l t s are shown w i t h r e s p e c t t o
s t r e a m f l o w , s o i l m o i s t u r e , d r a i n a g e p i p e r u n o f f and p i e z o m e t r i c heads.
I t may be concluded t h a t a comprnhensive t e s t i n g p r o c e d u r e was c a r r i e d
o u t i n t h e o r i g i n a l s t u d y , a l t h o u g h n o t i n s t r i c t compliance w i t h t h e method o l o g y recommended i n t h i s r e p o r t . The example i s , however, b e i n g c o n t i n u e d
f o r i l l u s t r a t i v e purposes.
Two model s i m u l a t i o n s were
and F i g . 5.4.1,
namely:
c a r r i e d out,
cf.
CASE
1 o f S u b s e c t i o n 5.4.2
o
SIM1:
One s i m u l a t i o n where t h e model p a r a m e t e r s a r e unchanged as compared
t o t h e r e f e r e n c e p e r i o d . T h i s i s done b y k e e p i n g t h e groundwater
a b s t r a c t i o n unchanged and e q u a l t o t h e v a l u e s v a l i d i n t h e . p e r i o d
1959-64.
o
SIM2:
Another s i m u l a t i o n where t h e a c t u a l groundwater a b s t r a c t i o n s a r e
i n t r o d u c e d . A l l o t h e r parameter v a l u e s a r e unchanged as compared t o
SIMl.
The s i m u l a t i o n r e s u l t s a r e g i v e n i n T a b l e 7.2.1.
STEP4: Trend t e s t
---------------_-
The model r e s u l t s were s u b j e c t t o t h e s t e p t r e n d t e s t s on t h e r e f e r e n c e and
t e s t p e r i o d s u s i n g d e v i a t i o n s between observed and s i m u l a t e d v a l u e s c a l c u l a t e d
as
DEVl
= OBS-SIM1
F o r t e s t i n g whether t h e DEVl samples can b e assumed i d e n t i c a l between t h e
t e s t and r e f e r e n c e p e r i o d s (H h y p o t h e s i s ) , t w o - s i d e d W i l c o x o n Rank Sum t e s t s
0
were c a r r i e d o u t , a c c o r d i n g t o t h e p r o c e d u r e o u t l i n e d i n S e c t i o n 4.2.
For
sample l e n g t h s n = 5 and m = 5 H i s accepted, i f t h e r a n k sum, W
i s within
0
t h e i n t e r v a l 18 5 W 2 37 ( B r a d l e y , 1 9 6 8 ) . The e s t i m a t e o f t h e d i f ? e r e n c e ben
tween t h e two s e r i e s can be o b t a i n e d f r o m t h e Hodges-Lehman e s t i m a t o r , A .
The s i m u l a t e d and observed d a t a a r e shown i n T a b l e 7.2.1
t h e DEV and DEV s e r i e s , t h e t e s t s t a t i s t i c s and t h e r e s u l t s .
1
2
together w i t h
From t h e t a b l e i t appears t h a t t h e t e s t on t h e observed d a t a d i r e c t l y
( t h e no model approach) does n o t g i v e a s t a t i s t i c a l l y s i g n i f i c a n t t r e n d i n t h e
a n n u a l f l o w s whereas t h e t r e n d on t h e l o w f l o w s i s s i g n i f i c a n t .
U t i l i z i n g t h e m o d e l l i n g r e s u l t s and a n a l y z i n g t h e d e v i a t i o n s (DEV1 columns) t h e t e s t shows t h a t t h e t r e n d i n b o t h annual f l o w s and l o w f l o w s i s
statistically significant.
7-7
Thus, i t c a n b e concluded t h a t t h e groundwater a b s t r a c t i o n h a s a s i g n i f i c a n t e f f e c t o n b o t h a n n u a l f l o w s and l o w f l o w s .
The example i l l u s t r a t e s how t h e models a b i l i t y t o e x p l a i n some o f t h e
c l i m a t e i n d u c e d v a r i a b i l i t y i n t h e h y d r o l o g i c a l s e r i e s reduces t h e v a r i a n c e i n
t h e DEV s e r i e s as compared t o t h e OBS s e r i e s and t h e r e b y i n c r e a s e s t h e power
1
o f t h e s t a t i s t i c a l t e s t so t h a t t h e e f f e c t o f t h e groundwater a b s t r a c t i o n on
t h e a n n u a l f l o w s can be d e t e c t e d .
Table 7.2.1
Recorded and s i m u l a t e d v a l u e s € o r t h e s t e p t r e n d t e s t o n K@ge A
R a i n f a 11
(mm)
Year
OBS
Annual R u n o f f (mm)
SIMl
SIM2
DEVl
DEV2
OBS
Annual Low F l o w ( l / s )
DEVl
DEV2
SIM
SIM
1
2
_____--_____----
Reference P e r i o d
494
842
723
805
652
105
229
173
223
171
101
161
166
199
110
101
161
166
199
110
4
68
7
24
61
4
68
7
24
61
18
35
67
140
60
48
58
80
133
63
48
58
80
133
63
-30
-23
-13
- 7
- 3
-30
-23
13
7
- 3
703
180
147
147
33
33
64
76
76
-12
-12
138
50
41
41
30
30
47
34
34
1974
1975
1976
1977
1978
772
530
502
703
768
143
117
24
98
180
242
181
68
155
201
182
143
25
90
129
-39
-26
- 1
8
61
5
1
0
1
4
67
56
57
82
76
4
3
3
3
4
-
-
99
64
44
57
21
Y
655
112
169
114
-
57
1
2
68
3
S
130
58
65
60
2
11
1
25
Yes
1959
1960
1961
1962
1963
X
sX
-----------
-
15
15
-
62
55
57
81
72
1
- 2
- 3
- 2
0
-
65
- 1
Test P e r i o d
W
Y
n
H accept?
0
A
-
37
-
-
29
39
35
40
341
Yes
No
73
-
88
Yes
-
33
-
-
1.1
2
40
40
201
No
No
59
-
52
STEPS:
Further hydrological analysis
-___---___----______---------------The m o d e l ' s a b i l i t y t o s i m u l a t e t h e e f f e c t o f t h e groundwater a b s t r a c t i o n was
e v a l u a t e d b y c o n s i d e r i n g t h e s i m u l a t i o n where t h e a c t . u a l groundwater a b s t r a c t i o n d a t a were a p p l i e d ( S I M ) . The t e s t s on t h e DEV s e r i e s (DEV, = O B S - S I M )
2
2
2
i n d i c a t e t h a t a h y p o t h e s i s o f unchanged c o n d i t i o n s i n t h e DEV s g r i e s between
2
t h e t w o p e r i o d s i s accepted b o t h € o r a n n u a l f l o w s and l o w f l o w s .
Yes
11
7-8
A n a n a l y s i s o f t h e e f f e c t s o f c l i m a t e and groundwater
s p e c t i v e l y , on t h e a n n u a l r u n o f f shows t h e f o l l o w i n g :
abstraction,
rc-
The average a n n u a l r a i n f a l l i s observed t o decrease f r o m 1959-63 t o 1974-78, a l t h o u g h n o t a s t a t i s t i c a l l y s i g n i f i c a n t t r e n d . I n s p i t e o f t h i s t h e
mean a n n u a l r u n o f f would have i n c r e a s e d f r o m 1 4 7 mm/year t o 169 mm/year
i f t h e r e h a d n o t been any groundwater a b s t r a c t i o n ( S I M 1 ) .
Thus, t h e
e f f e c t o f c l i m a t e i s (169-147) mm/year = + 2 2 mm/year change i n annual
r u n o f f from reference t o t e s t p e r i o d .
When a c c o u n t i n g f o r a c t u a l groundwater a b s t r a c t i o n ( S I M 2 ) t h e s i m u l a t e d
mean a n n u a l r u n o f f i s seen t o decrease f r o m 147 mm/year t o 114 mm/year.
Thus t h e s e p a r a t e e f f e c t o f t h e groundwater a b s t r a c t i o n i s (114-169)
mm/year = - 55 mm/year change i n a n n u a l r u n o f f f r o m r e f e r e n c e t o t e s t
period.
From t h e s t a t i s t i c a l t e s t , i t can b e e s t i m a t e d t h a t t h e e f f e c t o f t h e
groundwater a b s t r a c t i o n i s a change i n t h e mean a n n u a l f l o w o f A = - 88
mm/year
.
The q u a n t i t a t i v e c o n s i s t e n c y check i s made by comparing t h e model p r e d i c t e d e f f e c t o f groundwater a b s t r a c t i o n ( - 55 mm/year) t o t h e e s t i m a t e
f r o m t h e s t a t i s t i c a l t e s t ( - 88 mm/year). The d i f f e r e n c e between t h e s e
two f i g u r e s i n d i c a t e s t h a t t h e r e i s n o t f u l l c o n s i s t e n c y . The reason f o r
t h i s d i f f e r e n c e i s m a i n l y due t o a t o o l o w r u n o f f s i m u l a t i o n i n t h e r e f e r e n c e p e r i o d , w h i c h a l s o r e s u l t e d i n a l a r g e , but n o t s t a t i s t i c a l l y
significant, test s t a t i s t i c W
on t h e DEV
series. As a conclusion a
n
q u a n t i t a t i v e c o n s i s t e n c y w i t h i n t h e acceptez u n c e r t a i n t y l i m i t s h a s been
o b t a i n e d . However, t h e a n a l y s i s a l s o i n d i c a t e d t h a t scope f o r f u r t h e r
improvements e x i s t s i n t h e model work.
C o r r e s p o n d i n g l y , t h e e f f e c t s o f groundwater a b s t r a c t i o n and o f t h e c l i mate o n t h e a n n u a l l o w f l o w s c a n b e e s t i m a t e d as f o l l o w s :
Model s i m u l a t i o n s :
E f f e c t s o f climate:
Effects o f abstraction:
(a)
(b)
-
8 l/s
65 l / s
-
52 l / s
E s t i m a t e from s t a t i s t i c a l t e s t :
Effects o f abstraction:
(C)
I n t h i s case t h e r e i s seen t o b e a n a c c e p t a b l e ( a n d b e t t e r t h a n € o r
a n n u a l r u n o f f v a l u e s ) q u a n t i t a t i v e c o n s i s t e n c y between t h e model s i m u l a t i o n s
and t h e s t a t i s t i c a l t e s t , where a l s o observed l o w f l o w v a l u e s a r e u t i l i z e d .
7.2.3
Example 2: Suss a t V e t t e r s l e v
....................................
No w e l l f i e l d s t o Regnemark a r e l o c a t e d w i t h i n t h e Suss catchment upstream o f
V e t t e r s l e v . However, some o f t h e w e l l f i e l d s a r e l o c a t e d i n t h e same r e g i o n a l
a q u i f e r . Furthermore, t h e l o c a l a b s t r a c t i o n s f r o m t h e a q u i f e r t a k i n g p l a c e
w i t h i n o r c l o s e t o t h e catchment a r e a l s o i n c r e a s e d s l i g h t l y w i t h t i m e , c f .
I
7 -9
Hence, t h e purpose of t h i s example i s t o a n a l y s e whether t h e i n F i g . 7.2.2.
creased groundwater a b s t r a c t i o n has had any s i g n i f i c a n t e f f e c t on t h e a n n u a l
f l o w s and l o w f l o w s a t Suss, V e t t e r s l e v .
D i s c h a r g e d a t a were a v a i l a b l e f o r one p e r i o d , 1974-80.
A s t e p t r e n d t e s t was s e l e c t e d .
STEP2: S e l e c t i o n o f model t y p e
..............................
A s streamflow
approach i s a
model.
d a t a were o n l y a v a i l a b l e f o r one p e r i o d t h e o n l y p o s s i b l e
d i s t r i b u t e d , p h y s i c a l l y based model - i n t h i s case t h e SusA
The model c a l i b r a t i o n and v a l i d a t i o n i n t h e o r i g i n a l s t u d y i s d e s c r i b e d u n d e r
Example 1 above.
I t i s r e c a l l e d f r o m S u b s e c t i o n 5.4.2 Case 2 t h a t t h e t e s t r e q u i r e m e n t s
a r e a d i f f e r e n t i a l s p l i t - s a m p l e t e s t f o r c l i m a t e change i n t h e t e s t p e r i o d and
p r o x y - b a s i n d i f f e r e n t i a l s p l i t - s a m p l e t e s t s f o r groundwater a b s t r a c t i o n u s i n g
d a t a f o r two o t h e r b a s i n s . A s d i s c u s s e d under Example 1 t h e s e t e s t r e q u i r e ments have n o t been s t r i c t l y f u l f i l l e d , y e t a comprehensive t e s t i n g p r o c e d u r e
was c a r r i e d o u t . Thus, t h e s p e c i f i c r e s u l t s i n t h e f o l l o w i n g w i l l have t o be
t a k e n w i t h some r e s e r v a t i o n s , however t h e p r o c e d u r e i 1 l u s t r a . t i n g t h e methodology i s s t i l l valid.
The model s i m u l a t i o n s f o l l o w s t h e p r o c e d u r e o u t l i n e d as Case 2 o f
s e c t i o n 5 . 4 . 2 and F i g . 5.4.1,
namely:
Sub-
0
SIM1:
One s i m u l a t i o n w i t h p a r a m e t e r s c o r r e s p o n d i n g t o a c o n s t a n t
groundwater a b s t r a c t i o n e q u a l t o t h e v a l u e s v a l i d i n 1950.
0
SIM
Another s i m u l a t i o n where t h e a c t u a l groundwater a b s t r a c t i o n s a r e
introduced.
2:
Trend t e s t
-_--------------STEP4:
No s t a t i s t i c a l t r e n d t e s t i s c a r r i e d o u t u n d e r STEP4. Hence no s t a t i s t i c a l l y
based s t r i c t c o n c l u s i o n r e g a r d i n g t h e e f f e c t s o f c l i m a t e v e r s u s man i s
obtained.
Instead a hydrological
under STEP5 below.
analysis
and
statistical
tests
are
carried
out
7-10
_-_______________-------------------
STEPS: F u r t h e r h y d r o l o g i c a l a n a l y s i s
I n o r d e r t o a n a l y s e t h e e f f e c t s o f t h e groundwater a b s t r a c t i o n on t h e f l o w
regime t h e t w o s e r i e s o f d e v i a t i o n s between observed and s i m u l a t e d v a l u e s were
calculated
DEVl = OBS-SIM1
DEV2 = OBS-SIM2
Two-sided W i l c o x o n Rank
t h a t t h e PEV
hypothesis,
HO
a selected s i g n i f i c a n c e l e v e l
accepted i f t h e r a n k sum W
n
1968).
Sum t e s t s a r e then c a r r i e d o u t w i t h t h e n u l l
and DEV samples can b e assumed i d e n t i c a l . W i t h
2
o f 5% and sample l e n g t h s n = 7 and m = 7, H,
i s
i s w i t h i n t h e i n t e r v a l 37 5 W
2 68 (BradYey,
n
The r e s u l t s a r e shown i n T a b l e 7.2.2.
The e f f e c t o f t h e groundwater pumping o n t h e mean a n n u a l r u n o f f i s e s t i mated t o be A =
11 mm/year. However, t h i s e f f e c t i s s o s m a l l compared t o unc e r t a i n t i e s i n t h e model p r e d i c t i o n s t h a t , i f d a t a had e x i s t e d f o r a r e f e r e n c e
p e r i o d a l s o a n a n a l y s i s b y use o f t h i s model would p r o b a b l y n o t have been a b l e
t o d e t e c t t h i s e f f e c t as a s t a t i s t i c a l l y s i g n i f i c a n t trend.
-
The e s t i m a t e d e f f e c t on t h e groundwater a b s t r a c t i o n on t h e l o w f l o w s i s a
r e d u c t i o n , A = - 4 1 l / s . I n c o n t r a r y t o t h e e f f e c t on t h e annual flows t h e
e f f e c t on t h e l o w f l o w s would p r o b a b l y have been d e t e c t e d as s t a t i s t i c a l l y
s i g n i f i c a n t if
d a t a h a d e x i s t e d i n a r e f e r e n c e p e r i o d and model analyses were
made.
T a b l e 7.2.2
Year
Recorded and s i m u l a t e d v a l u e s f o r t h e s t e p t r e n d t e s t on Sus;
Rainfall
(mm)
OBS
Annual R u n o f f (mm)
SIMl
S I M 2 DEVl
DEV2
OBS
a t Vetterslev
Annual Low F l o w ( l / s )
SIMl
SIM2
DEVl
DEV2
T est P e r i o d
-----_-----
1974
1975
1976
1977
1978
1979
1980
-
772
530
502
703
768
710
913
236
189
77
167
248
244
355
272
199
73
180
235
240
397
262
192
65
166
221
227
384
-
36
10
4
13
13
4
42
700
217
228
217
-
143
86
98
97
-
-
26
3
12
1
27
17
29
154
137
66
131
137
202
295
181
148
150
197
180
186
356
148
109
109
155
139
159
297
11
0
160
200
159
21
21
72
71
64
-
-
-
27
11
84
66
43
16
61
-
39
-
-
-
-
6
28
43
24
2
43
2
X
sx
-
45
n
'
H
0
A
accept?
60
1
35
29
363
684
Ih_c_
Yes
No
-11
-41
7-11
7.2.4
References
....................
B r a d l e y , J.V.
(1968) : D i s t r i b u t i o n - f r e e
Enqlewood C l i f f s , New J e r s e y .
statistical
tests.
Prentice-Hall,
Hansen, E. and D y h r - N i e l s e n , M. ( 1 9 8 3 ) : The Sus; p r o j e c t : M o d e l l i n g f o r w a t e r
r e s o u r c e s arrangement. N a t u r e and Resources, V o l . 19, No. 3, pp. 10-18.
Refsgaard, J . C .
(1981) : The s u r f a c e w a t e r component o f an i n t e g r a t e d h y d r o l o g i c a l model. D a n i s h Committee f o r H y d r o l o g y . R e p o r t SUSA H 1 2 , 108 pp.
Refsgaard, J . C . ,
and Hansen, E.
(1982): A d i s t r i b u t e d g r o u n d w a t e r / s u r f a c e
w a t e r model € o r t h e Sus;-catchment.
P a r t I:model d e s c r i p t i o n and P a r t 11:
S i m u l a t i o n s o f s t r e a m f l o w d e p l e t i o n due t o groundwater a b s t r a c t i o n . N o r d i c
H y d r o l o g y , V o l . 1 3 , No. 5, pp. 299-322.
and Stang, 0 . ( 1 9 8 1 ) : A n i n t e g r a t e d q r o u n d w a t e r / s u r f a c e w a t e r
Refsgaard, J . C . ,
h y d r o l o g i c a l model. D a n i s h Committee f o r H y d r o l o g y . R e p o r t SUSA H 1 3 , 1 2 2 pp.
Stang, 0 . ( 1 9 8 1 ) : A r e g i o n a l groundwater model € o r t h e Susb-area.
m i t t e e f o r Hydrology. R e p o r t SUSA H 9, 1 1 2 pp.
D a n i s h Com-
7-12
7.3
The B l u e R i v e r B a s i n , Nebraska, USA
The L i t t l e and B i g B l u e R i v e r b a s i n s ( B l u e R i v e r b a s i n ) , l o c a t e d i n southe a s t e r n Nebraska ( F i g u r e 7 . 3 . 1 ) , i s an a r e a o f i n t e n s i v e groundwater development f o r i r r i g a t i o n . Groundwater c o n d i t i o n s t h r o u g h 1962 were used by Emery
(1966) t o c a l i b r a t e an e l e c t r i c a n a l o g f l o w model. The model was used t o make
p r e d i c t i o n s o f w a t e r - l e v e l changes and s t r e a m f l o w d e p l e t i o n s due t o groundw a t e r pumping a s o f t h e y e a r s 1982 and 2022.
A subsequent e x a m i n a t i o n o f t h e m o d e l ' s p r e d i c t i v e c a p a b i l i t i e s was done
a p p r o x i m a t e l y t w e n t y y e a r s l a t e r by A l l e y and Emery ( 1 9 8 6 ) . Because streamflow
d e p l e t i o n was a m a j o r o b j e c t i v e o f t h e m o d e l l i n g , t r e n d s i n s t r e a m f l o w were
examined as p a r t o f t h i s p o s t - a u d i t a n a l y s i s and compared t o t h e e a r l i e r p r e d i c t i o n s by Emery ( 1 9 6 6 ) .
S t r e a m f l o w r e c o r d s were examined f o r t h e f i v e s t a t i o n s l i s t e d i n T a b l e
7.3.1.
F o u r o f t h e s t a t i o n s a r e shown on F i g . 7.3.1.
S t a t i o n 8820, n o t shown
on F i g . 7 . 3 . 1 ,
i s l o c a t e d o n t h e B l u e R i v e r n e a r t h e Nebraska-Kansas S t a t e
l i n e about 50 k m e a s t o f s t a t i o n 8840.
T r e n d a n a l y s i s u s i n g t h e Mann-Kendall t e s t was p e r f o r m e d on t w o . s t r e a m f l o w s t a t i s t i c s during t h e 1963-1982 w a t e r y e a r s : Annual s t r e a m f l o w volume and
combined October t h r o u g h December s t r e a m f l o w volume. The l a t t e r volume r e p r e s e n t s s t r e a m f l o w during months t h a t o c c u r a f t e r t h e i r r i g a t i o n season, and
t h u s r e d u c t i o n s i n f l o w s would n o t be due t o s u r f a c e w a t e r d i v e r s i o n s . Streamf l o w during t h e s e months may i n c r e a s e o v e r t i m e as a r e s u l t o f r e t u r n f l o w s
f r o m s u r f a c e w a t e r i r r i g a t i o n ; however, t h i s t e n d s t o make e s t i m a t e s o f downt r e n d s more c o n s e r v a t i v e .
...............................................................
STEP 1: D e t e r m i n a t i o n o f s t e p t r e n d o r monotonic t r e n d a n a l y s i s
A monotonic t r e n d t e s t was s e l e c t e d because t h e changes i n s t r e a m f l o w deplet i o n o c c u r r e d g r a d u a l l y over time.
STEP 2: S e l e c t i o n o f model t y p e
-----------_---_--------------Two s e p a r a t e a n a l y s e s o f t r e n d s i n t h e a n n u a l f l o w s t a t i s t i c s were made. The
f i r s t a n a l y s i s t e s t e d f o r t r e n d s i n t h e f l o w s themselves. I n t h e second anal y s i s an a t t e m p t was made t o remove t h e v a r i a b i l i t y o f f l o w s due t o c l i m a t i c
f l u c t u a t i o n s b e f o r e p e r f o r m i n g t h e t r e n d t e s t . The l a t t e r a n a l y s i s was p e r formed by f i r s t e s t i m a t i n g a n n u a l s t r e a m f l o w s f o r each s t a t i o n u s i n g a s i m p l e
m o n t h l y w a t e r b a l a n c e model ( T h o r n t h w a i t e and Mather, 1955; Mather, 1 9 8 1 ) .
STEP 3 : Model c a l i b r a t i o n , v a l i d a t i o n , and a p p l i c a t i o n
......................................................
Parameters i n t h e w a t e r b a l a n c e model were based on r e g i o n a l i z e d e s t i m a t e s
used by t h e U.S. Departments o f Commerce and A g r i c u l t u r e i n t h e computation o f
t h e Palmer D r o u g h t S e v e r i t y I n d e x . A r e g r e s s i o n e q u a t i o n between t h e observed
a n n u a l f l o w s and t h o s e from t h e w a t e r b a l a n c e model was t h e n developed f o r
each s t a t i o n as:
.
Qi
= a
+
bQ. + e
1
i
(7.3.1)
7-13
where Q . and Q . a r e t h e o b s e r v e d and s i m u l a t e d a n n u a l f l o w f o r y e a r i,
a and b
1
1
a r e r e g r e s s i o n c o e f f i c i e n t s , and e i s t h e r e s i d u a l f o r y e a r i.
The r e g r e s s i o n
i
c o e f f i c i e n t s were always s i g n i f i c a n t a t t h e CL = 0 . 0 1 l e v e l .
STEP 4: Trend t e s t
-----------------The r e s u l t s a r e i n The t r e n d t e s t was a p p l i e d t o t h e r e s i d u a l s o f Eq. 7 . 3 . 1 .
c l u d e d i n T a b l e 7.3.1.
The p - v a l u e s shown a r e t h e p r o b a b i l i t i e s o f i n c o r r e c t l y
r e j e c t i n g t h e n u l l hypothesis t h a t t h e r e i s no t r e n d i n t h e d a t a .
W i t h one m i n o r e x c e p t i o n , a l l s l o p e s f r o m t h e t r e n d a n a l y s i s i n d i c a t e d
decreases i n s t r e a m f l o w o v e r t i m e . Trends w i t h p - v a l u e s l e s s t h a n 0.10 were
d e t e c t e d a b o u t h a l f t h e t i m e . The average r a t e s o f s t r e a m f l o w d e p l e t i o n e s t i mated by t r e n d a n a l y s i s were t y p i c a l l y an o r d e r o f magnitude o r more g r e a t e r
t h a n t h o s e e s t i m a t e d by Emery ( 1 9 6 6 ) . There was f a i r c o n s i s t e n c y among t h e
t r e n d s l o p e e s t i m a t e s , p a r t i c u l a r l y among t r e n d s w i t h l o w p - v a l u e s .
Trend
s l o p e e s t i m a t e s i n d i c a t e d i n c r e a s e s i n s t r e a m f l o w d e p l e t i o n downstream, as
expected. Mote t h a t t h e observed t r e n d s i n a n n u a l s t r e a m f l o w volume r e p o r t e d
i n Table 7.3.1
when u s i n g t h e October-December f l o w s were computed as t h e
t r e n d observed d u r i n g t h e 3-month p e r i o d m u l t i p l i e d by f o u r .
The t r e n d s l o p e d a t a suggest ay ayfrage r a t e o f decrease o f a n n u a l
p e r y e a r f o r t h e combined B i g and
s t r e a m f l o w volume on t h e o r d e r o f 8 h m y r
L i t t l e Blue River basins.
U s i n g t h i s e s t i m a t e and s u b t r a c t i n g e s t i m a t e d
s t r e a m f l o w d e p l e t i o n s due t o s u r f a c e w a t e r d i v e r s i o n s , y i e l d s an e s t i a t e o f
t o t a l s t r e a m f l o w d e p l e t i o n d u r i n g t h e 1963-1982 w a t e r y e a r s o f 700 hm
This
i s t e n t i m e s l a r g e r t h a n t h e v a l u e p r e d i c t e d by Emery's a n a l o g model. F u r t h e r
h y d r o l o g i c p e r s p e c t i v e s on t h i s d i s c r e p a n c y a r e d i s c u s s e d by A l l e y and Emery
(1986).
Y.
References
A l l e y , W.M. , and Emery, P.A.
(1986) : Groundwater model o f t h e B l u e R i v e r bas i n , Nebraska-twenty y e a r s l a t e r . J o u r n a l o f H y d r o l o g y , 85, pp. 225-249.
Emery, P.A.
(1966) : Use o f a n a l o g model t o p r e d i c t s t r e a m f l o w d e p l e t i o n ,
and L i t t l e B l u e R i v e r b a s i n , Nebraska. Ground Water, 4, pp. 13-20.
Mather, J . R .
( 1 9 8 1 ) : Usirig computed s t r e a m f l o w i n watershed a n a l y s i s .
Resources B u l l e t i n , 1 7 , pp. 474-482.
T h o r n t h w a i t e , C.W.,
and Mather, J.R.
( 1 9 5 5 ) : The w a t e r b a l a n c e
t i o n s i n C l i m a t o l o g y , L a b o r a t o r y o f C l i m a t o l o g y , C e n t e r t o n , N.J.,
In:
Big
Water
Publica8 , 1 0 4 pp.
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Index Map
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7.3.1
L o c a t i o n o f t h e B i g and L i t t l e B l u e R i v e r b a s i n s .
APPENDIX A
Influence o f Global C l i m a t e
Changes o n Water Resources
A p p e n d i x A i s p r e p a r e d by
M.I.
B u d y k o and K.Ya. V i n n i k o v ,
1987
A- 1
INFLUENCE O F GLOBAL CLIMATIC CHANGES ON WATER
RESOURCES
M . I . Budyko and K. Ya. V i n n i k o v
( S t a t e H y d r o l o g i c a l I n s t i t u t e , L e n i n g r a d , USSR)
The f i r s t q u a n t i t a t i v e e s t i m a t e s o f t h e e x p e c t e d a n t h r o p o g e n i c change o f mean
g l o b a l s u r f a c e a i r temperature were d e r i v e d by i n d i v i d u a l s c i e n t i s t s . Accord0
i n g t o t h e f o r e c a s t p u b l i s h e d i n 1972 (Budyko, 1972) a 0.8 C i n c r e a s e i n temp e r a t u r e due t o carbon d i o x i d e by 2 0 0 0 , 1.5OC by 2025 and 2OC by 2050 s h o u l d
be observed. A subsequent f o r e c a s t r e f l e c t i n g t h e agreed p o s i t i o n o f USSR
s c i e n t i s t s s t u d y i n g t h i s p r o b l e m was p u b l i s h e d i n 1 9 8 1 and i t c o n t a i n e d t h e
f o l l o w i n g e s t i m a t e s of changing mean a i r t e m p e r a t u r e : 0.9OC by 2000, 1.8OC by
0
2025 and 2.8 C by 2050 (Budyko e t a l . , 1981)
I n 1 9 8 1 a j o i n t U.S./USSR
forec a s t was o b t a i n e d showing t h a t t h e most p r o b a b l e t e m p e r a t u r e changes w i l l b e
i n c r e a s e s o f l 0 C by 2000, 2OC by 2025 and 3OC by 2050 (The C l i m a t i c E f f e c t s o f
1982). T h i s f o r e c a s t was based on e s t i m a t i n g a combined e f f e c t
Increased
o f CO and o t h e r gases t a k i n g i n t o a c c o u n t t h e t h e r m a l i n e r t i a o f t h e c l i m a t e
2
system. L a t e r on, i n 1985 a t t h e UNEP, WMO and ICSU meetings i n V i l l a c h
( A u s t r i a ) t h e f o r e c a s t was adopted t h a t t h e g l o b a l warming e q u i v a l e n t t o t h e
e f f e c t o f d o u b l i n g atmospheric CO2 c o n c e n t r a t i o n (1.5-4.5OC)
would p r o b a b l y b e
reached by a p p r o x i m a t e l y 2030.
.
....,
A new e s t i m a t e r e f l e c t i n g updated knowledge f r o m t h e USSR i s proposed i n
a j o i n t monograph (Man-induced c l i m a t i c changes, 1987) by r e s e a r c h w o r k e r s o f
r e s e a r c h i n s t i t u t e s o f t h e S t a t e Committee o f Hydrometeorology and C o n t r o l o f
t h e N a t u r a l Environment and t h e USSR Academy o f Sciences. A c c o r d i n g t o t h i s
e s t i m a t e , as compared w i t h t h e g r e i n d u s t r i a l epoch, t h e mean s u r f a c e a i r temp e r a t u r e had i n c r e a s e d by 0.5 C by t h e :id-1970s
t h e anthropogenic g l o b a l
0
warming amount t o a b o u t 1.3 c by 2000, 2.5 C by 2025 and 3-4OC by 2050.
Thus, t h e a v a i l a b l e e s t i m a t e s o f expected change o f mean a i r t e m p e r a t u r e
a r e r e l a t i v e l y c o n s i s t e n t . They a r e g r a d u a l l y improved due t o more c o r r e c t
c o n s i d e r a t i o n o f t h e most i m p o r t a n t f a c t o r s i n f l u e n c i n g i t . I t i s i m p o r t a n t
t h a t a l l o f t h e f o r e c a s t s p r e d i c t a warming f a r exceeding t h o s e c o m p a r a t i v e l y
s m a l l v a r i a t i o n s i n mean t e m p e r a t u r e t h a t a p e a r due t o n a t u r a l reasons. There
i s l i t t l e q u e s t i o n whether t h e warming o f 1 , 2 o r 3OC w i l l come, t h e p r o b l e m
i s t h e t i m e when i t w i l l o c c u r i n t h e f u t u r e . The f a c t i t s e l f o f f u r t h e r
development o € anthropogenic g l o b a l warming seems t o b e undoubted, a t l e a s t
f o r t h e n e x t hundred y e a r s .
8
0
Less c e r t a i n a r e t h e e s t i m a t e s o f t h e p o s s i b l e r e g i o n a l changes o f t h e
c l i m a t i c c o n d i t i o n s . B o t h t h e c l i m a t e models and e m p i r i c a l d a t a a r e u s e d t o
o b t a i n them.
R e g i o n a l Changes o f S u r f a c e A i r Temperature and P r e c i p i t a t i o n
I n r e c e n t y e a r s , d e t a i l e d comparisons have been made o f t h e r e s u l t s o f u s i n g
c l i m a t e models t o o b t a i n e s t i m a t e s o f t h e e f f e c t o f i n c r e a s i n g CO c o n c e n t r a 2
t i o n i n t h e atmosphere on t h e g e o g r a p h i c a l d i s t r i b u t i o n o f s u r f a c e a i r t-emper a t u r e and p r e c i p i t a t i o n . I t p r o v e d t h a t f o r t h e a i r t e m p e r a t u r e f i e l d t h e
r e s u l t s o f a p p l y i n g d i f f e r e n t models agree a t l e a s t q u a l i t a t i v e l y , whereas f o r
t h e p r e c i p i t a t i o n f i e l d t h e r e s u l t s o f u s i n g even v a r i o u s v e r s i o n s o f t h e same
model have f r e q u e n t l y l i t t l e i n common ( S c h l e s s i n g e r , 1 9 8 4 ) . T h i s p r e s e n t s an
e s s e n t i a l d i f f i c u l t y i n u s i n g c l i m a t e models t o e s t i m a t e r e g i o n a l c l i m a t i c
changes w h e n a n t h r o p o g e n i c g l o b a l warming develops.
A- 3.
~n i m p o r t a n t r e s u l t o b t a i n e d b y u s i n g c l - i m a t e models i s t h e c o n c l u s i o n
t h a t t h e c l i m a t i c system has a l m o s t t h e same response t o a d d i t i o n a l h e a t
f l u x e s s p r e a d d i f f e r e n t l y by l a t i t u d e . Manabe and Wetherald ( 1 9 8 0 ) , have shown
by s i m u l a t i o n s w i t h a g e n e r a l a t m o s p h e r i c c i r c u l a t i o n model, t h a t changes i n
l a t i t u d i n a l d i s t r i b u t i o n o f mean a n n u a l s u r f a c e a i r t e m p e r a t u r e and o t h e r c l i mate elements w i t h d o u b l i n g CO
c o n c e n t r a t i o n i n t h e atmosphere p r a c t i c a l l y
2
c o i n c i d e s w i t h t h o s e caused b y a 2 % i n c r e a s e i n t h e s o l a r c o n s t a n t . L a t e r ,
Hansen e t a l .
(1984) demonstrated t h a t t h i s c o n c l u s i o n c o u l d be a p p l i e d t o
l a t i t u d e s e a s o n a l and s p a t i a l d i s t r i b u t i o n o f t e m p e r a t u r e change and, p r o b a b l y , o t h e r c l i m a t e elements. Moreover, t h e r e i s no s t a t i s t i c a l l y s i g n i f i c a n t
d i f f e r e n c e s between e m p i r i c a l e s t i m a t e s ( d e r i v e d from d a t a on modern c l i m a t e
change) o f l a t i t u d e - s e a s o n a l d i s t r i b u t i o n o f s u r f a c e t e m p e r a t u r e s e n s i t i v i t y
t o v a r i a t i o n s i n a t m o s p h e r i c CO
c o n c e n t r a t i o n and i t s t r a n s p a r e n c y ( V i n n i k o v
and Groisman, 1982; V i n n i k o v , 1&36).
T h i s r e s u l t gave u s wide p o s s i b i l i t i e s € o r o b t a i n i n g t h e e m p i r i c a l e s t i mates o f r e g i o n a l changes o f c l i m a t e c o n d i t i o n s a t d i f f e r e n t stages o f development o f q l o b a l a n t h r o p o g e n i c warming. These e s t i m a t e s a r e based on d a t a
on changing c l i m a t i c c o n d i t i o n s over t h e p e r i o d o f i n s t r u m e n t a l m e t e o r o l o g i c a l
o b s e r v a t i o n s and on p a l e o c l i m a t i c r e c o n s t r u c t i o n f o r warmer epochs of t h e
past.
Even t h e f i r s t p r e d i c t i o n o f r e g i o n a l c l i m a t i c changes f r o m t h e USSR t e r r i t o r y was based o n e m p i r i c a l e s t i m a t e s o b t a i n e d f r o m d a t a on modern c l i m a t i c
0
changes f o r a 0.5 C g l o b a l warming and on p a l e o c l i m a t i c r e c o n s t r u c t i o n s f o r
g l o b a l warming b y s e v e r a l degrees (Budyko e t a l . , 1975). A t p r e s e n t , schematic
c h a r t s o f changing mean a n n u a l and s e a s o n a l c h a r a c t e r i s t i c s o f d i f f e r e n t c l i m a t i c elements f o r much o f t h e N o r t h e r n Hemisphere a r e c o m p i l e d b y u s i n g d a t a
on modern c l i m a t i c changes ( V i n n i k o v and Groisman, 1979; Groisman, 1981;
V i n n i k o v and Kovyneva, 1983; Kovyneva, 1984, V i n n i k o v , 1 9 8 6 ) .
These schematic c h a r t s can b e used t o e s t i m a t e p r o b a b l e v a r i a t i o n s i n
0
r e g i o n a l c l i m a t i c c o n d i t i o n s a t an i n c r e a s e d mean a i r t e m p e r a t u r e o f 0.5 C
compared w i t h i t s average v a l u e f o r t h e l a s t hundred y e a r s . The c l i m a t i c cond i t i o n s o f t h e Holocene optimum, 5-6 thousand y e a r s ago, o f t h e l a s t i n t e r g l a c i a l epoch ( t h e M i k u l i n o i n t e r g l a c i a l ) , 1 2 5 thousand y e a r s ago, and o f t h e
P l i o c e n e optimum, 3-4 thousand y e a r s ago (Borzenkova and Zubakov, 1984, 1985;
V e l i c h k o e t a l . , 1982, 1983, 1984) a r e t h e p a l e o c l i m a t i c analogues o f c l i m a t i c
c o n d i t i o n s f o r t h e p e r i o d s o f t i m e when t h e mean g l o b a l a i r t e m p e r a t u r e w i l l
0
0
0
b e 1 . 2 C, 2.0 C and 3-4 C above t h e modern.
S i n c e c l i m a t e during t h e p r e s e n t epoch h a s changed c o n s i d e r a b l y , we w i l l
assume t h a t t h e t e r m "modern c l i m a t e " r e f e r s t o t h e l a t e p a r t o f t h e p r e v i o u s
c e n t u r y and t h e f i r s t h a l f o f t h e c u r r e n t one. I n t h i s case, i f we use t h e
f o r e c a s t o f c h a n g i n g t h e mean a i r t e m p e r a t u r e , we f i n d t h a t t h e schematic
c h a r t s o f t e m p e r a t u r e and p r e c i p i t a t i o n v a r i a t i o n s f o r a 0.5 0C g l o b a l warming
c o n s t r u c t e d by d a t a on modern c l i m a t i c change s h o u l d be used f o r p r e d i c t i n g
r e g i o n a l c l i m a t i c changes i n t h e l a t e 1 9 8 0 ' s . I n f o r m a t i o n o n changing c l i m a t i c
0
c o n d i t i o n s f o r t h e Holocene optimum ( a 1 . 2 C warming) y i e l d s d a t a f o r f o r e c a s t i n g r e g i o n a l c l i m a t i c changes f o r t h e e a r l y 2000's a p p r o x i m a t e l y . C h a r t s
0
f o r t h e M i k u l i n o i n t e r g l a c i a l ( a 2 C warming) can serve t h e b a s i s f o r f o r e c a s t i n g t h e changes i n r e g i o n a l c l i m a t i c c o n d i t i o n s around 2 0 2 0 . The m i d d l e of
t h e n e x t hundred y e a r s can be compared w i t h t h e r e c o n s t r u c t e d c l i m a t i c c o n d i t i o n s o f t h e Holocene c l i m a t i c optimum.
A- 3
. T h e q u e s t i o n o f p o s s i b i l i t y o f u s i n g i n f o r m a t i o n on c l i m a t i c c o n d i t i o n s
o f t h e epochs w i t h warmer c l i m a t e t o e s t i m a t e f u t u r e c l i m a t i c c o n d i t i o n s i s
n o t v e r y s i m p l e . The warmings u n d e r c o n s i d e r a t i o n were caused by d i f f e r e n t
reasons. The 1 9 3 0 ' s warming was i n d u c e d m a i n l y b y i n c r e a s i n g t r a n s p a r e n c y o f
t h e atmosphere. The Holocene optimum and t h e M i k u l i n o i n t e r g l a c i a l w e r e caused
m a i n l y b y a l t e r a t i o n s i n t h e E a r t h ' s o r b i t p a r a m e t e r s . The P l i o c e n e optimum
r e s u l t e d , p r o b a b l y , f r o m t h e g r o w t h o f a t m o s p h e r i c CO
concentration. It i s
2
necessary t o s t u d y i n d e t a i l t h e s t a b i l i t y o f t h e r e l a t i o n s h i p between r e g i o n a l c l i m a t i c changes and g l o b a l t e m p e r a t u r e v a r i a t i o n s due t o v a r i o u s f a c t o r s .
N o t i n g d i f f i c u l t i e s o f c h o o s i n g analogues of
anthropogenic c l i m a t i c
changes, i t i s necessary t o i n d i c a t e l i m i t e d a c c u r a c y o f t h e a v a i l a b l e d a t a on
s p a t i a l d i s t r i b u t i o n o f m e t e o r o l o g i c a l elements during warm epochs. I t i s nat u r a l t h a t e r r o r s o f t h e s e d a t a grow as t h e age o f t h e epochs under c o n s i d e r a t i o n increases.
I n f l u e n c e o f g l o b a l warming on p r e c i p i t a t i o n p a t t e r n o v e r t h e c o n t i n e n t s
i s f o u n d t o b e v e r y c o m p l i c a t e d as compared t o i t s e f f e c t s on s u r f a c e a i r t e m p e r a t u r e . F i g . A-1 r e p r e s e n t s a c h a r t o f v a r i a t i o n s i n a n n u a l p r e c i p i t a t i o n
0
w i t h i n c r e a s i n g g l o b a l t e m p e r a t u r e by 0 . 5 C c o n s t r u c t e d by d a t a on modern c l i m a t i c changes.
T h i s chart. shows a v e r y c o m p l i c a t e d system of i s o l i n e s , however, h e r e can
b e n o t i c e d t h e tendency f o r some i n c r e a s e i n p r e c i p i t a t i o n o v e r a g r e a t e r p a r t
o f Western Europe, i n U k r a i n e , i n t h e n o r t h o f European USSR and i n C e n t r a l
S i b e r i a . P r e c i p i t a t i o n decreased o v e r a g r e a t e r p a r t o f a C e n t r a l Europe as
w e l l as i n t h e c e n t r a l r e q i o n o f t h e European USSR and i n a number o f r e g i o n s
o f West S i b e r i a and Kazakhstan.
O v e r t h e a r e a o f t h e Holecene optimum warming ( F i g . A-2)
the region o f
i n c r e a s i n g p r e c i p i t a t i o n i s d i v i d e d i n t o two zones, one i n t h e n o r t h o f Europe
and A s i a and t h e o t h e r , i n C e n t r a l A s i a and o v e r a p a r t o f Kazakhstan. Over a
g r e a t e r p a r t o f Western Europe and i n t h e USSR p r e c i p i t a t i o n i n t h e m i d l a t i t u d e s decreased.
A reversed p r e c i p i t a t i o n p a t t e r n i s discovered i n c h a r t s c o n s t r u c t e d f o r
much warmer epochs: t h e M i k u l i n o i n t e r g l a c i a l ( F i g . A-3 and t h e P l i o c e n e c l i m a t i c optimum ( F i g . A - 4 ) .
D a t a p r e s e n t e d i n t h e f i r s t o f t h e s e c h a r t s show
t h a t a l m o s t o v e r t h e e n t i r e a r e a under c o n s i d e r a t i o n p r e c i p i t a t i o n i n c r e a s e s ,
t h e g r e a t e s t i n c r e a s e i n a n n u a l p r e c i p i t a t i o n b e i n g i n C e n t r a l Europe. D a t a
g i v e n i n t h e c h a r t f o r t h e P l i o c e n e demonstrate a v e r y s i m i l a r p r e c i p i t a t i o n
p a t t e r n . The c h a r t d e p i c t e d i n F i g . A-4 i s c o n s t r u c t e d b y N.A. Yefimova and
r e p r e s e n t s an improved v e r s i o n o f h e r c h a r t p u b l i s h e d e a r l i e r (The C l i m a t i c
E f f e c t s of Increased
1982).
....,
I t s h o u l d be p o i n t e d o u t t h a t t h e i d e a o f a n o n - l i n e a r r e l a t i o n s h i p between p r e c i p i t a t i o n and t h e g l o b a l . t e m p e r a t u r e has been r e p e a t e d l y c o n c e i v e d
i n a number o f s t u d i e s (Budyko, 1 9 8 0 ; Drozdov, 1981; The C l i m a t i c E f f e c t s o f
Increased
1 9 8 2 ) . T h i s i d e a i s based on a r a t h e r o b v i o u s t h o u g h t t h a t w i t h
g l o b a l warming t h e t e m p e r a t u r e d i f f e r e n c e between t h e p o l e s and t h e e q u a t o r
decreases. T h i s r e s u l t s i n v a r i e d a t m o s p h e r i c p r e s s u r e p a t t e r n and changes i n
g e n e r a l c i r c u l a t i o n o f t h e atmosphere, w h i c h c o n s i d e r a b l y a f f e c t s p r e c i p i t a t i o n patterns.
...,
O n e can b e l i e v e t h a t w i t h a comparative1.y s m a l l warming t h e s u b t r o p i c a l
zone o f h i g h p r e s s u r e i n t h e N o r t h e r n Hemisphere moves t o h i g h e r l a t i t u d e s .
A-4
Fig. A-1
Changes i n a n n u a l p r e c i p i t a t i o n p a t t e r n (cm)
0
0.5 C ( V i n n i k o v and Groisman, 1979)
,i.o 0
F i g . A-2
M
110
w
4
Chan P S i n a n n u a l p r e c i p i t a t i o n p a t t e r n ( c m )
o f 1 C (Borzenkova and Zubakov, 1984)
8-
w i t h g l o b a l warming o f
w i t h a g l o b a l warming
A- 5
00
ICO
100
-.
F i g . A-3
Changes i n a n n u a l p r e c i p i t a t i o n p a t t e r n (cm) w i t h g l o b a l warming o f
1.5OC ( V e l i c h k o e t a l . , 1982, 1983, 1984)
F i g . A-4
Changes i n a n n u a l p r e c i p i t a t i o n p a t t e r n (cm) w i t h a g l o b a l warming
0
of 3-4 C (Yefirnova, The c l i m a t e e f f e c t s o f
1982)
......,
A- 6
T h i s promotes i n c r e a s i n g t h e f r e q u e n c y o f d r o u g h t s i n some c o n t i n e n t a l m i d l a t i t u d e r e g i o n s . A c o n s i d e r a b l e warming i n d u c e s a n o t i c e a b l e g r o w t h o f absol . u t e a i r h u m i d i t y , w h i c h causes a c o n s i d e r a b l e i n c r e a s e i n a i r mass p r e c i p i t a t i o n . I n t h i s case m o i s t u r e c o n d i t i o n s on t h e c o n t i n e n t s become more homogeneous.
I t should b e mentioned t h a t i n t h e p r e s e n t s t a t e - o f - t h e - a r t ,
very general
c o n c l u s i o n s about g e o g r a p h i c a l d i s t r i b u t i o n o f changes i n p r e c i p i t a t i o n w i t h
i n c r e a s i n g a t m o s p h e r i c CO c o n c e n t r a t i o n can b e drawn b y u s i n g c l i m a t e models
2
( S c h l e s i n g e r , 1984; Manabe, 1983, e t c . ) I t t h i s case t h e e m p i r i c a l methods
y i e l d c o n s i d e r a b l y more d e t a i l e d and r e l i a b l e r e s u l t s .
Thus, t h e charts-schemes o f v a r i a t i o n s i n t h e annual p r e c i p i t a t i o n ( F i g s .
A-4)
can be c o n s i d e r e d a t e n t a t i v e and approximate f o r e c a s t o f v a r i a t i o n s i n norms o f r e g i o n a l p r e c i p i t a t i o n f o r v a r i o u s s t a g e s o f a n t h r o p o g e n i c
g l o b a l warming.
A-l
-
I n f l u e n c e o f Anthropogenic Changes i n G l o b a l C l i m a t e on t h e H y d r o l o g i c a l C y c l e
A l t h o u g h t h e q u e s t i o n o f t h e e f f e c t s o f c l i m a t e change on s u r f a c e w a t e r i s o f
g r e a t p r a c t i c a l importance, s t u d y i n g t h e i n f l u e n c e o f anthropogenic g l o b a l
warming on t h e h y d r o l o g i c a l c y c l e o f t h e E a r t h ' s c o n t i n e n t s p r e s e n t s g r e a t
d i f f i c u l t i e s . They a r e caused b y t h e c o m p l e x i t y of v a r i a t i o n s i n t h e atmospher i c g e n e r a l c i r c u l a t i o n as t h e c l i m a t e change and have n o t y e t been overcome
completely.
A t p r e s e n t , t o e v a l u a t e p r o b a b l e changes i n t h e h y d r o l o g i c a l c y c l e on t h e
c o n t i n e n t s , we can use e s t i m a t e s o f c h a n g i n g s u r f a c e a i r t e m p e r a t u r e and mean
a n n u a l p r e c i p i t a t i o n o b t a i n e d f r o m e m p i r i c a l d a t a on c l i m a t e s o f warmer epochs
of t h e past.
The f i r s t a t t e m p t a t e s t i m a t i n g changes i n p o t e n t i a l e v a p o r a t i o n and mean
a n n u a l r u n o f f f o r t h e 2 0 2 0 ' s was made a b o u t t e n y e a r s ago (Budyko e t a l . ,
1 9 7 8 ) . L a t e r , i n f o r m a t i o n on t h e f u t u r e c l i m a t i c c o n d i t i o n s a l l o w e d us t o c l a r i f y d a t a on t h e h y d r o l o g i c a l c y c l e o f t h e end o f t h e 2 0 t h and t h e b e g i n n i n g
of t h e 2 1 s t c e n t u r i e s .
The p r o b l e m o f e s t i m a t i n g p o s s i b l e changes i n annual r u n o f f can be s o l v e d
e a s i e r f o r t h e epochs when t h e mean g l o b a l a i r t e m p e r a t u r e i n c r e a s e d b y 0.5 0C
( r e l a t i v e t o t h e mean t e m p e r a t u r e o v e r t h e l a s t hundred y e a r s ) . I n t h i s case,
t h e p o s s i b i l i t y e x i s t s t o e s t i m a t e t h e dependency o f r i v e r r u n o f f on c l i m a t e
warming f r o m h y d r o l o g i c a l o b s e r v a t i o n a l d a t a .
A t p r e s e n t , t h e r e a r e a few r i v e r s i n t h e World whose h y d r o l o g i c a l c y c l e
h a s n o t been changed by i n c r e a s i n g a n t h r o p o g e n i c i n f l u e n c e on catchments, hyd r o t e c h n i c a l c o n s t r u c t i o n s and r e s e r v o i r s and i r r e t r i e v a b l e consumption o f
w a t e r b y a g r i c u l t u r e and i n d u s t r y . T h e r e f o r e o n l y a c o m p a r a t i v e l y s m a l l p o r t i o n o f t h e a v a i l a b l e l o n g t e r m s e r i e s o f t h e annual r u n o f f can be c o n s i d e r e d
homogeneous. P r i m a r i l y , t h i s r e f e r s t o a p a r t o f s m a l l r i v e r s . Besides, t h e
a v a i l a b l e h y d r o l o g i c a l methods sometimes a l l o w u s t o r e s t o r e t h e l o s t homog e n e i t y of measurement d a t a s e r i e s .
The r e s u l t s o f t h e s t a t i s t i c a l e s t i m a t i o n o f t h e r e l a t i o n s h i p between
a n n u a l r u n o f f and mean a i r t e m p e r a t u r e b y N.A. Speranskaya e n a b l e d us t o draw
A- 7
some c o n c l u s i o n s about p r o b a b l e v a r i a t i o n s i n a n n u a l r u n o f f f o l l o w i n g c l i m a t i c
0
changes when t h e warming o f t h e N o r t h e r n Hemisphere was 0.5 C h i g h e r compared
w i t h t h e l a s t hundred y e a r c l i m a t e ( V i n n i k o v , 1 9 8 6 ) :
1.
The r u n o f f o f r i v e r s i n C e n t r a l and Volgo-Vyatka
USSR has decreased by 10-20%.
region of
t h e European
2.
The r u n o f f o f t h e upper O b r i v e r h a s i n c r e a s e d by 2 - 7 % .
3.
The r u n o f f o f Yenisey i n t h e upper reaches has i n c r e a s e d b y 7 - 1 0 $ .
4.
The r u n o f f o f Amur has i n c r e a s e d b y 5 - 2 0 % ,
being the greatest.
changes i n i t s m i d d l e s t r e a m
r e p r e s e n t s t h e r e s u l t s o f t h e more d e t a i l e d c a l c u l a t i o n o f
F i g . A-5
0
changing mean a n n u a l c l i m a t i c r u n o f f i n t h e USSR t e r r i t o r y w i t h a 0.5 C i n crease i n mean g l o b a l a i r t e m p e r a t u r e . The c a l c u l a t i o n i s c a r r i e d o u t b y N.A.
Lemeshko who u s e d t h e complex method f o r d e t e r m i n i n g e v a p o r a t i o n f r o m l a n d . I n
t h e g i v e n c h a r t , t h e v a s t areas o f i n c r e a s i n g ( o r d e c r e a s i n g ) r u n o f f a r e d i s t i n c t l y seen w h i c h i n case o f a r e l a t i v e l y s m a l l warming p r o v e t o b e a l m o s t
d i g i t l y r e l a t e d t o t h e r e g i o n s o f i n c r e a s i n g ( o r decreasing) p r e c i p i t a t i o n .
60
F i g . A-5
80
100
E s t i m a t e s o f changing a n n u a l r u n o f f norms
temperature increase.
I eo
(cm) w i t h a 0 . 5
0
C global
A- 8
The i n d i c a t e d c h a r a c t e r o f changes i n a n n u a l r u n o f f would a l s o r e m a i n
0
w i t h a 1 C warming, f o r w h i c h t h e changes i n a n n0u a l p r e c i p i t a t i o n p a t t e r n r e m a i n m a i n l y s i m i l a r t o t h o s e o c c u r r i n g w i t h a 0 . 5 C warming. I-Iowever, f o r more
c o n s i d e r a b l e g l o b a l warming t h e c h a r a c t e r o f t h e g e o g r a p h i c a l d i s t r i b u t i o n o f
a n n u a l p r e c i p i t a t i o n and r u n o f f would change: d e t a i l e d c a l c u l a t i o n s s h o u l d b e
c a r r i e d o u t t o e s t i m a t e t h e a n n u a l r u n o f f changes t h a t appear i n t h i s case.
E a r l i e r , c o n s i d e r i n g a n t h r o p o g e n i c changes i n w a t e r r e s o u r c e s , h y d r o l o g i s t s have n o t t a k e n i n t o a c c o u n t t h e a n t h r o p o g e n i c changes of g l o b a l c l i m a t e
and r e s t r i c t e d themselves t o e s t i m a t i n g man's i m p a c t on watersheds. However,
a s t h e g l o b a l warming develops, s t u d y i n g t h e g l o b a l a s p e c t s of t h e problem o f
a n t h r o p o g e n i c changes i n w a t e r r e s o u r c e s a c q u i r e s g r e a t p r a c t i c a l i m p o r t a n c e .
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