Agricultural and Forest Meteorology, 36 (1986) 241--248
Elsevier Science Publishers B.V., Amsterdam --Printed in The Netherlands
241
ESTIMATES OF ROUGHNESS LENGTH AND ZERO PLANE DISPLACEMENT FOR A FOLIATED AND NON-FOLIATED OAK CANOPY
A.J. DOLMAN
Department of Physical Geography and Soil Science, State University of Groningen,
Melkweg 1, 9718 EP Groningen (The Netherlands)
(Received May 20, 1985; accepted September 7, 1985)
ABSTRACT
Dolman, A.J., 1986. Estimates of roughness length and zero plane displacement for a
foliated and non-foliated oak canopy. Agric. For. Meteorol., 36: 241--248.
Measurements of wind speed were made above the canopy of an oak forest in foliated
and non-foliated conditions. Zero plane displacement height was estimated at 7.2 and
5.5 m, while roughness length was estimated at 1.0 and 0.9m, for foliated and nonfoliated conditions respectively. Mean tree height was 9.6 m. The effect of both parameters on evaporation of intercepted rainfall is evaluated.
INTRODUCTION
P r o b a b l y t h e m o s t i m p o r t a n t result arising f r o m studies o f f o r e s t h y d r o l o g y in t h e last d e c a d e is t h e finding t h a t i n t e r c e p t i o n a n d t r a n s p i r a t i o n n e e d
s e p a r a t e d e s c r i p t i o n (e.g. S h u t t l e w o r t h and Calder, 1979). D u r i n g e v a p o r a t i o n o f i n t e r c e p t e d rainfall t h e e v a p o r a t i o n r a t e is highly d e p e n d e n t o n t h e
a e r o d y n a m i c t r a n s f e r r e s i s t a n c e w h i c h is generally an o r d e r o f m a g n i t u d e
smaller t h a n t h e s u r f a c e r e s i s t a n c e w h i c h d e t e r m i n e s t h e t r a n s p i r a t i o n rate.
T h i s p a r t l y e x p l a i n s w h y i n t e r c e p t i o n p l a y s such an i m p o r t a n t p a r t in t h e
w a t e r b a l a n c e o f forests. I n t e r c e p t i o n losses m a y b e as high as 20 t o 40% o f
a n n u a l gross rainfall.
T h e i n t e r c e p t i o n p r o c e s s has b e e n m o d e l l e d b y a n u m b e r o f a u t h o r s
( R u t t e r e t al., 1 9 7 1 ; G a s h , 1 9 7 9 ; Mulder, 1983). T h e s e m o d e l s m a k e use o f
t h e M o n t e i t h - - P e n m a n f o r m u l a describing l a t e n t h e a t fluxes f r o m w e t
surfaces
k E = A R n + pcp 6 e / R a
A+ 7
(1)
where, R n = flux density of net radiation, A = change of saturation vapour
p r e s s u r e w i t h t e m p e r a t u r e , 7 = p s y c h r o m e t r i c c o n s t a n t , p -- d e n s i t y o f air,
cp = specific h e a t o f air at c o n s t a n t p r e s s u r e , 5e = s a t u r a t i o n v a p o u r pressure deficit, R a - a e r o d y n a m i c r e s i s t a n c e o f c a n o p y , XE = f l u x d e n s i t y o f
latent heat.
Businger ( 1 9 5 6 ) s u g g e s t e d f o r Ra t h e f o l l o w i n g e x p r e s s i o n
Ra
1
= k i u {ln [ ( z - - d ) / z o ] } 2
"0168-1923/86/$03.50
© 1986 Elsevier Science Publishers B.V.
(2)
242
80
2 40
~S o8o i
0 40!
Aerodynomlc reslstonce sin-'
Fig. 1. Dependence of evaporation rate on aerodynamic resistance; calculation performed
according to eq, 1. R n : 100Jm -2 s-1 ;Be = 100Pa;u : 1.5 ms -1 ; T = 15°C.
where k : yon Kbxman's constant, u = wind speed mea~Jred at height z,
z : measurement height, d : zero plane displacement, z0 : roughness
length.
Figure 1 shows calculated evaporation rates for a wide range of values of
R~. Especially with low values of R~ evaporation rates change drastically
with small changes in aerodynamic resistance. Typical values of Ra for
forests lie b e t w e e n 5 and 10 s m -1 (Stewart and Thorn, 1973).
Equation 2 is formally only valid for conditions of neutral stability and
describes transfer o f m o m e n t u m not of mass. T w o corrections should thus
be applied. The first correction consists of the addition of a s t a b ~
factor,
the second should take into a c c o u n t the incomplete analogy b e t w e e n transfer of mass and m o m e n t u m . In the latter case a so-called excess resistance
(Chamberlain, 1966) has to be introduced.
Conditions under which most evaporation of intercepted rainfall occurs
are likely to be near neutral, i.e. cloudy weather. The stability factor would
then approach unity, b u t it m a y be as low as 0.5 (Thorn et al., 1975). R u t t e r
et al. (1975) state that the result of applying the second correction on R~ is
a value o f R~ n o t very different from that derived from eq. 2. Neglecting
b o t h corrections, or assuming that they are compensating does not lead to
serious errors in calculat'mg evaporation of intercepted rainfall ( R u t t e r et al.,
1975; see also Gash, 1979; Mutder, 1983).
In the absence of wind profile data, d and z0, the surface roughness
parameters, are usually estimated according to empirical formutae which
relate b o t h parameters to mean tree height (e.g. Jarvis et al., 1976). However, uncertainty in these empirical relationships has been identified as a
major source of systematic error in estimating evaporation of intercepted
rainfall (Gash et al., 1980).
Most wind profile data on which these relationships are based stem from
measurements above coniferous forests. Above deciduous forests, the effect
of leaf fall on the shape of the wind profile is not well known. This paper
243
deals with wind measurements above an oak canopy under foliated and
non-foliated conditions. Estimates of z 0 and d are given and the effect of
leaf fall on the aerodynamic resistance is evaluated.
THEORY
The log-linear equation, relating wind speed to height, is given by
u
= ( u * / k ) In { ( z - - d ) / z 0 }
(3)
where, u * = friction velocity; all other symbols are previously defined.
Strictly, eq. 3 is only valid under conditions of neutral stability. Under
other stability conditions empirical corrections may be applied (Thom et al.,
1975).
There appears to be some controversy regarding the effects of different
stability conditions on the shape of the wind profile and, consequently, on
the estimates of z0 and d. Theoretically it is to be expected that under stable
conditions turbulence decreases thereby producing steeper wind gradients
and higher values of z0. Under unstable conditions the reverse would be the
case.
Above forests temperature gradients are generally small, typically of the
same order of magnitude as the dry adiabatic lapse rate. This is a direct
consequence of the turbulence instigated by the height and roughness of
the canopy surface. As a result, Richardson numbers remain close to zero
and "it is questionable whether any real improvement is obtained in the
estimation of z0 and d for forest by the application of empirical stability
corrections obtained for completely different kinds of surface such as grass
and stubble" (Jarvis et al., 1976). Furthermore, stability corrections on
aerodynamic resistance prove to be o f little numerical importance in evaporation modelling, according to Shuttleworth et al. (1984). These authors
attribute the scatter in the empirical determination of aerodynamic resistance largely to instrumental errors, especially at low wind speed. In view
of these arguments and the fact that the present measurements were made
in the first few meters above the canopy surface, where temperature gradients are very small, stability influences are ignored.
A simple m e t h o d o f calculating d derives from the relation
U 1
--
U 2
ul -- u3
--
In (zl -- d) -- In (z 2 -- d)
In (z 1 - - d ) -- In (z3 - - d )
(4)
where the subscripts refer to the measurement levels (Monteith, 1973;
Landsberg and Jarvis, 1973). Equation 4 can be solved using an iterative
procedure which can easily be programmed on a computer. When In (z -- d)
is plotted against wind speed (u), the corresponding value of z0 can be found
from the intercept.
244
SITE DESCRIPTION AND MEASUREMENTS
The experimental site is located near Castricum in the north-west of the
Netherlands at the Iysimeter site of the Provincial Water Supply Board of
North Holland (Fig. 2).
The vegetation consists of oak (Quereus robur). Mean tree height in 1984
was 9.6 m (s.d. = 1.6) and tree density is high, ca. 3000 trees ha -1 .
The surrounding vegetation consists of oak in the immediate vicinity,
while f u r t h e r away it consists of pine and oak occasionally mixed with
shrubs. The change f r om one vegetation t y p e to the o t h e r is mostly gradual.
Winds are p r e d o m i n a n t l y f r om the south-west. A t o w e r was erected where,
besides o th er meteorological instruments, three cup anemometers were
installed at f o u r levels. The a n e m o m e t e r s were placed on one-meter boom s
away from the tower. T he size of the t o w e r is small and its structure very
light, so it is unlikely t hat t he a n e m o m e t e r readings will be influenced by
the tower. The a n e m o m e t e r s were supplied with a calibration graph from the
m a n u f a c t u r e r and two o f t h e m were intercalibrated showing no substantial
differences between the t w o a n e m o m e t e r readings. Errors in the readings are
ca. 0.1 m s -I . No a t t e m p t was made t o interchange the a n e m o m e t e r during
the e x p e r i m e n t b u t it is n o t e d t ha t the instrumental set up in winter differs
from that in the summer. Fifteen-minute averages o f wind speed were
stored on an automatic data recording system. From 9th July 1984 until
3rd O c t o b e r 1984 the measuring heights were 10.5, 11.7, 13.6 and 15.2 m.
A f t er leaf fall the upper a n e m o m e t e r was removed and placed at 8.2 m.
r
oAikmoor
Co~tricum
Fig. 2. Location of the experimental site (latitude 52°33'N, longitude 4°38'E).
245
Under non-foliated conditions data were collected from l l t h
1984 until 24th December 1984.
November
RESULTS
The analysis of wind speed data was performed on values averaged over
30 min. Typical profiles for foliated and non-foliated conditions are shown
in Fig. 3. A computer program in PASCAL was written to calculate the lefthand side of eq. 4 and, for 0.1-m increments of d, the right-hand side of (4).
When the two sides were equal, the value of d employed was taken as the
actual zero plane displacement, z0 was found by fitting a regression line to
the log-linear profile, using least-squares analysis. For foliated conditions,
only profiles obtained between 8.00--18.00 hours (local time) were used.
For non-foliated conditions only profiles obtained between 8.00--16.00
hours were used.
Equation 4 can be solved if at least three measurements levels are used.
As in the present experiment four levels were used, eq. 4 can be solved for
five possible combinations of measurement levels. From these combinations,
the combination was selected which gave most often a solution to eq. 4 (i.e.
the difference between the two sides being zero} and which gave the smallest
standard deviation o f the estimate o f d. For foliated conditions the combination selected consisted of the lowest three anemometers. This can also be
seen in Fig. 3; the upper part of the profile curves away after 1 3 . 6 m . For
non-foliated conditions the level at 11.7 m had to be excluded. The reason
for this is unclear.
A further selection of profiles consisted of excluding values of d which
were an artefact of the computing procedure. Thus, for foliated conditions
only values lying in the interval 0.1--9.9 m were used; for non-foliated conditions the interval was 0.1--8.2 m. This selection criterion was incorporated,
because the physical interpretation of values lying outside both ranges seems
35
15.2
,o l / ,,z' ,,J/>-'v
8.3
l
l/
,, J
J
J
J
..-"
_.---~"
.-"
o',
T~
5 -- Fohafed
Non foliafed
2
3
4
5
~,
t
8
9
~o
Wind velocity m/sec
Fig. 3. Typical wind profiles for foliated and non-foliated conditions of the canopy.
Horizontal lines are measurement levels.
246
TABLE I
Estimates of d and z0 for foliated and non-foliated conditions of canopy
Foliated
Mean
Median
Stand. dev.
Non-foliated
zu
d
z0
d
1.0
0.7
1.0
7.2
7.5
1.9
0.9
0.5
0.9
5.5
6.5
1.7
%
5O F
f ~i,oted
4~L
......
40-
'!or
~o'~clet2
35~
30k
26L
.
.
.
J 1
I I :
~0~
I
51
.
,.,-'- J---J !
.
.
15 2 5
05
I
.
.
35
{
.
45
.
5'5
i .
65
75
~.5
95
Fig. 4. Relative frequency distributions of zero plane displacement for foliated and nonfoliated conditions.
unclear. For foliated conditions 9 7 1 profiles were used; for non-foliated
conditions 262.
Table I shows estimates of d and z 0 for both conditions of the canopy. A
general lowering of the profile, as can be inferred from Fig. 3 can also be
seen in the estimates o f d. Considering the large standard deviation involved
in both estimates of z0, no difference between the t w o estimates can be
substantiated.
DISCUSSION
According to Thorn (1976) the zero plane displacement level can be looked
upon as the level o f the mean m o m e n t u m sink, while roughness length is a
measure of the effectiveness o f the canopy as a m o m e n t u m absorber. The
general lowering of the zero plane displacement after leaf fall, as ~ o w n in
Fig. 4, is thus much as one would expect. As foliage density decreases, the
area o f m o m e n t u m sink also will decrease.
The rather high value found for the ratio zero plane displacement/tree
height, 0.75 for foliated conditions can probably be attributed to the structure of the forest which is very dense. Furthermore, the leaves are heavily
247
TABLE II
Estimates of aerodynamic resistance at 10 m for foliated (Ras) and non-foliated (Raw)
conditions and at a level 2.8 m above the zero plane displacement height for non-foliated
conditions.
u
(m s -1 )
1
Ras (10)
Raw (10)
Raw (8.3)
( s m -1 )
(s m -1 )
(s m -1 )
6.3
15.4
7.7
2
3
4
5
3.2
7.7
3.9
2.1
5.1
2.0
1.0
3.9
1.9
1.3
3.0
1.5
concentrated in the top of the canopy, providing an effective m o m e n t u m
sink.
The values of z0 for foliated and non-foliated conditions do not differ.
This is not as one would expect. The leafless canopy is as effective a moment u m absorber as the leaved canopy. Sellers (1981) derived an equation
relating z0 and d with stand height and leaf area index. Sellers' equation is
based on Goudriaan's (1977) equation which relates z0 and d to canopy
characteristics. The calculated variations of z0 with leaf area index were very
small at low wind speeds. This may partly explain w h y in this experiment
no difference in z0 for foliated and non-foliated conditions can be substantiated. Most of the wind profile data were obtained at relatively low wind
speeds.
Jaeger (1984) analysed data on wind profiles above a pine forest obtained
over a period o f nearly ten years. His data on stability suggest a daily course
of the local Richardson number with values near zero a few hours after
sunrise and a few hours before sunset. Selecting these hours for analysis did
not result in substantially different values of z0 and d as presented in Table
I. Furthermore, the scatter in values of d is evenly distributed over the hours
used in the analysis (i.e. 8.00--16.00 hours in winter and 8.00--18.00 hours
in summer). The origin of the scatter is thus presumably not to be sought
in stability effects.
Instrument errors, are probably thus responsible for a large part of the
scatter in the calculated roughness length. Especially at low wind speeds,
stalling effects may easily contribute to errors in the order of 200%. Naturally, this error also applies to estimates of d but apparently this estimate is
less sensitive to measurement error. However, the values obtained in this
experiment can be used in evaporation modelling, if wind speeds are of
the same order of magnitude as those used to estimate the surface roughness
parameters. Table II gives an indication of how the value of aerodynamic
resistance will change with leaf fall. Ra is calculated for wind speeds at
10 m and for non-foliated conditions also at a level 2.8 m above the zero
plane displacement height (i.e. the same height above the zero plane displacement height as for foliated conditions). Table II shows that aerodynamic canopy resistance in foliated conditions is of the same order of magnitude as in non-foliated conditions. This implies that, other environmental
24~
variables remaining the same, t h e e v a p o r a t i o n rates f r o m w e t surfaces in
s u m m e r and w i n t e r m a y be o f the same o r d e r o f m a g n i t u d e . This m i g h t
p a r t l y explain w h y i n t e r c e p t i o n losses in w i n t e r are a l m o s t equal to t h o s e
in s u m m e r .
ACKNOWLEDGEMENT
T h e help o f G.J. van d e n Burg in collecting d a t a and assisting in s o m e
o f t h e c o m p u t i n g is g r a t e f u l l y a c k n o w l e d g e d .
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