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1-2015
Dynamics of MODIS evapotranspiration in South
Africa
Nebo Jovanovic
Qiaozhen Mu
Richard D. H. Bugan
Maosheng Zhao
Follow this and additional works at: http://scholarworks.umt.edu/ntsg_pubs
Recommended Citation
Jovanovic, N., Mu Q., Bugan R. D. H., and Zhao M. (2015). Dynamics of MODIS evapotranspiration in South Africa. Water SA:
41(1): 79-90, doi: 10.4314/wsa.v41i1.11
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Dynamics of MODIS evapotransplratlon In South Africa
N e b o J o v a n o v i c ' * Q i a o z h e n M u ^ R ic h a r d DH B u g a n ' a n d M a o s h e n g Z h ao ^
'CSIR, N atu ral Resources a n d Environment, PO B o x3 2 0 ,7599 Stellenbosch, South Africa
^Numerical Terradynamic S im ulation Group, College o f Forestry and Conservation, University o f M ontana, 32 Campus Drive, Missoula, M T 59812, USA
^D epartm ent o f G eographical Sciences, University o f M aryland, 2181 SamuelJ. LeFrak Hall, College Park, M D 20742, USA
ABSTRACT
This paper describes the dynam ics o f ev ap o tran sp iratio n (ET) in South A frica using MOD16 ET satellite-derived data,
an d analyses the inter-dependency o f variables used in the E T alg o rith m o f M u et al. (2011). A nnual evapotranspiration
is strongly dependent on rain fall an d potential ev ap o tran sp iratio n (PET) in 4 clim atically different regions o f South
Africa. Average E T in South A frica (2000-2012) was estim ated to be 303 m m -a ' or 481.4 x 10’ m ’-a' (14% o f P ET an d 67%
o f rainfall), m ainly in the form o f p lan t tra n sp ira tio n (T, 53%) an d soil evaporation (Soil E, 39%). E vapotranspiration (ET)
show ed a slight tendency to decrease over the period 2000-2012 in all clim atic regions, except in the south o f the co u n try
(w inter rainfall areas), although an n u al variations in E T resulted in the 13-year trends n o t being statistically significant.
E v ap o transpiration (ET) was spatially dependent on PET, T an d vap o u r pressure deficit (VPD), in p a rticu lar in w inter
rain fall an d arid to sem i-arid clim atic regions. A ssum ing a n average rainfall o f 450 m m -a ', an d considering cu rre n t best
estim ates o f ru n o ff (9% o f rainfall), groundw ater recharge (5%) an d w ater w ithdraw al (2%), MOD16 ET estim ates were
ab o u t 15% short o f the w ater balance closure in South Africa. The E T alg o rith m can be refined an d tested for applications in
restricted areas th a t are spatially heterogeneous an d by accounting for soil w ater supply lim iting conditions.
Keywords: M O D16, p o te n tia l e v a p o tra n s p ira tio n , soil ev ap o ra tio n , tra n s p ira tio n , w a ter balance
IN T R O D U C T IO N
S ustainable m a n a g e m e n t o f w a ter re so u rce s re q u ire s carefu l
p la n n in g , m o n ito rin g a n d m a n a g em e n t, as w a te r is a finite
re so u rce in q u a lity a n d q u an tity . E n v iro n m e n ta l ch an g e d riven
by a n th ro p o g e n ic global w a rm in g im p o ses a d d itio n a l c o n ­
stra in ts, for exam ple, in crease in ex tre m e w e ath e r o c cu rre n ce s
(d ro u g h ts a n d floods), in cre ase in te m p e ra tu re a n d p o te n tia l
ev ap o ra tio n , ch an g es in ra in fa ll a m o u n ts a n d d istrib u tio n ,
etc. The q u a n tifica tio n o f th e w a te r cycle c o m p o n e n ts is a
fu n d a m e n ta l re q u ire m e n t in th e assessm ent a n d m an a g em e n t
o f w a te r re so u rces, in p a rtic u la r, u n d e r th e im p a c ts o f h u m a n in d u c e d lan d -u se a n d c lim ate change.
E v a p o tra n sp ira tio n (ET) is a k ey p ro c ess w ith in th e
h y d ro lo g ical cycle a n d a rg u ab ly th e m o st difficult c o m p o n e n t
to d e te rm in e , especially in a rid a n d se m i-a rid areas w here a
large p ro p o rtio n o f low a n d sp o rad ic p re cip ita tio n is re tu rn e d
to th e a tm o sp h e re v ia ET. In th ese areas, vegetation is often
subject to w a ter stress a n d p la n t species a d ap t in differen t w ays
to p ro lo n g ed d ro u g h t c o n d itio n s (Jovanovic a n d Israel, 2012).
E v a p o tra n sp ira tio n (ET) is e stim a te d to be >60% o f ra in fa ll on
a global scale (K o rz o u n et al., 1978; L vovich a n d W h ite , 1990)
a n d c an re ac h n e arly 100% o f ra in fa ll in a rid reg io n s (B ugan et
al., 2012). In a d d itio n , E T v aries d e p e n d in g on th e h e te ro g e n e ­
ity o f th e lan d sca p e a n d to p o g ra p h y clim ate, ty p e o f vegetation
a n d soil p ro p e rtie s (M u et al., 2007a). T his m ak e s th e p ro c ess
o f E T very d y n a m ic over tim e a n d variab le in space. By u n d e r­
sta n d in g ho w th is p a ra m e te r v aries in space a n d tim e , w e w ill
im p ro v e o u r u n d e rs ta n d in g o f a c ritica l c o m p o n e n t o f th e
w a ter cycle.
*
S
To w hom all correspondence should be addressed.
27 21 888 2506; Fax: +27 21 888 2682;
e-m ail: niovanovic(a)csir.co.za
R e c e iv e d 13 M a y 2014; a cc ep ted in revise d fo r m 10 D e c e m b e r 2014.
http://dx.doi.org/10.4314/w sa.v41il.ll
Available o n website http://www.wrc.org.za
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ISSN 1816-7950 (On-line) = W ater SA Vol. 41 No. 1 January 2015
Besides th e FL U X N E T n e tw o rk (B aldocchi et al., 2001),
m ea su re m e n ts o i E T are scarce a n d localised. H ow ever, o u r
a b ility to use in fo rm a tio n fro m satellite sen so rs to e stim a te ET
is developing ra p id ly a n d offers th e o p p o rtu n ity to u n d e rs ta n d
h o w E T v a rie s across space a n d tim e , red u ce u n c e rta in ty levels,
in cre ase sp atial d e ta ils a n d scale-up to large areas. The accuracy
a n d u n c e rta in ty o f sa tellite-b ased e stim a te s o f E T w ere ev alu ­
a te d in specific stu d ies for different a lg o rith m s a n d p ro d u c ts,
e.g., SEBAL (B astiaan ssen et al., 1998a a n d b), M E T R IC (A llen
e t al., 2007a a n d b), SEBS (Su, 2002), a n d M O D IS ET (M u et
al., 2007a), as w ell as for c o m p o n e n ts o f E T calcu la tio n such as
M O D IS fra c tio n o f ab so rb ed p h o to sy n th e tic a lly active ra d ia ­
tio n (FPAR) a n d le a f area in d e x (LAI) (M y n e n i et al., 2002).
T his w as g en erally d o n e by c o m p a riso n b etw een re m o te sensin g -b a s e d e stim a te s o f E T a n d g ro u n d -b a s e d m e a su re m e n ts
o f E T o r o th e r v ariables. M u eller et al. (2011) a n d Jim enez et
al. (2011) also c o m p a re d g lobal E T d a ta se ts a n d su rface fluxes
o b ta in e d w ith satellite-b ased p ro d u c ts a n d la n d surface m odels
for large riv er b asin s o f th e w orld.
The C o u n c il for S cientific a n d In d u s tria l R esearch (CSIR)
h a s re ce n tly in itia te d resea rc h a im e d at e v alu atin g , v a lid a tin g
a n d im p ro v in g th e M O D 16 ET p ro d u c t, one o f th e free satelliteba se d E T p ro d u c ts w ith re ad ily available E T d a ta for th e p a st 13
years. These tim e series w ere seldom a pplied to e stim a te E T in
A frica, especially in a rid a n d se m i-a rid regions. The M O D 16 ET
p ro d u c t e stim a te s global E T fro m g ro u n d -b a s e d m ete o ro lo g i­
cal o b se rv atio n s a n d re m o te -se n sin g d a ta fro m th e M o d erate
R esolution Im a g in g S p e c tro ra d io m e te r (M O D IS) lo ca ted on
NASA’s T erra a n d A qua satellites (Justice e t al., 2002). The
M O D IS se n so r w orks on a sp atial re so lu tio n o f a p p ro x im ate ly
1 k m , m a k in g it p o te n tia lly suitable for a p p lic atio n s in w ater
re so u rce m an a g em e n t. The im ages c o n ta in 36 sp e c tra l b a n d s
in th e w avelen g th ra n g e o f 0.4 to 14.4 pm . The M O D 16 ET
a lg o rith m w as developed by M u et al. (2007a) fro m th e o rig in a l
m o d el o f C leugh et al. (2007), a n d la te r im p ro v e d by M u et al.
79
(2011). T his p a p e r p re sen ts th e first ev alu atio n o f
th e M O D 16 ET d o n e in S o u th A frica at c o u n try ­
w ide scale. The aim s w ere: (i) to d escrib e th e
a n n u a l a n d sp atial tre n d s o f E T a n d its c o m p o n e n ts
e stim a te d w ith th e m o d ifie d E T a lg o rith m o f M u
et al. (2011) for S o u th A frica, a n d (ii) to assess th e
lim itin g ran g es o f a lg o rith m key v ariab les in rela­
tio n to E T a n d its c o m p o n en ts.
MATERIA L A N D M E T H O D S
MOD16ET algorithm
B rief description o f the M O D IS ET algorithm
The d e ta ile d a lg o rith m d e sc rip tio n c an be fo u n d
in M u et al. (2007a) a n d M u et al. (2011). In th is
study, o n ly th e v ariab les u se d in th e analysis are
described. The M O D 16 ET a lg o rith m is based
on th e p hysically s o u n d th e o ry o f th e P e n m an M o n te ith en erg y b alan ce (M o n te ith , 1965; A llen et
a l , 1998):
A +YX (l+rs/ra)
w here:
E T is in m m
X is th e la te n t h e a t o f v a p o risa tio n o f w ater
(!•% ')
A is th e g ra d ie n t o f th e sa tu ra tio n v a p o u r
p re ssu re -te m p e ra tu re fu n c tio n ( P a ° C ')
is th e n e t ra d ia tio n (J-m ^-s ')
G is th e soil h e a t flux (J-m ^-s')
is th e a ir d e n sity (kg-m ^)
is th e specific h e a t o f th e a ir (J-kg^'-K i)
is th e sa tu ra te d v a p o u r p re ssu re o f th e a ir
(Pa), a fu n c tio n o f a ir te m p e ra tu re m e a su re d at
h e ig h t z
is th e m e a n a ctu al v a p o u r p re ssu re o f th e air
m e a su re d at h e ig h t z (Pa)
( e - e ) is v a p o u r p re ssu re deficit {VPD; Pa)
is th e a ero d y n a m ic re sistan c e to w a ter
v a p o u r diffusion in to th e a tm o sp h e ric b o u n d ­
a ry layer (s-m ')
Y is th e p sy c h ro m e tric c o n sta n t (0.066 k P a -K ')
r is th e surface re sistan c e to w a te r v a p o u r
tra n s fe r (s-m ')
The M O D 16 ET a lg o rith m (M u e t al., 2011) c al­
c u lates E T u sin g g lobal d a ily te m p e ra tu re , actu al
v a p o u r p re ssu re a n d in c o m in g solar ra d ia tio n , a n d
rem o tely -sen sed E A R FPAR, albedo, a n d la n d cover
ty p e. The available en erg y at th e la n d surface {R^ is
p a rtitio n e d in to v eg etatio n surface a n d soil surface
u sin g FPAR (M O D IS 15A p ro d u c t, a ssu m e d to be
e q u al to c a n o p y cover F^. The te rm r fro m Eq.
(1) is d efin ed as an effective su rface resistan ce to
e v ap o ra tio n fro m th e soil surface a n d tr a n s p ira tio n
fro m th e p la n t canopy. C a n o p y r d ecreases as VPD
decreases, a n d it is also lim ite d by low te m p e ra tu re
(M u e t a l , 2007a; M u e t a l , 2011).
E v ap o ratio n fro m th e w et c an o p y o c cu rs after
c e rta in c o n d itio n s (e.g. after ra in fa ll, w h en air
relative h u m id ity >70%) a n d c a n be a su b sta n tia l
c o m p o n e n t w h en le a f area is large. In o rd e r to
80
calculate d a y tim e a n d n ig h t-tim e FT, d aily average a ir te m p e ra tu re (Tavg)
is a ssu m e d to be th e average o f d a y tim e a ir te m p e ra tu re (Tday) a n d n ig h t­
tim e te m p e ra tu re (M u et al., 2011). D ay-tim e a n d n ig h t-tim e E T are th e n
a d d ed u p to get d a ily E T values.
A soil e v ap o ra tio n {Soil E) c o m p o n e n t is also c alcu la te d in th e M O D16
ET a lg o rith m (M u e t al., 2011), w h ich m ay be im p o rta n t in areas w ith a
sparse canopy. The p o te n tia l e v ap o ra tio n fro m th e soil is first c alcu la te d
w ith a n e q u atio n th a t fu lly resem bles th e P e n m a n -M o n te ith en erg y b a l­
ance e q u atio n (Eq. (1)). A c tu a l Soil E is th e n c alcu la te d as a fu n c tio n o f
a ir relative h u m id ity {RET). The a lg o rith m also co n sid ers th e w et surface
fra c tio n (E
,) c alcu la te d as a fu n c tio n o f R H . The w et su rface fra c tio n (E
,)
'
w e t'
'
w e t'
re p re se n ts th e fra c tio n o f c a n o p y o r soil covered by w ater. In th e case o f
th e canopy, E^^^ is u se d to sep arate e v ap o ra tio n o f w a ter in te rc e p te d by th e
c a n o p y a n d tra n s p ira tio n (T). In th e case o f th e soil, E^^^ is u se d to sep arate
e v ap o ra tio n fro m sa tu ra te d a n d m o ist soil surface. The late n t h e a t fluxes
fro m vegetation c a n o p y a n d soil (p a rtitio n e d th ro u g h P^ a n d F^J are
finally su m m e d u p to calculate E T for th e p a rtic u la r v egetation.
M O D 16 ET is th e sum o f 3 co m ponents:
E T — Tr + Ec + Ei
(2)
w here:
T , E^, a n d E . are c a n o p y tra n s p ira tio n (T), soil e v ap o ra tio n {Soil E), a n d
in te rc e p tio n e v ap o ra tio n {C anopy E), respectively.
({ARnFc + pCpVPD
ATr =
s -h y X
F c /E ic ) ( 1 ~ F w e t )
(3)
(1 -h r .J V a c )
{^RnEc + p C p V P D F c /r a w c ) F w e t
XEi =
A -h (1
-h
^
(4)
)
' *awc'
The te rm E^ c o n sists o f Soil E fro m d ry soil su rface a n d w et soil surface:
(5)
^ w e t _ s o i l 4" ^ S o i L p o t fs m
(A(i?„(l - FJ - G) + pCp(1.0 - Fc) VPD/rgs)Fwet
AE.S O IL p o t
(i(B „ (l - FJ - C) +()C,(1,0 - Fc) I'f P /r „ )(l - Fwet)
(6)
(y,
'
»+
w here:
Ej, is th e fra c tio n a l v eg etatio n cover
Ew e ,t is relative surface w etness (EEP)
'
'
r ^ are th e a ero d y n a m ic a n d c a n o p y resistan c es o f th e d ry c a n o p y
is m o d ifie d RET™ to th e one in F isher et al. (2008)
r a w e a n d rs w c are th e a ero d y' n a m ic a n d w et c a n o -Tp y/ resistan ces o f th e w et
canopy
ET^^j soi7
are th e w et a n d p o te n tia l Soil E
ra s a n d r ss are th e soil a ero d y' n a m ic c o n d u c ta n c e a n d soil to ta l
resistan ces
The p o te n tia l p la n t tra n s p ira tio n {T^J is c alcu la te d follow ing th e P riestleyT aylor (P riestley a n d Taylor, 1972) e q uation:
a A P n F c il - Fwet)
s -h y
^
1.26
(8)
The to ta l d a ily p o te n tia l E T (PET) is c alcu la te d w ith Eq. (9):
P E T — AEi + ATpQi + AEy^^
+ XE<S O I L p o t
(9)
http://dx.doi.org/10.4314/w sa.v41il.ll
Available on website http://www.wrc.org.za
ISSN 0378-4738 (Print) = W ater SA Vol. 41 No. 1 lanuary 2015
ISSN 1816-7950 (On-line) = W ater SA Vol. 41 No. 1 lanuary 2015
L egend
I TVopicarW et
I S u m m e r R ainfall
I W inter R ainfall
' A rid to Sem i-A rid
720Kllom«»(S
Figure 1
Legend
T av g ( d e g C)
v a lu e
B H ig h : 2 6 .6
Low : 13.4
720 KilematAis
GMAO MERRA m eteorological inp u t d ata
N A SA /G M A O M o d e rn E ra R etrospective A nalysis (M ERRA )
at sp atial re so lu tio n o f 0.5°x 0.66° p ro v id e d every h o u r w as u se d
as m eteo ro lo g ical in p u t to th e M O D 16 ET a lg o rith m . M u et al.
(2011) p ro c e sse d th e h o u rly d a ta to d a ily level. The tec h n iq u e
p ro p o se d by Z h ao e t al. (2005) w as u se d to in te rp o la te d ata
fro m co arse sp atial re so lu tio n to 1 k m , to fit M O D IS pixels,
to rem ove a b ru p t ch an g es fro m one side o f a G M A O p ixel to
a n o th e r, a n d to im p ro v e th e a cc u rac y o f th e se pixels.
M eth o d o lo g y and stu d y area
S o u th A frica covers a w ide ra n g e o f c lim atic a n d h ydro lo g ical
co n d itio n s. The S o u th A frica n D e p a rtm e n t o f W ater A ffairs
classified th e c o u n try ’s w a te r reso u rce s in to 19 w a te r m a n a g e ­
m e n t areas (W M A s) in 2004 (DW AF, 2004, since re g ro u p e d
in to 9 W M A s). The W M A b o rd e rs w ere u se d to delineate 4
clim atic reg io n s (Fig. la). The w estern a n d c e n tra l W M A s fall
in a rid a n d se m i-a rid regions. The so u th e rn W M A s are in an
area w ith a M e d ite rra n e a n (w in ter ra in fa ll) clim ate. The e ast­
e rn co asta l area h a s a tro p ic a l w et clim ate, w h ilst th e n o rth e rn
reg io n s are in th e su b -tro p ica l (su m m er ra in fa ll) belt. Such
clim atic div ersity is ideal for th e analysis o f a w ide ra n g e o f E T
values. The d ivision in to 4 c lim atic re g io n s is c o rro b o ra te d by
th e c h a ra c te ristic g ra d ie n t in a n n u a l ra in fa ll fro m w est (a rid
a n d se m i-a rid clim ate) to east (tro p ic al w et clim ate) (Fig. lb;
L ynch a n d S chulze, 2006). It is e v id e n t th a t average a ir te m ­
p e ra tu re s are ty p ic a lly m o d e ra te in th e so u th a n d e ast o f th e
c o u n try , a n d h ig h in th e n o rth -w e s t (Fig. Ic).
T h irte en y ears (2000-2012) o f a n n u a l M O D 16 ET a n d
G M A O M E R R A m ete o ro lo g ica l d a ta w ere c o llected a n d p r o ­
cessed for th e w hole c o u n try , as w ell as for in d iv id u a l clim atic
http://dx.doi.org/10.4314/w sa.v41il.ll
Available o n website http://www.wrc.org.za
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a) C lim atic regions o f South
A frica delineated based on Water
M a nagem ent Areas (South A frican
D epa rtm e nt o f Water A ffairs and
Forestry; DWAF, 2004); b) mean a nnual
ra in fa ll fo r the period 1960-2014
(Lynch a n d Schulze, 2006); c) average
a ir tem perature (Tavg, MODIS) fo r a
typica l year (2009)
re g io n s as classified in Fig. la , on a 0.912 k m x 0.912 k m pixel
basis. For each yearly d a ta set, th e follow ing v ariab les w ere
extracted :
E v a p o tra n sp ira tio n (ET)
P o te n tia l e v a p o tra n s p ira tio n (PET)
E v ap o ra tio n fro m w et c a n o p y surface {Canopy E)
Soil e v ap o ra tio n (Soil E)
D ry soil e v ap o ra tio n (D ry soil E)
W et soil e v ap o ra tio n ( W et soil E)
T ra n s p ira tio n (T)
A verage a ir te m p e ra tu re (Tavg)
D a y tim e average a ir te m p e ra tu re (Tday)
D a y tim e average v a p o u r p re ssu re deficit (VPD)
T he v ariab les w ere selected b a se d on th e im p ro v e m en ts in tr o ­
d u c ed by M u et al. (2011) to th e o rig in a l a lg o rith m . Yearly a n d
sp atial c h an g es in E T w ere a n aly se d a n d c o rre la te d to th e yearly
values fo r each v ariab le in o rd e r to assess th e sen sitiv ity a n d
d ep en d e n ce o f F T to th e selected variables. The d a ta w ere a n a ­
lysed for th e w hole c o u n try as w ell as p e r clim atic region.
Statistical an alysis
T he te m p o ra l (an n u al) ch an g es in E T a n d a sso ciated v ariables
w ere assessed u sin g lin e a r reg ressio n fu n c tio n s a n d teste d
for sta tistica l significance. F or th e assessm en t o f d ep en d en ce
betw een E T a n d a sso ciated v ariables over tim e , th e S p e a rm a n
ra n k c o rre latio n coefficient (r^) w as u se d b ecause it is suitable
for sm all d a ta series th a t m ay n o t n e ce ssa rily have a n o rm a l
d istrib u tio n . The In fo S tat softw are (D i R ienzo et al., 2012) w as
u se d for th e c alcu la tio n o f a n d sta tistica l significance.
F or th e sp atial analysis it w as n o t p ossible to gen erate a
d a ta se t by av eraging th e a n n u a l d a ta for 13 y ears because th e
81
TABLE 1
P oten tial ev a p o tra n sp ira tio n (PET), a ctual eva p o tra n sp ira tio n (ET), c a n o p y and soli ev a p o ra tio n
(Canopy E a n d Soil E) a n d transp iration (T) e stim a te d w ith MODIS p rod u cts for Sou th Africa.
S lo p es o f th e linear r eg r essio n are sh ow n (p > 0.05 in ail ca ses). Total area is 1 2 2 8 297 km^.
Y ear
PET
(mnti’a ')
ET (b liilo n
m = a ')
ET
(mnti’a ')
C anopyE
(mnti’a ')
2000
2 173
428.1
349
41
139
169
2001
2 174
411.9
335
30
138
167
2002
2 292
340.3
277
18
103
156
2003
2 321
299.2
244
14
93
137
2004
2 285
342.2
279
21
95
2005
2 266
340.4
277
24
2006
2 156
434.3
354
42
2007
2 268
347.1
283
2008
2 211
377A
307
2009
2 236
377.6
307
2010
2 262
369.8
301
2011
2 209
393.5
320
2012
2 250
368.8
Average
2 239
371.6
Slope
0.649
-0 .0 9 7
S o iiE
(mnti’a ')
T (mnti’a ')
Canopy
EIET
SoiiE/ET
0.16
0.12
0.40
0.48
0.15
0.09
0.41
0.50
0.12
0.07
0.37
0.56
0.10
0.06
0.38
0.56
163
0.12
0.07
0.34
0.58
107
146
0.12
0.09
0.39
0.53
142
169
0.16
0.12
0.40
0.48
22
110
151
0.12
0.08
0.39
0.53
27
129
151
0.14
0.09
0.42
0.49
30
122
156
0.14
0.10
0.40
0.51
27
116
159
0.13
0.09
0.38
0.53
26
119
175
0.15
0.08
0.37
0.55
300
24
115
162
0.13
0.08
0.38
0.54
303
27
117
158
0.14
0.087
0.387
0.526
-0 .0 7 9
-0.153
-0 .2 0 3
0.277
-lE -0 4
-2 E -0 4
-3 E -0 4
5E -04
n u m b e r o f m issin g d a ta (out o f range) v a rie d b etw een years,
a n d th is m ay have in tro d u c e d in co n sisten cies a n d bias. The spa­
tia l analysis w as th e n p e rfo rm e d for a y e ar w h en a n n u a l E T a n d
asso ciated c o m p o n e n ts e x h ib ite d th e least d ev ia tio n fro m th e
13-year average. T his ty p ic a l y e ar w as 2009 a n d it w as a ssu m e d
th a t it w o u ld give a realistic a n d rep re se n tativ e d e sc rip tio n
o f sp atial differences. Average, m e d ia n , sta n d a rd d eviation,
coefficient o f v a ria tio n , skew ness a n d k u rto sis o f all relev an t
v ariab les w ere d e te rm in e d u sin g all d a ta pixels. The spatial
d ep en d en ce b etw een v ariab les w as assessed for all y ears u sin g
th e coefficient o f d e te rm in a tio n (R^) o f reg ressio n fu n c tio n s a n d
P earso n c o rre latio n coefficient (r). In th is in stan c e, r w as u se d
in ste a d o f to red u ce c o m p u ta tio n tim e because o f th e v ery
large d a ta se t («>100 000) a n d to b e tte r a cc o u n t for o u tliers (the
effects o f o u tlie rs m ay be m a sk e d by th e ra n k in g in r^). B oth th e
coefficient o f d e te rm in a tio n (R^) a n d th e c o rre latio n coefficients
w ere re p o rte d to be suitable to in d ic a te w h e th e r tw o d a tasets
have sim ila r te m p o ra l o r sp atial p a tte rn s (Ji a n d G allo, 2006).
ET/
PET
T/ET
400
300
as
I
200
LU"
1LU
— 100
o
o
O
m
o
O
O
O
(N m
Year
■ET
-C a n o p y E
-S oil E
Figure 2
Thirteen-year trends in a n n u a l evapotranspiration (ET), canopy
evaporation (canopy E), soil evaporation (soil E) and transpiration
(T) estim ated w ith M ODIS fo r South Africa
R ESULTS A N D D IS C U S S IO N
Tem poral c h a n g es o f MOD16 ET an d ET c o m p o n e n ts
T h irte e n y e ars o f a n n u a l PET, E T a n d its c o m p o n e n ts w ere
e s tim a te d w ith M O D IS p ro d u c ts a n d are sh o w n in T able 1.
ft w as e s tim a te d th a t th e average E T in S o u th A frica is
303 m m - a r a n g i n g fro m 2 4 4 m m - a ' in 2003 to 354 m m - a '
in 2006. O n ly 14% o f th e p o te n tia l a tm o sp h e ric d e m a n d for
w a te r e v ap o ra te s (E T/P E T). T he la rg e st c o m p o n e n t o f E T w as
tr a n s p ir a tio n o f p la n ts (53% on average), follow ed b y Soil E
(39% on average). D ire c t e v a p o ra tio n fro m th e v e g etatio n
c a n o p y w as a m in o r c o m p o n e n t o f E T (9% on average).
A n n u a l v alues in d ic a te d th a t E T w as ra th e r stable in th e
p e rio d 2 00 0 -2 0 1 2 (Fig. 2), d e p e n d in g on ra in fa ll a m o u n ts
a n d d istrib u tio n . E v a p o tra n sp ira tio n (ET), C anopy E a n d Soil
E show ed a slight te n d e n c y to decrease b a se d on th e negative
slope o f th e lin e a r reg ressio n (Table 1), w h ilst P E T a n d T w ere
slightly in cre asin g (positive slope in Table 1). H ow ever, a n n u a l
v a ria b ility w as m u c h la rg e r th a n th e o b serv ed c h an g es a n d
82
th e se tre n d s w ere n o t sta tistica lly significant (p>0.05). T ables
2 to 5 show 13 years o f a n n u a l PET, E T a n d its c o m p o n e n ts
for each c lim atic region. E v a p o tra n sp ira tio n (E T) d isplayed
a slight te n d e n c y to decrease in all c lim atic regions, except
in w in te r ra in fa ll areas w here th e C anopy E a n d Soil E w ere
in creasin g . H ow ever, n o n e o f th e tre n d s w as sta tistica lly signifi­
c a n t (p>0.05). N atio n -w id e average values (Table 1) are b iased
to w a rd s th e values e stim a te d in th e a rid a n d se m i-a rid clim ate,
w h ich re p re se n ts th e larg est c lim atic reg io n in e x te n t (Fig. la).
The re la tio n s b etw een v ariab les w ere d e te rm in e d u sin g
a n d th e re su lts are s u m m a rise d in Table 6. The values below th e
m a in d iag o n al in Table 6 re p re se n t r^. A p ositive n u m b e r r e p ­
re sen ts p ositive c o rre latio n a n d vice versa. G o o d co rre latio n s
te n d to +1 (positive co rrelatio n ) a n d -1 (negative correlation).
The values above th e m a in d iag o n a l re p re se n t th e p ro b a b ility
a sso ciated w ith th e n u ll h y p o th esis. V alues <0.05 re p re se n t
sta tistica lly significant re la tio n s at p ro b a b ility o f 95% o r m ore,
a n d th e se are h ig h lig h te d in b o ld in T able 6. ft is e v id en t th a t
th e re is gen erally a negative c o rre latio n betw een P E T a n d all
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TABLE 2
P oten tial ev a p o tra n sp ira tio n (PET), actual eva p o tra n sp ira tio n (ET), ca n o p y and soil e v a p o ra tio n (Canopy E
an d SotVE) an d transp iration (T) e stim a te d w ith MODIS p rod u cts for t h e su m m er rainfall area o f S ou th Africa.
S lo p es o f th e linear reg ressio n are sh ow n (p > 0.05 in ail ca ses). Total area is 2 9 9 693 km^.
Y ear
PET
(m m -a ')
ET (b illio n
m =-a')
ET
(m m -a ')
C anopyE
(m m -a ')
2000
2157
105.9
460
2001
2200
93.1
405
2002
2370
66.7
290
2003
2396
59.5
2004
2263
80.6
2005
2312
72.5
315
2006
2147
103.1
448
2007
2329
73.5
320
2008
2244
86.7
2009
2231
2010
2260
2011
2303
2012
2329
76.3
332
13
95
224
Average
2272
83.5
363
24
115
224
Slope
3.278
-0 .0 6 8
-0 .2 9 6
-0 .2 5 6
-0 .7 4 6
0.705
-5 E -0 4
S oilE
(m m -a ')
T
(m m -a ')
ET/
PET
Canopy
E/ET
S o il E/ET
T/ET
46
161
254
27
139
239
0.21
0.1
0.35
0.55
0.18
0.07
0.34
8
83
198
0.59
0.12
0.03
0.29
0.68
259
6
72
181
0.11
0.02
0.28
0.7
350
17
93
241
0.15
0.05
0.26
0.69
15
97
203
0.14
0.05
0.31
0.64
53
162
233
0.21
0.12
0.36
0.52
12
95
213
0.14
0.04
0.3
0.67
377
28
135
213
0.17
0.08
0.36
0.57
94.1
409
40
141
229
0.18
0.1
0.34
0.56
89.5
389
26
117
246
0.17
0.07
0.3
0.63
84.6
368
20
105
243
0.16
0.05
0.29
0.66
0.14
0.04
0.29
0.68
0.16
0.06
0.31
0.63
-5 E -0 5
- lE - 0 3
-2 F -0 3
TABLES
P oten tial ev a p o tra n sp ira tio n (PET), actual eva p o tra n sp ira tio n (ET), ca n o p y and soil e v a p o ra tio n (Canopy E
and SoilE) and transp iration (T) e stim a te d w ith MODIS p ro d u cts for th e tropical w e t area o f S ou th Africa.
S lo p es o f th e linear reg ressio n are sh ow n (p > 0.05 in ail ca ses). Total area is 132 913 km^.
Y ear
PET
(m m -a ')
ET (b illio n
m = .a ')
2000
1 834
2001
1 869
2002
1 935
ET
(m m -a ')
C anopyE
(m m -a ')
S oilE
(m m -a ')
T
(m m -a ')
ET/
PET
Canopy
EIET
108.4
816
192
101.5
764
148
90.6
682
98
180
S o il E/ET
T/ET
249
375
0.44
220
395
0.41
0.24
0.31
0.46
0.19
0.29
404
0.35
0.52
0.14
0.26
0.59
2003
1 970
80.9
609
77
181
351
0.31
0.13
0.3
0.58
2004
1 906
92.5
696
107
179
410
0.37
0.15
0.26
0.59
2005
1 905
92.2
694
130
212
352
0.36
0.19
0.31
0.51
2006
1 823
104.5
787
178
234
375
0.43
0.23
0.3
0.48
2007
1 935
92.2
694
108
200
385
0.36
0.16
0.29
0.56
0.48
2008
1 853
91.9
691
126
234
331
0.37
0.18
0.34
2009
1 880
96.2
724
140
211
373
0.39
0.19
0.29
0.52
2010
1 922
94.8
713
136
216
362
0.37
0.19
0.3
0.51
2011
1 857
94.2
709
119
201
389
0.38
0.17
0.28
0.55
2012
1 910
94.8
713
118
199
396
0.37
0.17
0.28
0.56
Average
1 892
95.0
715
129
209
377
0.38
0.18
0.29
0.53
Slope
0.002
-0 .3 1 3
-2 .3 5 6
-1.292
-0 .3 6 8
-0 .6 9 6
- l F - 0 .3
-6 F -0 4
2 F -0 4
4 F -0 4
v ariab les except T/ET. The re m a in in g v ariab les w ere g enerally
p ositively correlated. A nalysis by clim atic region in d ic a te d th a t
th e c o rre latio n s o f ra tio s (C anopy E/ET, Soil E /T a n d T/E T)
to o th e r v ariab les w ere g enerally n o t significant in th e w in te r
ra in fa ll a n d especially a rid a n d se m i-a rid clim ates.
In absolute te rm s, M O D 16 ET e stim a te d an average w a ter
loss to th e atm o sp h e re o f 371.6 x 10® m m -a ' for th e c o u n try
(Table 1). A ssu m in g an average ra in fa ll o f 450 m m - a c o r r e ­
sp o n d in g to 553 X 10® m m - a i t w as c alcu la te d th a t 67% o f
ra in fa ll w a ter evaporates. It w as e stim a te d th a t ru n o ff is a bout
50 X 10® m m -a ' o r 9% o f ra in fa ll (DW AF, 2004) a n d th a t
g ro u n d w a te r re ch a rg e is ab o u t 30 x 10® m m -a ' o r 5% o f ra in fa ll
(Vegter, 1995; DW AF, 2005). F re n k e n (2005) e stim a te d w ater
w ith d ra w a l in S o u th A frica to be 12.5 x 10® m m - a ' in 2000.
C o n sid e rin g m issin g d a ta (about 3% o f th e to ta l n u m b e r o f
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pixels), M O D 16 ET e stim a te s w ere ab o u t 15% sh o rt o f th e w ater
b a la n ce c losure fo r S o u th A frica, possibly due to in ac cu ra c ie s
in th e a lg o rith m a n d in p u t d a ta (e.g. la n d cover).
Spatial ch an ges o f MOD16 ET and ET c o m p o n e n ts
F igure 3 (a to g) displays e n v iro n m e n ta l v ariab les o b ta in e d
fro m M O D IS for a ty p ic a l y e ar (2009) w h e n a n n u a l E T a n d
a sso ciated c o m p o n e n ts e x h ib ited th e least d ev iatio n s from
th e 13-year average (Table 1). C lim atic c o n d itio n s drive P F T
e x h ib itin g a g ra d ie n t fro m th e so u th e a st to th e n o rth w e st
(Fig. 3a). The g ra d ie n t is inverse for E T (Fig. 3b), w h ich is d riven
by a tm o sp h e ric e vaporative d e m a n d , b u t d ep en d s on ra in fa ll
(Fig. lb) a n d v egetation cover (Fig. 3c). H ig h ra in fa ll areas
(Fig. lb) are g en erally asso ciated w ith a m o re h u m id
83
TABLE 4
P oten tial eva p o tra n sp ira tio n {PET), actu al ev a p o tra n sp ira tio n {ET), c a n o p y a nd soli ev a p o ra tio n
{C anopy E a n d Soil E) a n d transp iration (T) e stim a te d w ith MODIS p r o d u c tsfo r th e w in ter rainfall area
o f S ou th Africa. S lo p es o f th e linear reg ressio n are sh ow n (p > 0.05 in ail ca ses). Total area is 2 4 9 637 km^.
Y ear
PET
(m m -a ')
ET (b liilo n
m = .a ')
ET
(m m -a ')
C anopyE
(mnti’a ')
2000
1 886
103.4
414
43
191
180
2001
1 899
102.7
411
36
189
186
2002
1 965
94.2
377
27
162
189
2003
1 963
87.5
351
21
156
2004
2 001
90.1
361
25
156
2005
1 940
95.0
380
33
170
2006
1 856
109.0
436
49
203
2007
1 933
97.2
389
34
181
2008
1 898
99.2
397
34
2009
1 957
89.6
359
2010
1 960
91.6
367
2011
1 836
106.5
2012
1 869
Average
Slope
S oilE
(m m -a ')
T
(m m -a ')
ET/
PET
Canopy
EIET
SoiiE/E T
T/ET
0.22
0.1
0.46
0.43
0.22
0.09
0.46
0.45
0.19
0.07
0.43
0.5
173
0.18
0.06
0.45
0.49
180
0.18
0.07
0.43
0.5
111
0.20
0.09
0.45
0.46
184
0.24
0.11
0.47
0.42
175
0.20
0.09
0.46
0.45
187
176
0.21
0.09
0.47
0.44
27
172
160
0.18
0.07
0.48
0.45
29
185
154
0.19
0.08
0.5
0.42
426
40
194
193
0.23
0.09
0.45
0.45
106.6
427
40
193
194
0.23
0.09
0.45
0.46
1 920
97.9
392
34
180
179
0.20
0.08
0.46
0.46
-3.719
0.297
1.188
0.235
1.323
-0 .3 6 9
lE -0 3
3E -04
2E-03
-2 E -0 3
TABLE 5
P oten tial eva p o tra n sp ira tio n {PET), actu al ev a p o tra n sp ira tio n {ET), c a n o p y a nd soli ev a p o ra tio n
{Canopy E a n d Soil E) and transp iration (T) e stim a te d w ith MODIS p rod u cts for th e arid and sem i-arid area
o f S ou th Africa. S lo p es o f th e linear reg ressio n are sh ow n (p > 0.05 in ail ca ses). Total area is 5 4 6 0 5 4 km^.
Y ear
PET
(m m -a ')
ET (b liilo n
m = .a ')
T (m m -a ')
ET/
PET
Canopy
EIET
SoiiE/E T
T/ET
2000
2 400
2001
2 365
77
70
0.06
0.01
0.52
0.47
93
66
0.07
0
0.58
2002
0.41
0
67
58
0.05
0
0.53
0.47
97
0
52
45
0.04
0
0.54
0.46
55.7
102
0
47
55
0.04
0
0.47
0.54
2 485
59.2
108
0
56
52
0.04
0
0.52
0.48
2 384
87.9
161
2
80
79
0.07
0.01
0.5
0.49
2007
2 477
62.2
114
0
62
52
0.05
0
0.54
0.46
2008
2 430
74.2
136
0
72
64
0.06
0
0.53
0.47
2009
2 458
71.0
130
0
66
63
0.05
0
0.51
0.49
2010
2 490
68.3
125
0
58
67
0.05
0
0.46
0.54
2011
2 424
83.0
152
1
70
81
0.06
0
0.46
0.53
2012
2 473
68.0
125
0
67
57
0.05
0
0.54
0.46
Average
2 457
70.7
129
0
67
62
0.05
0.00
0.52
0.48
Slope
1.528
-0.018
-0 .0 3 2
-0 .0 1 4
-0 .6 1 4
0.596
-8 E -0 5
-3 E -0 4
-4 E -0 3
4E-03
ET
(m m -a ')
C anopyE
(mnti’a ')
S oiiE
(m m -a ')
80.3
147
1
87.6
160
1
2 494
68.4
125
2003
2 537
53.0
2004
2 524
2005
2006
e n v iro n m e n t, low er P E T a n d d e n se r v eg etatio n cover c o m p a re d
to d ry areas. A s a resu lt, E T is h ig h e r in th e tro p ic a l w et easte rn
region c o m p a re d to th e a rid a n d se m i-a rid n o rth w e st region
(Fig. 3b). B oth c o m p o n e n ts o f ET, n a m e ly T (Fig. 3d) a n d Soil
E (Fig. 3e), ex h ib it th e sam e g ra d ie n ts, i.e., th e y are h ig h in th e
h ig h ra in fa ll area o f th e east co ast a n d low in th e a rid n o rth w e st
o f th e co u n try .
The M O D IS la n d cover m ap (Fig. 3c) classifies th e largest
p o rtio n o f in la n d S outh A frica (cen tral a n d w e ste rn regions) as
open sh ru b la n d a n d g ra ssla n d , w ith sav a n n a o c c u rrin g in th e
n o rth e a s t p a r t o f th e c o u n try . L an d cover is classified as c ro p ­
la n d m o stly alo n g th e w est a n d east co ast a n d in th e n o r th ­
east. The m a in u rb a n areas are clearly visible in th e n o rth e a s t
(Jo h a n n esb u rg ), so u th w est (C ape Town) a n d on th e east coast
(D u rb an ). V alues o f M O D IS v ariab les w ere o u t o f ra n g e for
84
pixels c o in c id in g w ith u rb a n areas a n d th e se w ere d isc ard e d
fro m th e analysis. A n o th e r area w ith freq u e n t m issin g d a ta (out
o f range) is visible in th e n o rth w e st in la n d a n d classified as b a r­
re n o r sparsely vegetated. The ra tio T /E T te n d s to be h ig h in th e
n o rth e rn , su m m e r ra in fa ll p a rts o f th e c o u n try w here g ra ss­
la n d s c o m m o n ly occur, a n d low in th e d ry sou th w est w here
sparse vegetation o ccu rs (Fig. 3f). The opposite tr e n d is visible
for th e Soil E /E T ra tio (Fig. 3g). In th e c e n tra l a n d n o rth w e st­
e rn p a rts o f th e c o u n try , lin e s follow ing m ajo r riv er system s
(O ran g e a n d V aal) are clearly visible p ro v id in g excep tio n al
values o f h ig h T /E T a n d low Soil E /E T (Figs 3f a n d g).
Table 7 show s th e sta tistica l analysis o f M O D IS sp a tia l d ata
for a ty p ic a l y e ar (2009). For E T a n d re la te d v ariables {Soil E
a n d T), th e large sta n d a rd d ev iatio n s a n d coefficients o f v a ria ­
tio n in d ic a te d th e w ide ra n g es o f values observed. The m e d ia n
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a)
b)
Legend
ET Immia)
Legend
P E T 4m m /a)
v a lu e
V alu e
— High ; 2007.7
H ig h : 3 0 3 8 .4
L o w : 13 6 6 .8
720 K iio rrete rs
c)
d)
Legend
T (mm/a)
H igh : 1 4 1 3 .2
Low : 3
7ZD K ilo m eters
e)
f)
Legend
Sqm
Legend
E (mm/a)
T/ET
v alu e
V a lu e
— High :0.d
— H ig h : 3 24.1
Low : 6
720 KlloinAMfs
g)
’
Legend
V alu e
y
0
1B0
— High :0.£
360
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720 K ilo m e te rs
Figure 3
a) A nnu al p o te n tia l evapotranspiration (PET); b) a n nual
evapotranspiration (ET); c) la n d cover; d) a n nual transpiration
(T); e) a n n u a l soil evaporation (Soil E); f) T/ET ratio; a n d g) Soil
E/ET ra tio o b tained w ith MODIS fo r a typica l year (2009).
85
TABLE 6
Spearm an correlation c o efficie n ts o f a nnuai p o te n tia i ev a p o tra n sp ira tio n {PET), actuai
ev a p otran sp iration {ET), ca n o p y a nd soii e v a p o r a tio n (£) and transp iration (T) e stim a te d
w ith MODiS p ro d u cts for th e p eriod 2 0 0 0 -2 0 1 2 for Sou th Africa
V ariab le
PET
ET
C anopy E
Soil E
T
ET/PET
C anopy
E/ET
Soil E/ET
T/ET
4.8E-03
1
7.5E-04
l.lE -0 3
8.1E-04
0 .0 2
5.7E-04
1.9E-03
0 .0 2
ET
-0 .9 7
1
1.2E-03
8.7E-04
0 .0 1
6.6E-04
2.2E-03
0.04
0 .0 1
C anopy E
-0 .9 4
0.93
1
8.1E-04
0.06
1.3E-03
6.1E-04
0 .0 1
1.6E-03
Soil E
-0 .9 7
0.96
0.97
1
0.04
7.5E-04
1.2E-03
0 .0 1
2.2E-03
T
-0 .7
0.74
0.54
0.59
1
0 .0 1
0.12
0.98
0.46
PET
-0 .9 9
0.98
0.93
0.97
0.7
1
2.3E-03
0 .0 2
0 .0 1
C a n o p y E /E T
-0 .9
0.88
0.99
0.93
0.45
0.88
1
0 .0 1
1.3E-03
Soil E /E T
-0 .6 5
0.6
0.76
0.77
-0 .0 1
0.65
0.77
1
1.4E-03
0.81
-0 .7 6
-0 .9 1
-0 .8 8
-0 .2 1
-0 .8
-0 .9 3
-0 .9 2
1
E T/PE T
T /E T
TABLE 7
A verage, m ed ian , stan dard d e v ia tio n , c o efficie n t o f variation , sk ew n e ss a nd ku rtosis
o f sp atiai M O D iS v a ria b ie so b ta in e d for Sou th Africa fo r a typicai year (2009); n= 1 591 184
ET
PET
SoilE
D ry soil E
W et soil E
T
Tavg
Tday
Average
S ta tistic a l p a r a m e te r
307
2 236
122
92
29
156
20.21
22.31
1.97
M ed ian
238
2 251
109
89
20
120
20.00
22.20
1.94
S ta n d a rd d eviation
238
303
77
49
31
151
2.97
2.94
0.82
C oetficient o f v a ria tio n
0.78
0.14
0.63
0.53
1.07
0.97
0.15
0.13
0.42
Sicewness
1.33
-0 .0 1
0.85
0.48
1.61
2.27
0.16
0.04
0.12
K urtosis
2.00
-1.05
0.57
-0 .1 5
2.64
8.46
-1.20
-1.16
-0 .9 5
values low er th a n averages a n d th e p ositive sicewness in d ic a te d
th a t th e freq u e n c y o f o b se rv atio n s is b iased to w a rd s th e low
value range. For clim atic v ariab les {PET, Tavg, Tday a n d VPD),
th e freq u e n c y d istrib u tio n te n d e d to be sy m m etrica l. K u rto sis
is an in d ic a tio n o f th e shape (peaic) o f th e d istrib u tio n a n d
v a rie d fro m a negative n u m b e r fo r th e c lim atic v ariab les (fre­
quen cy d istrib u tio n fu n c tio n w ith a shape o f a n in v e rte d bell
w ith no ex tre m e ta il values) to 8.64 for T (freq u en cy d is trib u ­
tio n fu n c tio n w ith a sh a rp peaic).
A n n u a l v alues o f PET, E T a n d its c o m p o n e n ts are stro n g ly
d e p e n d e n t on clim ate (Tables 2 to 5). The h ig h e st P E T values
o c c u rre d in th e se m i-a rid a n d a rid areas (2 457 m m -a ' on aver­
age) a n d th e low est u n d e r tro p ic a l w et c o n d itio n s (1 892 m m - a ')
(Fig. 3a, Tables 3 a n d 5). T his is c o n sisten t w ith isoreference
e v ap o ra tio n m ap s p ro d u c e d by Savva a n d Frenicen (2002) u sin g
g ro u n d -b a s e d m eteo ro lo g ical m ea su re m e n ts, a n d th e h isto ric
p a n e v ap o ra tio n d a ta p ro c essed by W aticins (1993). C o n c e rn in g
E T a n d its c o m p o n e n ts, an inverse sp atial tre n d w as observed.
The h ig h e s t ET, C anopy E, Soil E a n d T w ere u n d e r tro p ic a l
c o n d itio n s a n d th e low est in a rid a n d se m i-a rid clim ate. E T w as
h ig h e r in su m m e r ra in fa ll areas c o m p a re d to w in te r ra in fa ll
areas in som e y ears, a n d low er in oth ers, d e p e n d in g on ra in fa ll
p a tte rn a n d d istrib u tio n . C anopy E a n d Soil E w ere g enerally
h ig h e r a n d T w as low er in w in te r ra in fa ll areas c o m p a re d to
su m m e r ra in fa ll. This w as due to th e lo w -in te n sity ra in fa ll
ty p ic a lly o c c u rrin g in w in te r areas (fro n tal ra in b ro u g h t by cold
fro n ts fro m th e ocean) c o m p a re d to tro p ic a l th u n d e rs to rm s o f
h ig h in te n sity o c c u rrin g in su m m e r ra in fa ll areas. C anopy E in
w in te r ra in fa ll areas (8% o i E T on average. Table 4) w as co n sist­
en t w ith th e m e a su re m e n t o f 6% m ad e by Jovanovic et al. (2013)
on fy n b o s vegetation e n d em ic to th is area. C anopy E in a rid
a n d se m i-a rid areas w as b asically negligible due to low ra in fa ll
a n d sparse v e getation. The h ig h e s t E T /P E T a n d C anopy E /E T
86
VPD
ra tio s w ere in tro p ic a l areas (0.38 a n d 0.18 on average) a n d th e
low est in a rid areas (0.05 a n d 0). The h ig h e s t Soil E /E T ra tio w as
in a rid areas due to sparse vegetation (0.52), follow ed by w in te r
ra in fa ll areas (0.46) due to low in te n sity ra in fa ll. The h ig h est
T /E T ra tio w as in su m m e r ra in fa ll areas (0.63) w ith h ig h
in te n sity ra in fa ll c o in c id in g w ith p e rio d s o f h ig h atm o sp h e ric
e vaporative d e m an d .
in co m p a rativ e te rm s, A h m a d e t al. (2005) e stim a te d E T to
be 3.51 m m - d ' on average for th e d o m in a n t la n d class (forest
a n d w o o d la n d s) in th e O lifan ts c a tc h m e n t (su m m e r ra in fa ll
area), u sin g a L andS at im age a n d SEBAL on 7 Ja n u a ry 2002.
M eijn in g er a n d Ja rm a in (2014) e stim a te d E T o i d o m in a n t vege­
ta tio n u sin g M O D iS a n d SEBAL. A n n u a l E T w as e stim a te d to
be 575 m m fo r native thicicet, 520 m m for e n d em ic fy n b o s a n d
>800 m m fo r alien invasive a n d exotic forest p la n ta tio n species
in th e W este rn C ape P ro v in ce (southw est co asta l zone o f th e
w in te r ra in fa ll region), in th e K w aZ uIuN atal P ro v in ce (east
co ast tro p ic a l w et region), a n n u a l E T w as e stim a te d to be
875 m m for alien invasive species, 755 for n ativ e thicicet,
685 m m for sav a n n a a n d 640 m m fo r g rasslan d s. The d o m in a n t
fa rm in g talcing place alo n g th e east co ast is w ith sugarcane.
O liv ier a n d Singels (2012), u sin g lysim eters, m e a su re d a sea­
so n al E T o f irrig a te d su g a rca n e o f b etw een 1 061 a n d 1 378
m m d e p e n d in g on cro p m an a g em e n t. These lite ra tu re d ata
w ere c o llected for specific p u rp o se s, over differen t areas a n d
ta rg e te d to specific ty p e s o f v e getation, so a d irec t c o m p a riso n
w ith M O D 16 ET is difficult. H ow ever, th e v alues re p o rte d in
th e lite ra tu re give a co arse in d ic a tio n th a t th e ran g es o i E T w ere
co m p a rab le to th o se e stim a te d w ith M O D 16 ET.
D ata for E T a n d re la te d c o m p o n e n ts w ere c o rre late d to te st
th e in te rd e p e n d e n c y o f icey v ariab les in th e alg o rith m . Table 8
su m m a rise s r o b ta in e d for E T a n d re la te d v ariab les p e r year.
F or co nvenience, |r| values >0.7 w ere m ariced in b o ld in
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TABLES
Pearson correlation c o efficie n ts (r) b e tw e e n y eariy ev a p o tra n sp ira tio n (ET) (rows)
and variab ies u sed in th e M 0D 16 ET aigorithm (coium ns) (p<0.01)
Year
E T vsP E T
ET v s S o ilE
ET vs D ry
S o ilE
E T vs W et
SoilE
2000
-0 .7 3
0.67
0.56
2001
0.71
0.56
0.41
2002
-0 .7 2
-0 .7 4
0.56
2003
E T v sT
ET vs Tavg
ET vs Tday
E T v s VPD
0.76
0.91
-0 .4 3
-0 .5 3
-0 .7 7
0.71
0.92
-0 .4 3
-0 .6 0
0.82
0.45
0.68
-0 .5 8
-0 .6 5
0.60
0.52
0.67
0.94
0.93
-0 .4 2
-0 .4 8
0.79
-0 .7 4
2004
0.76
0.61
0.53
0.69
0.94
-0 .4 8
-0 .5 6
0.76
2005
-0 .7 5
0.66
0.57
0.73
0.91
-0 .6 0
-0 .6 8
0.80
2006
-0 .7 3
0.63
0.50
0.74
0.91
-0 .3 8
-0 .4 7
-0 .7 7
2007
-0 .7 3
0.62
0.53
0.72
0.92
-0 .5 8
-0 .6 5
0.80
2008
-0 .7 3
0.65
0.56
0.73
0.89
-0 .5 6
-0 .6 5
0.80
2009
-0 .7 2
0.65
0.55
0.72
0.91
-0 .4 5
- 0 .5 4
-0 .7 7
2010
-0 .7 3
0.64
0.56
0.72
0.90
-0 .4 6
- 0 .5 4
-0 .7 4
2011
-0 .6 8
0.59
0.49
0.70
- 0 .4 4
-0 .5 3
2012
-0 .7 2
0.60
0.50
0.71
0.91
0.91
-0 .5 3
-0 .5 8
0.79
-0 .7 8
Table 8. T his v alue w as ch o sen a rb itra rily to re p re se n t m o d era te
to h ig h c o rre latio n betw een variables. A tte m p ts to fit n o n ­
lin e a r reg ressio n fu n c tio n s w ere m ade; how ever th is d id n o t
re su lt in su b sta n tia l in creases o f R^. Significance te sts re su lte d
in p ro b a b ility v alues te n d in g to 0 in ail cases due to th e large
d a ta se ts a n d degrees o f free d o m (p o p u la tio n n u m b e r >100 000).
The effects o f large sam ple sizes on th e p -v alu e w ere d isc u sse d
by Lin e t al. (2003), w ho suggested p ro c e d u re s a n d g u id elin es to
overcom e th is problem .
it is e v id e n t fro m Table 8 th a t E T w as d riv en by a tm o s­
p h e ric ev aporative d e m a n d (PET) a n d stro n g ly c o rre la te d to T
a n d VPD. A n alysis by clim atic reg io n s in d ic a te d th a t th is w as
p a rtic u la rly tr u e for w in te r ra in fa ll a n d a rid areas. D a y tim e
average te m p e ra tu re (Tday) h a d h ig h e r r c o m p a re d to Tavg
(exception w as tro p ic a l w et clim ate). The c o rre latio n s betw een
E T a n d Soil E w ere g en erally po o r, w ith th e ex cep tio n o f som e
years in a rid areas. C o n c e rn in g th e d ire c tio n s o f th e relations,
r w as positive in th e re la tio n s o f E T to Soil E a n d T; an ex cep ­
tio n w as th e tro p ic a l w et c lim ate w h e re E T w as negatively a n d
w eaid y c o rre la te d to Soil E, possibly due to th e effects o f dense
vegetation a n d c a n o p y cover u n d e r h u m id c o n d itio n s. The c o r­
re la tio n s b etw een E T a n d clim atic v ariables (PET, Tavg, Tday
a n d VPD) h a d v ariab le stre n g th a n d w ere negative, w ith th e
excep tio n o f th e tro p ic a l w et clim ate, w here h ig h e r te m p e ra ­
tu re s re su lte d in h ig h e r E T in m o st years.
E xam ples o f c o rre latio n s b etw een icey a lg o rith m v a ri­
ables are show n in Fig. 4 for tw o d istin c t clim atic regions
(tro p ical w et a n d a rid to sem i-arid ) for a ty p ic a l y e ar (2009).
E v a p o tra n sp ira tio n (E T) is w eaid y d riv en by PET, p a rtic u la rly
u n d e r tro p ic a l w et c o n d itio n s. The negative slope o f th e lin e a r
reg ressio n in d ic a te s th a t E T is h ig h e r w h en th e atm o sp h e ric
evap o rativ e d e m a n d is low er (Figs 4a a n d b). The c o rre latio n
coefficient b etw een E T a n d VPD w as m o d era te in a rid reg io n s
(Fig. 4c) a n d weaic in th e tro p ic a l c lim ate (Fig. 4d). ffow ever,
th e d ire c tio n o f chan g e w as th e sam e: h ig h e r VPD c o rre ­
sp o n d e d to low er E T (T a n n e r a n d S inclair, 1983). The VPD
d eriv ed fro m th e global c o arse -re so lu tio n (0.5°x0.66°) M E R R A
m eteo ro lo g ical d a ta c a n n o t alw ays reflect sm all-scale (1 icm)
VPD v a ria tio n s. As a resu lt, sm all areas o f w e tla n d , sp rin g s or
irrig a te d c ro p la n d m ay cause splices in E T at h ig h VPD v a l­
ues especially in th e a rid a n d se m i-a rid region. F or exam ple,
th is is visible in Fig. 4c at VPD ~ 3.25 icPa. A lth o u g h outliers
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are visible in Figs 4c a n d d, th e bulic o f th e d a ta p o in ts are in
th e low er p a r t o f th e g raphs. S im ila r re la tio n s w ere g enerally
o b serv ed for E T in re la tio n to d aily average a n d d a y tim e te m ­
p e ra tu re (data n o t show n). Figures 4e to h show th e relatio n s
betw een E T a n d its c o m p o n e n ts Soil E a n d T. The d a ta d is trib u ­
tio n o i E T vs. Soil E h a s a fanshape: it is c o n tro lle d by T in th e
low er ra n g e o f Soil E, w h ilst Soil E is u su a lly th e lim itin g fa cto r
in th e h ig h ra n g e o f its values. The m o d e ra te R ^in th e a rid cli­
m ate (Fig. 4e) in d ic a te s th a t Soil E is an im p o rta n t c o m p o n e n t
o f E T w here v eg etatio n is sparse a n d c a n o p y cover is low. T his is
n o t th e case in th e tro p ic a l c lim ate (Fig. 4f), w here a low
w as
o b serv ed w ith a negative slope o f th e lin e a r regression, in d ic a t­
in g th a t, in p re d o m in a n tly d en se v e getation, T is th e m a in c o n ­
tro llin g factor. S im ila r d ire c tio n s a n d re la tio n s w ere o bserved
betw een E T a n d th e se p a ra te c o m p o n e n ts o f D ry Soil E a n d W et
Soil E (data n o t show n). A m o n g st ail factors analysed, E T h a d
th e stro n g e st d ep en d e n ce on T (Figs 4g a n d h). The fa n sh ap e o f
th e d a ta p lo t is visible for a rid areas (Fig. 4g), w here th e E T is
c o n tro lle d by Soil E in th e low er ra n g e o f T. in areas w ith dense
v e getation, th e R^ o f th e lin e a r reg ressio n b etw een E T a n d T
w as h ig h a n d th e fa n sh ap e o f th e d a ta p lo t a lm o st stra ig h te n e d
com pletely (Fig. 4h). The T p o rtio n o f th e a lg o rith m a p p ea rs to
be suitable for h u m id re g io n s w here E T is lim ite d by available
en erg y a n d sto m a ta l resistan ce is re g u la te d by a ir te m p e ra tu re
a n d VPD. H ow ever, in d ry regions, a d d itio n a l c o n tro llin g fac­
to rs liice soil w a ter supply play a role in th e e stim a tio n o i E T
(M u et al., 2007b).
C O N C L U S IO N S
Satellite E a rth o b se rv atio n s w ill be o f huge im p o rta n c e in
a v a rie ty o f a p p licatio n s in fu tu re. R em ote se n sin g -b a se d
m e th o d s have scope in ro u tin e ap p licatio n s fo r w a ter a n d la n d
re so u rce p la n n in g a n d m an a g em e n t, as w ell as in scientific
re sea rc h on physical, biogeo ch em ical a n d ecological processes,
in th is study, w e p re se n te d a first ev alu atio n o f M O D 16 ET a n d
re la te d p ro d u c ts for S o u th A frica.
A verage E T in S o u th A frica (2000-2012) w as e stim a te d
to be 303 m m - a ' o r 371.6 x 10® m m -a ' (14% o f P E T a n d
67% o f ra in fa ll), m a in ly in th e fo rm o f p la n t tr a n s p ira tio n
(53%) a n d Soil E (39%). D irect e v ap o ra tio n fro m th e v egeta­
tio n c a n o p y w as a m in o r c o m p o n e n t o f £ T (9% on average).
87
a)
b)
900
V = -0 .2 2 3 8 x + 5 7 9 .9 1
800
V = -0.4869x + 1639.4
R^ = O.OS
700 -
E,
p=0
p=0
600 T
1500 -
500 E
\n
300
200
100 0
0
500
lOOO
1500
2000
2500
3000
3500
4000
0
500
1000
t
1500
PET (m m )
2000
2500
3000
3500
4000
PET (m m )
c)
d)
V = -7 6 .9 0 2 k + 331.4
y = -2 0 1.83x-i-908.73
R^ = 0.11
r= -0 .3 4
p=0
R^ = 0.41
r = -0.64
p=0
E 500
E,
1000
0 .0
0 .5
1.0
VPD (kPa)
1.5
2.0
2.5
VPD(kPa)
e)
f)
V = -1 .3 2 1 x + 1 0 0 3
R^ = 0.19
r = -0.44
p=0
700 500 E 500 400 V = 1.1529 x + 53.571
R^ = 0.44
r = 0.66
p=0
200 100
-
200
300
400
500
400
600
600
Soil E (mm)
Soil E (m m )
h)
g)
y = 0 .9 5 6 4 x + 367.28
R^ = 0.80
r = 0.89
p =0
800 -
— 1500
E 500
y = 1.1134x + 59.422
R^ = 0.67
r = 0.82
p=0
0
100
200
300
400
500
500
700
800
900
600
T (mm)
900
T (mm)
Figure 4
Linear regressions o f MODiS evapotranspiration (ET) vs. potentiai evapotranspiration (PET), vapour
pressure deficit (VPD), soii evaporation (Soii E) a n d transpiration (T) for arid a n d sem i-arid region
(a, c, e, g) a n d tropicai w e tc iim a te (b, d, f h) for a typicai year (2009).
E v a p o tra n sp ira tio n show ed a slight te n d e n c y to decrease over
th e p e rio d 2 0 00-2012 in all c lim atic re g io n s except in th e so u th
o f th e c o u n try (w in ter ra in fa ll areas), a lth o u g h a n n u a l v a ria ­
tio n s in E T re su lte d in th e 13-year tre n d s n o t b e in g statistically
significant. R ain fall a n d atm o sp h e ric evap o rativ e d e m a n d are
th e m a in c lim atic v ariab les d riv in g E T a n d p a rtic u la rly its
tra n s p ira tio n c o m p o n e n t. The h ig h e st PET values o c c u rre d in
th e se m i-a rid a n d a rid areas (2 457 m m -a ' on average) a n d th e
low est u n d e r tro p ic a l w et c o n d itio n s (1 892 m m -a '). Inversely,
th e h ig h e s t ET, C anopy E, Soil E a n d T w ere u n d e r tro p ic a l c o n ­
d itio n s a n d th e low est in a rid a n d se m i-a rid clim ate. V ap o u r
p re ssu re deficit (VPD) is a n im p o rta n t c lim atic v ariab le in a rid
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a n d w in te r ra in fa ll areas. The re la tio n o i E T to d a y tim e aver­
age te m p e ra tu re g enerally h a d a h ig h e r c o rre latio n coefficient
c o m p a re d to Tavg in all c lim atic areas, except u n d e r tro p ic a l
co n d itio n s. E v a p o tra n sp ira tio n (ET) is stro n g ly d e p e n d e n t on
T in all c lim atic regions, a n d occasionally on Soil E in d ry areas
w ith sparse v egetation.
The M O D 16 ET a lg o rith m c an be suitable to id en tify
te m p o ra l changes a n d for relative c o m p a riso n s o f d a ta b etw een
clim atic regions. In absolute te rm s, M O D 16 ET u n d e re stim a te d
E T b y 15% for w a te r b a lan ce c losure at n a tio n a l scale. These
results, how ever, open u p th e o p p o rtu n ity to im p ro v e a n d test
th e a lg o rith m for E T e stim a tio n , by a cc o u n tin g for b o th a tm o s­
p h e ric d e m a n d lim itin g a n d soil w a ter supply lim itin g c o n d i­
tio n s in th e n e x t re sea rc h p hase. The relatively c o arse re so lu tio n
o f ~1 km ^ pixels m ay have im p lica tio n s for a p p lic atio n s in
re stric te d areas, especially in h e te ro g en e o u s v e getation, la n d
use/cover a n d land scap e.
ACKNOW LEDGM ENTS
The a u th o rs acknow ledge fu n d in g from th e CSIR P a rlia m en tary
G ra n t a n d th e N a tio n a l R esearch F o u n d atio n o f S outh A frica.
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