A Land Surface Water Deficit Model for an Arid and Semiarid Region

7/29/2019 A Land Surface Water Deficit Model for an Arid and Semiarid Region

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244 VOLUME 12J O U R N A L O F C L I M A T E

1999 American Meteorological Society

A Land Surface Water Deficit Model for an Arid and Semiarid Region: Impact ofDesertification on the Water Deficit Status in the Loess Plateau, China

QINXUE WANG* AND HIDENORI TAKAHASHI

Laboratory of Geoecology, Graduate School of Environmental Earth Science, Hokkaido University, Sapporo, Japan

(Manuscript received 18 April 1997, in final form 3 March 1998)

ABSTRACT

A land surface water deficit model was developed for a large-scale heterogeneous arid and semiarid area withvarious soil, vegetation, and land use types, and used to simulate seasonal and spatial variability in potential(E0 ) and actual (Ea) evapotranspiration and an index of water deficit (WDI). Comparisons with the results ofother commonly used models and natural vegetation conditions suggest that this model can give an estimate ofthe success for large-scale regional studies. By using the model, the authors estimated E0, Ea , and WDI in a

grid cell of 0.25 lat 0.25 long over the Loess Plateau, China. Finally, the sensitivities of the model to botha vegetation parameter and an assumed desertification case were simulated, and several highly sensitive areaswere found to be the risk regions to desertification.

1. Introduction

It is widely recognized that land usecover changes(LUCC), such as desertification in arid and semiaridregions and deforestation in tropical zones, may exertan influence on regional or even global environmentalchange by changing the hydrological cycle and surfaceenergy balance. The desire to gain a better understand-ing of the impact of LUCC on the global environment

has stimulated many studies of land surfaceatmosphereinteractions using coupled soilvegetationatmospheretransfer (SVAT) models. Over the past decades, therehas been significant progress in the development ofSVAT parameterizations, which differ in their descrip-tion of surface processes, amount of input data required,and time and space scales (Braud et al. 1995). Theyrange from simple big-leaf models to multilayer modelswith higher-order closure formulations, and their spatialscale ranges from local small-scale homogeneity to re-gional macroscale heterogeneity, and even to a globalscale. The simple models usually describe soils coveredwith one or two vegetation layers, and solve the energybalance equation for each layer (Deardorff 1977; Ta-

conet et al. 1986; Serafni 1987; Noilhan and Planton

* Current affiliation: Eco Frontier Fellow, National Institute forEnvironmental Studies, Japan.

Corresponding author address: Dr. Qinxue Wang, Institute of Ge-ography, Hokkaido University of Education, Asahikawa, Hokkaido070-8621, Japan.E-mail: [email protected]

1989). Other models, such as BATs of Dickinson (1984)and SiB1 of Sellers et al. (1986), include detailed ra-

diation transfer schemes to estimate the incoming andoutgoing short- and longwave radiation components. Inthe revised SiB2 model of Sellers et al. (1996), satellite

data are used to specify the canopy photosynthetically

active radiation, leaf area index (LAI), and canopy

greenness fraction. All of these models were derived for

a realistic description of the interacting processes at thesoilvegetationatmosphere interface. Use of these

models to investigate the impact of Amazonian defor-

estation and Sahel desertification (e.g., Dickinson and

Henderson-Sellers 1988; Nobre et al. 1991; Xue and

Shukla 1993; Xue 1996) has shown that land surface

changes play an important role in regional climatic

anomalies.

Land usecover changes have seriously occurred in

arid and semiarid regions of northern China mainly due

to intensive and continuous human-induced distur-

bances such as excessive reclamation, overgrazing, and

denudation. According to aerial photographs, TM im-

agery analysis and field investigation (Zhu and Wang

1993), sandy desertified land in the arid and semiarid

regions of northern China has increased by 25 200 km 2

from 1975 to 1987, an annual average increase of 2100

km 2 . The desertified area in some regions has almost

doubled in size over the last few decades. The main

areas of desertified land on the Loess Plateau are ex-

tending to 47 counties on the Mu Us sandy land and

the area along the Great Wall. According to GISLPs

(1991) investigation, the total area of desertified land is

118 000 km 2, of which 35 000 km 2 is severely deser-


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JANUARY 1999 245W A N G A N D T A K A H A S H I

TABLE 1. Several commonly used indices of aridity.

Authors and reference Ranges Equation

De Martonne (IM) (1925) 05 desert510 grass30 forest

IM P

T 10a

(1)

Penman (IP) (1948)IP

E0

P

(2)

Budyko (IB) (1956) 1.1 forest1.12.3 grass2.33.4 semidesert3.4 desert

IB Rn

LP

(3)

CNC (IZ) (1959) 1.0 the boundary of subhumid and humid zone IZ 0.16 T

10

P(4)

FIG. 1. A theoretical scheme showing different land use types vsWDI and vegetation fraction (veg), and the direction of desertificationand deforestation vs these two indices.

tified, 29 500 km 2 is moderately desertified, and 52 800km 2 is slightly desertified.

Impacts of desertification are most clearly manifestedby the land surface water status. The aim of this studywas to establish a water deficit index (WDI) by usinga regional water deficit model and to evaluate the impactof desertification on the WDI. The regional model is asimplified but interdisciplinary one, which combinedmeteorological measurements with soil, vegetation, andland use data derived from remote-sensing measure-ments.

WDI, recently used by Moran et al. (1994) to definea soil-canopy water deficit status, was derived from theoriginal concept of Crop Water Stress index (CWSI)introduced by Jackson et al. (1981). CWSI is directly

determined by the minimal, maximal, and mean valuesof the foliage and air temperature difference. However,it is only applicable to conditions of full vegetationcoverage. Moran et al. (1994) developed a graphic meth-od that allowed the index to be estimated for a partialcanopy incorporating, in addition, fractional vegetationcoverage. Based on the simulation results, however,Moran et al. (1994) pointed out that further refinementof WDI should take into account coupled flux exchangesbetween the soilvegetationatmosphere continuum(SVAC). The present study presents a new approachthat combines major land surface properties for esti-mating the index in a large heterogeneous arid and semi-arid area with various soil, vegetation, and land usetypes. The concept of the model is described in section2. Parameterization of the model is shown in section 3.Study area, parameters, and data processing are givenin section 4. The feasibility of the model is discussedin section 5, and the sensitivity of the models outputsto desertification is analyzed in section 6.

2. Basic model

There have been many studies of land-surface aridityusing various indices such as those of De Martonne(1925), Budyko (1956), Penman (1948), and CNC(1959) (Table 1). However, these indices were devel-oped from empirical or semiempirical relationships be-tween measured evapotranspiration and climatic factorssuch as net radiation, air temperature, and precipitation,and do not capture physical processes in the SVAC.

In the present study, a physically based index rep-resenting the water deficit status of a large-scale het-erogeneous area was derived based on the results ofrecent SVAT studies. The water deficit index of Moranet al. (1994) is defined as

EaWDI 1 , (5)

E0

where E0 and Ea are the potential and actual evapo-transpiration. WDI varies from 0 to 1. WDI 0 meansthat the land surface is extremely humid and covered


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TABLE 2. Land cover types and their characteristic parameters. Values of these parameters were determined according to BATs (Dickinsonand Henderson-Sellers 1988).

Vegetation types Z0i vii nii LAImaxi LAImini Rsmini

Deciduous broad-leaf treeDeciduous needle-leaf treeDeciduous shrubCropsTypical grassShort grassSemidesertDesert

0.81.00.30.060.10.020.10.05

0.080.050.080.080.080.10.170.2

0.280.230.280.280.30.30.340.4

66644210

1110.50.50.50.20

100150

80404040

250250

TABLE 3. Monthly coefficients a and b for calculation of global radiation over northern China.

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

a1a2

0.060.7

0.020.76

0.190.47

0.090.62

0.030.73

0.070.65

0.110.54

0.040.68

0.120.57

0.090.6

0.120.56

0.080.64

by well-watered forest or water-saturated soil, and WDI 1 means that the surface is in an extremely arid con-dition or completely covered by desert. Figure 1 illus-trates a theoretical scheme showing the relationship be-tween WDI and the vegetation fraction (veg), which canbe used to show different land use types versus differentWDI and veg. The directions (arrows in Fig. 1) of land

use changes such as deforestation and desertification canalso be shown by this scheme.

To estimate WDI, we developed a regional land sur-face parameterization, which is described in the follow-ing section.

3. Parameterization

The parameterization includes three main parts: landsurface resistances, radiation transfer, and energy bal-ance in the evapotranspiration processes.

a. Estimation of surface resistances

1) AERODYNAMIC RESISTANCES

From the point of view of diffusion, the aerodynamicresistances of momentum (ram ), heat (rah ), and watervapor (rav ) have the following relationships (Grace etal. 1981; Thom 1972):

r 0.93r ,av ah

2/ 3r r 6.266u , (6)ah am *

where the friction velocity, (symbols are listed inu*

appendix), can be calculated from the reference levelwind speed using similarity theory (Monin and Obu-khov 1954). Thom (1975) gave a simplified function:

z du* u ln . (7) z 0

Here is the von Karman constant (0.41); z 0 is the

roughness length, which depends on the vegetationtypes (Table 2); and d is surface displacement height,which can be estimated by (Wollenweber 1995)

d 1.1h ln[1 (Cd LAI)1/4 ]. (8)

The aerodynamic resistance of momentum (ram ) was de-termined by using Monteiths (1981) Eq. (5), which has

been proven by Lu (1992), by a comparison of its resultswith seven other models with consideration to stratifi-cation stability, to be appropriate for regional study:

z d z d2r ln u 1.6 ln u. (9)am z z0 0

2) CANOPY RESISTANCES

Among land surface resistances, canopy resistancesthat is, stomatal and leaf boundary resistancesplay aspecial role in surface interactions. A physically basedstomatal resistance, which depends on incoming solarradiation (Q), maximum irradiance (Qmax ), soil moisture(ws), wilting point (wwilt), and leaf area index (LAI),was selected with c1 0.03 (Taconet et al. 1986) asfollows:

2Q 1.2 w 1 0.5LAImax wilt

r r , (10)st sto [ ]c Q Q w LAI1 max swhere the minimum stomatal resistance rsto depends onvegetation types (Table 2).

The leaf boundary resistance (rlb ) was calculated ac-cording to Kustas (1990) formula for estimating latentheat fluxes over a partial canopy cover:

rlb A (l/u)1/2 , (11)

where l is a characteristic length scale for an averageleaf width (0.05 m) and A is a constant (90 s1/2 m1).


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FIG. 2. Location and climatic classification of the Loess Plateau(Zhang and Wang 1989) and the distribution of 107 meteorologicalstations used in the present study.

TABLE 4. Main soil types and their depth, textures, and clay content in the Loess Plateau of China (GISLP 1991).

Soil texture Soil type Soil depth Clay content wsat wfc wwilt

Heavy loam BurozemDrab soilsManured loessial soilsOasis soils

100150250200

4555

4854

0.4760.4760.4760.476

0.1460.1460.1460.146

0.130.130.130.13

M ed ium loa m G ra y-d ra b f ore st s oilsChernozemsMeadow soilsYellow loessial soilsAlpine meadow soilsChestnut soils

10070

120200

50150

2038

2238

2040

0.4510.4510.4510.4510.4510.451

0.1230.1230.1230.1230.1230.123

0.080.080.080.080.080.08

Light loamSandy loam

Sandy soil

Dark loessial soilsSierozemsGray desert soilsBrown soilsAeolian sandy soils

250150100100

20

31422425

1021810

0.4350.410.410.3590.359

0.1030.0930.0930.0620.062

0.050.040.040.030.03

3) SOIL SURFACE RESISTANCE

Soil surface resistance was estimated by the empiricalformula of SiB2 (Sellers et al. 1996):

rsoil .exp(8.206 4.255w )s (12)

b. Effective parameters for vegetation and soil

To compute regionally averaged fluxes over a largearea, averaging operators were chosen to calculate ef-fective parameters. It is assumed that one grid cell canbe classified into several land use classes for which the

fractions are i (i f, gs, c, d, etc., which representforest, grass, cultivated land, desert, etc., respectively)of each category is known, together with its surfaceproperties i, rstoi , LAIi , and z 0i (Table 2). Then, theeffective parameters of surface properties , rsto , LAI,and z 0 can be estimated as the mean weighted by thefractional coverage of the different vegetation types(Noilhan and Lacarrere 1995):

a a , (13) i ii

LAI LAI , (14) i ii

ln(z ), ln(z ), (15)0 i 0ii

1 1 . (16) i

r risto stoi

Seasonal changes in the parameters were consideredcalculated using the monthly time series of total andgreen-leaf area indices, vegetation coverage, albedo, andsurface roughness length for the major SiB vegetationtypes (Dorman and Sellers 1989).

c. Radiation transfer

A semiempirical model is used to describe the netradiation transfer with respect to vegetation and bare

soil surface (Shuttleworth and Wallace 1985):(0.7LAI)R R [1 e ],nv n

R R R , (17)ns n nv

where Rn, which is total net radiation, can be writtenas


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FIG. 3. Dominant soil textures (a) and vegetation types (b) derived from the Soil and Vegetation Map of China.

sR [R (1 ) R (1 )] a an vi vi ni ni 1 2 S

s4 T (0.36 0.08 e ) 0.10 0.90 . (18)a S

Shortwave radiation is divided into visible (Rvi ) and

near-infrared (Rni ) components, which are estimated by(Ferenc 1994)

R 0.52(Q q)vi

R 0.48(Q q), (19)ni

where Q and q are potential direct solar radiation andindirect shortwave radiation in clear sky (W m2), anda and b are the empirical coefficients (Liu et al. 1991)shown in Table 3.


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FIG. 4. Schematic procedures used to generate surface parameters,evapotranspiration, and WDI.

d. Estimation of evapotranspiration

A modified version of the PenmanMonteith equationwas derived for vegetation and bare soil surface:

R C [e (T ) e ]/rnv p s a a ahE (20)av

(r r r )/rst lb av ah

(R G) C [e (T ) e ]/rns p s s a ahE (1 ) . (21)as

(r r )/rsoil av ah

The total actual evapotranspiration can then be esti-mated by

Ea Eav Eas . (22)

However, if the surface is saturated by water vaporthat is, rst rlb rsoil 0 and rav rahthen Eqs.

(20) and (21) become

R C [e (T ) e ]/rnv p s a a ahE (23)0v

(R G ) C [e (T ) e ]/rns p s s a ahE (1 ) . (24)0s

Then, the potential evapotranspiration can be calculatedby

E0 E0 E0s. (25)

One important parameter in Eqs. (20)(24), , whichis called the shielding factor (Ben Mehrez et al. 1992),is calculated by

1 e (LAI). (26)

This factor changes from 0 to 1 depending on the leaf

area index (LAI) and , a weight coefficient of LAI thatdepends on soil, vegetation, and land use types. Here 0 means vegetation has no leaves or bare soil, and 1 means full-leafed vegetation ground. In section 5,the dependence of Ea and WDI on this parameter willbe discussed. Soil heat flux (G ) can be estimated simplyas a fraction of Rn dependent only upon the range ofannual air temperature.

e. Treatment of soil water content

Many studies (e.g., Mahrt and Pan 1984; Wetzel andChang 1987) have shown that the relationship betweensoil moisture and evapotranspiration depends strongly

on soil, atmospheric, and vegetation conditions. In thepresent study, soil moisture is estimated by the so-calledforce restore method proposed by Deadroff (1977) andmodified by Noilhan and Planton (1989):

dw C C s 1 2 (P E ) (w w )as s 2

dt d w 1

when 0 w ws sat

dw 12 (P E E ) when 0 w w , (27)as av 2 sat

dt dw 2

where P should be treated as the difference betweenprecipitation and runoff. According to the China Map

of Runoff (Jiang 1989), the annual runoff is less than50 mm in most of study area and is around 100 mm foronly a small area in the subhumid zone. Because thismodel is developed mainly for an arid and semiaridregion, we neglected the runoff in this study. The neglectmight cause a small increase in Ea and decrease in WDI.The two dimensionless coefficients C1 and C2 were es-timated for different soil textures by

b/21wsat

C C ,1 1sat wsw2

C C , (28)2 2 ref

w

w

0.001sat 2

and values and parameters used in Eqs. (27)(28) versussoil textures were employed from Noilhan and Planton(1989). The initial data of ws (199091) was obtainedfrom 24 agricultural meteorological stations in the LoessPlateau of China.

4. Study area, parameters, and data

The Loess Plateau of China was selected as the studyarea because of its heterogeneity of land surface and its


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FIG. 5. Distribution of annual-mean E0, Ea, and WDI estimated by the regional water deficit model.

sensitive ecological and environmental conditions. Theplateau is located in northern China (3441N, 100115E) with a total area of 632 520 km 2, accounting for6.3% of the entire land area of China (Fig. 2). Most ofthe plateau lies on the transitional border between the

monsoon climatic zone and the continental arid climatezone. The annual precipitation is 200600 mm, and themean temperature range is 512.5C from northwest tosoutheast. According to climatic classification (Zhangand Wang 1989), the plateau can be divided into four


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FIG. 6. (a) Seasonal changes in E0 , Ea, and WDI in the whole studyarea (mean value of 107 grid cells) and (b) changes in WDI in fourclimatic subzones (ART, averages of 28 stations; SAT, 28 stations;SAW, 35 stations; and SHW, 16 stations).

subzones (Fig. 2): arid temperate zone (ART), semiarid

temperate zone (SAT), semiarid warm temperate zone(SAW), and subhumid warm temperate zone (SHW).From ART to SHWthat is, from northwest to south-eastglobal solar radiation decreases gradually, where-as air and soil temperatures, precipitation, and humidityincrease. There are no apparent differences in the meanwind speed over the whole plateau. The coverage offorest and shrubs in SAW is greater than that in otherzones due to more mountainous regions. The fractionof typical-grass land and cultivated land increases fromART to SHW, whereas that of short-grass land decreasesgradually.

Meteorological data from 107 stations, includingmonthly mean (195191) air and ground temperatures,

precipitation, sunshine duration, wind speed, and air va-por pressure, were used in this simulation. It should berecognized that the data from meteorological stationscannot logically be applied to the various vegetationtypes being studied. Using this dataset is just due todifficulty to obtain ground-based observations over sucha large heterogeneous area for its very pilot study. The-oretically the application of remote-sensing data mightgreatly complement this shortage, which leaves us manyproblems to be solved in the next step. Soil and vege-tation parameters were mainly derived from the domi-

nant soil textures and vegetation types in each 0.25 lat 0.25 long grid cell. The map of soil texture wasderived from the Soil Map of China (Li et al. 1989) andinvestigated data (Table 4) of GISLP (1991). The clas-sification is based on the dominant soil texture and dis-tinguishes between five types (Fig. 3a): sand, sandyloam, light loam, medium loam, and heavy loam. Thesoil moisture parameters, wsat , wfc , and wwilt , are pre-scribed from this map with reference to Clapp and Horn-bergers (1978) experiment. Land cover classification(Fig.3b) was based on the Vegetation Map of China (He1989) and was then used to construct maps of param-eters. The values of parameters assigned to each typeof dominant vegetation were determined based on thoseof BATs shown in Table 2. The fraction coverage ofeach land-cover category i , which was derived fromremote-sensing measurements (GISLP 1991), was usedto compute effective parameters with Eqs (13)(16).

5. Implementation and discussion

a. Implementation of the model

1) FLOWCHART OF SIMULATION

Fundamentally, the model equations are based on mi-crometeorology, and are used on short timescale (timestep 1 day). However, some meteorological factorssuch as S and P are monthly total values, which needto be interpolated into diurnal values. In the presentstudy, we simply used monthly total values divided bythe number of days in each month and obtained diurnalvalues. On the other hand, the meteorological measure-ments of 107 stations were interpolated into each 0.25

lat 0.25 long grid cell with the distance weight leastsquares methods, and the land surface parameters ineach grid cell were derived from various maps of Chinamentioned above. Figure 4 shows the flowchart of dataprocessing and simulation.

2) DISTRIBUTION OF ESTIMATED VALUES

Monthly E0, Ea, and WDI in each grid cell of 0.25lat 0.25 long were estimated based on our datasetand the annual-mean distributions are shown in Fig. 5.As seen in Fig. 5, all of the estimated values have ap-parent regional differences. Here E0 was large (about1000 mm) in the southeast (SHW), then decreased to

700900 mm in the middle (SAW), and finally increasedto a maximum of about 1400 mm in the northwest(ART); Ea ranged from a maximum of about 500 mmin the SHW to a minimum of about 100 mm in the ART;and WDI ranged from a minimum of about 0.5 to amaximum of about 0.9. The reason for the peakval-leypeak pattern ofE0 was due to a higher temperaturein the SHW zone and larger solar radiation in the ARTzone. However, Ea was dependent to a large extent onsoil moisture conditions and the vegetation fraction. Un-der natural conditions, Ea decreases gradually from


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TABLE 5. Some commonly used evapotranspiration equations.

Name References Periods Equations

Schreiber (Lu and Gao 1987) Annual R /LPnE P(1 e )a (29)

Budyko (Budyko 1955) AnnualP

E /P0E E tg P(1 e )a 0

E0

(30)

Thornthwaite (Thornthwaite 1944) Monthly

c10T

E 1.62 ,a I1.51412 T

I i, i 5i13 2c 0.000000675I 0.0000771I 0.0179I 0.49 (31)

CNC (CNC 1959) Annual E 0.16 Ta 10 (32)

TABLE 6. A comparison of the estimated Ea in different climaticzones by various models (ART, averages of 28 stations; SAT, 28stations; SAW, 35 stations; SHW, 16 stations, and total area, 107stations).

Schreiber Budyko CNCThorn-thwaite Our model

ARTSATSAWSHWTotal area

313.6404.6467.8493.8410.8

335.9435.7522.3551.3451.5

434.1441.4501.5559.6503.5

520.4524.2564.9610.0568.1

338.5401.3430.3493.1425.3

southeast to northwest (from SHW to ART) due to themonsoon climate. As a result, WDI in the four regionsis clearly in the order of ART SAT SAW SHWthroughout the year. Although the area near Yinchuan

is in the ART, the estimated values of WDI are relativelysmaller than other parts of the ART. This exception isdue to intensive irrigation in this area, a major graingrowing area in China.

3) SEASONAL CHANGES IN ESTIMATED VALUES

Seasonal variations in E0 , Ea, and WDI were veryclear in the study area. The averages of 107 grid cellsover the whole plateau are shown in Fig. 6a, in whichE0 and Ea had the lowest values in January and thehighest values in June, whereas WDI had the lowestvalue in July and highest value in December.

To analyze regional differences in seasonal changes,

the averages ofE0 , Ea, and WDI in four subzones (ART,28 stations; SAT, 28 stations; SAW, 35 stations; andSHW, 16 stations) were computed. The results showedthat the characteristics of seasonal variation were similarin the four subzones but their amplitudes were differentaccording to the zone. One interesting characteristic isthat regional differences are small in winter, but largein summer (Fig. 6b).

b. Discussion on the feasibility of the model

The validity of the model was usually demonstratedby comparing the estimated values with ground-based

measurements. Since the outputs of the model, such asEa and WDI, are difficult to observe for various vege-tation types in a large-scale area, the feasibility of ourmodel can be only partially validated by 1) comparing

the estimated value of Ea with those of other commonlyused equations listed in Table 5 and 2) analyzing thecorrespondence between estimated WDI and naturalvegetation condition.

1) COMPARISON WITH THE RESULTS OF OTHEREVAPOTRANSPIRATION EQUATIONS

In past decades, the lack of basic data and the diffi-culties in measurement required in field methods haveaccounted for the great efforts made to develop evapo-transpiration equations that can relate the evapotran-spiration with some readily available climatic data.There are many methods of estimating potential and

actual evapotranspiration, including physically basedtheoretical approaches, water, and heat balance analyt-ical approaches and empirical approaches based on therelation between measured evapotranspiration and cli-matic conditions. However, theoretical approaches aredifficult for large time and spatial scales. A number ofequations have been suggested for different purposesand scales (Veihmeyer 1964). Some typical ones com-monly used are listed in Table 5. Many studies con-ducted in China on these equations have been reviewedby Lu and Gao (1987), who suggested that the meanerrors of these methods are within about 15%, inwhich Budykos and Scheibers methods are better withthe mean errors of0.2% to 5.5% and 5.2% to 13.3%,

respectively. The results of these methods were used tocompare with those of the present model, which wasshown in Table 6. It can be clearly seen that the averagevalues of the present model are very close to these ofBudykos and Scheibers equations in different climaticzones, which suggests that our model can output rea-sonable values of Ea, comparable to those estimated byother commonly used models. Here it should be stressedthat the present model has its advantage of being ableto output regional evapotranspiration values because ithas been coupled with land surface properties.


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FIG. 7. Correspondence between frequencies of the grid cells of dominant vegetation types and the estimated WDI.

2) CORRESPONDENCE WITH NATURAL VEGETATIONCONDITION

According to the definition, WDI indicates the waterdeficit status of land surface, which is most easily man-ifested on natural vegetation conditions. Different waterdeficit conditions are correspondence with different veg-etation types, thus the relationship between the esti-mated WDI and the distribution of vegetation types willconvince us whether this model can output reasonablevalues or not. For this reason, we counted the frequen-cies of grid cells for dominant natural vegetation typesillustrated in Fig. 7. It can be found that different veg-etation types have different distribution patterns ofWDI; for example, the large fraction of forest has smallWDI (0.70), whereas that of semidesert and desertland have large WDI (0.75). Shrubs have a large range(0.600.86), whereas the major part of grassland is inthe range between forest and desert. This result is con-sistent with the actual situation, thus supporting WDIas an indicator of the surface water deficit on the re-gional scale.

Finally, note that high variability of land surface and

difficulty of measuring Ea in such a large-scale areamakes the complete validation very complex. Attemptsmade above provide only a partial validation of the mod-el for large-scale regional studies.

6. Sensitivity analysis: Impact of desertification

The results of this study confirmed that the land sur-face water deficit is closely related to both climatic con-ditions and surface properties. The land surface is un-dergoing great changes due to land use and can influence

the exchange of momentum, energy, and water fluxeswith the atmosphere. We concentrate in this study on ,the weighted coefficient of LAI, and the fractional areaof desert land (d). The sensitivity to will give us ageneral concept of the transition from completely bareground to full-leafed vegetation ground. The sensitivityto d is of particular interest because the effect of de-sertification can be taken into account through variationof this parameter. Theoretically, removing vegetation

would be expected to be accompanied by an increasein surface temperature, which should increase E0 . How-ever, there is another negative feedbackthat is, re-moving vegetation would lead to an increase in albedo,then a decrease in net radiation, and hence a reductionin E0. As a result, the sensitivity of E0 to both and dwas found to be very small. For this reason, sensitivityanalysis was carried out only for Ea and WDI. Here notethat meteorological factors and soil parameters are usedas average values in the sensitivity study.

a. Sensitivity to

As mentioned in section 3d, changes from 0 to 1

that is, from off-leafed vegetation or bare ground to full-leafed vegetation ground. Changes in would at firstcause changes in the shielding factor of and wouldthen influence each flux. Figure 8 shows the change inaveraged Ea and WDI of 107 stations corresponding tothe change in . It can be clearly seen that Ea increaseswhile WDI decreases exponentially when varies from0 to 1. This change was especially notable in summer.Therefore, it can be stated that the larger the vegetationleaf area is, the bigger is the actual evapotranspiration,and the smaller is the water deficit index.


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FIG. 8. Sensitivity of (a) Ea and (b) WDI to the weight coefficient in Jan, Apr, Jul, and Oct.

FIG. 9. Fraction of desert (%) in total area both at control and desertification cases.

b. Sensitivity to d

To analyze the sensitivity of the model to desertifi-cation, the fraction of desert in each grid cell was as-sumed to expand gradually from a control case (d)that is, current conditions, to a desertification case (d d 2d), that is, doubling of the desert fraction.Here it is assumed that if d d 100, then d d 100. With an increase in the fraction of desertland, on the contrary, it can be assumed that the grass-land fraction is g d, which physically means that

desertification occurs only at desert edges and is pre-ceded by progressive degradation of grassland. Ofcourse, if there is no desert in a grid cell, then, d d 0. Thus, the case where desertification occursinitially in a grid cell was not taken into consideration.Figure 9 shows fraction of desert in total area both atcontrol and desertification cases.

Differences [dEa (%) and dWDI] between desertifi-cation case and control case were simulated under theassumption mentioned above. Figure 10 shows the re-sults of dEa (%) and dWDI in summer over the wholeplateau. It can be found that there are highly sensitiveareas distributed in the north central part of the plateaunear Yulin and the northwestern boundary area of theLoess Plateau. In these regions, vegetation destructionmight cause an obvious decrease in evapotranspiration(5%20%) and an increase of WDI (0.010.1)that is, an aggravation of land surface water stress.Therefore, these regions should be carefully treated or

protected. Unfortunately, due to the continuous increasein population and exploration of natural resources, theseregions are being subject to intensive human activities,which will continue in the future.

7. Conclusions

A regional water deficit model has been developedfor a large arid and semiarid region with heterogeneousland surface properties. This model can be used to es-timate the regional evapotranspiration (E0, Ea ) and wa-ter deficit index (WDI) with a grid cell of 0.25 lat 0.25 long by combining meteorological measurements,soil, vegetation, and land use data derived from remote-sensing observations.

The feasibility of the model has been partially verifiedby comparisons with the results of other commonly usedmodels and natural vegetation condition, which suggeststhat the model can give a reasonable estimate for large-scale regional studies.

Sensitivity analysis showed that changes in Ea andWDI caused by desertification are larger in arid and


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FIG. 10. Changes in Ea and WDI after the fraction of desert doubled.

semiarid subzones than in subhumid zones, and alsolarger in summer than in other seasons. Several highlysensitive geomorphic units, such as the area near Yulinand the northwestern boundary area of the Loess Pla-teau, were investigated. These regions can be regardedas risk regions that are easily affected by vegetationdestruction.

Finally, we would like to point out that this is a pilotstudy on SVAT in the Loess Plateau of China, an areafor which there are insufficient measurements for SVATparameterizations. Needless to say, the comparisons

made above only partially show the validity of the mod-el, but we can say that on a regional scale, this modelis an interesting first attempt to bridge the gap betweenLUCC and climate changes in regions where there hasbeen no intensive investigation such as that carried outin the Amazonian and Sahel regions. In the future, it isexpected that this model can be improved in terms ofboth resolution and precision along with the progressof remote sensing and ground-based measurements.

Acknowledgments. As a joint researcher of the Group


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for Integrated Survey of the Loess Plateau, ChineseAcademy of Sciences (CISLP, CAS), the first author par-ticipated in investigation and data collection for a project,Rational Utilization of Agricultural Climate Resources inthe Loess Plateau, during 198691, which enabled us toconduct this research. Thanks are also due to the TokaFoundation of Education and Cultural Exchange, Japan,which provided financial aid for this project.

APPENDIX

List of Symbols

A Constant for leaf boundary resistance(90 s1/2 m1)

a1, a2 Empirical coefficient for global radiationb Slope of the retention curve for soil types

(Clapp and Hornberger 1978)c Empirical coefficient for Thornthwaite

equation (Thornthwaite 1944)c1 Coefficient for stomatal resistance

(0.03)C1, C2,

C1sat, C2ref

Parameters in soil moisture equations(Noilhan and Planton 1989)

Cd Mean drag coefficient for individualleaves ( 0, 2)

Cp Specific heat at constant pressure (J kg1

K1)d Surface displacement height (m)d1 Depth of top soil layer (10 cm)d2 Depth of subsoil layer (50 cm)E0, E0,

E0s

Potential evapotranspiration from landsurface, vegetation, and bare soil (mm)

Ea, Eav,Eas

Actual evapotranspiration from land sur-face, vegetation, and bare soil (mm)

ea Air vapor pressure at level za (hPa)es(Ta) Saturated vapor pressure at temperature Ta

(Pa)G Surface soil heat flux (W m2)h Mean height of vegetation (m)I Thornthwaites temperature-efficiency in-

dexIB Budykos radiative aridity indexIM De Martonnes aridity indexIP Penmans aridity indexIZ CNCs aridity index

L Latent heat of vaporization (J kg1

)l A characteristic length scale for an aver-age leaf width (0.5 m)

LAI Leaf area indexP Precipitation reaching the soil surface

(mm)Q Potential direct solar radiation in clear sky

(W m2)q Potential indirect shortwave radiation in

clear sky (W m2)Qmax Maximum irradiance (W m

2)

ram, rah,rav

Aerodynamic resistance for momentum,heat, and vapor, respectively (s m1)

rlb Leaf boundary resistance (s m1)

Rn, Rns,Rnv

Total net radiation, net radiation for thebare soil, and vegetation, respectively (Wm2)

rsoil Soil surface resistance (s m1)

rst Stomatal resistance (s m1)

rsto Minimum stomatal resistance (s m1)

RviRni Visible and near-infrared shortwave radi-ation, respectively (W m2)

S Possible sunshine duration (h)s Sunshine duration (h)T10 Accumulated temperature of10C

TsTIa Soil surface temperature and air temper-ature, respectively (K)

u Wind speed at height zu

*Friction velocity (m s1)

veg Vegetation fraction

WDI Water deficit indexws Volumetric water content (cm3 cm3)

wsat Saturated volumetric water content (cm3

cm3)wwilt Wilting point (cm

3 cm3)z Height of the atmosphere reference level

(m)z0 Roughness length for momentum Time step (1 day) Von Karmans constant (0.41) Weight coefficient of leaf area indexvb, nt Albedo to visible and near-infrared radi-

ation, respectively The psychrometer constant (hPa K1)

Rate of change in saturated vapor pressurewith temperature Ta (hPa K

1) Shielding factor of vegetationd Fraction area of desert landi Fractional area of each land use category

in a grid cell Emissivity of surface Density of dry air (kg m3)w Density of soil water (kg m

3) StefanBoltzmann constant (5.67 108

W m2 K4)

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A Land Surface Water Deficit Model for an Arid and Semiarid Region

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