continental scale water balance model

8/3/2019 Continental Scale Water Balance Model

1/13

3rdWaterNet/Warfsa Symposium 'Water Demand Management for Sustainable Development', Dar es Salaam, 30-31 October 2002

A Continental Scale Water Balance Model: A GIS-Approach for Southern Africa 1

A Continental Scale Water Balance Model:a GIS-Approach for Southern Africa

B.F. Alemaw1 and T.R. Chaoka2

Geology Department, University of BotswanaP. O. Box 0022, Gaborone, Botswana

E-mail:1

[email protected]@mopipi.ub.bw

ABSTRACT: A distributed GIS-based hydrological model is developed using GIS and computational

hydrology techniques. The model is based on water balance consideration of the surface andsubsurface processes. The surface water balance processes include precipitation infiltration, overlandrunoff and canopy surface interception losses on daily time steps; The subsurface process considers

soil moisture accounting on a monthly basis. The model was used to estimate generated runoff frommatrix of specific geo-referenced grids representing southern Africa. All regional and seasonaldispensation of water balances have been based on standard GIS formats for storage, spatial display

and interpretation of results. Considering the 1961-90 climatic period, we have mapped the regionalvariation of the mean annual soil moisture (SM), actual evapo-transpiration (AET), and generated runoff(ROF) across the SADC. The model estimates the mean SM of the region to be about 148 mm per year.

There is a wide spatial range in the distribution of SM over the due to the fact that the absolute soil

moisture is dependent on the water retention properties of the soils considered across the region. Themodel prediction of the mean annual AET in the region reaches a maximum of 1500 mm, with mean

420 mm. The mean annual generated runoff from the land catchment in the region is about 151mm/year although there is a significant inter-regional variation among the SADC countries, which is afunction of the variation in the vegetation cover, soil and climate variation. Lower runoff regimes are

dominant in arid areas in Botswana, Namibia and south-western part of the Republic of South Africa.Higher runoff regimes are the northern and western Tanzania, along the east coastal portions ofMozambique, central Mozambique, western Zambia and Malawi.

Key words: water balance model; GIS; regional hydrology; Southern Africa; runoff; soil moisture;evapotranspiration

1. Introduction

Water balance models have been widely used to simulate regional water balances and to study hydrologic effectof climatic change. The Thornthwaite and Mather (1957) conceptualisation of the catchment water balance for

long term monthly climatic condition has become one of the outstanding research areas of water balancemodeling of a catchment, region or of a continent. Typical examples are (1) a grid-based model for Latin Americaof Vorosmarty et al. (1989); (2) the Rhine flow model of Van Deursch and Kwadijk. 1993); and (3) the large scale

water balance model for the upper Blue Nile in Ethiopia of Conway (1997).

With the advent of increasing computing power and GIS technique, physical based hydrologic modeling has

become important in contemporary hydrology for assessing the impact of human intervention and/or possibleclimatic change on basin hydrology and water resources.

The use of distributed physically based (conceptual) hydrological modelling with prudent simplification is

appropriate for providing a reasonable solution to large scale hydrological problems associated with planningand optimal allocation of resources. The present work concerns the development of such a model for the region

of Southern Africa. The model can enable one to estimate expected monthly soil moisture, actual evapo-transpiration and runoff. Such a model may be used for planning and decision support system in the region.

Generally distributed type models can be developed either on the basis of dividing the drainage basin into gridmeshes of specified resolution or by identifying as many as possible recognisable upstream sub-catchments in awatershed. A water balance model is developed in this study based on grid cell size of 30 by 30 minutes

resolution, covering the region of southern Africa in a view to document the seasonal regimes of soil moisture,actual evapotranspiration and runoff.


2/13



2. Methodology

Model formulationThe distributed GIS-based hydrological model (DGHM) developed in this study is based on consideration ofsurface and subsurface processes. In the subsurface zone, soil moisture accounting technique of Thornthwaite

and Mather (1957), modified as part of this study, is used in computing the water balance components like actualsoil moisture (SM), evapo-transpiration (AET) and runoff (TRO). The surface abstractions in terms of overlandrunoff and interception are accounted for by DGHM by using the SCS curve number method (SCS, 1985). The

model leads to the creation of high-resolution data sets of SM, AET and TRO over the several catchments in the

southern African region, which are represented by geographically referenced grids of 0.5X0.5 degree resolution.

The Distributed GIS-based Hydrological Model (DGHM) for the southern African region proposed in this study isbased on the combination of: (1) daily overland runoff computation using the curve number (CN) method anddaily canopy evaporation or interception losses estimated from normalised vegetation indices (NDVI), in the

surface processes; and (2) monthly soil moisture accounting approach in the subsurface zone,

The model handles the temporal and spatial variations of the water balance components by first solving the

temporal variation of each hydrological component for a single grid cell spatially over the region. This eventuallyallows for hydrologic regime establishment for the region of southern Africa.

When written in volumetric units, water balances can be given by:

FAETTROPPTtSM = )( (1)where PPT is volume (depth) of precipitation, TRO is volume of runoff, AET is amount actual Evapo-transpiration, F is commutative infiltration. S with a subscript denotes component of storage with the subscript Mfor soil moisture storage. Equation (1) is in the form, which explains that the central idea of water balance

modelling is monthly accounting of soil moisture.

The water balance model given by Equation (1) can be rearranged to estimate the total run off as follows:

)( AETSMPPTTRO += (2)

In Equation (2) PPT is replaced with EPPT, which is the effective precipitation, the precipitation in excess of

interception loss and that flows overland, thus infiltrates to the soil.

Description and Structure of the Model

The model development procedure and algorithm of the water balance computation at a grid cell (using the gird

runoff generation (RG) component) is schematically shown in Figure 3.

The precipitation input is first separated into the portion that is runoff over land (DRO) and the portion that

infiltrates into the soil and enters the water balance calculation called effective precipitation (EPPT). EPPT isobtained from grid precipitation (PPT) by subtracting daily evaporation as interception losses (ES) and dailyoverland runoff (DRO) computed by CN method of rainfall abstraction, and aggregating for month of simulation.

The subsurface processes of soil moisture, actual evapotranspiration and generated runoff are presented in thesubsequent sections.

Interception lossThe net precipitation that enters the soil, or infiltration, is the aggregate effect of surface processes namely,incoming precipitation, and losses through surface evaporation as interception and direct runoff. In DGHM,

therefore, the daily precipitation (P) input is first separated into the following. (i) The portion that is runoff overland(Qo), (ii) The portion that infiltrates (I) and enters the soil, and (iii) The daily wet canopy surface evaporation orcanopy interception losses (ewct). Interception is estimated with the assumption of absence of drainage with the

water balance at the canopy described by:

SCwc

epdt

dC= 0)1( (3)


3/13



where pis the precipitation rate, ewc is the wet canopy evaporation rate, Sis the canopy water storage capacity,

Cis the actual amount of water intercepted by canopy andis the free throughfall coefficient (the proportion of

rain which falls to the ground without striking the canopy). From measurements of and LAI of different

landuses tabulated in Rutter et al. (1975), Biftu (1998) established 997.0;139.0997.0 2 == RLAI as aregression equation between them, and this is adopted in this study.

Fig. 1 Representation of Water balance at a grid cell in the distributed GIS-based water balance model (DGHM).

Modeling daily overland runoff in DGHMBefore entering the estimation of the water balance components, the daily precipitation (P) is separated into thedirect runoff (Qo) and the portion that infiltrates and so enters the water balance computation as the effective

rainfall.

The US Soil Conservation Service (SCS) has prepared a series of tables and nomographs by which the amount

of daily overland runoff from intense precipitation can be estimated from information on slope, ground cover, soiltype and antecedent precipitation. This method is usually called the SCS-CN curve method (CN formula). Thismethod is usually recommended for daily overland runoff estimation.

Estimation of the overland runoff using the CN formula for daily overland runoff is given by:

sPforQo

sPforsP

sPQo

2.00.0

2.08.0

2.0

=

>+

=(4)

where s is a parameter related to curve number (CN) [ SCS (1985) ,Chow et al. (1988)] as:

= 1100

254CN

s (5)

The constant, 254, in Equation (5) gives s in mm. Thus, P and Qo are also expressed in mm. Thus, the monthly

volume of overland runoff is the sum of the daily overland runoff, DRO; that is, =

=nd

i

iQoDRO1

, where, nd is

the number of days in the month under consideration.

Regional information

(PET, PPT, SOIL, NDVI)

Surface process Eva otrans iration

Soil Moisture SM

Runoff storage(RO)

Direct runoff

Excess

Runoff from a grid (TRO)

Eff. Precipitation(EPPT)


4/13



The importance of this approach in developing the distributed GIS-based model (DGHM) is more explained interms of the subsurface processes. It is based on the assumption that if one computes overland runoff from the

total precipitation falling, then it forms the effective precipitation that goes to replenish the soil moisture.

Modeling soil moisture

Soil moisture is determined from the interaction between effective PPT and PET. During wet months (wheneffective PPT in excess of PET), soil moisture can increase up to a maximum of field capacity determined by soiltexture and rooting depth.

FCEPPTwhenPET-EPPT=dt

dSM

(6)

FC=SMwhen0=dt

dSM (7)

PET PET. During this time it is assumed that EPPT is in sufficient abundance to satisfy all the potential

water demands of the resident vegetation. During dry season when EPPT < PET, the monthly average AET ismodified down wards from its potential value as shown below.

PETEPPTwhenPETAET >= (10)


5/13



PETEPPTFC=SMwhenPET)-(EPPT+(D=RO &)*5.0 (12)

PET


6/13



Table 1. Distribution of textural soil classes in the southern African region.

Sand Sandy

loam

Clay Clay

loam

Silt

loam

Lithosol

No. of grids 831 320 331 1432 365 122

% coverage 24 10 9 42 11 4

To set broader rooting depths, two rooting depth categories in compliance with Vorosmarty et al. (1989) havebeen created. These are: (1) VEG1 - this includes farmlands (or extensive crop production area), savannah with

scattered trees, shrub lands, etc., and percentage forest of 50% or less of NDVI. (2) VEG2 -dense forest, naturalvegetation cover and deciduous forest cover, and percentage of forest above 50% of mean annual NDVI haveused as a criterion.

The nature of soil at a particular location and for a given vegetation cover affects the rooting depth. This hasbeen noted in Vorosmarty et al. (1989) and is adopted. Based on the above vegetation grouping, the root depth

for each soil is assigned based on the values. The SCS soil groupings for the overland flow module is assignedaccording to the definition given in Singh (1992) and is tabulated in Table 2.

Table 2. Rooting depth assigned for various soil textures and SCS soil groupings.

Assigned Root Depth (M) For Different Soil TypesVeg.Group

NDVI

Sand Sandy Loam SiltyLoam

Clay Loam Clay Lithosol

VEG2 >50% 2.5 2.0 2.0 1.6 1.2 0.1VEG1 50% 1.0 1.0 1.3 1.0 0.7 0.1SCS soil group

(Singh, 1992) A B D C C B

Satellite data have been used extensively for mapping the land use and for monitoring the seasonal change ofvegetation of river basins (Nemani & Running, 1989). The Normalized Difference Vegetation Index (NDVI) is

commonly applied to derive the leaf area index (LAI) from channels 1 and 2 of NOAA-AVHRR data at 1-km2

resolution. Monthly twelve NDVI images, expressed in percentage, for 1987 are acquired from USGS webpages. Based on NDVI values the LAI for different land use groups can be estimated by empirical formulae.

Derivation of soil retention parametersThe ultimate importance of the textural reclassification of soils and vegetation is to derive retention parameters of

the soils such as field capacity (FC) and wilting point (WP) values for each soil group to determine the soilmoisture capacities.

Based on field measurements, Saxton et al. (1986) have developed a technique to estimate the matrix potentialof different soils by using multiple regression techniques. So at a matrix potential equivalent to field capacity (33KPa) and wilting point (1500 KPa) for a unit meter depth of soil, approximate values of FC and WP for the

various soil textures have been extracted [see Table 1]. Accordingly, the FC and WP values as per the rootingdepth is then derived for the whole region as summarised in Table 3.

5 E 10 E 15 E 20 E 25 E 30 E 35 E 40 E 45 E 50 E-35 S

-30 S

-25 S

-20 S

-15 S

-10 S

-5 S

1100200300400500

Field Capacity (mm)

Derived field capacity

5 E 10 E 15 E 20 E 25 E 30 E 35 E 40 E 45 E 50 E-35 S

-30 S

-25 S

-20 S

-15 S

-10 S

-5 S

050100150200

Available water content (mm) = FC-WP

Available water content

(a) field capacity (FC) (b) available water content (AWC)

Fig. 2 Distribution of derived (a) field capacity (FC) and (b) available water content (AWC) in the SADC regionused in water balance calculation.


7/13



The maximum retention capacity of soils depends on the type of soil and the vegetation cover of the area. It isobtained by multiplying the UFC and UWC values by the corresponding root depth. Derived field capacity (FC)

distribution in the SADC region used in water balance calculation is presented in Figure 2a. On the other hand,Figure 2b shows the spatial variation of the derived available water content (AWC) distribution across the SADCregion used in DGHM.

Table 3. Relationship linking vegetation class, soil texture, rooting depth and moisturecapacities of various soil groups in southern Africa.

Sand Sandy Loam Silt Loam Clay Loam Clay Lithosol

Veg. Group The Root depth (m)

GRP1 2.5 2.0 2.0 1.6 1.2 0.1

GRP2 1.0 1.0 1.3 1.0 0.7 0.1

FC and AWC of soils as % of total volume of soils / m

% (FC)/m

%(AWC)/m

14.1

6.3

20.0

9.1

27.3

13.2

35.2

35.8

48.5

35.8

27.3

13.2

Field Capacity and AWC per root depth of the plant

GRP1 (FC)

(AWC)

353

196

400

218

546

282

563

243

582

153

27

14

GRP2 (FC)

(AWC)

141

78

200

109

355

183

352

152

339

89

27

14

(a) runoff (b) evapotranspiration

O N D J F M A M J J A S

0

2

4

6

8

10Grid: at lat/long 10.25 S / 35.75 E

PET

PPT

TR O

mm/day

O N D J F M A M J J A S

0

2

4

6

8

10Grid: at lat/long 10.25 S / 35.75 E

PET

PPT

AET

mm/day

(c) Soil moisture

0

2

4

6

8

1 0

1 2 3 4 5 6 7 8 9 1 0 1 1 1 2

PPT

&

PET(mm/day

0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

3 0 0

soilm

oisture,

SM(

mm

P E T

P P T

S M

Fig. 3Seasonal variation of precipitation and PET versus model derived (a) runoff, (b) actual evapotranspiration,

and (c) soil moisture for a selected grid cell the SADC region centred on Eastern Tanzania, which is dominatedwith soil of field capacity of 349 mm.


8/13



4. MODEL APPLICATION AND DISCUSSION OF RESULTS

General principleFor a single geographically referenced grid cell, the model is run independently for the 30-year periodbetween 1961-90 to derive a regional map of hydrologic regimes. In each simulation year, the model in the

subsurface zone, is run for a time loop of 12 months, by applying the PPT and PET. If a dynamic state is notachieved in soil moisture (SM), actual evapotranspiration (AET) and runoff (TRO) between subsequentsimulations, simulation proceeds until a dynamic steady state is achieved with in 0.01 % error in all of these

variables. When the steady state situation is arrived, the outputs SM, EAT and TRO are maintained, and the

spatial control module is invoked and computation for another grid cell continues. The model is then appliedfor 7000 grids that represent the study area according to their spatial identifier.

In order to establish the hydrologic regimes of the study region, the available 1961-1990 average hydro-climatological information, on monthly basis, has been used as input to the model DGHM. The seasonal

variation of TRO, AET and SM for corresponding PET and PPT for a typical region in eastern Tanzania is shownin Figures 3a,b & c, respectively.

Soil moistureThe variation of 1961-90 mean annual soil moisture (MASM) in Southern African region, computed by the model,is shown in Figure 4. The MASM of the basin is estimated by the model is about 148 mm. The frequency

distribution of MASM over the region portrays a significance spatial variation [Figure 4]. This is due to the factthat the absolute soil moisture depends on the water retention property of the soil, and hence on the field

capacity of the soil. If the actual soil moisture is segregated by its field capacity value of the corresponding soiltype, the actual regional variation can be observed clearly.

It can be observed from Figure 4 that DGHM simulates the majority of the area northwestern Tanzania west ofthe Lake Victoria extending to west of Zaire and Central Mozambique to exhibit higher annual soil moisture

regimes. The highland areas in Northern and eastern Tanzania have moderate soil moisture and most part ofcentral and southern Africa from Zimbabwe to southern most of Republic of South Africa are dominated by lowsoil moisture regimes. Generally, the map of annual average soil moisture to some extent follows the pattern of

precipitation. The variation of mean annual SM with respect to the mean annual PPT is depicted in Figure 5.

5 E 10E 15E 20E 25E 30E 35E 40E 45E 50E

-30S

-25S

-20S

-15S

-10S

-5S

0 S

100200300400500

Mean annual soil moisture - 1961-90

Soil moisture (mm)

Fig. 4Mean annual soil moisture variation for the baseline 1961-90 over southern Africa

It can also be inferred from Figure 5 that high precipitation grids experience high SM, explained by relatively highvalues of the ratio mean annual SM/FC. However, because PPT alone is a poor indicator of SM in absolute

terms, and the variation of SM with PPT is not distinctively related, either linearly, or not otherwise. This can alsobe attributed because of the high variation of FC in the region shown in Figure 4, which ranges from 27 to 563mm that can affect the ratio of actual SM to FC. But the dependence of SM on PPT becomes more vivid if it is

segregated by the field capacity.


9/13



0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 00

1

2

3

4

5

6

7

8

Mean annual SM vs PPT

Precipitation

(mm

/day)

Soil moisture (mm)

Fig. 5The relationship between precipitation and model derived mean annual soil moisture

Actual evapotranspiration

The variation of mean annual actual evapotranspiration (MAET) in the Southern African region, simulated by themodel DGHM, is shown in Figure 6. The model prediction of the mean annual (AET) in the region reaches amaximum of 1500 mm, with mean 420 mm.

0 1 2 3 4 5 6 70

1

2

3

4

5

6

7

Mean annua l AET vs PPT

Precipitation

(mm/day)

Evapot ransp i ra t ion (mm/day)

Fig. 6 The relationship between 1961-90 mean annual precipitation and DGHM model derived mean annualAET over the Southern African region.

Considering the whole region, the actual mean annual AET accounts for 41 % of the mean annual PET over theregion. The spatial variation of the computed annual AET over the Southern African region is shown in Figure 7.It can be seen that, PET is high in the area near the shore areas surrounded by the oceans and decreases

towards hinterland. Nearly northern half of southern African region experiences higher evaporation than theremaining southern half of the region which experiences lower evaporation.

The variation of the ratio of annual AET to PET is shown in same figure [Figure 7]. The regional variation of thisratio follows a similar tendency of the actual evaporation. It is higher in the areas surrounding the oceans and


10/13



tends to decrease hinterland as one goes from the periphery of the ocean shore areas, which reaches nearer toa value of 1.0. Since the mean annual AET values depend both on the distribution pattern of the rainfall as well

as PET values, no general conclusion can be derived from PET alone with out involving the role of PPT & SM.

5E 10E 15E 20E 25E 30E 35E 40E 45E 50E

-30S

-25S

-20S

-15S

-10S

-5S

0S

0.51.01.52.02. 53.03. 54.04.55. 0

Mean annual AET - 1961-90

Actual ET (mm/day)

5E 10E 15E 20E 25E 30E 35E 40E 45E 50E

-30S

-25S

-20S

-15S

-10S

-5S

0S

0.10.20.30.40.50.60.70.80.91.0

Mean annual AET/PET ratio - 1961-90

AET/PET ratio

Fig. 7Mean annual actual evapotranspiration and relation to Penman (AET/PET) variation over southern Africanregion.

RunoffThe mean annual runoff and the actual runoff coefficient variation for each grid (as computed from the ratio of

the total runoff (TRO) to (PPT) is given in Figure 8a and 8b, respectively. The runoff coefficient map shown hereis the ratio of the actual runoff generated from precipitation within each grid cell before starting to form a streamflow.

(a) (b)

5E 10E 15E 20E 25E 30E 35E 40E 45E 50E

-30S

-25S

-20S

-15S

-10S

-5S

0S

0.51.01.52.02.53.03.54.04.55.0

Mean annual runoff - 1961-90

Grid runoff (mm/day)

5E 10E 15E 20E 25E 30E 35E 40E 45E 50E

-30S

-25S

-20S

-15S

-10S

-5S

0S

-0.050.000.050.100.150.200.250.300.350.40

Mean annual runoff coefficient - 1961-90

mean annual runoff coefficient

Fig. 8 Spatial variation of mean annual generated runoff and runoff coefficient over southern African regionderived from the baseline 1961-90 climatology.

The mean annual generated runoff from the land catchment in the region is about 151 mm/year although there isa significant inter-regional variation among the SADC countries. Nevertheless, the variation of the runoff

generation for each grid varies greatly. Lower runoff regimes are dominant in arid areas in Botswana, Namibiaand south-western part of the Republic of South Africa. Higher runoff regimes are the northern and westernTanzania, along the east coastal portions of Mozambique, central Mozambique, western Zambia and Malawi.


11/13



0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 9 0 0 1 0 0 00

5 0 0

1 0 0 0

1 5 0 0

m e a n = 1 5 1 m m , s t . d e v . 2 4 6 , s i z e = 3 4 0 1 g r i d s

Noofgridsin

SADC

Mean annual runof f (mm)

Fig. 9Frequency distribution of mean 1961-90 annual runoff of the SADC region simulated by the developed

model DGHM.

0

1

2

3

4

5

6

0 1 2 3 4 5 6

Rainfall (mm)

Runoff(mm)

Fig. 10Mean annual generated runoff in relation to the rainfall of the baseline 1961-90 climatology at the grids ofsouthern African region.

Figure 9 shows the frequency distribution of the mean 1961-90 annual runoff of the SADC region simulated bythe developed model DGHM. It demonstrates the mean annual runoff in the region of southern Africa is 151 mm

with majority dominated with low runoff regime below 500 mm per year.


12/13



It has been observed that the runoff generation is highly influenced by the distribution pattern of precipitation inthe region. The mean annual variation of runoff generated is linear at high and low precipitation regimes in the

region. In the medium precipitation regimes, there is a wide variation in runoff generation as depicted in Figure10. The annual variation of runoff as a function of the annual precipitation in mm/day at grids across southernAfrica is presented in Figure 10. It offers the relative runoff volume generated at each grid. However, a clear

conclusion can not be drawn for the region, as to the inter-grid and regional variation of input informationresponsible for the runoff generation dictated by the processes in surface as well as in subsurface soil moisturevariation.

5. CONCLUSION

A distributed GIS-based hydrological model (DGHM) is developed using GIS and computational hydrologytechniques. The model is based on water balance consideration of the surface and subsurface processes.

The model has been used to create a GIS-based high resolution data sets of monthly soil moisture,evapotranspiration and grid runoff in the region. Considering the 1961-90 climatic period, we have mapped the

regional variation of the mean annual soil moisture (SM), actual evapo-transpiration (AET), and generated runoff(ROF) across the SADC. The model estimates the mean SM of the region to be about 148 mm per year. Thereis a wide spatial range in the distribution of SM in the region due to the fact that the absolute soil moisture is

dependent on the water retention properties of the soils considered across the region. The model prediction ofthe mean annual AET in the region reaches a maximum of 1500 mm, with mean 420 mm.

The mean annual generated runoff from the land catchment in the region is about 151 mm/year although there isa significant inter-regional variation among the SADC countries, which is a function of the variation in thevegetation cover, soil and climate variation.

The model enables one first to establish the hydrologic regimes of the region, and finally to deal with theprediction of discharge from the various drainage basins. It ultimately permits a through assessment of theregion's water resources availability. Such models can be externally coupled with Atmospheric Global

Circulation Models (AGCM) and can be used to study the impact of possible climatic change conditions on theregions water resources.

Acknowledgments: The authors thank DAAD for the research grant to fund part of the study, and Dr. MikeHulme at University of East Anglia for providing climatic data of Southern Africa.

REFERENCES

Biftu, G.F. (1998) Semi-distributed hydrological modelling using remoteley sensed data and GIS.UnpublishedPhD thesis. University of Alberta.

Conway, D. (1997) A Water Balance Model of the Upper Blue Nile in Ethiopia, Hydrological Science Journal,

42(2).

Eastman, J.R. (1997) IDRISI for windows users guide. Clark University, Graduate School of Geography,Worcester, Massachusetts 06610, USA.

FAO (of United Nations) (1988) World Soil Resources, An explanatory Notes on the FAO world soil referencemap, World Soils Resources Report, No. 66.

Hulme, M., Arntzen, J., Downing, T., Leemans, R., Malcolm, J., Reynard, N., Ringrose, and Rogers, D. (1996)

Climate Change and Southern Africa: An exploration of some potential impacts and implications in theSADC region, University of East Anglia, Norwich, UK.

Nemani, R. R., and Running, S. W. (1989). Testing a theoretical climate-soil-leaf area hydrologic equilibrium of

forests using satellite data and ecosystem simulation. Agricultural and Forest meteorology, 44: 245-260.

Rutter, A. J., Morton, A. J., and Robins, P. C. (1975) A Predictive model of rain interception in forests, 1.Generalization of the model and comparison with observations in some coniferous and hardwood stands. J.

Appl. Ecol, 12:364-380.

Saxton,K.E., Rawls, W.J., Romberger, J.S. and Papendick, R.I. (1986). Estimating generalized Soil-WaterCharacterstics from Textre. Soil SCI. SOC. AM. J., Vol. 50


13/13


Singh, V. J. (1992) Elementary hydrology. Prentice hall, Inc., Englewood Cliffs, pp. 973

Thornthwaite, C.W. and Mather, J.R. (1957) Instructions and Tables for computing potential evapotranspiration

and the water balance, Drexel Inst. Techno. Publ. Clim., X(3).

Thornthwaite, C.W. (1948) An approach toward a rational classification of climate. Geographical review, 38(1):55-94.

Van Deursch, W.P.A., and Kwadijk, J.C.J.(1993) An Integrated GIS Water Balance Model for the River Rhine,Proceeding of Viena Conference, IAHS Publ., No.211.

Vorosmarty, C.J., More, B., Grace, A.L., Gildea, M.P., Melillo, J.M., Peterson, B.J., Rasteller, E.B., and Steudler,P.A. (989). A Continental Scale Models of Water Balance and Fluvial Transport: An Application to SouthAmerica, Global BioGeochemical Cycles, 3(3) 241-265.

continental scale water balance model

Documents