Journal of Water Resource and Protection, 2012, 4, 516-522
http://dx.doi.org/10.4236/jwarp.2012.47060 Published Online July 2012 (http://www.SciRP.org/journal/jwarp)
Hydrological Modeling of Large Drainage Basins
Using a GIS-Based Hybrid Atmospheric and Terrestrial
Water Balance (HATWAB) Model
Berhanu F. Alemaw
Department of Geology, Faculty of Science, University of Botswana, Gaborone, Botswana
Received March 26, 2012; revised April 27, 2012; accepted May 29, 2012
ABSTRACT
A Hydrological model is proposed to study the sp atial and temporal variability of the water budget co mponents of large
drainage basin systems from atmospheric and terrestrial water balances. In order to understand the water balances that
include, surface runoff, actual evapotranspiration and soil moisture, a GIS-based simple water balance model which is
referred as Hydrological Model from Hybrid Atmospheric and Terrestrial Water Balances with acronym HATWAB is
presented. The spatio-temporal climatology database was created from a network of climate stations from CLIMWAT
data base to reconstruct the monthly primary inputs to HATWAB model, rainfall and potential evapotranspiration. The
modeling princip les and HATW AB model are d emonstrated us ing the Limp opo and Congo basins in Africa. The model
was used to simulate water balance components by taking rainfall-runoff processes in the basin including soil-texture
controlled moisture in the terrestrial system, and the vertical integrated moisture convergence that accounts for the net
water vapor flux from the basins in order to close the hydrologic water budget.
Keywords: HATWAB; Water Budget; Large Drainage Basin; Soil Moisture; Vertical Integrated Moisture
Convergence; Water Flux; GIS
1. Introduction
Hydrological modeling of large drainage basins is used
to understand the complex hydrological processes that
control the distribution and availability of hydrologic
components and water resources availability in terms of
atmospheric and terrestrial water balances. It is princi-
pally undertaken through precipitation partitioning into
surface and groundwater flows, soil moisture and evapo-
transpiration. Spatial and temporal variations of regional
water and energy balances over long and short time
scales play an important role in changes in the stream
flow of a basin. Precipitation being rainfall, evapotran-
spiration, runoff, percolation and soil moisture are the
main components of the hydrologic cycle within semi
arid regions. Their overall role to the hydrologic cycle
are influenced by their interaction with soil, vegetation,
topography and climate of the given area and to some
extent by human interaction on the dry-land being crops,
pastures and forestry.
Complex hydrologic systems have always been sim-
plified in order to understand water balances within a
catchment. To understand the spatial water balance com-
ponents hydrological models have been employed for
precipitation-runoff modeling based on GIS [1-3]. Among
the most earlier catchment water balancing approach un-
dertaken based on long term monthly climatic cond itions
was the one by [4], which then led to many researches on
water balance models for similar conditions on a catch-
ment, a region or a continental scale. Typical examples
are 1) the USGS micro-computer Thornthwaite Water
Balance model [5]; 2) a grid-based model for Latin
America [6-8]; 3) a GIS-based water balance model at
southern Africa scale [9]; 4) the Rhine flow model [10];
and 5) the large-scale water balance model for the upper
Blue Nile in Ethiopia [11]. In South Africa, the Depart-
ment of Water affairs and Forestry (DWAF) has deve-
loped a Water Balance Situation Assessment Model
(WSAM) [12]. WSAM is widely used model in southern
Africa to simulate streamflow, which allows calibration
based on parameters for partitioning of precipitation into
surface and subsurface components. The Famine Early
Warning System Network (FEWS NET) hydrological
model for the Limpopo basin [13], which is still under
development, is one standard rainfall-runoff model that is
expected to provide a continuous daily simulation of
stream flow mainly developed for flood forecasting.
Increasing computer technology including use of GIS
technique and physical (or quasi-physical) based hydro-
C
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B. F. ALEMAW 517
logic modeling has become important in contemporary
hydrology research for assessing the impact of human
and/or possible climatic change on basin hydrology and
water resources. This approach is widely used in the hy-
drologic research community compared to the systems-
type black box models. Another adv antage of physical or
quasi-physical hydrological modeling is also its useful-
ness for investigating large-scale hydrological modeling
thereby helping with planning, allocation and manage-
ment of water resources.
In this manuscript results of a simplified water balan ce
model, named Hydrological Model from Atmospheric
and Terrestrial Water Balance (HATWAB) model [14],
is presented and demonstrated for two basins, 1) the
Limpopo river basin based on previously reported origi-
nal data for the basin [15]; and 2) the Congo basin, based
on previously presented data [16]. The model is capable
of estimating monthly soil moisture, actual evapotranspi-
ration, runoff and the vertical integrated moisture con-
vergence. Such a model may be used for planning and
decision support system in the region. HATWAB model
was developed based on the approach proposed in [9],
but was upgraded to cater for seasonal variation of verti-
cally integrated moisture convergence (C) as well as
correcting the imbalances in the closure of the water
budget which are catered for precisely to address a com-
mon challenge in water budget modelling at a basin scale.
Perhaps this aspect remains one important contribution
and attribute of this paper.
The major objective of this study was to understand
the hydrological budget and processes in large drainage
basins using HATWAB. The specific benefits of HAT-
WAB and the objectives presented in this manuscript
include: 1) determining the available spatial and tem-
poral hydro-climatic information and data gaps to under-
take water budget study, which is based on available
sparse data; 2) mapping the spatial and temporal vari-
ability of rainfall, effective rainfall and potential evapo-
transpiration a basin scale; 3) assessing the spatial and
temporal variability basin water budget in terms of soil
moisture, actual evapotranspiration, runoff, and vertically
integrated moisture con vergence.
By doing so a number applications of HATWAB can
be sought that include mainly: 1) Assessment of water
availability and distribution in a drainage basin; and 2)
Assessment of climate change and large scale human-
induced changes.
2. Approach and Methodology
Selecting a Template
The modeling approach followed was based on parame-
terizations to compute temporal and spatial variability of
water budgets at geo-referenced grid cells covering a
drainage basin. The model computes the integrated moi-
sture convergence (C) and soil moisture in solving the
water budgets in the atmospheric and terrestrial compo-
nents, respectively. Uncertainties on atmospheric water
balance estimates and imbalances are also investigated.
The atmospheric component of the water balance is
expressed as follows [14]:
ddWt PEC 
CQ
(1)
where dW/dt is the storage change (LT-1). C is the ver-
tical integrated moisture convergence (LT-1) and was
expressed as a function of a variable Q which is the water
vapour flux (LT-1), as follows:

 
PEC
(2)
The storage change, dW/dt is usually ignored because
changes in precipitable water are quite small in averages
over time scales of a month or more [8]. Then Equation
(1) reduces to
(3)


The terrestrial water balance model on a monthly time
scale can be written as
ddStPER (4)
where S is soil moisture storage (L); P is precipitation
(LT-1); E is actual evapotranspiration (LT-1); and R is
the observ ed runoff (LT-1). The monthly E can be calcu-
lated once the soil moisture is determined. Then by com-
bining Equations (3) and (4), it follows that the vertical
integrated moisture con vergence, C is computed as:
ddCStR (5)


In a steady state P – E = R. Changes in storage could
however lead to P – E being different from R. These
could also be due to certain errors in represen ting rainfall
within a basin under consideration. These lead to the
expression of an imbalance equation


dd dd 1
mb
CStR CSt
IRRR


 
(6)
Contrary to the formulation adopted in this study
based on Equation (6), [8] assumed that dS/dt is neg-
ligible for monthly time scales and applied it to the
Amazon basin, which reported unaccounted residuals in
water budgets. Whereas in the proposed model in this
study, the soil moisture variation dS/dt is varying from
season to season as a function of the prevailing Ep and P
at a given location according to Equation (4), in which
the imbalance should also cater for this variability ac-
cording to Equation (6). One of the contributions of this
study is that, once the imbalance (Equation (6)) is kept to
a minimum in the water balance computation at each grid,
then the simula ted variables and water balances, P, E, R,
R/P, E – P, E/Ep, S and C can then be used to investigate

B. F. ALEMAW 518
the seasonal and temporal variability of a basin’s water
budget.
The amount of precipitation and potential evapotran-
spiration determine soil moisture availability, which in
turn is controlled by the water holding capacity of the
soils. Solution of the mass balance equation was solved
for E, R and S based on procedures given in [6,9,17].
3. The Study Area and Data
The study area considered, the Limpopo river basin and
the Congo basin, are two of the major drainage systems
in Africa (Figure 1) with huge interest for regional de-
velopment among the riparian states. The Limpopo basin
represents predominately arid to semi arid regions with
low rainfall regimes where as Congo basin predomi-
nately represents high rainfall regimes.
In order to so lve the water budget equations an d cover
the study area with the minimum available information
and effort, gauged data from the FAO CLIMWAT data-
base [18] within each basin was resampled and used. A
total of 66 stations in Limpopo and 145 stations in the
Congo basin were used in the analysis. The extracted
data was based on a rectangular region in which the ba-
sins are located. The data includes long-term average
monthly rainfall, effective rainfall (Pe), Ep and other cli-
matic variable such as temperature (minimum, mean and
maximum), wind speed, sunshine hours and solar radia-
tion. The point distributed hydroclimatic data were spa-
tially interpolated using the Inverse distance squared
(IDS) method.
One of the main inputs required in the proposed water
balance model is the effective precipitation (Pe). At a
monthly time scale, the effective precipitation is calcu-
lated as per the formula of the USDA soil conservation
available from FAO manual [20]. The reference evapo-
transpiration (Eo) is computed according to the FAO’s
Penman-Monteith method [20]. These soil textural classes
have been extracted from agronomical soil classes of
soils databases of FAO/UNESCO [21] according to the
methodology proposed in [9]. The soils data were origi-
nally available at 10 minutes spatial resolution, which
was further regridded using pixel thinning algorithm [22].
From textural reclassification of soils and vegetation
cover data (based on the NDVI imagery data of 1987),
soil-water retention parameters such as field capacity
(FC), wilting point (WP) and available moisture content
(AMC) values were extracted at each grid cell was within
the basin according to soil-water relations [9,23]. All the
spatial data were compiled in a GIS raster grid format at
a spatial resolution of 5’ by 5’ (9.2 km by 9.2 km) repre-
senting the study basins.
4. Analysis of Results and Discussions
For a single geographically referenced grid cell, the
model is run independently for the simulation period of
30-years to derive a basin-wide map of water balances.
The water balances were conducted for a period of 30
years assuming that the mean does not change during this
normal period. This was important as 30 years is the
mean record length of the data obtained from CLIM-
WAT database [18], which represents the rainfall and
other climatic variables. In each simulation year, the model
Figure 1. Location map of the Limpopo and Congo basins and flow direction grid maps (own Figures: [16,19], modified).

B. F. ALEMAW 519
in the soil moisture zone is run for a time loop of 12
months, by applying the P and Ep. If a dynamic state is
not achieved in soil moisture storage term (S), actual
evapotranspiration (E) and runoff (R) between subse-
quent simulations, the simulation proceeds until a dy-
namic steady state is achieved within 0.01% error in all
of these variables. When the steady state situation is ar-
rived, the outputs S, E and R are maintained, and the spa-
tial control module is invoked and computation for an-
other grid cell cont i n ues.
The model is then applied for all grids that represent
the basin under consideration according to the spatial
identifier of such grids.
Computation of monthly water balances throughout all
the identified grids with each basin has been undertaken,
and results for geo-referenced grids in the each basin
have been stored in the results database. The actual eva-
poration which was computed from the mass-balance
equations, whose value as a ratio to its potential value,
Ep is assumed to change linearly with the soil moisture
storage for the given month that satisfies Equation (4).
For each grid, the soil moisture was computed on a
monthly basis in such a way that closure of the water
budget is achieved as stipulated by mass balance equa-
tions (Equation (4)) until close of the hydrological bud-
get is achieved.
Typical variations of temporal/seasonal water balances
at selected grids is shown in Figure 2(a) and Figure 2(b)
for grid cells centered on 29.03˚E/19.93˚S and 29.12˚E/
26.33˚S, respectively. A common feature of all the sea-
sonal portrayals of these water balances components is
that the actual E values are less than the Ep values for
any given month, which is as expected. The same applies
between the rainfall and generated runoff.
The reference evapotranspiration (Ep) computed based
on the FAO Penman-Monteith method [20] at 66 climate
stations in the Limpopo basin and 145 climate stations in
the Congo basin, which were further resampled at the
corresponding p ixels in the same format as the other spa-
tial information. For Limpopo basin, the annual Ep va-
lues reach above 1100 mm with almost 50% of the basin
having higher values ranging from 600 to 900 mm. Soil
moisture is found to range between 50 an d 450 mm with
most of the area dominated with higher moisture ranges.
The actual evapotranspiration computed for the Lim-
popo Basin using the developed water balance model is
shown in Figure 3. The actual evapotranspiration is
found to be varying with in the entire basin. The E varies
from 400 to 1100 mm per year with most of the basin,
accounting about 60% of the basin area having the high-
est E.
For the Congo basin, the simulated annual to tal runoff
in relation to precipitation is shown in Figure 4. The
mean annual Runoff for the Congo basin varies between
Figure 2. Temporal variation of water balance components
computed in the Limpopo basin at a grid cell centered on (a)
29.03˚E/19.93˚S and (b) 29.12˚E/26.33˚S (own figure, modi-
fied from [15]).
Figure 3. Annual actual evapotranspiration variation in the
Limpopo basin (mm).
1 and 1945 mm with a mean annual runoff of 342 mm.
The annual simulated runoff show a general trend
strongly influenced by the distribution pattern of precipi-
tation. The highest valu es are concentrated in the heart of
the equatorial forest along the Middle Congo river branch.
This area records higher rainfalls in the whole basin. The
lowest value is simulated in the southern hemisphere
around the grid of coordinate 31˚E and 6.73˚S (western
part of Tanzania). A part the lakes, the highest values of
runoff are simulated in the heart of the equatorial forest
across the equator, and decrease progressively towards
the tropics. This trend is relatively disturb ed with the soil

B. F. ALEMAW 520
10 15 20 25 30 35
-15
-10
-5
0
5
10
0
100
200
350
400
525
650
750
850
1050
1250
1350
Total Annual Rainf
[mm/year]
-15
-10
-5
0
5
10
all and Runoff
10 15 20 25 30
Rainfall
Runoff
35
Figure 4. The simulated runoff and areal precipitation in the Congo river basin.
(a) (b)
Figure 5. The simulated vertically integrated moisture convergence C in the Congo river basin (a) Dec to Feb (left); (b) Jun to
Aug (right) (Source: Own data, [16]).
types especially in the south-eastern, the extreme north
region and along the main Congo River.
The corresponding grid-based vertical integrated the
moisture convergence (C) computed during water ba-
lance calculations for the Congo basin are shown in Fig-
ure 5. The moisture convergence corresponds to the ne-
gative values whereas the positive values correspond to
the moisture divergence. This clearly is displayed in the
see-saw fluctuation of C between the above and below
equator during the different quarters, winter and summer
occurring in the two climatic regimes of the basin.
5. Summary
HATWAB, though simple in form and easy to implement
with Fortran, it can be used to solve and answer basin

B. F. ALEMAW 521
water resources planning questions of determining water
resources availability and distribution at a basin level
with localized various spatial and temporal scales de-
pending on the need.
The changes in the input climatic Changes variables
such as precipitation and potential ET can easily be in-
corporated in the model structur e in order to simulate the
effect on runoff under climate change scenarios. Effects
of land cover and land use change as a result of human
activity can be considered in HATWAB.
As the grid water balance computations are compatible
with raster GIS platforms, the extended application of
HATWAB model for hydro-morp hologic parameters that
control surface runoff can be explored.
However, the model, even if it is at its early stage of
development, it is potentially suitable to incorporate hu-
man induced changes such as land use land cover and
climate impacts in the rainfall-runoff processes of and
integrated water resources management of large drainage
basins. It is also possible to study transboundary interests
in joint management o f shared water resources especially
in data scarce Africa where this gap is overcome by the
approach presented in this man uscript.
6. Acknowledgements
The author appreciates the support of the University of
Botswana, Department of Meteorological Services, the
NUFU project (NUFUPRO-2007/10079) and the Chal-
lenge Programme on Water and Food (CPWF). The Uni-
versity of Dar es Salaam is also appreciated which men-
tored an d hos ted a Ph D rese arch of the au thor b ack in th e
late 1990s, from which some of the concepts of this
manuscript were developed, applied and tested.
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