Phys. Chem.Earth (B),gol. 25, No. 7-8, pp. 695-698, 2000 © 2000 ElsevierScience Ltd. All rights reserved 1464-1909/00/$ - see front matter
PII: S 1464-1909(00)00087-3
Water Balances Using GIS M. T. Pimenta
Instituto da Agua (INAG), Av. Almirante Gago Coutinho, 30, 1049-066 Lisboa, Portugal
Received 23 April 1999," revised 23 August 1999," accepted 27 September 1999 evapotranspiration. Model parameters are maximum soil water holding capacity, deep infiltration and groundwater flow coefficients. These parameters depend on the soil type. This model can be applied to studies ranging from catchment to regional scale.
Abstract. In order to identify the desertification prone areas for the establishment of the National and Regional Action Plan to combat the desertification a methodology based on indices was developed for Portugal. One of these indices is based on the number of months with water stress conditions. The distribution of the index for the country was obtained by the combination of the precipitation amounts, the potential evapotranspiration and the maximum soil water holding capacity in a water balance model, producing as intermediate results the maps of the actual evapotranspiration and the soil water storage for each period. Base information covers monthly data for 55 years and the procedures are sequentially performed month by month in each cell (1000 x 1000m). The data management is achieved using a programming language integrated in a GIS. The advantage of this procedure is that it is easy to update or modify the system variables. This approach allows the computation of the annual, the total, the average and the percentage of the number of months under stress conditions in the study period. © 2000 Elsevier Science Ltd. All rights reserved
2 Water balance model
2. l Model Description The water balance model applied is the Thornthwaite and Mather (1955) approach with some adaptations concerning the model parameters: maximum soil water holding capacity (MaxSS), groundwater flow coefficient (d) and deep infiltration coefficient (p). Figure 1 shows the scheme of water balance model used. Two different reservoirs are considered: an upper zone and lower zone reservoir (saturated). When the upper reservoir is full it allows the occurrence of deep percolation. A part (p) of the surplus is directed to the lower reservoir while the remaining (l-p) component generates overland flow, as shown in the scheme of Fig. 1. The subterranean water is discharged, as a rate d. During the sequential water balance it is considered that the actual evapotranspiration is lower than the potential whenever the water stored in the soil is lower than the maximum soil water holding capacity. In this case it is taking into account a month in stress conditions. The actual evapotranspiration is computed by the Thornthwaite and Mather method. The runoff is computed in a distributed cell-wise process as the sum of the d part of the water stored in the lower reservoir and the surplus percentage that does not infiltrate, i.e. surface runoff.
The goal of this study was to identify and group the regions in the Portuguese territory according to the within-year number of months under water stress conditions given by a spatial distributed, water balance model. This will, in turn, improve a methodology, previously developed (Pimenta et al, 1998), to identify desertification prone areas based on indices. To compute the number of months of water stress conditions and amounts of water involved in the different components of the hydrologic cycle and the fluxes between them, a distributed water balance model was developed, with a monthly time step, using a GIS programming language. GIS provides the storage and manipulation of huge amounts of spatial data allowing easy updating of the system and state variables. Depending on the characteristics of the input data it is possible to test the influence of different resolutions and scenarios. The simple model used requires minimal meteorologic input data: monthly precipitation and monthly potential
Correspondence to. M.T. Pimenta
The outputs of the model can be selected on the initial menu, Fig. 2, and they are all monthly distributed for each cell of the grid and through the study period. The water balance can be applied to any region taking into consideration the law of mass conservation, which states that the changes of water storage within the reservoirs must be equal to the difference between inflows and outflows. 695
M.T. Pimenta: Water Balances Using GIS
~ Precipitation PRE ~ DIGITAL ELEVATION MODEL
SSsup FLOW ACcoNIULATION
(l-p) * Surplus ~
PRECIPITATION.¢ A~ET ~
~= P R E ~ + S S s u p
Surplus, = SSsup ~- MaxSS
d * SSsub H =1
~-Deep infiltration = p Surplus
~= (l-d) SSsub ~_~- p * Surplus i
Kernels: MaxSS, p, d
i - time step
Fig. t Water balance model monthly performed for each watershed cell.
There are several potential uses for the model developed in this study, such as runoff estimation of ungaged basins, the generation of synthetic series to supplement short streamflow records or the simulation of different climatic (precipitation plus temperature) scenarios, making it appropriate for climatic change studies. It can also be applied to any spatial scale, with different resolutions.
The maximum soil water holding capacity, deep infiltration and groundwater flow coefficients are dependent on the soil hydrologic characteristics associated to each soil type that gives their spatial distribution. The soil map used is 1:1 000 000 scale. These parameters values have been calibrated for some river gauging stations made for each year (Pimenta et al, 1998). 2.3 Model application to Cunhas basin The water balance model, as applied to Cunhas basin, is developed in order to verify the distributed outputs at basin scale, for each cell of the basin (I00 x 100m). The study basin used for calibration, presented in Fig. 3, has an area of 338 km2. The study period comprises data from October 1950 to September 1990 (41 years).
Fig. 2 Initial Menu to select the outputs.
2.2 Description of the Input Data The inputs of the model are distributed monthly precipitation, distributed monthly potential evapotranspiration and the parameters: distributed maximum soil water holding capacity, deep infiltration and groundwater flow coefficients. The distributed monthly precipitation is obtained by the interpolation of 231 precipitation station data series. The potential evapotranspiration is obtained by the application of the Penman method and its spatial distribution given by the the interpolation of 87 climatological station data series within and near the study area.
? ~ !'
Fig. 3 Location of Cunhas basin in Portugal.
M.T. P i m e n t a : W a t e r Balances Using GIS
1950 to 1959
1960 to 1969
400 300 200 ~ 100 0 g
600 , 500 ~ 400 300 200 100 0
1980 to 1989
1970to1979 600 500 400 300 200
~;: " :
600 500 400 300 200 0o
a i ~ a ~ ~ ~}a*~a~ ~,~,~,~'~'='~,~,~'~,~,~'~,~'?,~'~''
Fig. 4 Comparisons between observed and computed runoff
The flow direction and the flow accumulation grids are obtained from the Digital Elevation Model of the basin, with the GIS tools, and the outlet is selected. The estimated runoff accumulated in the outlet is then calibrated against the measured runoff for each month. In the Fig. 4 the difference between observed and computed streamfiow is presented for Cunhas basin at the gauging station.
3 N u m b e r of m o n t h s under water stress conditions The number of months in water stress conditions, spatially distributed for all the country, is obtained through the water balance model. Information for the generalised used of the model to the Portuguese territory covers monthly data for 55 years, since 1940/41 to 1994/95. The procedures are sequentially performed month by month in each cell (1000 x 1000m). The result, Fig. 5, shows the average number of months for Portugal verified for the study period. The south and the northeast of Portuguese territory are the critical areas in terms of water stress prevailing in the areas where podzolic soils have lower water holding capacities. The number of months with water stress in these areas is about 6 months per year.
computed runoff values are rather good (Table l) although one may observe a general trend for underestimating the runoff. In general it provides a qualitative information about the space and time variability of all the components that are not revealed in an aggregate model. A difficulty of this model application is to consider the balance of groundwater in each defined cell. The simplification used may lead to important imprecision, especially in areas where groundwater is an important component. The use of GIS allows the computation of water balances in any region using complex spatial and time variant data.
The water balance model used in this study provides a quantitative evaluation of the partitioning of precipitation in the different components of the hydrologic cycle (runoff, evaporation and sub-surface and underground soil water storage). Comparisons between observed and
 4 CE2 5
F i g . 5 M e a n n u m b e r o f m o n t h s u n d e r stress c o n d i t i o n s .
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Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count
M. "12 Pimenta: Water Balances Using GIS Descrtpttve 3lattsttcs
73.46 3.92 40.36 4.97 87.06 7579.51 4.76 2.03 534.94 2.99 537.93 36141.86 492.00
KunoJJ Lsttmallon Lvalualton
Pearson Correlation (computed - observe ME (Mean Error) MSE (Mean Squared Error) MAE (%) (Mean Squared Error)
0.93 -8034.85 210225102.45 47.87
Table 1. Descriptive Statistics and Estimation Evaluation of the observed runoff
Pimenta, M.T., Santos, M.J. and Rodrigues, R. 1998 - Vulnerability to desertification process infered from water exchanges in the soil. Headwater98, Poster Volume, Hydrology, Water Resources and Ecology of Mountain Areas, European Academy Bozen/Bolzano, Section Alpine Environment, 21-24. Reed, Sean M., Maidment, David R. and Patoux, J6r6me, 1997
Spatial Water Balance of'lexas, CRWR (Center tbr Research in Water Resources) 97-1 Online Report: http://www.ce.utexas.edu/prof/maidment/gishyd97/library/wbtexas/wb texashtm Thornthwaite, C W. and Mather, J. R. 1955 - The water balance, Drexel Inst. Lab. Climatol. Centerton, N. J., Publ. Climatol., Vol. 8. 11°3.