HYDROLOGICAL PROCESSES Hydrol. Process. 23, 3718– 3727 (2009) Published online 1 December 2009 in Wiley InterScience (www.interscience.wiley.com) DOI: 10.1002/hyp.7517
A simple semi-distributed water balance model for the Ethiopian highlands Amy S. Collick,1,2 Zachary M. Easton,2 Tegenu Ashagrie,3 Biniam Biruk,3 Seifu Tilahun,1,2 Enyew Adgo,4 Seleshi B. Awulachew,5 Gete Zeleke6 and Tammo S. Steenhuis1,2 * 1 Department of Water Resources Engineering, Bahir Dar University, Bahir Dar, Ethiopia Department of Biological and Environmental Engineering, Riley Robb Hall, Cornell University, Ithaca, NY, USA 3 Integrated Watershed Management and Hydrology Program, Cornell University, Bahir Dar, Ethiopia 4 Department of Natural Resources, Faculty of Agriculture, Bahir Dar University, Bahir Dar, Ethiopia International Water Management Institute, Sub-regional Office for Nile Basin & Eastern Africa, ILRI campus Addis Ababa, Ethiopia 6 Ctr Int Agr Trop, AHI, POB 5689, Addis Ababa, Ethiopia 2
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Abstract: The discharge of the Nile River is highly dependent on the flow generated in the highlands of Ethiopia. However, little is known about the local (i.e. small scale) watershed hydrological response, due in part to a lack of long duration, continuous hydrological data. The goal of this paper was to develop a realistic, simple model that is useful as a tool for planning watershed management and conservation activities so that the effects of local interventions on stream flow can be predicted at a larger scale. The developed model is semi-distributed in that it divides the watershed into different regions that become hydrologically active given different amounts of effective cumulative rainfall after the start of the rainy season. A separate water balance is run for each of the hydrologic regions using rainfall and potential evaporation as the major inputs. Watershed parameters that were calibrated included the amount of water required before each region becomes hydrologically active, the fraction of soil water that becomes runoff and subsurface flow, and aquifer characteristics, Model validation indicated that daily discharge values were predicted reasonably well with Nash Sutcliffe values ranging from 0Ð56 to 0Ð78. Despite the large distance between the test watersheds, the input parameter values for the watershed characteristic were remarkably similar for the humid highlands, indicating that the model could be used to predict discharge in un-gauged basins in the region. As expected, the watershed in the semi-arid region behaved somewhat differently than the other three watersheds. Good quality precipitation data, even for short durations, were key to the effective modelling of runoff in the highland watersheds. Copyright 2009 John Wiley & Sons, Ltd. KEY WORDS
rainfall runoff; Thornthwaite–Mather; Upper Nile Basin; Nile; monsoonal climate
Received 14 October 2008; Accepted 5 October 2009
INTRODUCTION A better understanding of the hydrological characteristics of different watersheds in the headwaters of the Nile River is of considerable importance because of the international interest in the utilization of its water resources, the need to improve and augment development, and management activities of these resources, and the potential for negative impacts of climate change in the future. Conflicting views of water resource utilization and ownership has been challenging the development of appropriate management of the Nile River Basin for the countries that are most dependent on its resources including Egypt, Sudan, and Ethiopia. Egypt’s agricultural production and domestic requirements depends primarily (99%) on the waters of the Nile River, withdrawing up to 55Ð5 billion m3 /year (Gheith and Sultan, 2002); Sudan’s agriculture also relies heavily on these waters; while Ethiopia, at the Nile’s headwaters, is interested in further developing the water resources to meet development needs and attain ‘water * Correspondence to: Tammo S. Steenhuis, Department of Biological and Environmental Engineering, Riley Robb Hall, Cornell University, Ithaca, NY 14853, USA. E-mail:
[email protected] Copyright 2009 John Wiley & Sons, Ltd.
security’ through equitable sharing among the Nile countries (Arseno and Tamrat, 2005). Only 5% of Ethiopia’s surface water (0Ð6% of the Nile Basin’s water resource) is being currently utilized by Ethiopia, while cyclical droughts cause food shortages and intermittent famine (Arseno and Tamrat, 2005). The Ethiopian highlands are the origin, or source, of much of the river flow reaching the Nile River, contributing greater than 60% of Nile flow (Ibrahim, 1984; Conway and Hulme, 1993) possibly increasing to 95% during the rainy season (Ibrahim, 1984). As the Nile River discharge is highly dependent on the flow generated in the Ethiopian highlands, increases in utilization of water resources and management activities that alter discharge levels in Ethiopia may have a significant effect on the overall flow of the Nile, and consequently become a considerable concern for populations in the regions downstream in Sudan and Egypt. Thus, a better understanding of flow characteristics throughout the upper Nile River’s basins in Ethiopia that account for seasonal differences and different spatial scales is necessary. There have been limited studies on basin characteristics, climate conditions, and hydrology of the Upper
A SEMI-DISTRIBUTED WATER BALANCE MODEL FOR THE ETHIOPIAN HIGHLANDS
Nile Basin in Ethiopia (Antar et al., 2006; Mishra and Hata, 2006; Johnson and Curtis, 1994; Conway, 1997) with a very few being published relating to hydrological conditions in the Blue Nile and its tributaries (Conway, 2000; Mishra et al., 2003). To remedy these data gaps, several models of the Blue Nile Basin that simulate the hydrological responses of extreme climate and environmental changes have been developed, including the work by Conway (1997), Tarekegn and Tadege (2005), Johnson and Curtis (1994), Kebede et al. (2006), and others. These analyses indicated that water balance models were clearly the model format of choice to simulate watershed hydrology owing to its simplicity and effectiveness, even with limited data inputs. Both Mishra et al. (2004) and Conway (1997) developed grid-based water balance models for the Blue Nile Basin using monthly discharge data from the El Diem Station in Sudan, near the Ethiopian border, in order to study the spatial variability of flow parameters and the sensitivity of runoff to changes in climate, respectively. The El Diem Station collected discharge data from the whole Blue Nile Basin in Ethiopia from the 1960s to the present. Although the model predicted the discharge at the station well, it provided limited insight into the spatial variability and distribution of the flow within the basin itself. As an alternative to large-scale basin modelling, hydrological modelling of watersheds is also relevant, especially to gain insight into the particular hydrological conditions throughout the larger basin and how these conditions affect the important agricultural practices of many Ethiopian communities. Johnson and Curtis (1994) used short-duration ( PET) or the moisture content is above field capacity, the moisture storage, St , is determined from the addition of the previous day’s moisture Stt L to the difference between P and PET , during the time step. Conversely, when evaporation exceeds rainfall (i.e. P < PET) and the moisture content of the soil is at or below field capacity (dry conditions), actual evapotranspiration, AET , (mm), decreases linearly from the potential rate at field capacity to zero at the wilting point (Thornthwaite and Mather, 1955; Steenhuis and van der Molen, 1986): St AET D PET 2 Tmax The available soil storage capacity per unit area, Tmax , (L) is defined as the difference between soil storage at wilting point and the threshold value when the watershed becomes active and varies with landscape position and depth to a soil restrictive layer. On the basis of Equation 2, when the soils dry out (i.e. P < PET) the soil surface storage at time step t can be written as an Hydrol. Process. 23, 3718– 3727 (2009) DOI: 10.1002/hyp
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A SEMI-DISTRIBUTED WATER BALANCE MODEL FOR THE ETHIOPIAN HIGHLANDS
exponential function (Lyon et al., 2004): P PETt when P < PET St D Stt exp Tmax 3 In the original procedure of Thornthwaite and Mather (1955), accumulated potential water loss (APWL) was used to calculate the soil storage. Equation 3 gives identical results but is simpler to implement in a spreadsheet program. When rain exceeds evaporation, the net precipitation is added to the previous day’s storage St D Stt C P PETt when P < PET
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If the precipitation fully saturates the soil, any moisture above saturation becomes either surface runoff or percolates to the aquifers Exm , and can be determined by adding the change in soil moisture from the previous time step (Stt ) to the difference between precipitation and AET Exm D Stt C P PET St D Tmax
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Tmax is considered to be uniform across the watershed when the water balance is applied in temperate climates (Steenhuis and van der Molen, 1986). In monsoon climates, this assumption is not valid because the watershed dries out differentially, and runoff occurs only when the soil saturates, so that the watershed wets up differentially. In the modelling framework, this means that various parts of the watershed start to contribute at different times when they become hydrologically active. In other words, there is a ‘threshold’ effect at which the effective water storage of an area must be satisfied before it becomes active. The total runoff and percolation during a storm event is the sum of the runoff contributed by each of these watershed regions. As mentioned before, we assume that above the threshold Tmax value the excess moisture is partitioned between percolation and runoff. This is similar to the procedure developed by Easton et al. (2008) for SWAT that can simulate saturated areas. Percolation (Perc) and saturated excess runoff (R) are Perc D ˇ Exm R D 1 ˇ Exm
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where ˇ is the coefficient that determines the division between runoff and percolation and is used as a calibration parameter. Perc, (L/T) is added to a baseflow reservoir, RS, (L/T), at each time step (Easton et al., 2007): RSt D RStt C Perct BFtt t
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where BFt is the modelled amount of baseflow (LT1 ) and is calculated using a linear reservoir model as follows: [1 expa t] BFt D RSt 10 t Copyright 2009 John Wiley & Sons, Ltd.
where a (T1 ) is the recession coefficient, a property of the aquifer, and can be calibrated from the baseflow recession curve, and t is the time step. DATA INPUTS Rainfall and evaporation were key input data for modelling all the watersheds. Each watershed was also divided into a series of contributing areas with different Tmax , or effective soil moisture storage. This storage must be filled before runoff is created. Two base flow parameters—base flow recession and fraction of the water in excess of Tmax being lost to percolation—were also applied. The models are most sensitive to rainfall data. The rainfall data and other model inputs and parameters from each of the watersheds are described in the following sections. SCRP research sites Daily and weekly hydrology data, including rainfall (P), evaporation (ET ), and discharge (Q) from three research sites (Maybar, Anjeni, and Andit Tid) in the Nile basin were used to calibrate and validate the model. Hydrological data were collected from 1982 to 1993 with overlap for all three stations from 1985 to 1992. The SCRP watersheds all receive >1000 mm of rainfall per year, which is sufficient for sustainable crop production. The annual rainfall in both Andit Tid and Maybar watersheds commonly occurs in a bimodal distribution, with short rains between March and May contributing only 20% and 19% of the total rainfall. In the Anjeni watershed, the annual rainfall mostly occurred between May and October in a unimodal distribution. The major rainfall during the recognized main rainy season between June and September accounts for 61%, 75%, and 67% of the total annual rainfall in Andit Tid, Anjeni, and Maybar watersheds respectively. Table II provides a summary of the hydrological data for the three SCRP monitoring sites. Anjeni has the highest rainfall (P) and highest PET of the three catchments. However, the discharge was slightly less than the discharge at Andit Tid. Andit Tid has a humid climate with the lowest average daily temperature of the sites, but the greatest average annual discharge. Along with the lowest rainfall, Maybar also produced the lowest annual runoff (430 mm). The annual runoff coefficients from the data for Maybar, Anjeni, and Andit Tid are 30%, 42%, and 49% respectively. Yeku watershed In the Yeku watershed, the daily rainfall and evaporation data collected from June 2003 to May 2004 were Table II. Annual hydrological data for the SCRP monitoring sites
Maybar Anjeni Andit Tid
°C
P (mm)
PET (mm)
Q (mm)
16Ð4 16Ð0 12Ð6
1443 1663 1478
1177 1555 1159
430 700 723
Hydrol. Process. 23, 3718– 3727 (2009) DOI: 10.1002/hyp
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used in addition to daily and storm event flows. During the hydrological assessment, the daily rainfall was measured using both automatic and manual rain gauges. Potential evaporation rates were determined from pan evaporation values adjusted with a pan coefficient of 0Ð75. The runoff was gauged manually. Daily flow and storm events were measured near the terminus of two small rivers (Weleh tributary and Yeku) flowing through the watershed and totalled into weekly discharge volumes. The Yeku watershed is characterized by low rainfall and high evaporation compared to the other data sets in this study. Annual rainfall of 625 mm and annual evaporation of 1954 mm (average 5Ð1 mm/day) from June 2003 to May 2004 with nearly half (48Ð1%) falling in the month of August 2003. The annual rainfall amount was relatively low considering an average annual rainfall of 800 mm that was previously mentioned (Mekonnen et al., 1999). However, we have been unable to locate reliable hydrological data from studies other than those from the current research. Nevertheless, rainfall is very erratic and varies spatially and temporally over the watershed and throughout the region. As with rainfall, flow in the Yeku River is limited to the rainy season and persists at a very low rate after the rains have ended. Subsurface (inter and base flow) that causes the river flow after the surface runoff has stopped was measured to be approximately 0Ð06 mm/day in the rainy season.
CALIBRATION AND VALIDATION The data were divided to provide data sets for both calibration and validation: SCRP watersheds from 1988 to 1989 (Maybar has substantial missing data during 1990 and 1991) and from 1992 to 1996 for validation. The selection of the data sets for calibration and validation was based on the availability of continuous data. Because flow data for the Yeku watershed were available only for one season, these data were used to test the potential of the model only. Better calibration and validation is contingent on the availability of further data from Yeku. The threshold values (Tmax ) and contributing area (percent of total area) of each of the watershed sections were key parameters used to calibrate the model. Besides Tmax , the parameters affecting the baseflow (Equation 10) were also calibrated for the SCRP watersheds so that the model better predicted the river flow persisting after the end of the rainy season. In the Yeku River, the baseflow is generally a very small fraction of the total flow during the rainy season and nearly non-existent after October; so the recession coefficients described in Equation 6 and the baseflow reservoir (Rs ) in Equation 10 were zero. The fraction of the water in excess of Tmax being lost to percolation varied between the different watersheds, ranging from 0Ð4 in Yeku to as high as 0Ð8 in the SCRP watersheds (Table III). Table III summarizes the range of rainfall (P), PET , and discharge (Qobs ) observed in the watershed. Because most of the Copyright 2009 John Wiley & Sons, Ltd.
Table III. Description of the parameters and range of values for the parameters for Anjeni, Andit Tid, Maybar, and Yeku watersheds Anjeni Time step Daily Adjusted precipitation (mm) Maximum 87 Minimum 0 Mean 4Ð5 PET (mm) Maximum 7Ð0 Minimum 0Ð3 Mean 4Ð2 Discharge, Q (mm) Maximum 29 Minimum 0Ð1 Mean 1Ð9 Baseflow estimation Fraction of 0Ð8 excess to percolation Recession 0Ð1 coefficient
Andit Tid Daily
Maybar Daily
Yeku Weekly
102 0 4Ð1
71 0 3Ð8
143 0Ð0 12Ð0
7Ð0 0Ð0 3Ð2
7Ð0 0Ð0 3Ð2
67 18 37
61 0Ð0 2Ð4
38 0Ð0 1Ð1
28 0Ð0 3Ð3
0Ð8
0Ð8
0Ð4
0Ð2
0Ð2
0Ð0
available data begin in January, well into the dry season, the initial soil moisture was considered to be negligible. By running model simulations and varying Tmax for each section of the watershed with varying contributing areas, percolation fraction, and recession coefficient, a model efficiency coefficient (E) commonly used to assess the predictive power of hydrological models developed by Nash and Sutcliffe (1970) was optimized. For each watershed, an efficiency coefficient closest to 1 was sought because it indicated a good match between modelled and observed data. The performance of the model during the calibration and validation period was evaluated using the efficiency coefficient, the root mean squared error (RMSE), and the normalized RMSE%, or the RMSE divided by the range of the observed data. Means, standard deviations, minimums, and maximums of the model input parameters, including precipitation, evaporation, and discharge, were also calculated.
MODEL RESULTS The available precipitation, PET, and daily, weekly, or monthly discharge data of the four watersheds were incorporated into the model in several Microsoft Excel spreadsheets. The water balance model developed in this study was tested with data from different areas of Ethiopia with varying time steps. The model generated discharge from existing precipitation (P) and evaporation (E) data using available water content as a storage threshold within subdivided areas of a watershed. For each time step, an example of the model and the value of each of the parameters used for the different watersheds is presented. Hydrol. Process. 23, 3718– 3727 (2009) DOI: 10.1002/hyp
A SEMI-DISTRIBUTED WATER BALANCE MODEL FOR THE ETHIOPIAN HIGHLANDS
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1992, for Andit Tid (A), Anjeni (B), and Maybar (C) watersheds. The model often underestimates discharge generated from rainfall events greater than 50 mm/day. The comparison of observed and predicted data includes the calibration and validation periods, and, in the case of Anjeni, the validation period was decreased to 2 years (1992–1994) because there were missing data in 1995 and 1996. However, validation periods for Andit Tid and Maybar extended from 1992 to 1996. The calibration period for all three SCRP sites was the same (1988–1989). The Anjeni was divided into four separate areas with Tmax ranging from 100 to 4000 mm and
Figure 2. Comparison of observed (solid line) and predicted river discharge (shaded area) and rainfall (solid lines downwards) from 1988 to 1996 in the (A) Andit Tid Watershed, (B) Anjeni Watershed, and (C) Maybar Watershed. Observed discharge data was lacking from 1995 and 1996 for Anjeni, precipitation and observed discharge data was lacking from 1990 to 1991 for Maybar
SCRP watersheds: daily time step The SCRP monitoring watersheds provided the most comprehensive data compared, and the modelled period for this time step extended from 1988 to 1996. These watersheds are also small in area, all less than 500 ha. Figure 2A–C presents comparisons of the modelled discharge and the actual measured discharge (observed) data for Andit Tid (A), Anjeni (B), and Maybar (C) watersheds for daily values over the entire duration of analysed data. Figure 3A–C provides a comparison of modelled and observed discharge for a single year, Copyright 2009 John Wiley & Sons, Ltd.
Figure 3. Comparison of observed (solid line) and predicted river discharge (shaded area) and rainfall (solid lines downwards) from a single year, 1992, in the (A) Andit Tid Watershed, (B) Anjeni Watershed, and (C) Maybar Watershed Hydrol. Process. 23, 3718– 3727 (2009) DOI: 10.1002/hyp
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area contributions from 15–40%. The Tmax and area were optimized for each watershed. Although located several hundred kilometres apart, the three watersheds’ parameters were nearly identical except one value for the Andit Tid watershed. While Anjeni and Maybar tended to have higher Tmax values, Andit Tid required a very low value of Tmax in place of the highest value (4000 m with an area contribution of 20%) of Anjeni and Maybar. This was necessary to increase the area of shallow storage to compensate for the exposed subsoil in Andit Tid and subsequent runoff created from the first rainfall after the dry season. A summary of the Tmax and contributing areas for the three SCRP sites is shown in Table IV. The Tmax indicates that the evaporation during the dry season resulted in a 4000 mm moisture deficit that needed to be replaced before the area became hydrologically active. The shallow storage in over half the area of the watersheds simulated the higher runoff response producing more runoff, while the deeper storage capacity in 35% of Anjeni and Maybar may be necessary to offset shallower slopes and lower runoff coefficient in these watersheds.
Figure 4. Comparison of observed (solid line) and predicted discharge (shaded area) from the Yeku River for the 2003 rainy season
of the watershed cover a small area, and these soils have high infiltration capacity, delaying any flow from these areas. Consequently, the storage on these slopes is higher than that in other areas of the landscape. Model analysis
Yeku watershed: weekly time step
Parameterization of the model was based on optimizing the Nash–Sutcliffe efficiency coefficient (E) as it considers how well the fluctuations in the modelled discharge coincide with those of the observed data and how well the model predictions agree with the observed data. The RMSE and the normalized RMSE % indicate the degree to which the model predictions deviate from the observed data. The RMSE has limitations because different time steps were used in the simulations of different watersheds, which affect the RMSE . For example, the daily RMSE is much lower than monthly RMSE because the actual data points represent cumulative discharge over an individual time step. Therefore, RMSE % was used because it considers the error over the range of the data. Together, the E and RMSE (%) provide insight into the performance of the model. Table V provides the statistical analyses of the model performance for all four watersheds studied. The efficiency of the model is quite good in the watersheds, ranging in efficiency from 0Ð56 to 0Ð86 in either calibration or validation periods on a daily time step. However, a relatively high efficiency does not always indicate good model performance, as in the case of the Yeku Watershed (Table V). As the
Modelling the Yeku Watershed proved to be the most difficult because continuous data were lacking and the only available data were collected manually at variable time intervals (
