Determining watershed response in data poor environments with remotely sensed small reservoirs as runoff gauges

Transcription

1 WATER RESOURCES RESEARCH, VOL. 45,, doi: /2008wr007369, 2009 Determining watershed response in data poor environments with remotely sensed small reservoirs as runoff gauges J. R. Liebe, 1,2 N. van de Giesen, 3 M. Andreini, 4 M. T. Walter, 1 and T. S. Steenhuis 1 Received 18 August 2008; revised 15 February 2009; accepted 22 April 2009; published 14 July [1] In the semiarid regions of Africa, there are many small reservoirs used for irrigation. This study explores the practicality of using small reservoirs as runoff gauges by estimating their water storage changes using remote sensing imagery. A simple rainfall-runoff model is developed by observing the surface area and estimating the volume of eight small reservoirs in the Upper East Region of Ghana and in Togo using Envisat advanced synthetic aperture radar satellite images. The model is based on the Thornthwaite-Mather procedure and the assumption that with increasing precipitation, the contributing watershed area increases exponentially. The model parameters were estimated using the 2005 data and were validated using 2006 data. Although the total rainfall amounts were comparable in these 2 years, the rainfall and reservoir filling patterns were quite different. The model results indicate that the overall impact of the reservoirs largely depends on the ratios of reservoir to watershed areas. For this 2 year study, the reservoirs captured on average 34% of quick flow and 15% of overall runoff. Citation: Liebe, J. R., N. van de Giesen, M. Andreini, M. T. Walter, and T. S. Steenhuis (2009), Determining watershed response in data poor environments with remotely sensed small reservoirs as runoff gauges, Water Resour. Res., 45,, doi: /2008wr Introduction [2] In semiarid Africa, governments and communities have difficulty managing water supplies because of hydroclimatic variability and ever increasing population pressure. Uncertainty arises because of a lack of information, poor understanding of hydrological processes, and absence of suitable models for these environments. In international river basins, this uncertainty leads to unnecessary tension since equitable sharing and utilization of water resources is difficult in the absence of informed planning and coordinated development. [3] Although more and more data are becoming available on a regional basis with the World Hydrological Cycle Observing Systems (WHYCOS) framework [World Meteorological Organization, 2005], watershed interventions, such as the construction of small and intermediate sized reservoirs, cannot be studied using regional water balances. Small reservoirs increase the reliability of water supplies at the local level, but may reduce the overall yield from a watershed. In the Volta basin, the construction of small reservoirs is hotly debated because they may reduce 1 Biological and Environmental Engineering, Cornell University, Ithaca, New York, USA. 2 Department of Ecology and Natural Resource Management, Center for Development Research, University of Bonn, Bonn, Germany. 3 Water Resources Section, Civil Engineering and Geosciences, Delft University of Technology, Delft, Netherlands. 4 International Water Management Institute, Washington, D. C., USA. Copyright 2009 by the American Geophysical Union /09/2008WR the flow to Lake Volta that stores water for the major hydroelectric generating plant in Ghana. [4] In order to improve our understanding of the impact of small reservoirs on downstream flows, these reservoirs themselves can be used as runoff gauges by remotely measuring their surface areas and converting these measurements to volume estimates with the regional area-volume relationship developed by Liebe et al. [2005]. Several studies have been published on mapping or monitoring reservoir surface areas with satellite images of small reservoirs [White, 1978; McFeeters, 1996; Frazier and Page, 2000]. Mialhe et al. [2008] estimated small reservoir storage volumes from Landsat images in India. Meigh [1995] quantified the impact of small farm reservoirs in Botswana on larger reservoirs downstream using field data. None of the other studies quantified the reservoirs impact on the downstream water resources because of the lack of suitable hydrological models, and none used the reservoirs as runoff gauges. [5] Satellite images for mapping the small reservoirs can be obtained from optical (i.e., Landsat, Spot, Aster, ISS, etc.) or radar satellite systems (Envisat, ERS, Radarsat, etc.). While optical systems are easier to process, surface observations are often hindered by clouds. Radar remote sensing is not affected by cloud cover and has an advantage over optical remote sensing platforms of being capable of acquiring time series under frequently cloudy conditions. The detection of water bodies on radar images can be affected by windinduced waves, and vegetation context [Liebe et al., 2009]. [6] The objective of this research is to show how in a data scarce environment, such as Ghana, remote sensing of existing reservoirs can be used to characterize runoff 1of12

2 LIEBE ET AL.: DETERMINING WATERSHED RESPONSE IN DATA POOR ENVIRONMENTS Figure 1. Location of eight reservoirs (small solid circles) and the associated watersheds (shaded) in the eastern part of the Upper East Region of Ghana and northern Togo ( N N, W E). The numbers correspond to the reservoirs as numbered in the text. processes. In particular, we will see if existing reservoirs can be used as runoff gauges to test a runoff model by remotely sensing reservoir sizes over time. 2. Study Area and Hydrology [7] The Upper East Region of Ghana, and northern Togo (Figure 1) are characterized by a monomodal rain season from July to September with almost 1000 mm of average annual rainfall, and 2050 mm of average annual potential evaporation (data from Ghana Meteorological Agency, 2006). Small reservoirs are typically located at the top of larger watersheds. Overland flow commonly plays a secondary role in these regions, as infiltration rates are generally high and storm durations are short [Masiyandima et al., 2003; van de Giesen et al., 2000, 2005]. The quick response to rainfall is mainly due to interflow. Distinct inflow channels into the reservoirs are usually absent. Runoff generation in semiarid areas typically follows a distinct pattern. The first rains at the start of the wet season wet up the soil that is dried out after the extended dry season. These rains produce very little runoff. Only after the soils are above field capacity does water flow from the watershed to the reservoir. The contributing area increases with the size of the storms. [8] In the study region, small reservoir storage volumes can be estimated as a function of their surface areas [Liebe et al., 2005] with V ¼ 0:00857 A Res 1:4367 ð1þ where V is the volume of a reservoir (m 3 ), and A Res is its area (m 2 ). Since the sides of these reservoirs have gentle slopes, minor changes in depth result in relatively large surface area changes. 3. Materials and Methods 3.1. Determination of Small Reservoir Volumes, Watershed Sizes, and Climatological Data [9] The basic assumption behind this research is that small reservoirs can be used as runoff gauges. Reservoir surface areas were extracted from twelve Envisat advanced synthetic aperture radar (ASAR) images from 21 May 2005 to 15 August 2005, and from 13 June 2006 to 15 August 2006, covering the end of the dry season, the onset of the rainy season, and the early rainy season. Envisat ASAR is a C band radar, which provides images at a spatial resolution of 30 m [Gardini et al., 1995]. The images used in this study were acquired in dual polarization mode (HV/HH), which also has been found useful in flood studies by Henry et al. [2006]. The reservoir surface areas were extracted from the radar images using a quasi-manual classification approach, which is based on training areas digitized inside the water bodies [Liebe et al., 2009]. By combining reservoir surface areas with the known relationship between reservoir volume and surface area (equation (1)), changes in reservoir storage can be calculated. [10] The watershed of each reservoir was delineated using SRTM V3 elevation data (A. Jarvis et al., Hole-filled seamless SRTM data V3, 2006, which have a spatial resolution of 90 m, and a relative 2of12

3 LIEBE ET AL.: DETERMINING WATERSHED RESPONSE IN DATA POOR ENVIRONMENTS Table 1. Penman Reference Evaporation Rates From Long-Term Averages for the Meteorological Station Navrongo a Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Pen ET 0 (mm d 1 ) a Data are from Ghana Meteorological Agency (2006). Averages are for Navrongo station is at N, W, m asl. vertical accuracy of better than 10 m. After performing a pit removal procedure, the stream network was extracted, and the reservoirs watershed boundaries were determined with Idrisi software by choosing the dam wall as the seed point. The reservoir surface is included in the total watershed area, A (WS+Res). For the hydrological modeling, although the overall effect may be very small, a reduced watershed area, A WS, is used, which is obtained by subtracting the timedependent reservoir area, A Res, from the total watershed area A (WS+Res) (i.e., A WS = A (WS+Res) A Res ). [11] Rainfall estimates were obtained from the Famine Early Warning Systems Network (Satellite/image data, 2007, The FEWS NET rainfall estimates are a computer-generated product with a horizontal resolution of 10 km based on Meteosat infrared data, rain gauge reports, and microwave satellite observations [Xie and Arkin, 1997]. Monthly means of daily evaporation rates were obtained from the Meteorological Station in Navrongo, Ghana ( N, W, Table 1), and were generally in the range mm d 1 during the period of study from May to August Calculation of Watershed Discharge From Changes in Volume of a Small Reservoir [12] To determine the hydrological watershed response, the reservoir storage increase through direct rainfall on the reservoirs has to be subtracted. Since the remotely sensed reservoir surface areas are only available at intervals of approximately 14 days, and not necessarily on days when it rained, the reservoir area changes occurring between image acquisition dates were estimated. When reservoirs become larger, the reservoir areas are assumed to increase on dates with significant rainfall, while on the dry days, the reservoir areas were assumed to have remained the same: For A Res t > A Res t n and t n t t 8 A Res t 1 >< A Rest ¼ þ N n ð A Res t A Res t n Þ; for wet days >: A Res t 1 ; for dry days where n represents the number of days between two consecutive image acquisitions taken at time t and t n, N is the number of wet days in this time period, and A Res is the remotely sensed reservoir area. On the basis of Acheampong s [1988] definition of a wet month, a day is considered wet when the rainfall in the ten preceding days exceeds 34 mm, and rainfall exceeds potential evaporation on that day, i.e., ð2þ wet day t ¼ Xt 10 P i > 34 mm ^ P t E pott > 0mm ð3þ i¼t where on a day t, P t is the depth of precipitation and E pott is potential evaporation. When the reservoir decreases in size, a different interpolation procedure is followed with the reservoir area decreasing on dry days and remaining constant on wet days, i.e., for A Res t < A Res t n and t n t t A Rest 8 A Res t 1 ; for wet days >< ¼ >: A Res t 1 n N n ða Res t n A Res t Þ; for dry days [13] The volume of water in the reservoir increases because of quick flow which is interflow from the watershed and precipitation on the reservoir. The volume decreases because of evaporation from the reservoir. Reservoirs are used for irrigation during the dry season, but the abstraction for irrigation generally occurs between November and April and has no effect on the model calibration. The change in reservoir volume V between two subsequent images at time t n and t, equals DV t ¼ V t V t n where V is the total volume of the reservoir at the time indicated by the subscript. The increase in the volume of water due to inflow from the watershed, DV WS, can be calculated by taking the change of volume, DV t, estimated from the areas taken from the satellite imagery and equation (1), and then subtracting the net change due to evaporation and rainfall of the reservoir itself, DV Res : DV WS ¼ DV t DV Res DV Res (L 3 ) can be calculated as DV Res ¼ A Res t A Res t n 2 " # X t P t E pot t Ksat Dt t 1 where E pot (L/T) is the potential evaporation, P (L/T) is the rainfall and K sat (L/T) is the leakage from the reservoir. In this region, thick clay layers are typically found in the subsoil [Edmonds, 1956]. According to Rawls et al. [1983] saturated hydraulic conductivity, K sat, of clay is 0.1 mm d 1. This is equal to 3 mm month 1 and is small compared to the amount of evaporation. [14] Figure 2 shows the procedure of calculating DV t from DV Res and DV WS. Circles indicate the total reservoir storage, V, estimated from Envisat ASAR images. The storage volume on the first date represents the amount of water that remained in the reservoir after the end of the dry season, and serves as a reference level for storage change. ð4þ ð5þ ð6þ ð7þ 3of12

4 LIEBE ET AL.: DETERMINING WATERSHED RESPONSE IN DATA POOR ENVIRONMENTS Figure 2. Evolution of the water volume in reservoir 2 during the 2005 rainy season. Circles depict satellite-based reservoir storage volume estimates. V Res represents the water that fell directly on the reservoir minus the evaporation from the reservoir, and V WS is volume of water that flowed from the watershed. The part of the reservoir storage change, DV Res, due to rainfall and evaporation on the reservoir is calculated with equation (7). The volume entering the reservoir from interflow, DV WS, can be calculated by taking the difference with equation (6). The contribution of the watershed to the reservoir storage volume, DV WS, is used to estimate parameters for the rainfall-runoff method described below Prediction of Watershed Discharge [15] Data availability in Ghana is relatively poor. Fully distributed hydrological models are, therefore, not appropriate. Instead, we look for models with only a few parameters, which capture the main hydrological characteristics of the area. To do so, it is important to understand the hydrology of the landscape. The watershed plan view and profile in Figure 3 shows sandy soils overlaying an impermeable layer of clay or laterite, and exposed laterite in the other areas. The laterite has a relatively low conductivity but rainfall can infiltrate either during the storm or shortly thereafter. This water is not moving laterally because both the gradient and the conductivity are low. Most of this water is used by deep rooted shrubs that are green even in the long dry season, especially along the fissures in the rock. Some of the water ends up in springs. In the sandy area, the water percolates to the laterite layer and then moves laterally to the reservoir. The fact that there is still sand in some locations indicates that there is no significant overland flow. [16] We envision the runoff generating process as follows. After the long dry period the soils are dry (the moisture content at wilting point). The first rains wet up the soil and crops start growing. Water percolates down when the root zone is above field capacity, raising the water table, and inducing lateral flow to the valley bottom [Masiyandima et al., 2003]. Water flow stops again after either the water table is horizontal or the water table disappears. Field capacity changes throughout the watershed so the area that percolates to the groundwater increases with precipitation after the threshold of the soil with the lowest field capacity is exceeded. This is similar to the Figure 3. TM model scheme with plan view and cross section of conceptual watershed. The soils storage at field capacity (S max ) is defined in equation (9), and the available water in the soil reservoir is regulated by evaporation and precipitation. When S max is exceeded, the excess water is discharged of as percolation (P*), which can be separated into quick flow (Q f ) which reaches the reservoir and groundwater recharge (GW). The Q f fraction of P* depends on the extent of the saturated area, which is parameterized by a. 4of12

5 LIEBE ET AL.: DETERMINING WATERSHED RESPONSE IN DATA POOR ENVIRONMENTS concept of an expanding contributing area introduced by Hursh [1936] and Hoover and Hursh [1943]. Increasing contributing areas have also been observed in the semiarid climates by Masiyandima et al. [2003] and Liu et al. [2008]. [17] There are several studies showing that this type of conceptual model is reasonable. In Niger, Peugeot et al. [2003] and Cappelaere et al. [2003] observed that there was good agreement between storm rainfall and runoff [Peugeot et al., 2003, Figure 10]. Their observations are consistent with a variable contributing area concept where runoff is independent of rainfall intensity but depends on total rainfall. Masiyandima et al. [2003] observed a double peaked hydrograph in Côte d Ivoire where the first peak originated from saturation excess runoff from the inundated valley bottom and the second peak was delayed subsurface flow from the sandy soils bordering the valley bottom. [18] For our conceptual model, the water balance for the root zone can be written as S t ¼ S t Dt þ ðp E act P* ÞDt ð8þ where P is precipitation (L/T), E act is actual evaporation (L/T), and S t Dt is the previous time step storage in the root zone per unit area (L). P* is the percolation (L/T) out of the root zone, Dt(T) is the time step, and S t (L 3 /L 2 )is the volume of water stored in the root zone above wilting point per unit area at time t. For simplicity we do not use a subscript here other than for the storage in the root zone. The amount of water that is available for percolation is the fraction of net precipitation (i.e., precipitation minus actual evaporation) that exceeds the soil s field capacity. [19] One of the methods that works well for calculating percolation and actual evaporation in the water balance equation (8) is the Thornthwaite-Mather (TM) procedure [Thornthwaite and Mather, 1955] which has been successfully applied throughout the humid tropics [Peranginangin et al., 2004], and in semiarid areas [Norman and Walter, 1993; Taylor et al., 2006]. It is modified to predict the increasing fraction of the percolation water reaching the reservoir with increasing rainfall quantities. [20] In the TM procedure (Figure 3), the root zone storage at field capacity is called S max, and is equal to the volume of water between field capacity and wilting point in the root zone per unit area, e.g., S max ¼ d rz q fc q wp where d rz is the root zone depth (L), q fc is the moisture content at field capacity, and q wp is the moisture content at wilting point. [21] Percolation occurs when rainfall exceeds potential evaporation (i.e., P > E pot ), and actual evaporation, E act,is equal to potential evaporation, E pot. Percolation, P*, can then be written as ð9þ P* ¼ S t Dt S max þ P E pot Dt ð10þ [22] The soil always drains to field capacity within the time period, thus we find for the storage in the soil that S t ¼ S max ð11þ In the Thornthwaite and Mather procedure the actual evaporation, E act, is calculated when the potential evaporation exceeds rainfall (i.e., P < E pot )[Steenhuis and van der Molen, 1986]. In this method, E act decreases linearly with moisture content: S t E act ¼ E pot P þ P S max ð12þ [23] When P < E pot, the storage in the root zone (above the wilting point) can be obtained by integration of ds equation (12), recognizing that t dt = E act + P, and using the initial condition that on day t Dt the storage equals S t Dt : P E pot Dt S t ¼ S t Dt exp when P < E pot S max ð13þ [24] The original Thornthwaite-Mather procedure used a slightly different procedure for calculation by hand. Equation (13) gives the same results but is convenient for inclusion in spreadsheets. [25] Percolation through the root zone flows either to the deep groundwater or toward the reservoirs as quick flow or interflow. Quick flow, Q f, is the amount of percolation that reaches the reservoir (Figure 3). This leads to an increase in reservoir volume of DV WS. The fraction of the percolation that recharges the reservoir, Q f, increases with rainfall. Conceptually, as discussed above, we can explain this as an increase in contributing area to the reservoir, which becomes larger when rainfall amounts increase [Liu et al., 2008]. This relationship between contributing area and percolation amounts is not known. Such a relationship should meet the boundary conditions that the contributing area is zero when rainfall just wets up the soil to field capacity (and the percolation P* = 0), and the area should be equal to 1 when rainfall approaches infinity. Then the runoff rate should equal the precipitation rate. There are a limited number of expressions that have such a property. The well known SCS equation is an example of such an expression [Steenhuis et al., 1995]. Another such expression with a slightly more physical meaning that seemed to fit the data well is the following: Q f ¼ P* ð1 expð a P* ÞÞ ð14þ where a is a constant, which is an indicator of how fast the contributing area is increasing. Figure 4 depicts the production of Q f as a function of P* and different a values. As shown by Steenhuis et al. [1995], we can differentiate equation (14) with respect to P* to obtain the contributing area A f, i.e., A f ¼ 1 þ ða P* 1Þ expð a P* Þ ð15þ We can see that equation (15) has the required property of A f = 0 when P* = 0, and A f = 1 when P*!1. [26] The records for the eight reservoirs are divided into 2 years. The parameters S max and a are calibrated using the 2005 data, and then validated using 2006 data. In principle, one reservoir would have been sufficient for proof of 5of12

6 LIEBE ET AL.: DETERMINING WATERSHED RESPONSE IN DATA POOR ENVIRONMENTS Figure 4. Quick flow, Q f, as a function of the percolation, P*, for different watershed factor a (equation (14)). concept. Here, eight reservoirs were used to increase the trust in the overall method. This replication is especially needed because there is no independent measurement of the independent variable, being the cumulative runoff as measured through satellite observed changes in reservoir surface areas. The repeated concurrence of indirectly observed and modeled runoff shows that the errors are within acceptable margins. 4. Results 4.1. Watershed and Reservoir Sizes [27] The watersheds extracted from the SRTM DEM, including the reservoirs, range from 144 to 1829 ha (Table 2). The results of the reservoir surface area classification obtained from the radar image analysis are listed in Table 3. Reservoir storage volume estimates were made using equation (1) and the observed reservoir surface areas. This time series of reservoir storage volumes is the basis for the calibration of the runoff model Calibration and Validation of Watershed Discharge Predictions With the Simple Model Rainfall Characteristics [28] In 2005, the rainy season could be segmented into three to five wet periods with distinct dry spells in between. In 2006, there are only three wet periods, which were separated by only short dry spells. Figure 5 shows the results of the wet day, analysis for all watersheds, which is taken here as an indicator of the rainy season. Precipitation is scaled from 0 to 1 with respect to the maximum Table 2. Measured Watershed Area and Calibrated Root Zone Storage, S max, and Watershed Contributing Factor, a Reservoir a Watershed area (ha) S max mean (mm) S max low/high 35/55 35/50 40/50 40/45 20/45 15/35 35/55 20/55 (mm) a a The location of the reservoirs is given in Figure 1. rainfall observed within the 2 years. Although the rainfall in 2006 was, on average, only 3% below the rainfall in 2005, the rainfall patterns were distinctly different. Overall, the 2006 rainy season was shorter and occurred later in the year than the 2005 rainy season. In 2006 there were 67 wet days. Fifty nine percent of rain fell on those days. In 2005, 51% of the total precipitation fell on 63 wet days Model Calibration [29] The records for the eight reservoirs are divided into 2 years. The parameters S max and a are calibrated using the 2005 data, and then validated using the 2006 data. In calibration, the S max determines mainly the time of the first watershed contribution to the reservoir, while a is related to the total quantity of percolation that reaches the reservoir. [30] Figure 6 shows how the parameters are obtained. S max is determined in the time range when the reservoir rises first, i.e., when the first watershed response is observed in the reservoir. Initially, two S max values are determined with the Thornthwaite-Mather procedure. The maximum S max value is determined assuming that the first percolation occurs on the date that the first rise in the reservoir was observed with the satellite image, and the minimum S max values were calculated assuming that the rise occurred at the preceding satellite image acquisition date. In the Thornthwaite-Mather model the mean S max value was used. Table 3. Reservoir Surface Areas Classified From Envisat ASAR Images a Date Reservoir Surface Areas (ha) May Jun Jun Jul Jul Aug Jun Jun Jul Jul Aug Aug a The location of the reservoirs is given in Figure 1. 6of12

7 LIEBE ET AL.: DETERMINING WATERSHED RESPONSE IN DATA POOR ENVIRONMENTS Figure 5. Normalized precipitation patterns and occurrence of wet days for the eight reservoirs in 2005 and The precipitation is depicted with black bars and is scaled from 0 to 1 with respect to the maximum rainfall event observed within the 2 years (minimum 45 mm, maximum 66 mm, and average 56.6 mm). Wet days are depicted in gray. A day is considered wet when the rainfall in the 10 preceding days exceeds 34 mm and the rainfall exceeds potential evaporation on that day. [31] The shape factor value, a, is obtained by visually fitting predicted reservoir inflow with equation (14) to the observed inflow on the basis of volume increases determined with satellite images. The method does not apply once the reservoir is full, because inflows are then routed through the reservoirs over their spillways, and do not result in an increase in storage. For each watershed, the calibrated minimum, maximum and mean values S max, and the shape factor value a are reported in Table 2. The watersheds mean S max values range from 25 to 45 mm, and the a values range from 0.01 to It is remarkable that for these watersheds that are spread over the northern part of Ghana and western part of Togo, similar S max and a values can describe how and when the reservoirs fill up Model Validation [32] The runoff models of all eight watersheds are shown in Figure 7, with the calibration year 2005 (left), and the validation year 2006 (right). To check these predictions the quick flows are accumulated and compared to the observed volumetric storage contribution from the watersheds, DV WS, which were calculated from the remotely sensed reservoir areas with equation (6). The reservoir volumes DV WS are given as equivalent watershed depths (i.e., the reservoir volume divided by the watershed area). In 2005, the first inflow into the reservoirs occurred in early June. Both the increase in volume (obtained from the satellite image and indicated by the triangles) and the simulated results (solid line) are in good agreement. This is not surprising since the 2005 was used for calibration. In 2006, the same parameter sets were used to predict the reservoir response. For this year, the first predicted inflows were in mid July which was in accordance with the observed increase in reservoir storage from the satellite image. The intense rainstorm in the second week of August causes the reservoir to overflow. Also the filling pattern agreed well. Figure 6. Example of reservoir 6, 2005, for the calculations to determine the maximum storage of the root zone, S max, and the watershed parameter, a, that determines the rate at which the saturated areas expand. S max is determined in the period of first observed runoff. The predicted cumulative quick flow, Q f (bold line) is fitted with equation (14) to the observed quick flow volumes (triangles) using the parameter a as a calibration factor. 7of12

8 LIEBE ET AL.: DETERMINING WATERSHED RESPONSE IN DATA POOR ENVIRONMENTS Figure 7. Observed (triangles) and predicted cumulative quick flow (bold line) with equation (14) for (left) calibration year 2005 and (right) validation year In addition, the moisture deficit (gray line defined as E act E pot ), percolation (P*), and precipitation are shown. 8of12

9 LIEBE ET AL.: DETERMINING WATERSHED RESPONSE IN DATA POOR ENVIRONMENTS Figure 7. (continued) 9of12

10 LIEBE ET AL.: DETERMINING WATERSHED RESPONSE IN DATA POOR ENVIRONMENTS Figure 8. Observed and predicted cumulative runoff for (left) 2005 and (right) The year 2005 was the calibration year (r 2 = 0.83), and 2006 was used for validation (r 2 = 0.92). [33] The ability of the model to predict reservoir storages for the other watersheds was also satisfactory. Figure 8 compares the observed reservoir volumes with the predicted cumulative quick flow (Q f ) for the eight watersheds. In both years, the reservoirs were spilling water in August and therefore, images taken on 15 August 2005 and 15 August 2006 were omitted from the analysis, because reservoir area becomes constant and a full reservoir can no longer be used as a runoff gauge. The data obtained from the satellite images and the volumes predicted by the model were well correlated with overall r 2 values of 0.83 in 2005 and 0.92 in Discussion [34] Our results show that remotely sensed reservoirs can be used as a runoff gauges to better understand the hydrology of the landscape. In previous analyses such as by Taylor et al. [2006] it was assumed that the contributing area was constant. Figure 8 shows that after the dry season, at the time that quick flow starts, the Thornthwaite-Mather procedure can be used with a similar storage value for most of Northern Ghana and Northwestern Togo. The portion of the percolation (i.e., amount of rain after the soil is at field capacity) that becomes quick flow increases with rainfall amount because the area that contributes quick flow to the reservoir becomes larger as the storm progresses. [35] It is of interest to examine the rainfall pattern that caused the reservoirs to fill up. In 2005, a total of 211 mm of rain fell prior to 4 June, when the reservoirs started to fill. In 2006, 312 mm of rain fell prior to the first modeled runoff on 20 July. Clearly, total rainfall is not the parameter that determines when the reservoir starts to fill. The model helps us to understand what kind of rainfall pattern starts to fill the reservoir. In the model, quick flow is generated when the soil is at field capacity. This occurs when the precipitation is in excess of evaporation over a period that is more than the amount of water needed to bring the soil to field capacity. Thus, any time when P E pot over a period is more than S max, the reservoir will start filling up. In reality, the filling up will occur earlier, because the soil is not completely dry and the evaporation is not at the potential rate. Despite this, we can see that only during wet periods, when the rainfall is in excess of potential evaporation by an amount of the order 2 4 cm, the reservoirs will start to fill up. In 2006 (Figures 6 and 7) such a period did not occur until the middle of July. [36] The watershed model developed in this paper can be used to estimate the impact of small reservoirs on downstream flows. For each reservoir and year, Figure 9 depicts the fraction of quick flow Q f that is captured in the reservoirs, the fraction of quick flow Q f that spills, and the amount of deep groundwater recharge (P* Q f ). The Figure 9. Impact of reservoirs on water resources. A Res /A WS is the ratio of the reservoir area to the total watershed area, Q f is the quick flow, and GW is groundwater. 10 of 12

11 LIEBE ET AL.: DETERMINING WATERSHED RESPONSE IN DATA POOR ENVIRONMENTS reservoirs are sorted by decreasing A Res /A WS ratios from left to right. On average, small reservoirs captured 34% of the Q f produced in their watersheds, or 15% of the overall runoff. Despite the interannual variations, Figure 9 shows the decreasing impact of reservoirs on the total quick flow Q f and percolation with decreasing A Res /A WS ratios. This result is intuitive. Not included in the analysis is groundwater recharge through seepage from reservoirs, and inefficient application of water in small-scale irrigation systems [Faulkner et al., 2008], which remain available as groundwater downstream. The impact of small reservoirs on available water resources is, therefore, likely to be smaller than the captured Q f fraction shown in Figure 9. [37] An important consideration is to what extent the developed method can be used in other data scarce environments. We need to distinguish between the particular model used, and the method used to derive runoff volumes. The processes described can be found throughout West Africa [Masiyandima et al., 2003; Giertz et al., 2006] and also in Ethiopia [Liu et al., 2008]. The reduced importance of Hortonian flow in areas where it used to be seen as the main source of runoff, can also be found elsewhere, such as in Brazil [Wickel et al., 2008] and Japan [Sidle et al., 2007]. This implies that the region studied here is not an exceptional case. Still, although the method can be used to reject certain model structures, caution is needed because the method cannot be recommended for model identification purposes. The amount of information that can be extracted from storage changes is limited and can only be used for the calibration of relatively simple models. [38] Regarding the applicability of the method used to derive runoff volumes, the most crucial question is whether regional relations can be found that relate surface areas to stored volumes. Presently, we cannot predict such relations on the basis of readily available global data and must rely on bathymetric surveys. Regional area-volume equations have been developed for various regions in Africa, i.e., northern Ghana [Liebe et al., 2005; Annor et al., 2009], northern Côte d Ivoire [Cecchi, 2007], Botswana [Meigh, 1995], and southern Zimbabwe [Sawunyama et al., 2006]. These studies all show good correlations between satellite observable surface areas and stored volumes within given geomorphological regions. As such, we can surmise that the method can be used in most places where small reservoirs are common. It remains to be seen whether the extractable information from infrequently observed cumulative runoff is sufficient to calibrate models which adequately capture the most relevant runoff generating processes outside of West Africa. The strength of this method lies especially in the identification and parameterization of threshold behavior. 6. Conclusion [39] In ungauged basins, small reservoirs can be used as runoff gauges by monitoring their surface areas with remotely sensed time series, and regional area-volume relations. Together with publicly available rain records, the remotely sensed reservoir storage changes were used to calibrate a simple hydrological model. Despite different rain patterns in 2005 and 2006, our model was able to predict runoff in 2006 with the Thornthwaite-Mather parameters S max and a that were determined in the year The reservoir filling process is not determined by total rainfall. Our model is capable of reproducing the observed runoff generation with the concept of expanding contributing areas on the basis of soil moisture storage in the root zone and rainfall. The results developed with our simple hydrological model are consistent with field-based studies. This approach is especially useful in data poor environments. [40] Acknowledgments. This research was conducted as part of the Small Reservoirs Project (CP46), which is funded by GTZ through the Challenge Program on Water and Food. Cooperation with the GLOWA- Volta Project, the Center for Development Research at the University of Bonn, Germany, and the International Water Management Institute, Ghana, to support the field work is also gratefully acknowledged. Cornell University provided support in the form of an assistantship for part of the work. The Envisat images used in this research were obtained through ESA s TIGER Project References Acheampong, P. K. 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