Read Catchment Characteristics as Predictors of Base Flow Index (BFI) in Wabi-shebele River Basin, East Africa text version

Tropentag 2006 University of Bonn, October 11-13, 2006

Conference on International Agricultural Research for Development

CATCHMENT CHARACTERISTICS AS PREDICTORS OF BASE FLOW INDEX (BFI) IN WABI SHEBELE RIVER BASIN, EAST AFRICA

Adane Abebe1 and Gerd Foerch2 1,2 Research Institute for Water and Environment, Civil Engineering Department, University of Siegen, 57068 Siegen, Germany 1 [email protected]

Abstract

The Base Flow Index (BFI) is used as a measure of the base flow characteristics of catchments. It provides a systematic way of assessing the proportion of base flow in the total runoff of a catchment. It indicates the influence of soil and geology on river flows, and is important for low flow studies. Nowadays extreme low flow events are more diligently analysed and given focus in the emerging field of ecohydrology. However, many of the catchments in developing countries are ungauged, thus, it is often difficult to get recorded data on base flows of rivers. This paper seeks to establish a relationship between the climatic, morphologic and geologic features of a catchment to its base flow in the Wabi Shebele river basin, East Africa. It employs the parameters catchment size, stream density, climate index, hypsometric integral, normalized digital vegetation index (NDVI) extracted from satellite images and geologic features to derive the base flow index of a catchment. Values of base flow index determined for a network of stream flow gauges are matched to the composite morphometric and climatic data using spatial and regression analyses. To relate the BFI to a usable flow statistic, a relationship was derived between BFI and Q70, the point on the flow duration curve at which flows are exceeded 70% of the time. Q70 was chosen because it is the critical point that has been most often used in most previous works. The BFI has a strong relationship with NDVI, climate and geology. Catchments with high climate index (high rainfall or low evapo-transpiration) underlain with granites or basalt tend to give high base flow. Among the topographical parameters tested, drainage density index has better relationship with BFI. The developed relationship can be used for fairly estimating the base flows in the river basin considered. However, in view of the tremendous spatio-temporal heterogeneity of climatic and landscape properties extrapolation of response information or knowledge from gauged to ungauged basins remains fraught with considerable difficulties and uncertainties.

Key words: Base flow index, catchment characteristics, GIS, ungauged basins, Wabi-Shebele river

1. Introduction Understanding the relative importance that ground water discharge plays in maintaining stream flows is essential. River systems are often augmented by their base flows during lean seasons. The Base Flow Index (BFI) is used as a measure of the base flow characteristics of catchments. It provides a systematic way of assessing the proportion of base flow in the total runoff of a catchment. It indicates the influence of soil and geology on river flows, and is important for low flow studies. Nowadays extreme low flow events are more diligently analysed and given focus in the emerging field of ecohydrology. However, many of the catchments in developing countries are ungauged, thus, it is often difficult to get recorded data on base flows of rivers. This paper seeks to establish a relationship between the climatic, morphologic and geologic features of a catchment to its base flow in the Wabi-Shebele river basin, East Africa. It employs the variables catchment size, stream density, climate index, hypsometric integral, normalized digital vegetation index (NDVI) extracted from satellite images and geologic features to derive the base flow index of a catchment. 1

2. Study Area The Wabi Shebele river basin, located in East Africa, is a transboundary river basin shared between Ethiopia and Somalia. The part in Ethiopia lies between 4o45' N to 9o 45'N latitude and 38o45'E to 45o 30'E longitude, including the closed watershed of the Fafen and the Bio Ado (Figure 1).It springs from the Bale mountain ranges of the Galama and the Ahmar about 4000 m above mean sea level and drains into Indian ocean crossing Somalia. About 72% of the catchment (202,220 square kilometres) is lying in Ethiopia. The areal distribution of rainfall varies from 271 mm at lower arid portion (Gode) to 1320 mm in the upstream highlands of the basin (Seru). The study area is dominated by Mesozoic sedimentary formations, to some extent there are also volcanic rocks at the north west of the basin and isolated ridges and hills within the sedimentary basin. Metamorphic rocks outcrops in a small extent at the northern part of the study area. Alluvial deposits are also distributed linearly along the Wabi Shebele, Jerer, and Fafen rivers and fan deposits of seasonal floods and stream beds.

Figure 1: Location of the study area (a) Major river basins in Ethiopia (b) Rainfall characteristics in two typical months in April and August of the basin

Both meteorological and hydrological gauging stations are relatively more clustered in the upstream high lands. 3. Data and Methodology Unlike event based methods, continuous base flow separation techniques do not normally attempt to simulate the base flow conditions for a particular flood event, nor are they appropriate for the identification of the origin of base flow. These methods are rather aimed at the derivation of objective quantitative indices related to the long term base flow response of the catchment (e.g. base flow index -BFI) and at the estimation of continuous time series which specifically 2

characterize the high frequency, low amplitude base flow regime (Hughes, D.A, et al, 2003). Monthly base flow contribution to stream flow at gauged stations were estimated using automated analysis tool developed by USGS, HYSEP (Sloto and Crouse, 1996). In deriving the relation ship between catchment characteristics and base flow index, various variables are employed. These include the catchment size (A), stream density (Dd), climate index or aridity (humidity) index (AI), hypsometric integral (I), normalized digital vegetation index (NDVI) extracted from satellite images and geologic features. A number of morphometric indices have been used to summarize landform geometry. The hypsometric integral I is the area beneath the curve which relates the percentage of total relief to cumulative percent of area. This provides a measure of the distribution of landmass volume remaining beneath or above a basal reference plane. Integration of the hypsometric curve gives the hypsometric integral I. It is proved mathematically that the elevation-relief ratio E which is defined as (Pike and Wilson, 1971): (mean elevation - min elevation) (1) E= (max elevation - min elevation) is identical to the hypsometric integral I but has the advantage that it is much more easy to obtain numerically. In this work, E is therefore used instead of I.

.

Figure 2 Base flow index versus hypsometric integral and stream density in the Wabi Shebele river basin.

The base flow index is higher for places with an average hypsometric integral (0.48 - 0.54) and lower stream density. An increase in stream density and hypsometric integral is matched by an increase in base flow index (Figure 2).The coefficient of variation (CV) of base flow index in the basin ranges from 14% to 79%. Climate index, often denoted as aridity/humidity index, is the ratio of mean annual precipitation to potential evapotranspiration. It affects the base flow of catchments. A positive correlation between climate index and normalized digital vegetation index as high as 0.824 is noticeable in Wabi Shebele basin. Spectral measurements made in the red (580 ­ 680 nm) and near infrared (IR) (725 ­ 1100 nm) regions of the spectrum allow certain land and vegetation characteristics to be derived. Normalized digital vegetation index (NDVI) is the normalized differences between the reflectance of the red and near infrared spectrum.

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Wabi_1 is at the Wabi bridge (Station 61004) Wabi_2 is at Fruna (Station 61016) Wabi_3 is at Tebel (Station 62011) Wabi_4 is at Imi (Station 62015) Wabi_5 is at Gode (Station 63001)

Figure 3. Spatial and temporal correlation of base flow index (BFI) and normalized digital vegetation index (NDVI) at selected stations in Wabi Shebele basin (Month 1 is January).

A high negative correlation between BFI and NDVI is observed in the months of November to March in the middle valley of Wabi Shebele basin where as a positive correlation that gradually narrows in time upstream from Gode through June to September is noticeable (Figure 3).The rainfall season is mainly in June-September in the upstream portion of the river basin where as in the downstream it is predominantly falling in March-May. (See figure 1). It can be observed that the relationship between BFI and NDVI becomes highly negatively correlated in the dry seasons. This is also observed from time series plot of the two at the middle valley near Tebel station (Figure 4). During the famous drought years of 1990, 1991 and 1998 the correlation is appreciably higher than at other years.

1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 -0.10 -0.15 -0.20 -0.25 -0.30 -0.35 -0.40 -0.45 -0.50 -0.55 -0.60 -0.65 -0.70 -0.75 -0.80 -0.85 -0.90

Correlation coeffcient

Year of record

St at ion 62011

Figure 4 Time series plot of correlation between BFI and NDVI at the middle valley in Wabi Shebele basin.

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It was not easy to get data on aquifer properties. Pumping test results of most of the boreholes in the basin is missing. Thus it was not possible to include more rigorous parameters in the analysis like permeability that could better designate hydrogeological features of the basin. Thus average static water level (SWL) measured from ground surface is used. Values of base flow index determined for a network of stream flow gauges are matched to the composite morphometric and climatic data using spatial and regression analyses. To relate the BFI to a usable flow statistic, a relationship was derived between BFI and Q70, the point on the flow duration curve at which flows are exceeded 70% of the time. Q70 was chosen because it is the critical point that has been most often been used in most previous works.

4. Results and Discussion

Area of the catchment, average slope and drainage density were identified through factor analysis to affect base flows (Zecharias and Brutsaert, 1988). There is a strong negative correlation between catchment size and hypsometric integral, about -0.814, in Wabi Shebele basin. The average base flow index in the basin ranges from 0.375 to 0.856 where as the range of climate index is wider reaching from 0.134 to 0.980. The BFI has a strong relationship with climate and geology. Catchments with high climate index (high rainfall or low evapo-transpiration) underlain with granites or basalt tend to give high base flow. Among the topographical parameters tested, drainage density index has better relationship with BFI. Using least squares method different parameters were fitted against the base flow and it is found that the following relationship yielded the best result for the area under investigation:

BFI = 0.956 Dd + 2.795 I - 0.164 NDVI - 8.428SWL The standard error of this fit is 0.15. When flows are expressed as a percentage of the long term mean flow (standardised), the dependencies on the climatic variability across the basin and on the scale effect of catchment area are minimised. The shape of the standardised flow duration curve indicates the characteristic response of the catchment to rainfall. The gradients of the log normal flow duration curves for a range of catchments with differing geology illustrate that impermeable catchments have high gradient curves reflecting a very variable flow regime; low storage of water in the catchment results in a quick response to rainfall and low flows in the absence of rainfall. r2=0.97 (2)

Figure 5 Semi-log plot of Stream flow duration curves at different stations in Wabi Shebele river basin.

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Cathments around Erer (station 62013) and Jawis (station 62015) experience low variability and average base flow index as high as 0.84 (Figure 5). In Australia a fit of flow duration curve with an equation of the form

y=

1 a log(( ) - 1) b x

(3)

where y is log of normalised flow, x is exceedance probability (%), a and b are coefficients, yielded an interesting result (David post, 2005). The parameters a and b have somewhat physical connotation of the percentage at which the flow ceases to exist. The model is especially applicable for humid regions. In Zimbabwe, an exponential model of the following form can best describe the relationship between exceedance probability and stream flow (Mazvimavi, et al, 2005):

q = b exp(- b

p 0

1

p)

(4)

where qp is the dimensionless stream flow, p is the exceedance probability, b0 and b1 are coefficients. The above equation fits better for the low flow estimates (high exceedance probability). Equations 3 and 4 were applied to rivers in Wabi Shebele basin. Their performance is compared against a different variant of the exponential model (Table 2). Table 2. Goodness of fit of the different models between dimensionless flow and exceedance probability.

Sub-basin Name Lelisso Assasa Wabi at bridge Erer Fruna Hamaresa Jawis Tebel Imi Gode Average Sub-basin Code 61001 61005 61004 62013 61016 62007 62015 62011 62018 63001 Normalised flow m*log(x) + n b0*exp(-b1p) RMSE r2 RMSE r2 0.959 0.274 0.993 0.118 0.751 0.226 0.663 0.263 0.987 0.125 0.946 0.255 0.851 0.042 0.489 0.078 0.909 0.507 0.991 0.158 0.992 0.077 0.927 0.233 0.528 1.472 0.781 1.004 0.603 1.511 0.855 0.915 0.981 0.113 0.975 0.128 0.991 0.083 0.93 0.234 0.844 0.462 0.840 0.363 Log(Normalised flow) r2 0.994 0.751 0.997 0.981 0.997 0.996 0.983 0.959 0.975 0.991 0.959

a0*exp(a1p) + a2*exp(a3p) log((a/x)-1)/b

RMSE 0.106 0.226 0.055 0.015 0.091 0.053 0.281 0.488 0.128 0.086 0.158 r2 0.541 0.641 0.953 0.935 0.991 0.81 0.513 0.427 0.779 0.776 0.758 RMSE 0.443 0.203 0.237 0.027 0.158 0.171 0.238 0.312 0.187 0.212 0.194

It can be observed from Table 2 that the following equation has the highest coefficient of determination (r2) and the lowest root mean square error (RMSE).

q = a exp(a p ) + a

p 0 1

2

exp(a3 p )

(5)

Where qp is the flow exceeded p percent of the time, a0, a1, a2, a3 are coefficients. It better explains the relationship between the dimensionless flow and exceedance probability in Wabi Shebele river basin. The coefficients of these flow duration curve (FDC) are regressed against the base flow index for different sub-basins. These coefficients are relatively better estimated for the upper and middle valleys of Wabi Shebele basin using the following fits: a0 =110.95BFI ­ 63.83 r2 = 0.90; (6)

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a1 = -3.36BFI + 1.51 a2 = -20.41ln(BFI) ­ 3.084 a3 = -0.033BFI - 0.014

r2 = 0.71; r = 0.68; r2 = 0.68;

2

(7) (8) (9)

Station 63001 described well with the exponential model given in equation 3, but in the regional fit of the coefficients against the BFI it did not fit well with the above formulae. Thus it should be treated separately. The water level monitoring for one hydrologic cycle on two wells at Gode showed that the water level is deep always lower than the Wabi shebele river bed and the phreatic water level is practically the same during the hydrologic cycle and no interaction with Wabi shebele river water indicating the permeability is very low. (MoWR, 2004). Validation of the exponential fit in the basin using chi-square test between measured and calculated Q70, the point on the flow duration curve at which flows are exceeded 70% of the time, at four other stations including Gode, yielded 0.94. Thus it is fair to use the developed relationship for estimating the base flows. The availability of gauged stations with long years of record restricted the validation not to be carried out on more stations. Region of influence approach for estimating flow duration curves at ungauged sites is common. Delineating hydrogeologically similar catchments using soils data as surrogate of hydrogeological data yielded good results in UK (Holmes, et al, 2002). Analysis at hydrogeologically homogeneous catchment level may improve the search for a better estimate of base flow index at ungauged catchments.

5. Conclusions

Estimation of continuous time series of base flow index which specifically characterize the high frequency, low amplitude base flow regime are done at gauged catchments in Wabi Shebele basin. The relative strengths in association between the climatic, morphometric and geologic features of the catchment to the base flow estimates are weighted and a plausible relationship is produced. There is a strong negative correlation between BFI and NDVI which is even more pronounced during the dry seasons in the basin. Values of base flow index determined for a network of stream flow gauges are matched to the composite morphometric and climatic data using spatial and regression analyses. An exponential variant model fitted to the flow duration curves is used as an aid in deriving a relationship between BFI and Q70. The developed relationship can be used for fairly estimating the base flows in the ungauged portion of the river basin considered. However, in view of the tremendous spatio-temporal heterogeneity of climatic and landscape properties extrapolation of response information or knowledge from gauged to ungauged basins remains fraught with considerable difficulties and uncertainties.

6. Acknowledgement

The National Meteorological Services Agency and Ministry of Water Resources in Ethiopia are acknowledged for kindly providing the meteorological and hydrological data.

7. References

7.1. Hughes, D.A, Pauline Hannart and Deidre Watkins (2003) Continuous base flow separation from time series of daily and monthly stream flow data, Water SA 29(1). 7.2. Holmes, M.G.R., A.R. Young, A. Gustard and R. Grew (2002) A region of influence approach to predicting flow duration curves within ungauged catchments A region of influence Hydrology and Earth System Sciences, 6(4), 721­731. 7.3. Mazvimavi D., Meijerink, A.M.J., Savenije, H.H.G. and Stein, A. (2005) Prediction of flow characteristics using multiple regression and neural networks: a case study in

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Zimbabwe. Physics and Chemistry of the Earth, Parts A/B/C Volume 30, Issues 11-16 , pp 639-647. 7.4. MoWR (2003) Wabi Shebele river basin integrated master plan study project. Vol. VII Water resources, Part 3 Hydrogeology. 7.5. Pike, R.J., Wilson, S.E. (1971). Elevation-relief ratio, hypsometric integral, and geomorphic area-altitude analysis. Bull. Geol. Soc. Am. 82, 1079­1084. 7.6. Sloto, R.A., and Crouse, M.Y. (1996). HYSEP: A computer program for streamflow hydrograph separation and analysis, U.S. Geological Survey Water Resources Investigation Report 96-4040, 46p.

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