论文研究 - 通过降雨径流模型分析马拉河流域的行为.pdf

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Analyzing the Mara River Basin Behaviour through Rainfall-Runoff Modeling

Abstract

Keywords

1. Introduction

2. Materials and Methods

2.1. Application of Hydrologiska Byrans Vattenavdelning (HBV Light) Model

2.2. Model Run

3. Results and Discussions

3.1. Assessment of Model Performance

3.2. Water Balance Analysis

3.3. Sensitivity Analysis

3.4. Effect of Varying Time Steps

3.5. Partitioning of the Flow Hydrograph

3.6. Model Performance Efficiency

4. Conclusions

Acknowledgements

References

International Journal of Geosciences, 2017, 8, 1118-1132 http://www.scirp.org/journal/ijg ISSN Online: 2156-8367 ISSN Print: 2156-8359 Analyzing the Mara River Basin Behaviour through Rainfall-Runoff Modeling Anne M. Birundu1, Benedict M. Mutua2* 1Murang’a University College, Nairobi, Kenya 2Deputy Vice-Chancellor (Planning, Partnerships, Research and Innovation), Kibabii University, Bungoma, Kenya How to cite this paper: Birundu, A.M. and Mutua, B.M. (2017) Analyzing the Mara River Basin Behaviour through Rain- fall-Runoff Modeling. International Journal of Geosciences, 8, 1118-1132. https://doi.org/10.4236/ijg.2017.89064 Received: July 5, 2017 Accepted: September 19, 2017 Published: September 22, 2017 Copyright © 2017 by authors and Scientific Research Publishing Inc. This work is licensed under the Creative Commons Attribution International License (CC BY 4.0). http://creativecommons.org/licenses/by/4.0/ Open Access Abstract Hydrological models are considered as necessary tools for water and envi- ronmental resource management. However, modelling poorly gauged water- sheds has been a challenge to hydrologists and hydraulic engineers. Research done recently has shown the potential to overcome this challenge through in- corporating satellite based hydrological and meteorological data in the meas- ured data. This paper presents results for a study that used the semi-distributed conceptual HBV Light Model to model the rainfall-runoff in the Mara River Basin, Kenya. The model simulates runoff as a function of rainfall. It is built on the basis established between satellite observed and in-situ rainfall, evapo- ration, temperature and the measured runoff. The model’s performance and reliability were evaluated over two sub-catchments namely: Nyangores and Amala in the Mara River Basin using the Nash-Sutcliffe Efficiency which the model referred to as Reff and the coefficient of determination (R2). The Reff for Nyangores and Amala during the calibration and (validation) period were 0.65 (0.68) and 0.59 (0.62) respectively. The model showed good flow simula- tions particularly during the recession flows, in the Nyangores sub-catchment whereas it simulated poorly the short term fluctuations of the high-flow for Amala sub-catchment. Results from this study can be used by water resources managers to make informed decision on planning and management of water resources. Keywords Hydrological Models, Satellite Data, HBV Light Model, Mara River Basin 1. Introduction Kenya is characterized as water stressed country since the per capita water DOI: 10.4236/ijg.2017.89064 Sep. 22, 2017 1118 International Journal of Geosciences

A. M. Birundu, B. M. Mutua availability is at 792 m3 with a population of approximately 40 million people [1]. With the increasing population, expanding urbanization, modernised life- styles, climate changes and other global changes, the pressure for sustainable planning and management of the finite water resources is more evident than ever. This paper focuses on a study that was carried out in the Mara River Basin that cuts across Kenya and Tanzania. The Mara River Basin (MRB) covering a drainage area of 13,750 km2 is one of the catchments of Lake Victoria and forms part of the Upper Nile Basin. The Mara River (MR) which is about 395 km long is one of the Rivers supplying water into Lake Victoria throughout the year. The River originates from Mau Forest Complex which forms part of the upper basin. The Mara River Basin (MRB) is characterized by the extensive cultivated land and forested areas in the upper part, tropical savannah vegetation in the middle of the basin and one of the world famous Mara-Serengeti ecosystem towards the lower part of the Mara wetland form part of the extreme lower side of the Basin on the Tanzania side where the River drains into Lake Victoria. The Mara River Basin faces numerous interactions that require effective management to ensure sustainability of its water resources since many liveli- hoods depend on it. The basin has undergone several changes over the last 50 years as a result of increased human population [2]. The flow regime in the Mara River has changed over the years due to catch- ment degradation. For instance, [3] in the study on Modelling the Impact of Land-Cover and Rainfall Regime Change Scenarios on the Flow of Mara River found out that there has been a decline in the dry season flow and increased peak flood frequency in recent years. In another study by [4] where these re- searchers applied the USGS Geospatial Stream Flow Model in studying the im- pact of land use/cover on the hydrology of MRB, it was found out that forests and savannah grasslands have been cleared and turned into agricultural lands. In addition, the long-term monitoring also identified several areas of concern in the upper catchment of the basin. For instance, the results showed that the Amala sub-catchment has experienced higher decline in average monthly flow levels over the last 15 years, transported higher sediment load per unit catchment area and has generally lower water quality than the Nyangores sub-catchment, sug- gesting land degradation in this sub-catchment may be responsible for declines in water quantity and quality in the Mara River basin. In order to effectively plan for the water resource use and to protect it under the changing conditions, application of basin runoff models that can simulate flow regimes under different scenarios of change [5] is required. However, the availability of long term spatial and temporal quality hydro-meteorological data has been a challenge in many river basins in Kenya. In order to overcome this challenge, this study used the satellite observed rainfall products and the 30 m resolution Shuttle Radar Topography Mission (SRTM) DEM which were derived from open sources. The study applied a conceptual hydrological model, the Hy- 1119 International Journal of Geosciences DOI: 10.4236/ijg.2017.89064

A. M. Birundu, B. M. Mutua DOI: 10.4236/ijg.2017.89064 drologiska Byrans Vattenavdelning model (HBV Light Model) for run-off simu- lation of the measured rainfall. 2. Materials and Methods The Mara River Basin which is a trans-boundary basin covers approximately 13,750 km2. It lies between South Western Kenya and North Western Tanzania at between longitudes 33˚47'E and 35˚47'E and Latitudes 0˚28'S and 1˚52'S. The Napuiyapui swamp in the Mau Forest Complex, is the source for the Mara River where it flows at an altitude of approximately 3000 metres above sea level (m.a.s.l) South West before draining into Lake Victoria in Musoma Tanzania at an altitude of 1134 metres above sea level [6]. The Nyangores and Amala Rivers are the two main perennial tributaries of the Mara River and their respective sub-basins form part of the Upper catchment. The other tributaries are; Talek, Sand and Engare Ngobit rivers on the Kenyan side and the Bologonja River on the Tanzania side (Figure 1). The amount of annual rainfall in the basin varies from 1400 mm in the hills of the Mau Forest to 500 - 700 mm in the dry plains of north-west Tanzania [7]. The study used the HBV model which simulates the daily discharge using in- put variables of rainfall, temperature and potential evapotranspiration [8]. The input data collected were checked for consistency as well as filling in the missing data gaps for precipitation, discharge and temperature datasets. The main ap- proach used was the correlations between the three hydro-meteorological sta- tions (Narok, Kericho and Kisii) data. Thereafter, multiple linear regressions were used to develop relationship equations which were then used to fill the missing data gaps. The records of only three out of the thirty six hydro-meteorological stations on the Kenyan side as shown in Figure 2 were processed. The data was recorded daily at 0900 hours and was expressed in millimetres per day (mm/day). The area average precipitation Parea was calculated as weighted mean of precipitation stations in and around the catchment. This was achieved through use of the Thiessen polygons. The temperature was calculated as weighted mean of the stations in and around the catchment after the missing data was filled using multiple linear re- gressions. The data was obtained from the Kenya Metrological Department. Compared to other rivers within the Mara River basin, Nyangores and Amala Rivers have long term daily discharge data records. Readings of water levels for the two rivers were taken twice each day daily in the morning at 0600 hrs and in the evening at 1800 hrs. Rating curves were then used to estimate daily average discharges. 2.1. Application of Hydrologiska Byrans Vattenavdelning (HBV Light) Model The HBV light model which is a semi distributed conceptual model was selected 1120 International Journal of Geosciences

A. M. Birundu, B. M. Mutua Figure 1. Site Map of the trans-boundary Mara River Basin, showing the Mara River with its tributaries. Source: (Melesse, 2012). to simulate the rainfall runoff processes in the two sub-catchments. The model was selected because of its suitability that has been demonstrated under different hydro climatic conditions in the world [9] [10]. The general structure and equa- tions of HBV light model is summarized in Figure 3. The reservoirs are con- nected to each other by means of exchange fluxes which define the amount of water between the different zones. Equations (1) and (2) give the general water balance. The HBV light model has four routines which include; the snow pack (not used in this research), soil moisture, response function and routing routines [11] as summarized in Figure 3. S ∆ t ∆ = Input Output − (1) where; ∆S = Change in Storge and ∆t = Change over time P E Q − − = d dt ( SP SM UZ LZ lakes + + + + ) (2) where; P is precipitation, E is evaporation, Q is runoff, SP is the snow pack, and SM is the soil moisture. The UZ and LZ are the upper and lower ground water zones. The HBV light model uses sub-catchments as the primary hydrological units. 1121 International Journal of Geosciences DOI: 10.4236/ijg.2017.89064

A. M. Birundu, B. M. Mutua Figure 2. Processed SRTM DEM showing the Elevation, Rainfall gauging stations and the River gauging stations of the Mara River Basin. DOI: 10.4236/ijg.2017.89064 Figure 3. General structure of the HBV model. 1122 International Journal of Geosciences

A. M. Birundu, B. M. Mutua The catchments classifications of land use, and area-elevations are used as input into the model. The model can be run with daily precipitation time series data but higher resolution can also be used in the model. The channel routing is by a triangular weighing function through MAXBAS (length of weighing function). The soil moisture threshold for reduction of evapotranspiration defines LP. The maximal flow from the upper to lower groundwater box is defined by PERC; β is shape coefficient for the non-linear storage behaviour of the soil zone. The model uses a warming up period of one year [12]. The warm-up period refers to the time that the simulation will run before the final results are col- lected and it allows the acclimatization of input data-set to the running condi- tions normal to the system being simulated. 2.2. Model Run The model was run in dynamic mode on a daily basis in order to simulate a combined period of eleven (11) years translating to a total of 4017 time steps. The model calibration and validation was done by through trial and error method. The Monte Carlo runs were generated to investigate the catchment re- sponse characteristics, and to explore physically realistic model’s parameters ranges. Initial Monte Carlo simulations were generated using parameter values from the literature (tuned with preliminary model runs) to define possible pa- rameter ranges as shown in Table 1. However, the time dependent units change for simulations with more aggregated time steps (15 and 30 days) were applied. Table 1. Parameters and their ranges applied during the Monte Carlo Simulations. Explanation Unit Minimum Maximum Threshold for K0-outflow Maximal flow from upper to lower GW-box mm mm/d Routing routine: MAXBAS Routing, length of weighting function d 0 0 1 DOI: 10.4236/ijg.2017.89064 1123 International Journal of Geosciences Parameter Soil and evaporation routine: FC LP β Maximum soil moisture storage Soil moisture threshold for reduction of evaporation Shape coefficient Groundwater and response routine: Recession coefficient Recession coefficient Recession coefficient K0 K1 K2 UZL PERC mm 3/4 3/4 d−1 d−1 d−1 100 0.3 1 0.1 0.01 5.00E−05 550 1 5 0.5 0.2 0.1 70 4 2.5

A. M. Birundu, B. M. Mutua Different parameter sets were produced by running more than 300,000 Monte Carlo Simulations (MCS) for each catchment representation of the Nyangores and Amala sub-catchments on daily time steps. The efficiency Reff value was used for assessment of simulations by the HBV model. The Reff value compares the prediction by the model with the simplest possible prediction, a constant value of the observed mean value over the entire period. Several model parameter sets with Reff comparable to the highest values were obtained. 3. Results and Discussions The results show that in the Nyangores sub-catchment, a Reff > 0.65 was obtained after running, 250,000 MCS. In the case of Amala sub-catchment, a Reff > 0.59 was obtained after running 100,000 simulations of the Monte Carlos. Based on the Nash-Sutcliffe Efficiency criteria, the performance of the model was within acceptable range as per the selected performance criteria. In addition, to visual observation of the hydrographs and evaluation of low flows (log Reff), the values of Reff > 0.65 and Reff > 0.59 were considered satisfac- tory. The calibration results are shown in Figure 4 below and Table 2 together with their corresponding statistical measures for model performance assessment. (a) (b) Figure 4. (a) and (b). Simulated and Observed discharge in mm/day for Nyangores and Amala Sub-catchments re- spectively for the calibration. (a). Nyangores Sub-catchment; (b). Amala Sub-catchment. DOI: 10.4236/ijg.2017.89064 1124 International Journal of Geosciences

Table 2. Calibration and Validation parameters and model efficiency results for Nyan- gores and Amala Sub-catchments for the period of 1996-2008 and 2009-2013 respectively. A. M. Birundu, B. M. Mutua Calibration/Validation Parameters Parameters Calibration Validation FC LP β K0 K1 K2 UZL PERC MAXBAS Reff logReff R2 ∆Q Reff logReff R2 ∆Q Units (mm) (3/4) (3/4) (d−1) (d−1) (d−1) (mm) (mm/d) (d) (3/4) (3/4) (3/4) (mm/a) (3/4) (3/4) (3/4) Nyangores catchment 408.61 0.32 5.20 0.11 0.11 0.92 46.75 0.10 1.50 0.62 0.60 0.73 0.00 0.65 0.63 0.75 Amala catchment 350.00 0.9.00 12.00 0.05 0.99 0.99 56.36 0.45 15.00 0.48 0.46 0.65 0.00 0.59 0.57 0.69 (mm/a) −8.00 −131.00 From the visual observation of the hydrographs in Figure 4, it indicates gen- erally good flow simulations in particular during the recession flows, in the Nyangores sub-catchment with a bit of high peaks towards the end of the simu- lation period. In comparison to the Amala sub-catchment, the short-term fluc- tuations during the high-flow season were not modelled well. In fact, the model overestimated the discharge as clearly shown in the hydrograph. The mean an- nual (∆Q) differences between observed and simulated runoff was negligible. The results show a good relationship between the simulated and observed low flows in the Nyangores catchment with a log Reff > 0.63 compared to the log Reff > 0.57 for the Amala sub-catchment. The coefficient of determination R2 was >0.73 and >0.65 for the Nyangores and Amala sub-catchments respectively. The parameter values for which the model was highly sensitive (yielding good simulations) only for comparable small intervals, were related to the soil mois- ture storage and runoff generation routine as shown in the standardized pa- rameter values given in Table 2. The Table shows the smallest and largest pa- rameter values that produced Reff > 0.65 and >0.59 for the Nyangores and Amala respectively. A satisfactory model performance (Reff > 0.65) was attained in Nyangores with a soil moisture storage, FC, in the range of 408 mm < FC < 514 mm near the maximum parameter range whereas in Amala, the FC was lower, 1125 International Journal of Geosciences DOI: 10.4236/ijg.2017.89064

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