Optimization of rainfall spatial variability for daily streamflow estimation with a monthly water balance model

Abstract

Precipitation varies significantly over space and time within a watershed. Precipitation has a vital role in determining surface hydrological processes because of its influence on streamflow estimations using mathematical models. Though monthly rainfall data provides ease of access due to availability and affordability, daily data is the preferred option of engineers, planners and water managers. This is because daily time resolution is considered as a unit which reasonably represent the catchment time lag. If a water model calibrated using monthly data could estimate daily streamflow from a watershed, then this would be of immense value for sustainable water resources management. The three-parameter monthly water balance model (3PMWBM) proposed by (Dissanayake, 2017) has demonstrated the capability with an application on 2 watersheds in Sri Lanka while using Thiessen averaging method for rainfall input. Wijesekera and Musiake (1990a, 1990b) had optimized both rainfall station weights and model parameters for improved streamflow estimations by enabling the calibration of point rainfall measurements to generate a spatially averaged rainfall to reflect the response of the corresponding watershed. The study objective is to estimate streamflow in daily timescale using a monthly water balance model while optimizing the spatial variability of rainfall leading to enhanced water security and sustainable water management. Daily data from 2005 to 2014 of 4 rainfall stations of Badalgama watershed (1360 km2) in Ma Oya Basin, Sri Lanka are used to evaluate the streamflow predictions with the 3PMWBM when rainfall station weights are optimized. The 3PMWBM was developed, calibrated and verified with and without optimizing the rainfall gauging station weights. A spreadsheet tool and an object oriented modelling tool was used for the model development. Mean Ratio of Absolute Error (MRAE) was selected as the objective function during calibration and verification. The high, medium and low flow determined from observations and annual water balance were also were used during evaluation. The optimum value based on literature and analysis for Sc, C and k are 908, 2.5 and 0.69 respectively for monthly model. The MRAE calibration and verification results obtained at consecutive steps 0.41,0.409 and 0.36 and 0.60,0.62,0.50 i.e. optimizing model parameters, optimizing rainfall weights, optimizing model parameter and rainfall weights at the same time Thiessen weights are (0.26,0.19,0.20,0.35), (0.20,0.16,0.26,0.38) and (0.23,0.14,0.27,0.36) respectively for Ambepussa, Andigama, Aranayake and Eraminigolla stations. Daily streamflow estimations in Badalgama watershed using 3PMWBM with the optimization of rainfall station weights with optimum average MRAE 0.64. The study found that spatial variability of rainfall can significantly affect model results about 17% improvement in average MRAE at monthly scale when station weights and parameters are simultaneously optimized and under same case when the model is used for daily streamflow estimation, up to 8% improvements in average MRAE are noticed.