Regionalization of Parameters of Hydrological Models in South Indian River Basins

Abstract

Streamflow Prediction in Ungauged Basins (PUB) is imperative in developing countries such as India due to the sparse network of river gauging stations. Notwithstanding this limitation, accurate estimates of streamflow still need to be derived at all locations where either water development projects have to be constructed or optimal water management policies have to be implemented. Such activities require information on the Flow Duration Curve (FDC) and time-series of historical streamflows, which may however be unavailable if the location of interest is ungauged, i.e., historical discharge records are non-existent. While estimates of certain hydroclimatic variables (rainfall, temperature, soil moisture, etc.) at unsampled locations may be derived using spatial interpolation techniques, deriving estimates of streamflow at ungauged locations is not as straightforward and requires implementation of more sophisticated and involved procedures. In particular, a procedure known as Hydrologic Regionalization (also known as Top Down or Darwinian approach) is commonly used for this purpose and involves transfer of historical streamflow information from gauged stations which are hydrologically similar to the ungauged basin of interest. The present research was taken up with the specific objective of developing a comprehensive Hydrologic Regionalization-based methodology for deriving the FDC and streamflow time-series in ungauged basins located in the peninsular region of South India. The steps involved in the adopted methodology included: 1) compilation of a dataset comprising historical records of streamflow, climate data and catchment attributes of 50 gauged catchments in the study area, 2) delineation of the catchments into hydrologically homogeneous groups using a hierarchical agglomerative cluster analysis and evaluating the accuracy of the analysis, 3) deriving period-of-record FDCs for each catchment from historical streamflow records, 4) regionalization of 9 flow quantiles of the FDC by establishing multiple linear regression (MLR) relationships with relevant catchment Dept. of WROE, NITK, Surathkal, India ii attributes and evaluating the prediction accuracies of the developed MLR models, 5) cluster-wise evaluation of the reliabilities of the developed MLRs when applied to ungauged basins using jackknife cross validation procedures, 6) application and calibration of 3 popular conceptual rainfall-runoff models (ABWM, SIMHYD, Tank) in the 50 gauged catchments and evaluating their relative performances in simulating daily streamflow time series, 7) cluster-wise identification of dominant model parameters for use in ungauged basins in the region. For the purpose of this study, 50 catchments with largely unregulated flows located in Krishna, Cauvery, Godavari, East and West flowing river basins situated in South India were identified and a dataset of historical daily streamflow records was created for each of them. Depending on the consistency of the available data, the longest discharge record was from 1991 to 2018 (28 years), and the shortest was from 2000 to 2009 (10 years) for the selected catchments. SRTM-derived Digital Elevation Models were created for the purpose of delineating the catchment boundaries upstream of the gauging stations. The DEMs were also used to derive 15 physiographic attributes for each of the catchments. India Meteorological Department (IMD) gridded data products of historical daily rainfall (0.250x0.250) and daily maximum and minimum air temperatures (10x10) for the period 1981-2018 were obtained and used for carrying out the trend analysis. In addition, rainfall data and reference evapotranspiration (derived from gridded temperature data) were employed as inputs for the rainfall-runoff modeling. The Theissen polygon method was applied to ascertain the daily average values for all four climatic variables: rainfall, maximum and minimum temperatures, and reference evapotranspiration. A necessary first step in hydrologic regionalization is to group the gauged catchments into hydrologically homogeneous groups/clusters so as to ensure accurate information transfer to ungauged basins located within them. Therefore, a hierarchical agglomerative cluster analysis utilizing Ward's linkage method was implemented using carefully selected catchment attributes as clustering variables. This resulted in the grouping of the 50 gauged catchments into three homogeneous clusters with Cluster 1 comprising 17 catchments, Dept. of WROE, NITK, Surathkal, India iii followed by 11 catchments in Cluster 2, and 22 catchments in Cluster 3. Through the CV test and L-Discordancy measure using the L-Moment ratio, it was confirmed that all three clusters exhibited homogeneity without any discordant stations. A Flow Duration Curve (FDC) depicts the relationship between the percentage of time (or duration) for which a particular magnitude of discharge is equalled or exceeded at a particular gauging site. It is a valuable hydrological tool in the planning and design of water resources projects and therefore the present study focused on its estimation at ungauged locations. Initially, considering the historical records of daily discharge, frequency analysis was used to derive period-of-record FDCs for each of the 50 gauged catchments. Subsequently, nine flow quantiles representing the discharge magnitudes at durations of 10%, 20%....90% were extracted from the FDCSs of each catchment. The regionalization approach was then adopted, whereby using step-wise regression, each flow quantile was separately related to the catchment attributes through multiple linear regression (MLR) equations. Performances of the developed MLR models were evaluated using the coefficient of determination (R2), root mean square error (RMSE), and percentage bias (PBIAS) statistics. Cluster-wise performance analysis of the developed MLR models indicated excellent performance with average R2 values of 0.85, 0.97, and 0.8 for Cluster – 1, 2, and 3 respectively in comparison to poor performance when all 50 stations were considered to be in a single region. In an effort to evaluate the reliabilities of the developed MLR models when applied in ungauged catchments, a cluster-wise leave-one-out jackknife cross validation procedure was implemented. Results indicated mixed performances with regard to the reliability of developed models with performance being good for high flow quantiles and poor for low flow quantiles. Since historical records of streamflow time-series are also essential at ungauged sites, the present study also focused on the regionalization of conceptual rainfall-runoff (RR) models. For this purpose, the Australian Rainfall-Runoff Library (RRL) toolkit was identified from within which three popular conceptual RR models namely, AWBM, SIMHYD and Tank were selected for use in this study. Using inputs of catchment average Dept. of WROE, NITK, Surathkal, India iv rainfall and reference evapotranspiration the 3 lumped RR models were applied separately to each of the 50 gauged catchments for the periods for which historical discharge records were available using a daily time step. The in-built Shuffled Complex Evolution (SCEUA), Pattern Search Multi-Start (PS-Multi), and Rosenbrock optimization routine in RRL was used to calibrate the models using both split-sampling and full-period approaches and optimal model parameter values were obtained for each of the 50 catchments. Performance evaluation of the models was carried out using coefficient of determination (R2), Nash- Sutcliffe efficiency (NSE), and Kling-Gupta efficiency (KGE) metrics. Results indicated that the AWBM model exhibited satisfactory performance (average NSE 0.52) in 88% of the basins, surpassing the SIMHYD and Tank models, which showed satisfactory performance (average NSE 0.51) in 80% of the basins. Variabilities of the parameters of the best performing AWBM model across the catchments in each of the homogeneous clusters were examined and cluster-wise median values were extracted. It was assumed that these could be considered the optimal parameter values for application of the AWBM model in ungauged catchments located in a given cluster and thereby circumvent the need for model calibration using gauged flow records. The efficacy of this assumption was tested by applying the AWBM with the median parameter values in 3 gauged catchments located one each in the clusters. The performance of the model (without calibration) was evaluated and found to perform reasonably well in all 3 test catchments with NSE values of 0.55, 0.82, and 0.65 being obtained. This implies that the AWBM model with optimal model parameters derived through regionalization can yield reasonably accurate daily streamflow time-series in ungauged catchments in the study area. Overall results of this study indicate that hydrologic regionalization using historical flow records from a reasonably large number of unregulated catchments and possessing diverse attributes can lead to the development of reasonably accurate models for predicting flow duration curves and streamflow time series in ungauged catchments.