Effect of temporal scale on prediction using local approximation approach of hydrologic series in the Savitri basin in India

In this study, an attempt is made to examine the effect of temporal scale on the prediction of rainfall and runoff in the Savitri River basin, Maharashtra, India. The rainfall data from six stations and runoff data from four stations in the Savitri River basin are used here. The complexity of the series is analysed first with False Nearest Neighbour (FNN) method, then the nonlinear prediction method with a local approximation approach is employed, and one-time step-ahead predictions are made. The local approximation prediction involves the phase space reconstruction at optimum embedding dimension ‘m’ followed by identifying the nearest neighbours (k) based on the Euclidean distance between the vectors in the phase space. The one-time step ahead prediction is made by taking the mean of the ‘k’ number of neighbors in the phase space reconstructed at optimum dimension ‘m’. For each series, 80% of the data length is used for phase space reconstruction and then 20% of the data is used for testing the accuracy of prediction. Three statistical evaluation measures, correlation coefficient (CC), Nash-Sutcliffe efficiency (NSE), and normalized root mean square error (NRMSE), are used to determine the performance of the method. The FNN analysis reveals that the noise level in the hourly rainfall is more than the daily rainfall, whereas the noise level in the daily runoff series is more when compared to that of the hourly runoff series. Since noise in the data limits the accuracy of prediction (i.e., the prediction error is always greater than the noise level), the above may be an indication of better predictability of daily rainfall and hourly runoff than the hourly rainfall and daily runoff, respectively. The prediction results for the daily rainfall showed good prediction with CC values ranging between 0.56 and 0.69, whereas the hourly rainfall resulted in poor prediction with CC values between 0.46 and 0.51. In the case of daily runoff, the local approximation method gave good prediction (CC is in the range of 0.67 to 0.87), and hourly runoff showed very good prediction (CC is in the range of 0.98 to 0.99). The findings of the local approximation approach are in line with the predictability identified from the FNN analysis.