An Analytical S-Curve Approach for SUH Derivation

Abstract

Traditional S-curve/S-hydrograph method is used for deriving the desired duration (τ-hr) unit hydrographs (UHs) from known D-hr parent UH. Such D-hr UHs are seldom available for the ungauged basins. Hence, analytical S-curve approach/inflection S-shaped (IS) model (Patil and Mishra, J Hydrol Eng 21:06016010, 2016) has been proposed for smooth-shaped D-hr UH derivation over ungauged basins, where the optimal parameters of the S-curve were estimated using Central Water Commission (CWC)-based D-hr UHs peak discharge (Qp) and time to peak (tp) as constraints. The proposed analytical S-curve-based D-hr synthetic UH (SUH) proves its supremacy over CWC-based D-hr SUH by skipping the erratic manual fitting of SUH to preserve the unit runoff volume, unproductive time as well as efforts and unnecessary calculations involved. The sum of analytical S-curve-based D-hr SUH ordinates equals the volume of 1 cm direct runoff depth over the entire catchment area or equilibrium discharge of the S-curve justifies the SUH derived through proposed approach. The analytical SUHs are of comparable accuracy as CWC SUHs, as justified by the exact peaks (relative error = 0) and runoff volumes preserved with the SUH shapes generated.