Suitability of S-Shaped Functions for Fitting Smooth S-Hydrograph
- DOI
- 10.2991/978-94-6463-252-1_28How to use a DOI?
- Keywords
- Conventional or Classical S-Curve; Lower Incomplete Gamma Function; Modified S-Curve Function; Altered Duration Unit Hydrograph
- Abstract
In hydrologic analysis of floods, after having derived a unit hydrograph (UH) of a specified duration, one may wish to change the time step and define a new UH of desired duration. The conventional/classical S-hydrograph method used for the same always results in erroneous or fluctuating altered duration UHs with impaired unit volume. As effect of S-curve oscillations is transmitted in resultant altered duration UHs. Therefore, S-shaped lower incomplete gamma function (LIGF) and its analytically modified flexible version (modified S-curve function) are proposed for oscillation-free (hunting-free) fitting of D-hr S-curve against parent/conventional D-hr S-curve. The reliable function is selected on the basis of least deviation of analytical D-hr S-curve from the conventional D-hr S-curve, evaluated using Nash-Sutcliffe efficiency (ηNS). Herein, oscillation-free analytical D-hr S-curve and its lagged versions lead us to the smooth shaped altered duration UHs conserving unit volume. Proposed analytical S-curves outperform the conventional S-curve. However, the modified S-curve function (with ηNS = 99.85%) was found comparatively more reliable than LIGF (with ηNS = 99.62%) over 1st dataset (or UH) and hence used for analysis over 2nd dataset whereas; the LIGF was skipped. For 2nd dataset modified S-curve function rebuild the S-curve reliably with ηNS = 99.78%. Overall, the complexity associated with classical method i.e. lengthy calculations; erroneous lagging and incompatible interpolation of parent UH or S-curve; tedious manual/graphical smoothing of derived S-curve or altered duration UHs for sustaining unit volume has been justifiably resolved by proposed analytical approaches.
- Copyright
- © 2023 The Author(s)
- Open Access
- Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.
Cite this article
TY - CONF AU - Pravin R. Patil AU - S. K. Mishra AU - Sanjay K. Jain AU - Pankaj Mani PY - 2023 DA - 2023/11/09 TI - Suitability of S-Shaped Functions for Fitting Smooth S-Hydrograph BT - Proceedings of the Second International Conference on Emerging Trends in Engineering (ICETE 2023) PB - Atlantis Press SP - 251 EP - 263 SN - 2352-5401 UR - https://doi.org/10.2991/978-94-6463-252-1_28 DO - 10.2991/978-94-6463-252-1_28 ID - Patil2023 ER -