Su, Ninghu, and Zhang, Fengbao (2024) Random fractional kinematic wave equations of overland flow: The HPM solutions and applications. Journal of Hydrology, 645 (Part B). 132234.

Preview

PDF (Published Version) - Published Version Available under License Creative Commons Attribution Non-commercial No Derivatives. Download (1MB) | Preview

Abstract

This paper presents new findings from analyses of a random fractional kinematic wave equation (rfKWE) for overland flow. The rfKWE is featured with orders of temporal and spatial fractional derivatives and with the roughness parameter, the effective rainfall intensity and infiltration rate as random variables. The new solutions are derived with the aid of a numerical method named the homotopy perturbation method (HPM) and approximate solutions are presented for different situations. The solutions are evaluated with data from overland flow flumes with simulated rainfall in the laboratory. The results suggest that on an infiltrating surface the temporal nonlocality of overland flow represented by the temporal order of fractional derivatives diminishes over time while the spatial nonlocality manifested by the spatial order of fractional derivatives continue if there is overland flow. It shows that the widely used unit discharge-height relationship is a special case of the solution of the rfKWE. Procedures are demonstrated for determining the fractional roughness coefficient, nf , the order of spatial fractional derivatives, ρ, and the steady-state infiltration rate during the overland flow, As . The analyses of the data show that the mean spatial order of fractional derivatives is ρ = 1.25, the mean flow pattern parameter m = 1.50, and the mean fractional roughness coefficient is nf = 0.002 which is smaller than the conventional roughness coefficient, n = 0.108. With these average values of the parameters and their standard deviations, simulations were performed to demonstrate the use of the methods, which is also a comparison of the classic KWE and rfKWE models.

Item ID:	84848
Item Type:	Article (Research - C1)
ISSN:	0022-1694
Copyright Information:	© 2024 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Date Deposited:	11 Mar 2025 02:32
FoR Codes:	37 EARTH SCIENCES > 3707 Hydrology > 370704 Surface water hydrology @ 100%
SEO Codes:	18 ENVIRONMENTAL MANAGEMENT > 1803 Fresh, ground and surface water systems and management > 180399 Fresh, ground and surface water systems and management not elsewhere classified @ 50% 28 EXPANDING KNOWLEDGE > 2801 Expanding knowledge > 280107 Expanding knowledge in the earth sciences @ 50%
	More Statistics