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Development and Evaluation of an ODE Representation of 3D Subsurface Tile Drainage Flow Using the HLM Flood Forecasting System
Author(s) -
Fonley M. R.,
Qiu K.,
Velásquez N.,
Haut N. K.,
Mantilla R.
Publication year - 2021
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/2020wr028177
Subject(s) - ode , hydrograph , richards equation , ordinary differential equation , tile drainage , hydraulic conductivity , partial differential equation , flow (mathematics) , hydrology (agriculture) , geotechnical engineering , mathematics , geology , differential equation , flood myth , soil science , mathematical analysis , geometry , philosophy , theology , soil water , water content
We developed a new ordinary differential equation (ODE) to represent subsurface flows from a hillslope with artificial subsurface drainage (tiling) into an adjacent channel. Our ODE is based on a derived storage‐discharge relationship from high‐resolutions HYDRUS3D simulations that solve 3D partial differential Richards' equations for a hillslope (plot scale) with internal drainage surfaces, variable soil depth, hydraulic conductivity, and varying slope in the direction of flow. The ODE does not capture the hysteresis in the storage‐drainage relation that can only be captured using partial differential equations (PDEs), however the simplification does not have major impacts on the modeled flows. The nondimensional representation of the equation is consistent with, and provides an explanation for, the empirical equation used in classical hydrological models such as the ARNO (Arno River) and Variable Infiltration Capacity (VIC) model to simulate subsurface flows, which removes the need for parameter calibration. Our equation captures the features not captured by other ODE simplifications such as DRAINMOD. The ODE can be coupled to the Hillslope Link Model (HLM) flood forecasting system allowing real‐time regional simulation of streamflow fluctuations and floods over large domains. We show that (i) the new equation improves the capability to model watershed scale hydrograph recessions and to better capture the timing above flood thresholds for multiple spatial scales from 0.1 to 18,000 km 2 ; (ii)using realistic values of slope combined with typical values of tile separation and soil depth provides good predictive power at gauged basin outlets; and (iii) parameters can be derived for particular situations using the 3D PDE framework.