An analytical model for estimation of land surface net water flux from near-surface soil moisture observations

Morteza Sadeghi, Markus Tuller, Arthur W. Warrick, Ebrahim Babaeian, Kshitij Parajuli, Mohammad R. Gohardoust, Scott B. Jones

Research output: Contribution to journalArticlepeer-review

26 Scopus citations


The accurate determination of land surface water fluxes at various spatiotemporal scales remains a challenge in hydrological sciences. It is intuitive that land surface net water flux (i.e., infiltration minus evapotranspiration) directly affects near-surface soil moisture. However, there exists no hydrological model suitable to calculate net water flux based on measured near-surface soil moisture data. This is a consequence of the mathematical structure of existing models that use ‘boundary conditions’ to determine ‘internal conditions’ whereas what is needed is a model amenable to use near-surface soil moisture data (an internal condition) to determine the surface water flux (a boundary condition). To pursue the idea of utilizing remotely-sensed or in situ (i.e., sensor networks) near surface soil moisture data for estimation of net water flux, we derived an analytical model via inversion of Warrick's 1975 analytical solution to the linearized Richards’ equation for arbitrary time-varying surface flux boundary conditions. The applicability of the new analytical solution was evaluated based on actual water flux observations as well as HYDRUS-1D simulations for four vastly different sites in Arizona, California, Idaho, and Indiana. Our results demonstrate that the proposed model reasonably captures net water flux variations in natural settings, including layered and vegetated soils, especially at larger time scales (e.g., monthly). While the model works for a wide range of climatic conditions, the prediction accuracy is somewhat lower for extreme dry or wet conditions. A major advantage of the new model is that it does not require calibration, which provides an unprecedented opportunity for large scale estimation of land surface net water flux using remotely sensed near-surface soil moisture observations.

Original languageEnglish (US)
Pages (from-to)26-37
Number of pages12
JournalJournal of Hydrology
StatePublished - Mar 2019

Bibliographical note

Funding Information:
The authors gratefully acknowledge funding from National Science Foundation (NSF) grants no. 1521469 and 1521164. Additional support was provided by a FY17 Utah Agricultural Experiment Station (UAES) Seed Grant, Project # UTA01189 from Utah State University, Logan, Utah 84322-4810, approved as UAES journal paper #9093. MATLAB code for the forward and inverse calculations and model optimization are available upon request from the first author (

Publisher Copyright:
© 2019 Elsevier B.V.


  • Analytical model
  • Evapotranspiration
  • Infiltration
  • Near-surface soil moisture
  • Remote sensing
  • Richards’ equation


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