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Research Project: Improved Agroecosystem Efficiency and Sustainability in a Changing Environment

Location: Sustainable Agricultural Water Systems Research

Title: Vadose zone analytical algorithm (VZAA): A non-iterative algorithm for vadose zone soil moisture and groundwater recharge

Author
item SADEGHI, MORTEZA - California Department Of Water Resources
item BOYCE, SCOTT - University Of California, Davis
item DOGRUL, EMIN - California Department Of Water Resources
item HUANG, GUOBIAO - California Department Of Water Resources
item LIANG, LAN - California Department Of Water Resources
item BANDARA, UDITHA - California Department Of Water Resources
item ALTARE, CRAIG - California Department Of Water Resources
item HATCH, TYLER - Intera, Inc
item Bradford, Scott

Submitted to: Journal of Hydrology
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 4/8/2026
Publication Date: 4/8/2026
Citation: Sadeghi, M., Boyce, S.E., Dogrul, E.C., Huang, G., Liang, L., Bandara, U., Altare, C.R., Hatch, T., Bradford, S.A. 2026. Vadose zone analytical algorithm (VZAA): A non-iterative algorithm for vadose zone soil moisture and groundwater recharge. Journal of Hydrology. 673. Article 135467. https://doi.org/10.1016/j.jhydrol.2026.135467.
DOI: https://doi.org/10.1016/j.jhydrol.2026.135467

Interpretive Summary: Large-scale groundwater flow models require information about water flow from the unsaturated zone to groundwater (known as recharge), but typically do not rigorously simulate recharge because of computational challenges. This paper presents a simplified and efficient approach to simulate recharge that accounts for dominant factors. Incorporation of this new approach should improve the accuracy and utility of existing groundwater flow models without additional computational burden. This information should be of interest to federal, state, and local agencies that are concerned with the management of scarce water resources.

Technical Abstract: Conventional groundwater models often overlook the water flow dynamics within the unsaturated zone of the soil profile, referred to as “vadose zone”. Water flow in the vadose zone is often assumed to be uni-directional, always from the soil surface toward the groundwater, due to the gravitational force. In these tipping bucket models, the diffusive water flow due to the soil moisture gradient is neglected, because calculating the soil moisture gradient requires iterations and costly numerical schemes at large scales. This simplification, however, can lead to large errors in the simulated vadose zone soil moisture and recharge to the groundwater. In this paper, we introduce a novel algorithm, named “Vadose Zone Analytical Algorithm” (VZAA), that accounts for bi-directional exchanges of water between the saturated and unsaturated zones due to both gravitational force and soil moisture gradient. VZAA is based on a recently developed analytical relationship between soil moisture and soil water flux. It divides the soil profile into several computational layers and does the calculations layer by layer at each time step. It starts the calculations from the top layer and takes the surface net water flux (e.g., precipitation and irrigation minus evapotranspiration) as known input. It then calculates soil moisture and outflow for this layer based on the mass balance equation together with the analytical soil moisture-flux relationship. Having outflow from the top layer as the inflow to the next layer, the VZAA proceeds to subsequent layers and calculates their soil moisture and water flux until it reaches the groundwater table. Then, it updates the groundwater table based on the calculated recharge and goes to the next time step. Because all the calculations are based on closed-form algebraic relationships, this algorithm does not need an iterative optimization algorithm and is very fast. This algorithm was tested using HYDRUS-1D as a reference model for various soil and input flux scenarios. In most cases, VZAA showed a close agreement with HYDRUS-1D. VZAA’s performance was also compared with the tipping bucket model currently employed in the Integrated Water Flow Model (IWFM) and showed significantly better results than the bucket model. Therefore, VZAA can be potentially used in any existing large-scale groundwater model to improve the accuracy of these models at no additional computational cost.