Estimating and Forecasting Time‐Varying Groundwater Recharge in Fractured Rock: A State‐Space Formulation With Preferential and Diffuse Flow to the Water Table

• Published in: Water resources research Vol. 57; no. 9
• Main Authors: Shapiro, Allen M., Day‐Lewis, Frederick D.
• Format: Journal Article
• Language: English
• Published: 01.09.2021
• Subjects: groundwater; Kalman filter; preferential flow; recharge; state‐space model
• ISSN: 0043-1397; 1944-7973
• DOI: 10.1029/2020WR029110

Rapid infiltration following precipitation may result in groundwater contamination from surface contaminants or pathogens. In fractured rock, contaminants can migrate rapidly to points of groundwater withdrawals. In contrast to the temporal availability of groundwater quality chemical indicators, meteorological and groundwater level observations are available in real‐time to estimate time‐varying recharge, which can act as a surrogate to identify periods of rapid infiltration that may indicate contamination susceptibility. Estimating recharge using methods, such as base‐flow recession, unsaturated infiltration models, or water‐table fluctuations (WTF), cannot capitalize on currently available technologies and telecommunication infrastructure to conduct real‐time recharge estimation at scales relevant to characterizing rapid infiltration. We present a linear, physics‐based state‐space (SS) model of one‐dimensional infiltration to estimate recharge, which includes preferential and diffuse‐flow to the water table. The model can take advantage of real‐time data for water‐table altitude, precipitation, and evapotranspiration. Model parameters are calibrated over an observation period, and the Kalman Filter (KF) is subsequently applied to continuously update the observed (water‐table altitude) and unobserved (groundwater recharge) system states and predict future states as new data become available. The SS/KF algorithm is demonstrated at the Masser Groundwater Recharge Site in Pennsylvania, USA and comparisons are made with recharge estimates from WTF methods. Model results indicate that the frequency of observations (daily vs. sub‐daily) dictates the allocation between preferential and diffuse flow. Additionally, because infiltration processes encompass many nonlinearities, model parameters estimated from observation periods need to be updated at least seasonally to account for changing recharge conditions. Key Points A state‐space model interprets time series for water table altitude and meteorological inputs to estimate and forecast recharge Preferential and diffuse flow through the unsaturated zone are conceptualized using a precipitation rate threshold The frequency of observations dictates the recharge allocation between preferential and diffuse flow through the unsaturated zone