Incorporating Snowmelt into Daily Estimates of Recharge Using a State‐Space Model of Infiltration

Abstract

A state-space model (SSM) of infiltration estimates daily groundwater recharge using time-series of groundwater-level altitude and meteorological inputs (liquid precipitation, snowmelt, and evapotranspiration). The model includes diffuse and preferential flow through the unsaturated zone, where preferential flow is a function of liquid precipitation and snowmelt rates and a threshold rate, above which there is direct recharge to the water table. Model parameters are estimated over seasonal periods and the SSM is coupled with the Kalman Filter (KF) to assimilate recent observations (hydraulic head) and meteorological inputs into recharge estimates. The approach can take advantage of real-time hydrologic and meteorological data to deliver real-time recharge estimates. The model is demonstrated on daily observations from two bedrock wells in carbonate aquifers of northwestern New York (USA) between 2013 and 2018. Meteorological inputs for liquid precipitation and snowmelt are compiled from SNODAS (2021). Results for recharge during winter and spring seasons show preferential flow events to the water table from liquid precipitation, snowmelt, or a combination of the two. Recharge estimates summed annually are consistent with previous estimates of recharge reported from groundwater flow and surface-process models. Results from the SSM and KF point to errors in meteorological inputs, such as the snowmelt rate, that are not compatible with hydraulic head observations. Whereas liquid and solid precipitation are measured at discrete stations and extrapolated to 1-km 2 grid cells, snowmelt is a meteorological modeled outcome that may not represent conditions in the vicinity of monitoring well locations.

Application of Recursive Estimation to Heat Tracing for Groundwater/Surface‐Water Exchange

“…(2016) for a review of Kalman‐based applications in hydrology and to Shapiro et al. (2022), Shapiro and Day‐Lewis (2021), Kang et al. (2018), Kitanidis (2015), Ng et al.…”

Interpreting Concentrations Sampled in Long‐Screened Wells with Borehole Flow: An Inverse Modeling Approach

“…Our work could be extended to formulate the inverse problem using the process model for transient conditions (Equation 5), thus allowing for collection and analysis of samples under changing concentration conditions; this approach could capitalize on additional information available from the timing of breakthrough and evolution of concentration at different locations. The inversion of transient data lends itself to solution using filtering or smoothing approaches similar to the implementations in Shapiro et al (2022) and McAliley et al (2022). Compared to conventional sampling schemes, sampling procedures would require carefully controlled experimental operations and would produce significantly more samples for chemical analysis.…”

Benefits and Cautions in Data Assimilation Strategies: An Example of Modeling Groundwater Recharge

“…Although rapid infiltration is widely recognized for different unsaturated soil conditions (Mohammed et al 2018; Nimmo 2021), and process models of rapid infiltration have been formulated (Kung 1990; Dragila and Wheatcraft 2001; Nimmo 2010), the application of these models has required the characterization of complex unsaturated zone processes and their associated parameters. Instead, in this investigation, we use a DDMM of vertical infiltration and groundwater recharge as described in Shapiro and Day‐Lewis (2021) and Shapiro et al (2022). Young (2003) discusses concepts and advantages of applying a DDMM to complex physical processes.…”

“…Therefore, we limit the estimation of the model parameters over a period where meteorological conditions affecting infiltration are stable, and assume the model parameters are constant over this period. Shapiro and Day‐Lewis (2021) and Shapiro et al (2022) demonstrated that the model parameters vary seasonally, and thus, the parameters depend on recent meteorological conditions and need to be updated. In this investigation, parameters are estimated over an observation period up to current time, referred to as the Parameter‐Estimation Window (PEW) (Figure 1).…”

“…In the estimation of the expected values of the system states, the prediction step of the KF, as it is applied to the SSM, maintains mass conservation. However, the correction step of the KF, which assimilates the most recent observation of h , is not a mass conservative expression (Shapiro et al 2022). The correction step is analogous to reinitializing a groundwater model based on newly acquired information, which may violate previous assumptions of mass in the system.…”