Skip to main content
U.S. flag

An official website of the United States government

Algorithms for model parameter estimation, state estimation, and forecasting applied to a State-Space model coupled with the Kalman Filter for one-dimensional vertical infiltration to fractured rock aquifers

September 13, 2021

The algorithms and input data included in this data release are used to interpret time-series data (water- table altitude, precipitation, and potential evapotranspiration) over an observation period to estimate model parameters of a State-Space (SS) model of vertical infiltration to a fractured-rock aquifer. The SS model is coupled with a Kalman Filter (KF) to estimate system states (water-table altitude and groundwater recharge) over the observation period and forecast beyond the end of the observation period. This SS/KF model is formulated for one-dimensional vertical infiltration and includes preferential and diffuse flow through the unsaturated zone to the water table.
The analysis was conducted to demonstrate the application of the SS/KF model in characterizing responses of the groundwater table and estimating time-varying groundwater recharge following precipitation events. In fractured rock aquifers, rapid infiltration to the groundwater table following precipitation may result in groundwater contamination from surface contaminants or pathogens. The magnitude of the time-varying groundwater recharge can be used as surrogate to indicate time-varying contamination susceptibility of the groundwater, as microbial, particulate and other groundwater quality chemical indicators are unlikely to be available or are costly to develop with the temporal frequency needed to resolve responses to precipitation events. The SS/KF model can capitalize on currently available technologies and telecommunication infrastructure that deliver real-time data for water table altitudes and meteorological inputs to conduct real-time recharge estimation and forecasting.
Fourteen simulations are conducted to demonstrate the application of the SS/KF model to the interpretation of time series data for water table altitude, precipitation, and potential evapotranspiration. The data used in this demonstration are from a period of record in 1999 from the Masser Groundwater Recharge Site in Pennsylvania, USA, which is administered by the U.S. Department of Agriculture, Agricultural Research Service. Seasonal (Spring, Summer, and Fall) simulations using the SS/KF model are presented in this data release, along with the simulations that considered the continuous records between February and December 1999. The application of the SS/KF model is demonstrated with 30-mminute observations for the time series data, and also using daily observations of the time-series data. The daily observations for the water table altitude considered both daily average and daily maximum water table altitudes.
The algorithms used to formulate the SS/KF model and interpret the time-series data are prepared in the software MATLAB®, where functional calls are made to available algorithms that conduct the parameter estimation of the SS model parameters, followed by the application of the KF to perform the estimation and forecasting of models states. The MATLAB® files developed for the simulations are available in this data release. MATLAB® is a proprietary software, and thus, a stand-alone and executable version of the algorithms is not available in this data release. MATLAB can be downloaded from The source and description of the time-series data used in this data release are available in Baker et al. ( This USGS data release contains all input and output files for the simulations described in the associated journal article (https://xxxxx_journal).

Related Content