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Algorithms for model parameter estimation and state estimation applied to a state-space model for one-dimensional vertical infiltration incorporating snowmelt rate as a system input

May 13, 2022

The algorithms and input data included in this data release are used to interpret time-series
data (water-table altitude, precipitation, snowmelt, and potential evapotranspiration) over an
observation period to estimate model parameters of a State-Space Model (SSM) of vertical
infiltration to the groundwater table. The SSM model is coupled with a Kalman Filter (KF)
to estimate system states (water-table altitude and groundwater recharge) over the observation
period. This SSM and 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 SSM and KF model in
characterizing responses of the groundwater table and estimating time-varying groundwater
recharge due to the combination of liquid precipitation events and snowmelt events. The
SSM and KF are applied to daily information for water-table altitude, liquid precipitation,
snowmelt, and potential evapotranspiration. In fractured rock aquifers, rapid infiltration to
the groundwater table following precipitation and snowmelt events may result in groundwater
contamination from surface contaminants or pathogens. The magnitude of the time-varying
groundwater recharge can be used as a 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 and snowmelt events. The SSM
and KF 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.

Simulations are conducted to demonstrate the application of the SSM and KF to the
interpretation of time-series data for water-table altitude, liquid precipitation, snowmelt,
and potential evapotranspiration. The data used in this demonstration are from a period
of record in between January 1, 2013 and December 31, 2018 for groundwater monitoring
wells in northwestern New York, USA; the groundwater monitoring wells measure
groundwater responses in the carbonate aquifers that are used for watersupply in this
region. Water-table altitude data are available from the U.S. Geological Survey (USGS),
and meteorological data are available from the National Oceanic and Atmospheric
Administration (NOAA), and the Snow Data Assimilation System (SNODAS).
Seasonal (Spring, Summer, Fall, and Winter) simulations using the SSM and KF
are presented in this data release.

The algorithms used to formulate the SSM and KF 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 SSM parameters, followed by the application
of the KF to perform the estimation of model 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.
Details regarding the availability of MATLAB are available from
This USGS data release contains all input and output files for the simulations described in
the associated journal article (

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