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

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.  
		
Thirteen 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 https://www.mathworks.com.  The 
source and description of the time-series data used in this data release 
are available in Baker et al. (https://doi.org/10.5066/P9LLXCIC). This 
USGS data release contains all input and output files for the simulations 
described in the associated journal article (https://doi.org/10.1029/2020WR029110). 

Tags: broad-mountain-anticlinorium, environment, geoscientificinformation, groundwater, inlandwaters, mathematical-simulation, matlab, mississipian-age-sandstone, northumberland-county, pennsylvania, recharge, susquehanna-river-basin, time-series-analysis, usgs-2c2fd066-3a9f-46a7-b9ba-65cf6ab38385, usgsgroundwatermodel, valley-and-ridge-physiographic-province
Organization: Department of the Interior