Investigation of Data Assimilation Methods for Soil Parameter Estimation with Different Types of Data

Abstract

Groundwater level data require EnRML for better interpretation. Different methods perform similarly when assimilating surface soil moisture data. Soil water pressure head data are the most valuable in terms of parameter estimation. MCMC performs well in homogeneous soil but degrades in heterogeneous soil. The EnKF method relies more on a relatively large number of ensembles than does EnRML. In the past few decades, different data assimilation methods have been proposed to estimate soil parameters. It is not clear whether a straightforward sampling approach is sufficient or whether a linear filter or even an advanced nonlinear filter is needed to interpret the potential information carried by different data types (e.g., pressure head and water content data from multiple depths, easily available surface soil moisture data, and groundwater level data). In this study, three classical data assimilation methods, i.e., the ensemble Kalman filter (EnKF), the ensemble randomized maximum likelihood filter (EnRML), and the Markov chain Monte Carlo (MCMC), were investigated numerically in terms of the utility to cope with three different types of observations. Results show that, compared with the EnKF approach, EnRML is a superior method to extract the parameter information from observations. The MCMC approach performs well in homogeneous soil but not in heterogeneous soil. Regardless of the data assimilation methods and the soil heterogeneity, point‐scale soil water pressure head data are the most valuable in terms of soil parameter estimation, followed by groundwater level data, which require a nonlinear filter to interpret. A smaller observation error for groundwater level data leads to obviously improved parameter estimates by using EnRML with a slight improvement by using EnKF. The stable performance of the EnKF method relies more heavily on a relatively large number of ensembles than the EnRML method, whereas only a few ensemble members are needed for EnRML in a homogeneous soil column.

Data assimilation with multiple types of observation boreholes via the ensemble Kalman filter embedded within stochastic moment equations

“…The ensemble Kalman filter (EnKF; Evensen, 1994) is a powerful approach to parameter estimation in subsurface flow (Hendricks Franssen and Kinzelbach, 2008;Zheng et al, 2019) and solute transport (Liu et al, 2008;Li et al, 2012;Chen et al, 2018;Xu and Gomez-Hernandez, 2018) scenarios. Estimated system parameters can include conductivity (Botto et al, 2018), permeability (Zovi et al, 2017), porosity (Li et al, 2012), specific storage (Hendricks Franssen et al, 2011), dispersivity (Liu et al, 2008), riverbed conductivity (Kurtz et al, 2014), or unsaturated flow characteristic quantities (Zha et al, 2019;Li et al, 2020).…”

“…In this broad framework, it is noted that the accuracy of parameter estimation for a given environmental system is jointly determined by the ability of the mathematical model to describe the system of interest (Sakov and Bocquet, 2018;Alfonzo and Oliver, 2020;Luo, 2019;Evensen, 2019), the ability of the assimilation algorithm used (Emerick and Reynolds, 2013;Bocquet and Sakov, 2014), as well as by the quantity and quality of available observations (Zha et al, 2019;Xia et al, 2018, and references therein).…”

“…Data assimilation is performed by relying on an EnKF coupled with stochastic moment equations (MEs) of transient groundwater flow (e.g., Tartakovsky and Neuman, 1998a, b;Zhang, 2002;Ye et al, 2004). The latter are approximated at second order (in terms of the standard deviation of the natural logarithm of hydraulic conductivity) and are solved by an efficient numerical scheme proposed in this study.…”

“…While we refer to Zhang (2002) and Winter et al (2003) for reviews of MEs in heterogeneous conductivity fields, we recall that MEs of groundwater flow have been previously incorporated into geostatistical inverse modeling approaches (e.g., Hernandez et al, 2003) or stochastic pumping test interpretation (Neuman et al, 2004(Neuman et al, , 2007 and have been considered in field settings (Riva et al, 2009;Bianchi Janetti et al, 2010;Panzeri et al, 2015). More recent developments have allowed embedding stochastic MEs of steadystate groundwater flow in model reduction strategies (Xia et al, 2020).…”

Challenges with effective representations of heterogeneity in soil hydrology based on local water content measurements

“…In many cases, however, only one‐dimensional heterogeneity can be considered in parameter estimation based on information from local measurement profiles. For example, Zha, Zhu, Zhang, Mao, and Shi (2019) directly estimated a one‐dimensional parameter field, and Brandhorst, Erdal, and Neuweiler (2017), Erdal, Neuweiler, and Wollschläger (2014), and Zhang et al. (2019) estimated an additional bias to the state to consider model structural error, which can also stem from unresolved small‐scale heterogeneity.…”