Kalman filters for assimilating near-surface observations into the Richards equation – Part 1: Retrieving state profiles with linear and nonlinear numerical schemes

Chirico, Giovanni Battista; Medina, Hanoi; Romano, Nunzio

doi:10.5194/hess-18-2503-2014

Cited by 23 publications

(19 citation statements)

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“…Subsequently, time series of synthetic "true" matric head and soil moisture profiles are generated for 150 days, by setting the initial profile matric head uniformly equal to −50 cm, and by employing the nonlinear numerical scheme illustrated by Chirico et al (2014). Figure 1 also shows the time series of the generated matric pressure head values at 5 cm depth.…”

Section: Model Implementation and Synthetic Data Generationmentioning

confidence: 99%

“…A common assumption, also adopted in this work, is to set λ = 0.5 and pose m = 1 − 1/n. Chirico et al (2014) showed that the implementation of the filtering approach upon a linearized Crank-Nicolson finite difference scheme (CN) can be an efficient algorithm for onedimensional problems. The differentiation of Eq.…”

Section: Governing Equationmentioning

confidence: 99%

“…The DEnKF is implemented following the framework described by Moradkhani et al (2005), coupled with the fully implicit numerical representation of the Richards equation described by Chirico et al (2014). The DEnKF is run with ensembles of 12 members (hereafter referred to as DEnKF(12)) and 50 members (hereafter referred to as DEnKF(50)).…”

Section: Comparative Performance Analysesmentioning

confidence: 99%

“…The implementation of these large-scale assimilation systems is often described as a collection of independent low dimensional assimilation problems (Crow and Wood, 2003;Reichle and Koster, 2003;Kumar et al, 2008). Chirico et al (2014) show that the SKF, coupled with a Crank-Nicolson numerical scheme, can be an efficient choice for low dimensional applications, because it provides retrieval performances similar to those obtained with nonlinear schemes, but with less computational effort, also circumventing some issues which may arise with the sampling strategies used by the UKF and the EnKF. However, the UKF can be more flexible and computationally efficient than the EnKF in problems with low degrees of freedom, because it relies on ensemble sizes equal to twice the number of degrees of freedom plus one.…”

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confidence: 99%

“…Moving from the result of Chirico et al (2014), we hypothesize that the combination of SKF applied to a linearized numerical representation of the Richards equation, and UKF applied to handle the intrinsic nonlinearities between hydraulic parameters and soil water states, could provide a suitable strategy for optimizing the prediction of the state dynamics.…”

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confidence: 99%

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Kalman filters for assimilating near-surface observations into the Richards equation – Part 2: A dual filter approach for simultaneous retrieval of states and parameters

Medina

Romano

Chirico

2014

Hydrol. Earth Syst. Sci.

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Abstract. This study presents a dual Kalman filter (DSUKF -dual standard-unscented Kalman filter) for retrieving states and parameters controlling the soil water dynamics in a homogeneous soil column, by assimilating near-surface state observations. The DSUKF couples a standard Kalman filter for retrieving the states of a linear solver of the Richards equation, and an unscented Kalman filter for retrieving the parameters of the soil hydraulic functions, which are defined according to the van Genuchten-Mualem closed-form model. The accuracy and the computational expense of the DSUKF are compared with those of the dual ensemble Kalman filter (DEnKF) implemented with a nonlinear solver of the Richards equation. Both the DSUKF and the DEnKF are applied with two alternative state-space formulations of the Richards equation, respectively differentiated by the type of variable employed for representing the states: either the soil water content (θ) or the soil water matric pressure head (h). The comparison analyses are conducted with reference to synthetic time series of the true states, noise corrupted observations, and synthetic time series of the meteorological forcing. The performance of the retrieval algorithms are examined accounting for the effects exerted on the output by the input parameters, the observation depth and assimilation frequency, as well as by the relationship between retrieved states and assimilated variables. The uncertainty of the states retrieved with DSUKF is considerably reduced, for any initial wrong parameterization, with similar accuracy but less computational effort than the DEnKF, when this is implemented with ensembles of 25 members. For ensemble sizes of the same order of those involved in the DSUKF, the DEnKF fails to provide reliable posterior estimates of states and parameters. The retrieval performance of the soil hydraulic parameters is strongly affected by several factors, such as the initial guess of the unknown parameters, the wet or dry range of the retrieved states, the boundary conditions, as well as the form (h-based or θ-based) of the state-space formulation. Several analyses are reported to show that the identifiability of the saturated hydraulic conductivity is hindered by the strong correlation with other parameters of the soil hydraulic functions defined according to the van Genuchten-Mualem closed-form model.

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Section: Model Implementation and Synthetic Data Generationmentioning

confidence: 99%

Section: Governing Equationmentioning

confidence: 99%

Section: Comparative Performance Analysesmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Kalman filters for assimilating near-surface observations into the Richards equation – Part 2: A dual filter approach for simultaneous retrieval of states and parameters

Medina

Romano

Chirico

2014

Hydrol. Earth Syst. Sci.

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Inflation method based on confidence intervals for data assimilation in soil hydrology using the ensemble Kalman filter

Jamal

Linker

2020

Vadose Zone Journal

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The ensemble Kalman filter (EnKF) is a widely used data assimilation method in soil hydrology. However, underestimation of the modeling errors and of the sampling errors may cause systematic reduction of state variances and rejection of the observations. Inflation methods are used to alleviate this phenomenon. Here, we suggest a novel inflation method based on confidence intervals constructed using the collected ensemble of the measurements. The proposed method is illustrated via two synthetic examples of a three-layer soil with (i) precipitation and evaporation boundary condition and (ii) irrigation boundary condition. We present a comparison of two existing inflation methods and discuss the advantages and limitations of the proposed method. Basically, the suggested method behavior is superior to the behavior of the existing methods. Abbreviations: EnKF, ensemble Kalman filter. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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Geophysical and hydrological data assimilation to monitor water content dynamics in the rocky unsaturated zone

Carlo

Berardi

Vurro

et al. 2018

Environ Monit Assess

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In recent years, geophysics is increasingly used to study the flow and transport processes in the vadose zone. Particularly, when the vadose zone is made up of rocks, it is difficult to install sensors in the subsurface to measure hydrological state variables directly. In these cases, the electrical resistivity tomography (ERT) represents a useful tool to monitor the hydrodynamics of the infiltration and to estimate hydraulic parameters and state variables, such as hydraulic conductivity and water content. We propose an integrated approach aimed at predicting water content dynamics in calcarenite, a sedimentary carbonatic porous rock. The uncoupled hydrogeophysical approach proposed consists in 4D ERT monitoring conducted during an infiltrometer test under falling head conditions. Capacitance probes were installed to measure water content at different depths to validate the estimations derived from ERT. A numerical procedure, based on a data assimilation technique, was accomplished by combining the model (i.e., Richards' equation) with the observations in order to provide reliable water content estimations. We have used a new data assimilation method that is easy to implement, based on the ensemble Kalman filter coupled with Brownian bridges. This approach is particularly suitable for strongly non-linear models, such as Richards' equation, in order to take into account both the model uncertainty and the observation errors. The proposed data assimilation approach was tested for the first time on field data. A reasonable agreement was found between observations and predictions confirming the ability of the integrated approach to predict water content dynamics in the rocky subsoil.

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Kalman filters for assimilating near-surface observations into the Richards equation – Part 1: Retrieving state profiles with linear and nonlinear numerical schemes

Cited by 23 publications

References 50 publications

Kalman filters for assimilating near-surface observations into the Richards equation – Part 2: A dual filter approach for simultaneous retrieval of states and parameters

Kalman filters for assimilating near-surface observations into the Richards equation – Part 2: A dual filter approach for simultaneous retrieval of states and parameters

Inflation method based on confidence intervals for data assimilation in soil hydrology using the ensemble Kalman filter

Geophysical and hydrological data assimilation to monitor water content dynamics in the rocky unsaturated zone

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