Kalman filters for assimilating near-surface observations into the Richards equation – Part 3: Retrieving states and parameters from laboratory evaporation experiments

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

doi:10.5194/hess-18-2543-2014

Cited by 12 publications

(8 citation statements)

References 42 publications

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“…The soil hydraulic parameter uncertainty is identified as a major uncertainty source in vadose zone hydrology, and many studies have been focused on this topic. A highly relevant research area, inverse modeling, has been developed to reduce the uncertainty of the parameter by incorporating observational data (Erdal et al, 2014;Montzka et al, 2011;Margulis, 2011, 2013). Boundary conditions also introduce uncertainty during the simulation of soil water flow (Ataie-Ashtiani et al, 1999;Forsyth et al, 1995;Szomolay, 2008).…”

Section: Introductionmentioning

confidence: 99%

On the uncertainty of initial condition and initialization approaches in variably saturated flow modeling

Yang

Shi

et al. 2019

Hydrol. Earth Syst. Sci.

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Abstract. Soil water movement has direct effects on environment, agriculture and hydrology. Simulation of soil water movement requires accurate determination of model parameters as well as initial and boundary conditions. However, it is difficult to obtain the accurate initial soil moisture or matric potential profile at the beginning of simulation time, making it necessary to run the simulation model from the arbitrary initial condition until the uncertainty of the initial condition (UIC) diminishes, which is often known as “warming up”. In this paper, we compare two commonly used methods for quantifying the UIC (one is based on running a single simulation recursively across multiple hydrological years, and the other is based on Monte Carlo simulations with realization of various initial conditions) and identify the warm-up time twu (minimum time required to eliminate the UIC by warming up the model) required with different soil textures, meteorological conditions and soil profile lengths. Then we analyze the effects of different initial conditions on parameter estimation within two data assimilation frameworks (i.e., ensemble Kalman filter and iterative ensemble smoother) and assess several existing model initializing methods that use available data to retrieve the initial soil moisture profile. Our results reveal that Monte Carlo simulations and the recursive simulation over many years can both demonstrate the temporal behavior of the UIC, and a common threshold is recommended to determine twu. Moreover, the relationship between twu for variably saturated flow modeling and the model settings (soil textures, meteorological conditions and soil profile length) is quantitatively identified. In addition, we propose a warm-up period before assimilating data in order to obtain a better performance for parameter and state estimation.

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Section: Introductionmentioning

confidence: 99%

On the uncertainty of initial condition and initialization approaches in variably saturated flow modeling

Yang

Shi

et al. 2019

Hydrol. Earth Syst. Sci.

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“…The main advantage of testing the algorithm with a synthetic study is that, by knowing the true system, the results are not overshadowed by other sources of uncertainty: a fundamental aspect that should be addressed prior to evaluating algorithm performance with real data, as in the study presented by Medina et al (2014).…”

Section: Synthetic Experimental Frameworkmentioning

confidence: 99%

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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“…Soil water in the vadose zone exerts a large control on the water and energy balance of land-atmosphere systems over a wide range of space-time scales (e.g. Milly and Dunne, 1994;Entekhabi et al, 1996;Vrugt et al, 2001Vrugt et al, , 2003Rodriguez-Iturbe and Porporato, 2005). With the increasing availability of near-surface data from remote and ground-based sensors, unique opportunities emerge to predict the soil water dynamics (McLaughlin, 2002;Vereecken et al, 2008).…”

Section: Introductionmentioning

confidence: 99%

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

Chirico¹,

Medina²,

Romano³

2012

Preprint

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This paper examines the potential of different algorithms, based on the Kalman filtering approach, for assimilating near-surface observations in a one-dimensional Richards' equation. Our specific objectives are: (i) to compare the efficiency of different Kalman filter algorithms, implemented with different numerical schemes of the Richards equation, in retrieving soil water potential profiles; (ii) to evaluate the performance of these algorithms when nonlinearities arise from the nonlinearity of the observation equation, i.e. when surface soil water content observations are assimilated to retrieve pressure head values. The study is based on a synthetic simulation of an evaporation process from a homogeneous soil column. A standard Kalman Filter algorithm is implemented with both an explicit finite difference scheme and a Crank-Nicolson finite difference scheme of the Richards equation. Extended and Unscented Kalman Filters are instead both evaluated to deal with the nonlinearity of a backward Euler finite difference scheme. While an explicit finite difference scheme is computationally too inefficient to be implemented in an operational assimilation scheme, the retrieving algorithm implemented with a Crank-Nicolson scheme is found computationally more feasible and robust than those implemented with the backward Euler scheme. The Unscented Kalman Filter reveals as the most practical approach when one has to deal with further nonlinearities arising from the observation equation, as result of the nonlinearity of the soil water retention function

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Kalman filters for assimilating near-surface observations into the Richards equation – Part 3: Retrieving states and parameters from laboratory evaporation experiments

Cited by 12 publications

References 42 publications

On the uncertainty of initial condition and initialization approaches in variably saturated flow modeling

On the uncertainty of initial condition and initialization approaches in variably saturated flow modeling

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 in the Richards equation – Part 1: Retrieving state profiles with linear and nonlinear numerical schemes

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