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

Abstract

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.

Development and evaluation of an efficient soil-atmosphere model (FHAVeT) based on the Ross fast solution of the Richards equation for bare soil conditions

“…At longer term, the interest would be to enlarge the scope of the soil water and heat transfer model to other processes such as root uptake, solute transport, biogeochemical reaction and soil property dynamics. It was found that the main challenge in implementing a physically based model to estimate soil water content is the evaluation of soil hydraulic properties, requiring the development of estimation strategies such as using pedotransfer functions (PTF) and assimilation techniques (Witono and Bruckler, 1989;Zhu and Mohanty, 2004;Medina et al, 2014). Our work focuses on the innovation made in the FHAVeT (Fast Hydro Atmosphere Vegetation Temperature) model and does not consider those strategies that are already addressed in other studies (Chanzy et al, 2008).…”

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

“…However, several studies highlighted the instability and intractability of this approach as a result of the complex interactions between states and parameters in a nonlinear dynamic system (Moradkhani et al, 2005;Liu and Gupta, 2007). Medina et al (2014) have shown that the decoupled state-space representation in the dual KF provides higher flexibility since different Kalman filters can be selected for the states and parameters, respectively, according to the specific characteristics of both the observation and system equations.…”

“…Nevertheless, further improvements can be easily incorporated, as for instance reported by Kavetski et al (2002), who demonstrated that the reliability and the efficiency of these noniterative linearized schemes can be increased by adaptive truncation error control, and can be even more efficient than analogous time stepping schemes with iterative solvers. Medina et al (2014) provided valuable insights about the identifiability of the parameters featuring in the van Genuchten-Mualem soil hydraulic analytical relations (van Genuchten, 1980) by means of dual Kalman filters. This study also discussed the impact exerted by parameter initialization, observation depth, and assimilation frequency on the overall DSUKF retrieval performance, as well as the influence of the formulation of the Richards differential equation (either h-based or θ-based form).…”

“…Monztka et al (2011) and Plaza et al (2012) performed recursive state and parameter retrieval for the soil moisture estimation, but using a particle filter algorithm, which is another sequential method widely applied in the most recent studies (Vrugt et al, 2013). Medina et al (2014) performed a synthetic numerical study to evaluate a dual Kalman filter (named DSUKF) for real-time simultaneous prediction of soil water content or matric pressure head profiles and soil hydraulic parameters, by assimilating near-surface information in a onedimensional Richards equation. In this approach, a standard Kalman filter is implemented with a Crank-Nicolson numerical scheme to retrieve soil state profiles, while an unscented Kalman filter (UKF) Uhlman, 1997, 2004;van der Merwe 2004) is implemented for retrieving soil hydraulic parameters.…”

“…The method consists of a non-sequential inversion procedure, also implemented with a Crank-Nicolson numerical scheme, but using matric pressure head data instead of soil water content data. The evaporation experiments carried out by Romano and Santini (1999) have been selected mainly because soil water content values were also measured with a relatively high vertical resolution using the gamma ray attenuation method, thus providing a valuable experimental data set to test the DSUKF approach developed by Medina et al (2014).…”