Dual state-parameter estimation of root zone soil moisture by optimal parameter estimation and extended Kalman filter data assimilation

With well-determined hydraulic parameters in a hydrologic model, a traditional data assimilation method (such as the Kalman filter and its extensions) can be used to retrieve root zone soil moisture under uncertain initial state variables (e.g., initial soil moisture content) and good simulated results can be achieved. However, when the key soil hydraulic parameters are incorrect, the error is non-Gaussian, as the Kalman filter will produce a persistent bias in its predictions. In this paper, we propose a method coupling optimal parameters and extended Kalman filter data assimilation (OP-EKF) by combining optimal parameter estimation, the extended Kalman filter (EKF) assimilation method, a particle swarm optimization (PSO) algorithm, and Richards’ equation. We examine the accuracy of estimating root zone soil moisture through the optimal parameters and extended Kalman filter data assimilation method by using observed in situ data at the Meiling experimental station, China. Results indicate that merely using EKF for assimilating surface soil moisture content to obtain soil moisture content in the root zone will produce a persistent bias between simulated and observed values. Using the OP-EKF assimilation method, estimates were clearly improved. If the soil profile is heterogeneous, soil moisture retrieval is accurate in the 0-50 cm soil profile and is inaccurate at 100 cm depth. Results indicate that the method is useful for retrieving root zone soil moisture over large areas and long timescales even when available soil moisture data are limited to the surface layer, and soil moisture content are uncertain and soil hydraulic parameters are incorrect.     

Using a H∞ filter assimilation procedure to estimate root zone soil water content

Root zone soil water content impacts plant water availability, land energy and water balances. Because of unknown hydrological model error, observation errors and the statistical characteristics of the errors, the widely used Kalman filter (KF) and its extensions are challenged to retrieve the root zone soil water content using the surface soil water content. If the soil hydraulic parameters are poorly estimated, the KF and its extensions fail to accurately estimate the root zone soil water. The H‐infinity filter (HF) represents a robust version of the KF. The HF is widely used in data assimilation and is superior to the KF, especially when the performance of the model is not well understood. The objective of this study is to study the impact of uncertain soil hydraulic parameters, initial soil moisture content and observation period on the ability of HF assimilation to predict in situ soil water content. In this article, we study seven cases. The results show that the soil hydraulic parameters hold a critical role in the course of assimilation. When the soil hydraulic parameters are poorly estimated, an accurate estimation of root soil water content cannot be retrieved by the HF assimilation approach. When the estimated soil hydraulic parameters are similar to actual values, the soil water content at various depths can be accurately retrieved by the HF assimilation. The HF assimilation is not very sensitive to the initial soil water content, and the impact of the initial soil water content on the assimilation scheme can be eliminated after about 5–7 days. The observation interval is important for soil water profile distribution retrieval with the HF, and the shorter the observation interval, the shorter the time required to achieve actual soil water content. However, the retrieval results are not very accurate at a depth of 100 cm. Also it is complex to determine the weighting coefficient and the error attenuation parameter in the HF assimilation. In this article, the trial‐and‐error method was used to determine the weighting coefficient and the error attenuation parameter. After the first establishment of limited range of the parameters, ‘the best parameter set’ was selected from the range of values. For the soil conditions investigated, the HF assimilation results are better than the open‐loop results. Copyright © 2010 John Wiley & Sons, Ltd.     

Simultaneous estimation of surface soil moisture and soil properties with a dual ensemble Kalman smoother

In this paper, a new state-parameter estimation approach is presented based on the dual ensemble Kalman smoother(DEn KS) and simple biosphere model(Si B2) to sequentially estimate both the soil properties and soil moisture profile by assimilating surface soil moisture observations. The Arou observation station, located in the upper reaches of the Heihe River in northwestern China, was selected to test the proposed method. Three numeric experiments were designed and performed to analyze the influence of uncertainties in model parameters, atmospheric forcing, and the model's physical mechanics on soil moisture estimates. Several assimilation schemes based on the ensemble Kalman filter(En KF), ensemble Kalman smoother(En KS), and dual En KF(DEn KF) were also compared in this study. The results demonstrate that soil moisture and soil properties can be simultaneously estimated by state-parameter estimation methods, which can provide more accurate estimation of soil moisture than traditional filter methods such as En KF and En KS. The estimation accuracy of the model parameters decreased with increasing error sources. DEn KS outperformed DEn KF in estimating soil moisture in most cases, especially where few observations were available. This study demonstrates that the DEn KS approach is a useful and practical way to improve soil moisture estimation.     

A land surface soil moisture data assimilation framework in consideration of the model subgrid-scale heterogeneity and soil water thawing and freezing

The Ensemble Kalman Filter (EnKF) is well known and widely used in land data assimilation for its high precision and simple operation. The land surface models used as the forecast operator in a land data assimilation system are usually designed to consider the model subgrid-heterogeneity and soil water thawing and freezing. To neglect their effects could lead to some errors in soil moisture assimilation. The dual EnKF method is employed in soil moisture data assimilation to build a soil moisture data as- similation framework based on the NCAR Community Land Model version 2.0 (CLM 2.0) in considera- tion of the effects of the model subgrid-heterogeneity and soil water thawing and freezing: Liquid volumetric soil moisture content in a given fraction is assimilated through the state filter process, while solid volumetric soil moisture content in the same fraction and solid/liquid volumetric soil moisture in the other fractions are optimized by the parameter filter. Preliminary experiments show that this dual EnKF-based assimilation framework can assimilate soil moisture more effectively and precisely than the usual EnKF-based assimilation framework without considering the model subgrid-scale heteroge- neity and soil water thawing and freezing. With the improvement of soil moisture simulation, the soil temperature-simulated precision can be also improved to some extent.     

A soil moisture assimilation scheme based on the ensemble Kalman filter using microwave brightness temperature

This study presents a soil moisture assimilation scheme, which could assimilate microwave brightness temperature directly, based on the ensemble Kalman filter and the shuffled complex evolution method (SCE-UA). It uses the soil water model of the land surface model CLM3.0 as the forecast operator, and a radiative transfer model (RTM) as the observation operator in the assimilation system. The assimilation scheme is implemented in two phases: the parameter calibration phase and the pure soil moisture assimilation phase. The vegetation optical thickness and surface roughness parameters in the RTM are calibrated by SCE-UA method and the optimal parameters are used as the final model parameters of the observation operator in the assimilation phase. The ideal experiments with synthetic data indicate that this scheme could significantly improve the simulation of soil moisture at the surface layer. Furthermore, the estimation of soil moisture in the deeper layers could also be improved to a certain extent. The real assimilation experiments with AMSR-E brightness temperature at 10.65 GHz (vertical polarization) show that the root mean square error (RMSE) of soil moisture in the top layer (0–10 cm) by assimilation is 0.03355 m³ · m⁻³, which is reduced by 33.6% compared with that by simulation (0.05052 m³ · m⁻³). The mean RMSE by assimilation for the deeper layers (10–50 cm) is also reduced by 20.9%. All these experiments demonstrate the reasonability of the assimilation scheme developed in this study.     

Initialisation of Land Surface Variables for Numerical Weather Prediction

Land surface processes and their initialisation are of crucial importance for Numerical Weather Prediction (NWP). Current land data assimilation systems used to initialise NWP models include snow depth analysis, soil moisture analysis, soil temperature and snow temperature analysis. This paper gives a review of different approaches used in NWP to initialise land surface variables. It discusses the observation availability and quality, and it addresses the combined use of conventional observations and satellite data. Based on results from the European Centre for Medium-Range Weather Forecasts (ECMWF), results from different soil moisture and snow depth data assimilation schemes are shown. Both surface fields and low-level atmospheric variables are highly sensitive to the soil moisture and snow initialisation methods. Recent developments of ECMWF in soil moisture and snow data assimilation improved surface and atmospheric forecast performance.     

A dual-pass data assimilation scheme for estimating surface fluxes with FY3A-VIRR land surface temperature

In this work, a dual-pass data assimilation scheme is developed to improve predictions of surface flux. Pass 1 of the dual-pass data assimilation scheme optimizes the model vegetation parameters at the weekly temporal scale, and Pass 2 optimizes the soil moisture at the daily temporal scale. Based on ensemble Kalman filter(EnKF), the land surface temperature(LST) data derived from the new generation of Chinese meteorology satellite(FY3A-VIRR) are assimilated into common land model(CoLM) for the first time. Six sites, Daman, Guantao, Arou, BJ, Miyun and Jiyuan, are selected for the data assimilation experiments and include different climatological conditions. The results are compared with those from a dataset generated by a multi-scale surface flux observation system that includes an automatic weather station(AWS), eddy covariance(EC) and large aperture scintillometer(LAS). The results indicate that the dual-pass data assimilation scheme is able to reduce model uncertainties and improve predictions of surface flux with the assimilation of FY3A-VIRR LST data.     

Improving the estimation of hydrothermal state variables in the active layer of frozen ground by assimilating <Emphasis Type="Italic">in situ</Emphasis> observations and SSM/I data

The active layer of frozen ground data assimilation system adopts the SHAW (Simulteneous Heat and Water) model as the model operator. It employs an ensemble kalman filter to fuse state variables predicted by the SHAW model with in situ observation and the SSM/I 19 GHz brightness temperature for the purpose of optimizing model hydrothermal state variables. When there is little water movement in the frozen soil during the winter season, the unfrozen water content depends primarily on soil temperature. Thus, soil temperature is the crucial state variable to be improved. In contrast, soil moisture is heavily influenced by precipitation during the summer season. The simulation accuracy of soil moisture has a strong and direct impact on the soil temperature. In this case, the crucial state variable to be improved is soil moisture. One-dimensional assimilation experiments that have been carried out at AMDO station show that land data assimilation method can improve the estimation of hydrothermal state variables in the soil by fusing model information and observation information. The reasonable model error covariance matrix plays a key role in transferring the optimized surface state information to the deep soil, and it provides improved estimations of whole soil state profiles. After assimilating the 4-cm soil temperature by in situ observation, the soil temperature RMSE (Root Mean Square Error) of each soil layer decreased by 0.96°C on average relative to the SHAW simulation. After assimilating the 4-cm soil moisture in situ observation, the soil moisture RMSE of each soil layer decreased by 0.020 m³·m⁻³. When assimilating the SSM/I 19 GHz brightness temperature, the soil temperature RMSE of each soil layer during the winter decreased by 0.76°C, while the soil moisture RMSE of each soil layer during the summer decreased by 0.018 m³·m⁻³.     

Application of data assimilation with the Root Zone Water Quality Model for soil moisture profile estimation in the upper Cedar Creek,Indiana

Data assimilation techniques have been proven as an effective tool to improve model forecasts by combining information about observed variables in many areas. This article examines the potential of assimilating surface soil moisture observations into a field‐scale hydrological model, the Root Zone Water Quality Model, to improve soil moisture estimation. The Ensemble Kalman Filter (EnKF), a popular data assimilation technique for nonlinear systems, was applied and compared with a simple direct insertion method. In situ soil moisture data at four different depths (5, 20, 40, and 60 cm) from two agricultural fields (AS1 and AS2) in northeastern Indiana were used for assimilation and validation purposes. Through daily update, the EnKF improved soil moisture estimation compared with the direct insertion method and model results without assimilation, having more distinct improvement at the 5 and 20 cm depths than for deeper layers (40 and 60 cm). Local vertical soil property heterogeneity in AS1 deteriorated soil moisture estimates with the EnKF. Removal of systematic bias in the forecast model was found to be critical for more successful soil moisture data assimilation studies. This study also demonstrates that a more frequent update generally contributes in enhancing the open loop simulation; however, large forecasting error can prevent more frequent update from providing better results. In addition, results indicate that various ensemble sizes make little difference in the assimilation results. An ensemble of 100 members produced results that were comparable with results obtained from larger ensembles. Copyright © 2011 John Wiley & Sons, Ltd.     

Assimilation of near-surface temperature using extended Kalman filter

In order to improve the soil temperature profile predictions in land-surface models, an assimilation scheme using the extended Kalman filter is developed. This formulation is based on the discretized diffusion equation of heat transfer through the soil column. The scheme is designed to incorporate the knowledge of the uncertainties in both the model and the measurement. Model uncertainty is estimated by quantifying the model drift from observations when the model is initialized using the observed values. Furthermore, the initial error covariance has a significant influence on the performance of the assimilation scheme. It is shown that an inaccurate initial value for the error covariance can actually diminish the predictive capabilities of the model. When an appropriate initial error covariance is specified, using the top layer soil temperature observations in the assimilation scheme allows for improved predictive capabilities in lower layers. Observations at 30 min intervals have a significant effect on the model predictions in the lower layers. Assimilation of observations at 24 h intervals also has an effect on the lower layer predictive capability of the model, albeit more slowly than the 30 min assimilation scenario.     

Real-time assimilation of streamflow observations into a hydrological routing model: effects of model structures and updating methods

This paper comparatively assesses the performance of five data assimilation techniques for three-parameter Muskingum routing with a spatially lumped or distributed model structure. The assimilation techniques used include direct insertion (DI), nudging scheme (NS), Kalman filter (KF), ensemble Kalman filter (EnKF) and asynchronous ensemble Kalman filter (AEnKF), which are applied to river reaches in Texas and Louisiana, USA. For both lumped and distributed routing, results from KF, EnKF and AEnKF are sensitive to the error specification. As expected, DI outperformed the other models in the case of lumped modelling, while in distributed routing, KF approaches, particularly AEnKF and EnKF, performed better than DI or nudging, reflecting the benefit of updating distributed states through error covariance modelling in KF approaches. The results of this work would be useful in setting up data assimilation systems that employ increasingly abundant real-time observations using distributed hydrological routing models.     

Comparison of ensemble-based state and parameter estimation methods for soil moisture data assimilation

Model parameters are a source of uncertainty that can easily cause systematic deviation and significantly affect the accuracy of soil moisture generation in assimilation systems. This study addresses the issue of retrieving model parameters related to soil moisture via the simultaneous estimation of states and parameters based on the Common Land Model (CoLM). The state-parameter estimation algorithms AEnKF (Augmented Ensemble Kalman Filter), DEnKF (Dual Ensemble Kalman Filter) and SODA (Simultaneous optimization and data assimilation) are entirely implemented within an EnKF framework to investigate how the three algorithms can correct model parameters and improve the accuracy of soil moisture estimation. The analysis is illustrated by assimilating the surface soil moisture levels from varying observation intervals using data from Mongolian plateau sites. Furthermore, a radiation transfer model is introduced as an observation operator to analyze the influence of brightness temperature assimilation on states and parameters that are estimated at different microwave signal frequencies. Three cases were analyzed for both soil moisture and brightness temperature assimilation, focusing on the progressive incorporation of parameter uncertainty, forcing data uncertainty and model uncertainty. It has been demonstrated that EnKF is outperformed by all other methods, as it consistently maintains a bias. State-parameter estimation algorithms can provide a more accurate estimation of soil moisture than EnKF. AEnKF is the most robust method, with the lowest RMSE values for retrieving states and parameters dealing only with parameter uncertainty, but it possesses disadvantages related to increasing sources of uncertainty and decreasing numbers of observations. SODA performs well under the complex situations in which DEnKF shows slight disadvantages in terms of statistical indicators; however, the former consumes far more memory and time than the latter.     

Data assimilation with the ensemble Kalman filter in a numerical model of the North Sea

Coastal management and maritime safety strongly rely on accurate representations of the sea state. Both dynamical models and observations provide abundant pieces of information. However, none of them provides the complete picture. The assimilation of observations into models is one way to improve our knowledge of the ocean state. Its application in coastal models remains challenging because of the wide range of temporal and spatial variabilities of the processes involved. This study investigates the assimilation of temperature profiles with the ensemble Kalman filter in 3-D North Sea simulations. The model error is represented by the standard deviation of an ensemble of model states. Parameters’ values for the ensemble generation are first computed from the misfit between the data and the model results without assimilation. Then, two square root algorithms are applied to assimilate the data. The impact of data assimilation on the simulated temperature is assessed. Results show that the ensemble Kalman filter is adequate for improving temperature forecasts in coastal areas, under adequate model error specification.     

A particle batch smoother for soil moisture estimation using soil temperature observations

In this study, we present a particle batch smoother (PBS) to determine soil moisture profiles by assimilating soil temperatures at two depths (4 and 8 cm). The PBS can be considered as an extension of the standard particle filter (PF) in which soil moisture is updated within a window of fixed length using all observed soil temperatures in that window. This approach was developed with a view to assimilating temperature observations from distributed temperature sensing (DTS) observations, a technique which can provide temperature observations every meter or less along cables up to kilometers in length. Here, the PBS approach is tested using soil moisture and temperature, and meteorological data from an experimental site in Citra, Florida. Results demonstrate that the PBS provides a statistically significant improvement in estimated soil moisture compared to the PF, with only a marginal increase in computational expense ( < 3% of CPU time). This confirms that assimilating a sequence of temperature observations yields a better soil moisture estimate compared to sequential assimilation of individual temperature observations. The impact of observation interval was investigated for both PF and PBS, and the optimal window length was determined for the PBS. While increasing the observation interval is essential to maintain the spread of particle values in the PF, the PBS performance is best when all available observations are assimilated.     

Multi‐scale assimilation of root zone soil water predictions

When hydrology model parameters are determined, a traditional data assimilation method (such as Kalman filter) and a hydrology model can estimate the root zone soil water with uncertain state variables (such as initial soil water content). The simulated result can be quite good. However, when a key soil hydraulic property, such as the saturated hydraulic conductivity, is overestimated or underestimated, the traditional soil water assimilation process will produce a persistent bias in its predictions. In this paper, we present and demonstrate a new multi‐scale assimilation method by combining the direct insertion assimilation method, particle swarm optimisation (PSO) algorithm and Richards equation. We study the possibility of estimating root zone soil water with a multi‐scale assimilation method by using observed in situ data from the Wudaogou experiment station, Huaihe River Basin, China. The results indicate there is a persistent bias between simulated and observed values when the direct insertion assimilation surface soil water content is used to estimate root zone soil water contents. Using a multi‐scale assimilation method (PSO algorithm and direct insertion assimilation) and an assumed bottom boundary condition, the results show some obvious improvement, but the root mean square error is still relatively large. When the bottom boundary condition is similar to the actual situation, the multi‐scale assimilation method can well represent the root zone soil water content. The results indicate that the method is useful in estimating root zone soil water when available soil water data are limited to the surface layer and the initial soil water content even when the soil hydraulic conductivities are uncertain. Copyright © 2011 John Wiley & Sons, Ltd.     

Calibration of an integrated land surface process and radiobrightness (LSP/R) model during summertime

In this study, a soil vegetation and atmosphere transfer (SVAT) model was linked with a microwave emission model to simulate microwave signatures for different terrain during summertime, when the energy and moisture fluxes at the land surface are strong. The integrated model, land surface process/radiobrightness (LSP/R), was forced with weather and initial conditions observed during a field experiment. It simulated the fluxes and brightness temperatures for bare soil and brome grass in the Northern Great Plains. The model estimates of soil temperature and moisture profiles and terrain brightness temperatures were compared with the observed values. Overall, the LSP model provides realistic estimates of soil moisture and temperature profiles to be used with a microwave model. The maximum mean differences and standard deviations between the modeled and the observed temperatures (canopy and soil) were 2.6 K and 6.8 K, respectively; those for the volumetric soil moisture were 0.9% and 1.5%, respectively. Brightness temperatures at 19 GHz matched well with the observations for bare soil, when a rough surface model was incorporated indicating reduced dielectric sensitivity to soil moisture by surface roughness. The brightness temperatures of the brome grass matched well with the observations indicating that a simple emission model was sufficient to simulate accurate brightness temperatures for grass typical of that region and surface roughness was not a significant issue for grass-covered soil at 19 GHz. Such integrated SVAT-microwave models allow for direct assimilation of microwave observations and can also be used to understand sensitivity of microwave signatures to changes in weather forcings and soil conditions for different terrain types.     

Estimating soil moisture and soil thermal and hydraulic properties by assimilating soil temperatures using a particle batch smoother

This study investigates the potential of estimating the soil moisture profile and the soil thermal and hydraulic properties by assimilating soil temperature at shallow depths using a particle batch smoother (PBS) using synthetic tests. Soil hydraulic properties influence the redistribution of soil moisture within the soil profile. Soil moisture, in turn, influences the soil thermal properties and surface energy balance through evaporation, and hence the soil heat transfer. Synthetic experiments were used to test the hypothesis that assimilating soil temperature observations could lead to improved estimates of soil hydraulic properties. We also compared different data assimilation strategies to investigate the added value of jointly estimating soil thermal and hydraulic properties in soil moisture profile estimation. Results show that both soil thermal and hydraulic properties can be estimated using shallow soil temperatures. Jointly updating soil hydraulic properties and soil states yields robust and accurate soil moisture estimates. Further improvement is observed when soil thermal properties were also estimated together with the soil hydraulic properties and soil states. Finally, we show that the inclusion of a tuning factor to prevent rapid fluctuations of parameter estimation, yields improved soil moisture, temperature, and thermal and hydraulic properties.     

Soil moisture variability of root zone profiles within SMEX02 remote sensing footprints

Remote sensing of soil moisture effectively provides soil moisture at a large scale, but does not explain highly heterogeneous soil moisture characteristics within remote sensing footprints. In this study, field scale spatio-temporal variability of root zone soil moisture was analyzed. During the Soil Moisture Experiment 2002 (SMEX02), daily soil moisture profiles (i.e., 0–6, 5–11, 15–21, and 25–31 cm) were measured in two fields in Walnut Creek watershed, Ames, Iowa, USA. Theta probe measurements of the volumetric soil moisture profile data were used to analyze statistical moments and time stability and to validate soil moisture predicted by a simple physical model simulation. For all depths, the coefficient of variation of soil moisture is well explained by the mean soil moisture using an exponential relationship. The simple model simulated very similar variability patterns as those observed.As soil depth increases, soil moisture distributions shift from skewed to normal patterns. At the surface depth, the soil moisture during dry down is log-normally distributed, while the soil moisture is normally distributed after rainfall. At all depths below the surface, the normal distribution captures the soil moisture variability for all conditions. Time stability analyses show that spatial patterns of sampling points are preserved for all depths and that time stability of surface measurements is a good indicator of subsurface time stability. The most time stable sampling sites estimate the field average root zone soil moisture value within ±2.1% volumetric soil moisture.     

A land surface data assimilation framework using the land information system: Description and applications

The Land Information System (LIS) is an established land surface modeling framework that integrates various community land surface models, ground measurements, satellite-based observations, high performance computing and data management tools. The use of advanced software engineering principles in LIS allows interoperability of individual system components and thus enables assessment and prediction of hydrologic conditions at various spatial and temporal scales. In this work, we describe a sequential data assimilation extension of LIS that incorporates multiple observational sources, land surface models and assimilation algorithms. These capabilities are demonstrated here in a suite of experiments that use the ensemble Kalman filter (EnKF) and assimilation through direct insertion. In a soil moisture experiment, we discuss the impact of differences in modeling approaches on assimilation performance. Provided careful choice of model error parameters, we find that two entirely different hydrological modeling approaches offer comparable assimilation results. In a snow assimilation experiment, we investigate the relative merits of assimilating different types of observations (snow cover area and snow water equivalent). The experiments show that data assimilation enhancements in LIS are uniquely suited to compare the assimilation of various data types into different land surface models within a single framework. The high performance infrastructure provides adequate support for efficient data assimilation integrations of high computational granularity.