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.     

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.     

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.     

One-dimensional soil moisture profile retrieval by assimilation of near-surface observations: a comparison of retrieval algorithms

This paper investigates the ability to retrieve the true soil moisture and temperature profiles by assimilating near-surface soil moisture and surface temperature data into a soil moisture and heat transfer model. The direct insertion and Kalman filter assimilation schemes have been used most frequently in assimilation studies, but no comparisons of these schemes have been made. This study investigates which of these approaches is able to retrieve the soil moisture and temperature profiles the fastest, over what depth soil moisture observations are required, and the effect of update interval on profile retrieval. These questions are addressed by a desktop study using synthetic data. The study shows that the Kalman filter assimilation scheme is superior to the direct insertion assimilation scheme, with retrieval of the soil moisture profile being achieved in 12 h as compared to 8 days or more, depending on observation depth, for hourly observations. It was also found that profile retrieval could not be realised for direct insertion of the surface node alone, and that observation depth does not have a significant effect on profile retrieval time for the Kalman filter. The observation interval was found to be unimportant for profile retrieval with the Kalman filter when the forcing data is accurate, whilst for direct insertion the continuous Dirichlet boundary condition was required for an increasingly longer period of time. It was also found that the Kalman filter assimilation scheme was less susceptible to unstable updates if volumetric soil moisture was modelled as the dependent state rather than matric head, because the volumetric soil moisture state is more linear in the forecasting model.     

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.     

Improvement of TOPLATS‐based discharge predictions through assimilation of ERS‐based remotely sensed soil moisture values

In this paper, we investigate the possibility to improve discharge predictions from a lumped hydrological model through assimilation of remotely sensed soil moisture values. Therefore, an algorithm to estimate surface soil moisture values through active microwave remote sensing is developed, bypassing the need to collect in situ ground parameters. The algorithm to estimate soil moisture by use of radar data combines a physically based and an empirical back‐scatter model. This method estimates effective soil roughness parameters, and good estimates of surface soil moisture are provided for bare soils. These remotely sensed soil moisture values over bare soils are then assimilated into a hydrological model using the statistical correction method. The results suggest that it is possible to determine soil moisture values over bare soils from remote sensing observations without the need to collect ground truth data, and that there is potential to improve model‐based discharge predictions through assimilation of these remotely sensed soil moisture values. Copyright © 2002 John Wiley & Sons, Ltd.     

The effect of roughness in simultaneously retrieval of land surface parameters

Using remotely-sensed data, various soil moisture estimation models have been developed for bare soil areas. Previous studies have shown that the brightness temperature (BT) measured by passive microwave sensors were affected by characteristics of the land surface parameters including soil moisture, vegetation cover and soil roughness. Therefore knowledge of vegetation cover and soil roughness is important for obtaining frequent and global estimations of land surface parameters especially soil moisture.In this study, a model called Simultaneous Land Parameters Retrieval Model (SLPRM) that is an iterative least-squares minimization method is proposed. The algorithm estimates surface soil moisture, land surface temperature and canopy temperature simultaneously in vegetated areas using AMSR-E (Advance Microwave Scanning Radiometer-EOS) brightness temperature data. The simultaneous estimations of the three parameters are based on a multi-parameter inversion algorithm which includes model construction, calibration and validation using observations carried out for the SMEX03 (Soil Moisture Experiment, 2003) region in the South and North of Oklahoma.Roughness parameter has also been included in the algorithm to increase the soil parameters retrieval accuracy. Unlike other methods, the SLPRM method works efficiently in all land covers types.The study focuses on soil parameters estimation by comparing three different scenarios with the inclusion of roughness data and selects the most appropriate one. The difference between the resulted accuracies of scenarios is due to the roughness calculation approach.The analysis on the retrieval model shows a meaningful and acceptable accuracy on soil moisture estimation according to the three scenarios.The SLPRM method has shown better performance when the SAR (Synthetic Aperture RADAR) data are used for roughness calculation.     

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.     

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.     

Requirements of a global near-surface soil moisture satellite mission: accuracy,repeat time,and spatial resolution

Soil moisture satellite mission accuracy, repeat time and spatial resolution requirements are addressed through a numerical twin data assimilation study. Simulated soil moisture profile retrievals were made by assimilating near-surface soil moisture observations with various accuracy (0, 1, 2, 3, 4, 5 and 10%v/v standard deviation) repeat time (1, 2, 3, 5, 10, 15, 20 and 30 days), and spatial resolution (0.5, 6, 12 18, 30, 60 and 120 arc-min). This study found that near-surface soil moisture observation error must be less than the model forecast error required for a specific application when used as data assimilation input, else slight model forecast degradation may result. It also found that near-surface soil moisture observations must have an accuracy better than 5%v/v to positively impact soil moisture forecasts, and that daily near-surface soil moisture observations achieved the best soil moisture and evapotranspiration forecasts for the repeat times assessed, with 1–5 day repeat times having the greatest impact. Near-surface soil moisture observations with a spatial resolution finer than the land surface model resolution (∼30 arc-min) produced the best results, with spatial resolutions coarser than the model resolution yielding only a slight degradation. Observations at half the land surface model spatial resolution were found to be appropriate for our application. Moreover, it was found that satisfying the spatial resolution and accuracy requirements was much more important than repeat time.     

Investigating soil moisture sensitivity to precipitation and evapotranspiration errors using SiB2 model and ensemble Kalman filter

Accurate soil moisture information is useful in agricultural practice, weather forecasting, and various hydrological applications. Although land surface modeling provides a viable approach to simulating soil moisture, many factors such as errors in the precipitation can affect the accuracy of soil moisture simulations. This paper examined how precipitation rate and evapotranspiration rate affect the accuracy of soil moisture simulation using simple biosphere model with and without data assimilation through ensemble Kalman filter (EnKF). For each of the two variables, seven levels of relative errors (?20, ?10, ?5, 0, 5, 10 and 20 %) were introduced independently, thus a total of 49 combined cases were investigated. Observations from Wudaogou Hydrology Experimental site in the Huaihe River basin, China, were used to drive and verify the simulations. Results indicate that when the error of precipitation rate is within 10 % of the observations, the resulting error in soil moisture simulations is less significant and manageable, thus the simulated precipitation can be used to drive hydrological models in poorly gauged catchments when observations are not available. When the error of evapotranspiration rate is within 20 % of the observations, which is partly caused by model structural and parameterization errors, its impact on soil moisture simulation is less significant and can be acceptable. This study also demonstrated that the EnKF can perform consistently well to improve soil moisture simulation with less sensitivity to precipitation errors.     

Connecting Satellite Observations with Water Cycle Variables Through Land Data Assimilation: Examples Using the NASA GEOS-5 LDAS

A land data assimilation system (LDAS) can merge satellite observations (or retrievals) of land surface hydrological conditions, including soil moisture, snow, and terrestrial water storage (TWS), into a numerical model of land surface processes. In theory, the output from such a system is superior to estimates based on the observations or the model alone, thereby enhancing our ability to understand, monitor, and predict key elements of the terrestrial water cycle. In practice, however, satellite observations do not correspond directly to the water cycle variables of interest. The present paper addresses various aspects of this seeming mismatch using examples drawn from recent research with the ensemble-based NASA GEOS-5 LDAS. These aspects include (1) the assimilation of coarse-scale observations into higher-resolution land surface models, (2) the partitioning of satellite observations (such as TWS retrievals) into their constituent water cycle components, (3) the forward modeling of microwave brightness temperatures over land for radiance-based soil moisture and snow assimilation, and (4) the selection of the most relevant types of observations for the analysis of a specific water cycle variable that is not observed (such as root zone soil moisture). The solution to these challenges involves the careful construction of an observation operator that maps from the land surface model variables of interest to the space of the assimilated observations.     

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.     

Towards the estimation root-zone soil moisture via the simultaneous assimilation of thermal and microwave soil moisture retrievals

The upcoming deployment of satellite-based microwave sensors designed specifically to retrieve surface soil moisture represents an important milestone in efforts to develop hydrologic applications for remote sensing observations. However, typical measurement depths of microwave-based soil moisture retrievals are generally considered too shallow (top 2–5 cm of the soil column) for many important water cycle and agricultural applications. Recent work has demonstrated that thermal remote sensing estimates of surface radiometric temperature provide a complementary source of land surface information that can be used to define a robust proxy for root-zone (top 1 m of the soil column) soil moisture availability. In this analysis, we examine the potential benefits of simultaneously assimilating both microwave-based surface soil moisture retrievals and thermal infrared-based root-zone soil moisture estimates into a soil water balance model using a series of synthetic twin data assimilation experiments conducted at the USDA Optimizing Production Inputs for Economic and Environmental Enhancements (OPE³) site. Results from these experiments illustrate that, relative to a baseline case of assimilating only surface soil moisture retrievals, the assimilation of both root- and surface-zone soil moisture estimates reduces the root-mean-square difference between estimated and true root-zone soil moisture by 50% to 35% (assuming instantaneous root-zone soil moisture retrievals are obtained at an accuracy of between 0.020 and 0.030 m³ m⁻³). Most significantly, improvements in root-zone soil moisture accuracy are seen even for cases in which root-zone soil moisture retrievals are assumed to be relatively inaccurate (i.e. retrievals errors of up to 0.070 m³ m⁻³) or limited to only very sparse sampling (i.e. one instantaneous measurement every eight days). Preliminary real data results demonstrate a clear increase in the R² correlation coefficient with ground-based root-zone observations (from 0.51 to 0.73) upon assimilation of actual surface soil moisture and tower-based thermal infrared temperature observations made at the OPE³ study site.     

Improving the estimation of hydrological states in the SWAT model via the ensemble Kalman smoother: Synthetic experiments for the Heihe River Basin in northwest China

Data assimilation as a method to predict variables, reduce uncertainties and explicitly handle various sources of uncertainties has recently received widespread attention and has been utilized to combine in situ and remotely sensed measurements with hydrological models. However, factors that significantly influence the capability of data assimilation still need testing and verifying. In this paper, synthetic surface soil moisture data are assimilated into the Soil and Water Assessment Tool (SWAT) model to evaluate their impact on other hydrological variables via the ensemble Kalman smoother (EnKS), using data from the Heihe River Basin, northwest China. The results show that the assimilation of surface soil moisture can moderately improve estimates of deep layer soil moisture, surface runoff and lateral flow, which reduces the negative influences of erroneous forcing and inaccurate parameters. The effects of the spatially heterogeneous input data (land cover and soil type) on the performance of the data assimilation technique are noteworthy. Moreover, the approaches including inflation and localization are specifically diagnosed to further extend the capability of the EnKS.     

Root-zone soil moisture estimation from assimilation of downscaled Soil Moisture and Ocean Salinity data

The crucial role of root-zone soil moisture is widely recognized in land–atmosphere interaction, with direct practical use in hydrology, agriculture and meteorology. But it is difficult to estimate the root-zone soil moisture accurately because of its space-time variability and its nonlinear relationship with surface soil moisture. Typically, direct satellite observations at the surface are extended to estimate the root-zone soil moisture through data assimilation. But the results suffer from low spatial resolution of the satellite observation. While advances have been made recently to downscale the satellite soil moisture from Soil Moisture and Ocean Salinity (SMOS) mission using methods such as the Disaggregation based on Physical And Theoretical scale Change (DisPATCh), the assimilation of such data into high spatial resolution land surface models has not been examined to estimate the root-zone soil moisture. Consequently, this study assimilates the 1-km DisPATCh surface soil moisture into the Joint UK Land Environment Simulator (JULES) to better estimate the root-zone soil moisture. The assimilation is demonstrated using the advanced Evolutionary Data Assimilation (EDA) procedure for the Yanco area in south eastern Australia. When evaluated using in-situ OzNet soil moisture, the open loop was found to be 95% as accurate as the updated output, with the updated estimate improving the DisPATCh data by 14%, all based on the root mean square error (RMSE). Evaluation of the root-zone soil moisture with in-situ OzNet data found the updated output to improve the open loop estimate by 34% for the 0–30 cm soil depth, 59% for the 30–60 cm soil depth, and 63% for the 60–90 cm soil depth, based on RMSE. The increased performance of the updated output over the open loop estimate is associated with (i) consistent estimation accuracy across the three soil depths for the updated output, and (ii) the deterioration of the open loop output for deeper soil depths. Thus, the findings point to a combined positive impact from the DisPATCh data and the EDA procedure, which together provide an improved soil moisture with consistent accuracy both at the surface and at the root-zone.     

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.     

Data assimilation methods in the Earth sciences

Although remote sensing data are often plentiful, they do not usually satisfy the users’ needs directly. Data assimilation is required to extract information about geophysical fields of interest from the remote sensing observations and to make the data more accessible to users. Remote sensing may provide, for example, measurements of surface soil moisture, snow water equivalent, snow cover, or land surface (skin) temperature. Data assimilation can then be used to estimate variables that are not directly observed from space but are needed for applications, for instance root zone soil moisture or land surface fluxes. The paper provides a brief introduction to modern data assimilation methods in the Earth sciences, their applications, and pertinent research questions. Our general overview is readily accessible to hydrologic remote sensing scientists. Within the general context of Earth science data assimilation, we point to examples of the assimilation of remotely sensed observations in land surface hydrology.