Effect of simultaneous state–parameter estimation and forcing uncertainties on root-zone soil moisture for dynamic vegetation using EnKF

In this study, an EnKF-based assimilation algorithm was implemented to estimate root-zone soil moisture (RZSM) using the coupled LSP–DSSAT model during a growing season of corn. Experiments using both synthetic and field observations were conducted to understand effects of simultaneous state–parameter estimation, spatial and temporal update frequency, and forcing uncertainties on RZSM estimates. Estimating the state–parameters simultaneously with every 3-day assimilation of volumetric soil moisture (VSM) observations at 5 depths lowered the average standard deviation (ASD) and the root mean square error (RMSE) for RZSM by approximately 1.77% VSM (78%) and 2.18% VSM (93%), respectively, compared to the open-loop ASD where as estimating only states lowered the ASD by approximately 1.26% VSM (56%) and the RMSE by 1.66% VSM (71%). The synthetic case obtained RZSM estimates closer to the observations than the MicroWEX-2 case, particularly after precipitation/irrigation events. The differences in EnKF performance between MicroWEX-2 and synthetic observations may indicate other sources of errors in addition to those in parameters and forcings, such as errors in model biophysics.     

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.     

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.     

Comparison between gradient based UCODE_2005 and the ensemble Kalman Filter for transient groundwater flow inverse modeling

Gradient based UCODE_2005 and data assimilation based on the Ensemble Kalman Filter(EnKF) are two different inverse methods. A synthetic two-dimensional flow case with four no-flow boundaries is used to compare the UCODE_2005 with the Ensemble Kalman Filter(EnKF) for their efficiency to inversely calculate and calibrate a hydraulic conductivity field based on hydraulic head data. A zonal, random heterogeneous conductivity field is calibrated by assimilating the time series of heads observed in monitoring wells. The study results indicate that the two inverse methods, UCODE_2005 and EnKF, could be used to calibrate the hydraulic conductivity field to a certain degree. More available observations and information about the conductivity field, more accurate inverse results will be obtained for the UCODE_2005. On the other hand, for a realistic zonal heterogeneous hydraulic conductivity field, EnKF can only efficiently determine the hydraulic conductivity field at the first several assimilated time steps. The results obtained by the UCODE_2005 look better than those by the EnKF. This is possibly due to the fact that the UCODE_2005 uses observed head data at every time step, while EnKF can only use observed heads at first several steps due to the filter divergence problem.     

Improving hydrologic predictions of a catchment model via assimilation of surface soil moisture

This paper examines the potential for improving Soil and Water Assessment Tool (SWAT) hydrologic predictions of root-zone soil moisture, evapotranspiration, and stream flow within the 341 km² Cobb Creek Watershed in southwestern Oklahoma through the assimilation of surface soil moisture observations using an Ensemble Kalman filter (EnKF). In a series of synthetic twin experiments assimilating surface soil moisture is shown to effectively update SWAT upper-layer soil moisture predictions and provide moderate improvement to lower layer soil moisture and evapotranspiration estimates. However, insufficient SWAT-predicted vertical coupling results in limited updating of deep soil moisture, regardless of the SWAT parameterization chosen for root-water extraction. Likewise, a real data assimilation experiment using ground-based soil moisture observations has only limited success in updating upper-layer soil moisture and is generally unsuccessful in enhancing SWAT stream flow predictions. Comparisons against ground-based observations suggest that SWAT significantly under-predicts the magnitude of vertical soil water coupling at the site, and this lack of coupling impedes the ability of the EnKF to effectively update deep soil moisture, groundwater flow and surface runoff. The failed attempt to improve stream flow prediction is also attributed to the inability of the EnKF to correct for existing biases in SWAT-predicted stream flow components.     

Improvement of multi-layer soil moisture prediction using support vector machines and ensemble Kalman filter coupled with remote sensing soil moisture datasets over an agriculture dominant basin in China

Soil moisture prediction is of great importance in crop yield forecasting and drought monitoring. In this study, the multi-layer root zone soil moisture (0-5, 0-10, 10-40 and 40-100 cm) prediction is conducted over an agriculture dominant basin, namely the Xiang River Basin, in southern China. The support vector machines (SVM) coupled with dual ensemble Kalman filter (EnKF) technique (SVM-EnKF) is compared with SVM for its potential capability to improve the efficiency of soil moisture prediction. Three remote sensing soil moisture products, namely SMAP, ASCAT and AMSR2, are evaluated for their performance in multi-layer soil moisture prediction with SVM and SVM-EnKF, respectively. Multiple cases are designed to investigate the performance of SVM, the effectiveness of coupling dual EnKF technique and the applicability of the remote sensing products in soil moisture prediction. The main results are as follows: (a) The efficiency of soil moisture prediction with SVM using meteorological variables as inputs is satisfactory for the surface layers (0-5 and 0-10 cm), while poor for the root zone layers (10-40 and 40-100 cm). Adding SMAP as input to SVM can improve its performance in soil moisture prediction, with more than 47% increase in the R-value and at least 11% reduction in RMSE for all layers. However, adding ASCAT or AMSR2 has no improvement for its performance. (b) Coupling dual EnKF can significantly improve the performance of SVM in the soil moisture prediction of both surface and the root zone layers. The increase in R-value is above 80%, while the reduction in BIAS and RMSE is respectively more than 90% and 63%. However, adding remote sensing soil moisture products as inputs can no further improve the performance of SVM-EnKF. (c) The SVM-EnKF can eliminate the influence of remote sensing soil moisture extreme values in soil moisture prediction, therefore, improve its accuracy.     

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.     

Integrating a model with remote sensing observations by a data assimilation approach to improve the model simulation accuracy of carbon flux and evapotranspiration at two flux sites

Model simulation and in situ observations are often used to research water and carbon cycles in terrestrial ecosystems, but each of these methods has its own advantages and limitations. Combining these two methods could improve the accuracy of quantifying the dynamics of the water and carbon fluxes of an ecosystem. Data assimilation is an effective means of integrating modeling with in situ observation. In this study, the ensemble Kalman filter(En KF) and the unscented Kalman filter(UKF) algorithms were used to assimilate remotely sensed leaf area index(LAI) data with the Biome-BGC model to simulate water and carbon fluxes at the Harvard Forest Environmental Monitoring Site(EMS) and the Dinghushan site. After MODIS LAI data from 2000–2004 were assimilated into the improved Biome-BGC model using the En KF algorithm at the Harvard Forest site, the R2 between the simulated and observed results for NEE and evapotranspiration increased by 7.8% and 4.7%, respectively. In addition, the sum of the absolute error(SAE) and the root mean square error(RMSE) of NEE decreased by an average of 21.9% and 26.3%, and the SAE and RMSE of evapotranspiration decreased by 24.5% and 25.5%, respectively. MODIS LAI data of 2003 were assimilated into the Biome-BGC model for the Dinghushan site, and the R2 values between the simulated and observed results for NEE and evapotranspiration were increased by 6.7% and 17.3%, respectively. In addition, the SAE values of NEE and ET were decreased by 11.3% and 30.7%, respectively, and the RMSE values of NEE and ET decreased by 10.1% and 30.9%, respectively. These results demonstrate that the accuracy of carbon and water flux simulations can be effectively improved when remotely sensed LAI data are properly integrated with ecosystem models through a data assimilation approach.     

Heated distributed temperature sensing for field scale soil moisture monitoring

Characterizing both spatial and temporal soil moisture (θ) dynamics at site scales is difficult with existing technologies. To address this shortcoming, we developed a distributed soil moisture sensing system that employs a distributed temperature sensing system to monitor thermal response at 2 m intervals along the length of a buried cable which is subjected to heat pulses. The cable temperature response to heating, which is strongly dependent on soil moisture, was empirically related to colocated, dielectric-based θ measurements at three locations. Spatially distributed, and temporally continuous estimates of θ were obtained in dry conditions (θ≤ 0.31) using this technology (root mean square error [RMSE] = 0.016), but insensitivity of the instrument response curve adversely affected accuracy under wet conditions (RMSE = 0.050).     

Evapotranspiration models of different complexity for multiple land cover types

A comparison between half‐hourly and daily measured and computed evapotranspiration (ET) using three models of different complexity, namely, the Priestley–Taylor (P‐T), the reference Penman–Monteith (P‐M) and the Common Land Model (CLM), was conducted using three AmeriFlux sites under different land cover and climate conditions (i.e. arid grassland, temperate forest and subhumid cropland). Using the reference P‐M model with a semiempirical soil moisture function to adjust for water‐limiting conditions yielded ET estimates in reasonable agreement with the observations [root mean square error (RMSE) of 64–87 W m^?2 for half‐hourly and RMSE of 0.5–1.9 mm day^?1 for daily] and similar to the complex Common Land Model (RMSE of 60–94 W m^?2 for half‐hourly and RMSE of 0.4–2.1 mm day^?1 for daily) at the grassland and cropland sites. However, the semiempirical soil moisture function was not applicable particularly for the P‐T model at the forest site, suggesting that adjustments to key model variables may be required when applied to diverse land covers. On the other hand, under certain land cover/environmental conditions, the use of microwave‐derived soil moisture information was found to be a reliable metric of regional moisture conditions to adjust simple ET models for water‐limited cases. Further studies are needed to evaluate the utility of the simplified methods for different landscapes. Copyright © 2011 John Wiley & Sons, Ltd.     

A Modified Soil Moisture Model for Two‐Layer Soil

There can be marked variations in soil hydraulic properties in a soil vertical profile from the soil surface to the base of the root zone. Many existing two‐layer soil moisture (TLSM) models cannot well describe typical stratified soil profiles. A modified TLSM model is presented in this study. The modified model results and those from two existing models are compared with field observations. The modified TLSM model had the best agreement with the field observations. In both the surface layer and the root zone layer, the root mean square errors of soil moisture estimated by the modified model were smaller than those for the other models. The parameters in the modified TLSM model are relatively easy to determine. The modified TLSM model offers clear advantages over current TLSM models.     

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.     

Estimation of soil hydraulic properties and their uncertainty: comparison between laboratory and field experiment

Often the soil hydraulic parameters are obtained by the inversion of measured data (e.g. soil moisture, pressure head, and cumulative infiltration, etc.). However, the inverse problem in unsaturated zone is ill‐posed due to various reasons, and hence the parameters become non‐unique. The presence of multiple soil layers brings the additional complexities in the inverse modelling. The generalized likelihood uncertainty estimate (GLUE) is a useful approach to estimate the parameters and their uncertainty when dealing with soil moisture dynamics which is a highly non‐linear problem. Because the estimated parameters depend on the modelling scale, inverse modelling carried out on laboratory data and field data may provide independent estimates. The objective of this paper is to compare the parameters and their uncertainty estimated through experiments in the laboratory and in the field and to assess which of the soil hydraulic parameters are independent of the experiment. The first two layers in the field site are characterized by Loamy sand and Loamy. The mean soil moisture and pressure head at three depths are measured with an interval of half hour for a period of 1 week using the evaporation method for the laboratory experiment, whereas soil moisture at three different depths (60, 110, and 200 cm) is measured with an interval of 1 h for 2 years for the field experiment. A one‐dimensional soil moisture model on the basis of the finite difference method was used. The calibration and validation are approximately for 1 year each. The model performance was found to be good with root mean square error (RMSE) varying from 2 to 4 cm³ cm^?3. It is found from the two experiments that mean and uncertainty in the saturated soil moisture (θ_s) and shape parameter (n) of van Genuchten equations are similar for both the soil types. Copyright © 2010 John Wiley & Sons, Ltd.     

Applicability of cosmic-ray neutron sensor for measuring soil moisture at the agricultural-pastoral ecotone in northwest China

Accurate monitoring of soil moisture is crucial in hydrological and ecological studies. Cosmic-ray neutron sensors (CRNS) measure area-average soil moisture at field scale, filling a spatial scale gap between in-situ observations and remote sensing measurements. However, its applicability has not been assessed in the agricultural-pastoral ecotone, a data scarce semi-arid and arid region in Northwest China (APENC). In this study, we calibrated and assessed the CRNS (the standard N₀ method) estimates of soil moisture. Results show that Pearson correlation coefficient, R_P, and the root mean square error (RMSE) between the CRNS soil moisture and the gravimetric soil moisture are 0.904 and less than 0.016 m³ m⁻³, respectively, indicating that the CRNS is able to estimate the area-average soil moisture well at our study site. Compared with the in-situ sensor network measurements (ECH2O sensors), the CRNS is more sensitive to the changes in moisture in its footprint, which overestimates and underestimates the soil moisture under precipitation and dry conditions, respectively. The three shape parameters a₀, a₁, a₂ in the standard calibration equation (N₀ method) are not well suited to the study area. The calibrated parameters improved the accuracy of the CRNS soil moisture estimates. Due to the lack of low gravimetric soil moisture data, performance of the calibrated N₀ function is still poor in the extremely dry conditions. Moreover, aboveground biomass including vegetation biomass, canopy interception and widely developed biological soil crusts adds to the uncertainty of the CRNS soil moisture estimates. Such biomass impacts need to be taken into consideration to further improve the accuracy of soil moisture estimation by the CRNS in the data scarce areas such as agricultural-pastoral ecotone in Northwest China.

     

Data assimilation with the EnKF in a 1-D numerical model of a North Sea station

A series of numerical experiments for data assimilation with the Ensemble Kalman Filter (EnKF) in a shallow water model are reported. Temperature profiles measured at a North Sea location, 55°30ˊ North and 0°55ˊ East (referred to as the CS station of the NERC North Sea project), are assimilated in 1-D simulations. Comparison of simulations without assimilation to model results obtained when assimilating data with the EnKF allows us to assess the filter performance in reproducing features of the observations not accounted for by the model. The quality of the model error sampling is tested as well as the validity of the Gaussian hypothesis underlying the analysis scheme of the EnKF. The influence of the model error parameters and the frequency of the data assimilation are investigated and discussed. From these experiments, a set of optimal parameters for the model error sampling are deduced and used to test the behavior of the EnKF when propagating surface information into the water column.     

基于简化参数方法的蒙古干旱区土壤湿度被动微波遥感

卫星被动微波遥感土壤湿度,是准确分析大空间尺度上陆表水分变化信息的有效手段.美国航天局(NASA)发布的基于AMSR-E观测亮温资料的全球土壤湿度反演产品,在蒙古干旱区的实际精度并不令人满意.本文基于对地表微波辐射传输中地表粗糙度和植被层影响的简化处理方法,采用AMSR-E的6.9 GHz,10.7 GHz和18.7 GHz之V极化亮温资料,应用多频率反演算法,并以国际能量和水循环协同观测计划(The Coordinated Energy and Water Cycle Observations Project)即CEOP实验在蒙古国东部荒漠地区的地面实验资料作为先验知识,获取被动微波遥感模型的优化参数,以期获得蒙古干旱区精度更高的土壤湿度遥感估算结果.分析表明,本文方法反演的白天和夜间土壤湿度结果与地面验证值之间的均方根误差(RMSE)接近0.030 cm³/cm³, 证明所用方法在不需要其他辅助资料或参数帮助下,可较精确地反演干旱区表层土壤湿度信息,能够全天候、动态监测大空间尺度的土壤湿度变化,可为干旱区气候变化研究及陆面过程模拟和数据同化研究提供高精度的表层土壤湿度初始场资料.     

Assimilation of sea surface temperature into CECOM by flux correction

Sea surface temperature (SST) from a near real-time data set produced from satellites data has been assimilated into a coupled ice–ocean forecasting model (Canadian East Coast Ocean Model) using an efficient data assimilation method. The method is based on an optimal interpolation scheme by which SST is melded into the model through the adjustment of surface heat flux. The magnitude and space–time variation of the adjustment depend on the depth of heat diffusion into the water column in response to changes in surface flux, the correlation time scale of the data, and model and data errors. The diffusion depth is scaled by the eddy diffusivity for temperature. The ratio of the model and data errors is treated as an adjustable parameter. To evaluate the quality of the assimilation, the results from the model with and without assimilation are compared to independent ship data from the Atlantic Zone Monitoring Program and the World Ocean Circulation Experiment. It is shown that the assimilation has a significant impact on the modeled SST, reducing the root mean square difference (RMSD) between the model SST and the ship SST by 0.63°C or 37%. The RMSD of the assimilated SST is smaller than that of the satellite SST by 0.23°C. This suggests that model simulations or predictions with data assimilation can provide the best estimate of the true SST. A sensitivity study is performed to examine the change of the model RMSD with the adjustable parameter in the assimilation equation. The results show that there is an optimal value of the parameter and the model SST is not very sensitive to the parameter.     

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.     

Modelling soil moisture in a high‐latitude landscape using LiDAR and soil data

Soil moisture has a pronounced effect on earth surface processes. Global soil moisture is strongly driven by climate, whereas at finer scales, the role of non‐climatic drivers becomes more important. We provide insights into the significance of soil and land surface properties in landscape‐scale soil moisture variation by utilizing high‐resolution light detection and ranging (LiDAR) data and extensive field investigations. The data consist of 1200 study plots located in a high‐latitude landscape of mountain tundra in north‐western Finland. We measured the plots three times during growing season 2016 with a hand‐held time‐domain reflectometry sensor. To model soil moisture and its temporal variation, we used four statistical modelling methods: generalized linear models, generalized additive models, boosted regression trees, and random forests. The model fit of the soil moisture models were R² = 0.60 and root mean square error (RMSE) 8.04 VWC% on average, while the temporal variation models showed a lower fit of R² = 0.25 and RMSE 13.11 CV%. The predictive performances for the former were R² = 0.47 and RMSE 9.34 VWC%, and for the latter R² = 0.01 and RMSE 15.29 CV%. Results were similar across the modelling methods, demonstrating a consistent pattern. Soil moisture and its temporal variation showed strong heterogeneity over short distances; therefore, soil moisture modelling benefits from high‐resolution predictors, such as LiDAR based variables. In the soil moisture models, the strongest predictor was SAGA (System for Automated Geoscientific Analyses) wetness index (SWI), based on a 1 m² digital terrain model derived from LiDAR data, which outperformed soil predictors. Thus, our study supports the use of LiDAR based SWI in explaining fine‐scale soil moisture variation. In the temporal variation models, the strongest predictor was the field‐quantified organic layer depth variable. Our results show that spatial soil moisture predictions can be based on soil and land surface properties, yet the temporal models require further investigation. Copyright © 2017 John Wiley & Sons, Ltd.     

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.