The purpose of this paper is to provide a comprehensive presentation and interpretation of the Ensemble Kalman Filter (EnKF) and its numerical implementation. The EnKF has a large user group, and numerous publications have discussed applications and theoretical aspects of it. This paper reviews the important results from these studies and also presents new ideas and alternative interpretations which further explain the success of the EnKF. In addition to providing the theoretical framework needed for using the EnKF, there is also a focus on the algorithmic formulation and optimal numerical implementation. A program listing is given for some of the key subroutines. The paper also touches upon specific issues such as the use of nonlinear measurements, in situ profiles of temperature and salinity, and data which are available with high frequency in time. An ensemble based optimal interpolation (EnOI) scheme is presented as a cost-effective approach which may serve as an alternative to the EnKF in some applications. A fairly extensive discussion is devoted to the use of time correlated model errors and the estimation of model bias.

The Ensemble Kalman Filter: Theoretical formulation and practical implementation

The remarkable complexity of soil and its importance to a wide range of ecosystem services presents major challenges to the modeling of soil processes. Although major progress in soil models has occurred in the last decades, models of soil processes remain disjointed between disciplines or ecosystem services, with considerable uncertainty remaining in the quality of predictions and several challenges that remain yet to be addressed. First, there is a need to improve exchange of knowledge and experience among the different disciplines in soil science and to reach out to other Earth science communities. Second, the community needs to develop a new generation of soil models based on a systemic approach comprising relevant physical, chemical, and biological processes to address critical knowledge gaps in our understanding of soil processes and their interactions. Overcoming these challenges will facilitate exchanges between soil modeling and climate, plant, and social science modeling communities. It will allow us to contribute to preserve and improve our assessment of ecosystem services and advance our understanding of climate-change feedback mechanisms, among others, thereby facilitating and strengthening communication among scientific disciplines and society. We review the role of modeling soil processes in quantifying key soil processes that shape ecosystem services, with a focus on provisioning and regulating services. We then identify key challenges in modeling soil processes, including the systematic incorporation of heterogeneity and uncertainty, the integration of data and models, and strategies for effective integration of knowledge on physical, chemical, and biological soil processes. We discuss how the soil modeling community could best interface with modern modeling activities in other disciplines, such as climate, ecology, and plant research, and how to weave novel observation and measurement techniques into soil models. We propose the establishment of an international soil modeling consortium to coherently advance soil modeling activities and foster communication with other Earth science disciplines. Such a consortium should promote soil modeling platforms and data repository for model development, calibration and intercomparison essential for addressing contemporary challenges.

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Modeling Soil Processes: Review, Key Challenges, and New Perspectives

On the spatio-temporal dynamics of soil moisture at the field scale

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Michigan Geology: A Bibliography, March 2016

Soil moisture (SM) is a key hydrologic state variable that is of significant importance for numerous Earth and environmental science applications that directly impact the global environment and human society. Potential applications include, but are not limited to, forecasting of weather and climate variability; prediction and monitoring of drought conditions; management and allocation of water resources; agricultural plant production and alleviation of famine; prevention of natural disasters such as wild fires, landslides, floods, and dust storms; or monitoring of ecosystem response to climate change. Because of the importance and wide‐ranging applicability of highly variable spatial and temporal SM information that links the water, energy, and carbon cycles, significant efforts and resources have been devoted in recent years to advance SMmeasurement andmonitoring capabilities from the point to the global scales. This review encompasses recent advances and the state‐of‐the‐art of ground, proximal, and novel SM remote sensing techniques at various spatial and temporal scales and identifies critical future research needs and directions to further advance and optimize technology, analysis and retrieval methods, and the application of SM information to improve the understanding of critical zone moisture dynamics. Despite the impressive progress over the last decade, there are still many opportunities and needs to, for example, improve SM retrieval from remotely sensed optical, thermal, and microwave data and opportunities for novel applications of SM information for water resources management, sustainable environmental development, and food security.

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Ground, Proximal, and Satellite Remote Sensing of Soil Moisture

The Canadian Surface Prediction Archive (CaSPAr) is an archive of numerical weather predictions issued by Environment and Climate Change Canada. Among the products archived on a daily basis...

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The Canadian Surface Prediction Archive (CaSPAr): A Platform to Enhance Environmental Modeling in Canada and Globally

Many methods have been proposed to select sites for grid-scale soil moisture monitoring networks; however, calibration/validation activities also require information about where to place grid representative monitoring sites. In order to design a soil moisture network for this task in the Great Lakes Basin (522 000 km2), the dual-entropy multiobjective optimization algorithm was used to maximize the information content and minimize the redundancy of information in a potential soil moisture monitoring network. Soil moisture retrieved from the Soil Moisture and Ocean Salinity (SMOS) mission during the frost-free periods of 2010–2013 were filtered for data quality and then used in a multiobjective search to find Pareto optimum network designs based on the joint entropy and total correlation measures of information content and information redundancy, respectively. Differences in the information content of SMOS ascending and descending overpasses resulted in distinctly different network designs. Entropy from the SMOS ascending overpass was found to be spatially consistent, whereas descending overpass entropy had many peaks that coincided with areas of high subgrid heterogeneity. A combination of both ascending and descending overpasses produced network designs that incorporated aspects of information from each overpass. Initial networks were designed to include 15 monitoring sites, but the addition of network cost as an objective demonstrated that a network with similar information content could be achieved with fewer monitoring stations.

Design of an Optimal Soil Moisture Monitoring Network Using SMOS Retrieved Soil Moisture

Passive microwave satellites such as Soil Moisture and Ocean Salinity or Soil Moisture Active Passive observe brightness temperature (TB) and retrieve soil moisture at a spatial resolution greater than most hydrological processes. Bias correction is proposed as a simple method to disaggregate soil moisture to a scale more appropriate for hydrological applications. Temporal stability of soil moisture and TB was demonstrated at the Little Washita and Little River Experimental Watersheds using in situ observations and the Community Microwave Emissions Model. Decomposition of the mean square difference (MSD) between the watershed average soil moisture and TB showed that bias was a major contributor to differences between watershed average and local-scale soil moisture and TB, particularly at sites with high MSD. The mean RMSD between watershed average and local soil moisture was 0.04 m3 m−3 and 0.06 m3 m−3 at Little River and Little Washita, respectively. Following a simple bias correction the RMSD was reduced to 0.03 m3 m−3 at both sites. Considering multiple incidence angles at both horizontal and vertical polarization, bias correction of watershed average TBV reduced the RMSD by approximately 75% and 45% and TBH RMSD by 68% and 36% for Little River and Little Washita, respectively, at all incidence angles. Therefore, at subsatellite grid scale, bias correction can be considered a viable technique for downscaling passive microwave observations and soil moisture retrievals.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1002/2015JD023550

Potential of bias correction for downscaling passive microwave and soil moisture data

The assimilation of soil moisture and brightness temperature (TB) are expected to improve the modeling of land surface processes, but are only available at a resolution that is far coarser than the scale of many hydrological processes. Due to systematic differences between model states and satellite observations, a bias correction operator is a necessary step in land data assimilation schemes and was evaluated as a method to disaggregate coarse-scale satellite observations to fine-scale model grid cells ( ${\sim}\text{800}\;\text {m}$ ). This was done by coupling the Modelisation Environmentale Communautaire-Surface Hydrology (MESH) Hydrological Land-Surface Scheme to the Community Microwave Emissions Model (CMEM) to simulate soil moisture and TB. By comparison, MESH-CMEM was found to be in good agreement with observations from the Soil Moisture and Ocean Salinity (SMOS) satellite at the scale of SMOS data products ( ${\text R} \approx \text{0.55}$ ), with simulated TB being better correlated than soil moisture retrievals. Following bias correction, TB and soil moisture retrievals at 800-m resolution had comparable performance to coarse-resolution SMOS data. Bias correction of TB was more reliable than soil moisture. These findings indicate that both TB and soil moisture retrievals can be assimilated in a land surface model at moderate-to-high resolution with a simple observation operator.

Kurt C. Kornelsen

Papers

The Canadian Surface Prediction Archive (CaSPAr): A Platform to Enhance Environmental Modeling in Canada and Globally

Design of an Optimal Soil Moisture Monitoring Network Using SMOS Retrieved Soil Moisture

Potential of bias correction for downscaling passive microwave and soil moisture data

Application of SMOS Soil Moisture and Brightness Temperature at High Resolution With a Bias Correction Operator

The CAnadian Surface Prediction ARchive (CaSPAr): A Platform to Enhance Environmental Modelling in Canada and Globally