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

Advances in soil moisture retrieval from synthetic aperture radar and hydrological applications

The soil moisture state partitions both mass and energy fluxes and is important for many hydro-geochemical cycles, but is often only measured within the surface layer. Estimating the amount of soil moisture in the root-zone from this information is difficult due to the nonlinear and heterogeneous nature of the various processes which alter the soil moisture state. Data-driven methods, such as artificial neural networks (ANN), mine data for nonlinear interdependencies and have potential for estimating root-zone soil moisture from surface soil moisture observations. To create an ANN root-zone model that was nonsite-specific and physically constrained, a training set was generated by forcing HYDRUS-1D with meteorological observations for different soil profiles from the unsaturated soil hydraulic database. Ensemble ANNs were trained to provide soil moisture at depths of 10, 20, and 50 cm below the surface using surface soil moisture observations and local meteorological information. Insights into the processes represented by the ANNs were derived from a clamping sensitivity analysis and by changing the ANNs input data. Further model testing based on synthetic soil moisture profiles from three McMaster Mesonet and three USDA soil climate analysis network sites suggests that ANNs are a flexible tool capable of predicting root-zone soil moisture with good accuracy. It was found that ANNs could well represent soil moisture as estimated by HYDRUS-1D, but performance was reduced in comparison to in situ soil moisture observations outside the training conditions. The transferability of the model appears limited to the same geographic region.

Root‐zone soil moisture estimation using data‐driven methods

Having reliable water monitoring networks is an essential component of water resources and environmental management. A standardized process for the design of water monitoring networks does not exist with the exception of the World Meteorological Organization (WMO) general guidelines about the minimum network density. While one of the major challenges in the design of optimal hydrometric networks has been establishing design objectives, information theory has been successfully adopted to network design problems by providing measures of the information content that can be deliverable from a station or a network. This review firstly summarizes the common entropy terms that have been used in water monitoring network designs. Then, this paper deals with the recent applications of the entropy concept for water monitoring network designs, which are categorized into (1) precipitation; (2) streamflow and water level; (3) water quality; and (4) soil moisture and groundwater networks. The integrated design method for multivariate monitoring networks is also covered. Despite several issues, entropy theory has been well suited to water monitoring network design. However, further work is still required to provide design standards and guidelines for operational use.

Entropy Applications to Water Monitoring Network Design: A Review

Missing values in in situ monitoring data is a problem often encountered in hydrologic research and applications. Values in a data set may be missing because of sensor error or failure of data recording devices. Whereas various imputation techniques have focused on hydrometeorological data, very few studies have investigated gap-filling methods for soil moisture data. This paper aims to fill that gap by investigating well-established statistical and data-driven methods for infilling missing values in a high resolution, soil moisture time series. Since 2006, the authors collected hourly soil moisture data in the Hamilton-Halton Watershed, Southern Ontario, Canada at four research sites. Each site contained nine stations with time domain reflectometry (TDR) soil sensors at six soil depths. From these distributed data sets, the authors removed values randomly (∼5%) and systematically (∼20%) from the data to evaluate the effectiveness of the monthly average replacement (MAR), soil layer relative diffe...

Kurt C. Kornelsen

Papers

Advances in soil moisture retrieval from synthetic aperture radar and hydrological applications

Root‐zone soil moisture estimation using data‐driven methods

Entropy Applications to Water Monitoring Network Design: A Review

Comparison of Interpolation, Statistical, and Data-Driven Methods for Imputation of Missing Values in a Distributed Soil Moisture Dataset

Synthesis review on groundwater discharge to surface water in the Great Lakes Basin