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

found that field-scale dispersivities are several orders of.magnitude greater than lab-scale values for the same material; it is generally agreed that this difference is a reflection of the influence of natural heterogeneities which produce irregular flow patterns at the field scale. Consequently, laboratory measurements of dispersivity cannot be used to predict field values of dispersivity. Instead field-scale tracer tests are sometimes conducted to estimate dispersivity at a particular site. Early efforts to document the scale dependence of dispersivity [Lallemand-Barres and Peaudecerf, 1978; Anderson, 1979; Pickens and Grisak, 1981; Beims, 1983; Neretnieks, 1985] were based on field values of dispersivity reported in the literature and the test scales associated with those values. These studies were useful in that they indeed documented field evidence of the scale effect, but they were lacking in that they did not assess the reliability of the data presented. Because we felt that the data would be more

A Critical Review of Data on Field-Scale Dispersion in Aquifers

http://www.vliz.be/imisdocs/publications/242609.pdf

Seawater intrusion processes, investigation and management: Recent advances and future challenges

Over the past 15 years, artificial neural networks (ANNs) have been used increasingly for prediction and forecasting in water resources and environmental engineering. However, despite this high level of research activity, methods for developing ANN models are not yet well established. In this paper, the steps in the development of ANN models are outlined and taxonomies of approaches are introduced for each of these steps. In order to obtain a snapshot of current practice, ANN development methods are assessed based on these taxonomies for 210 journal papers that were published from 1999 to 2007 and focus on the prediction of water resource variables in river systems. The results obtained indicate that the vast majority of studies focus on flow prediction, with very few applications to water quality. Methods used for determining model inputs, appropriate data subsets and the best model structure are generally obtained in an ad-hoc fashion and require further attention. Although multilayer perceptrons are still the most popular model architecture, other model architectures are also used extensively. In relation to model calibration, gradient based methods are used almost exclusively. In conclusion, despite a significant amount of research activity on the use of ANNs for prediction and forecasting of water resources variables in river systems, little of this is focused on methodological issues. Consequently, there is still a need for the development of robust ANN model development approaches.

Review: Methods used for the development of neural networks for the prediction of water resource variables in river systems: Current status and future directions

A review of immiscible fluids in the subsurface: properties, models, characterization and remediation

Multi-time scale stream flow predictions: The support vector machines approach

Herein, a recently developed methodology, Support Vector Machines (SVMs), is presented and applied to the challenge of soil moisture prediction. Support Vector Machines are derived from statistical learning theory and can be used to predict a quantity forward in time based on training that uses past data, hence providing a statistically sound approach to solving inverse problems. The principal strength of SVMs lies in the fact that they employ Structural Risk Minimization (SRM) instead of Empirical Risk Minimization (ERM). The SVMs formulate a quadratic optimization problem that ensures a global optimum, which makes them superior to traditional learning algorithms such as Artificial Neural Networks (ANNs). The resulting model is sparse and not characterized by the “curse of dimensionality.” Soil moisture distribution and variation is helpful in predicting and understanding various hydrologic processes, including weather changes, energy and moisture fluxes, drought, irrigation scheduling, and rainfall/runoff generation. Soil moisture and meteorological data are used to generate SVM predictions for four and seven days ahead. Predictions show good agreement with actual soil moisture measurements. Results from the SVM modeling are compared with predictions obtained from ANN models and show that SVM models performed better for soil moisture forecasting than ANN models.

Soil Moisture Prediction Using Support Vector Machines

When operated properly, in situ soil venting or vapor extraction can be one of the most cost-effective remediation processes for soils contaminated with gasoline, solvents, or other relatively, volatile compounds. The components of soil-venting systems are typically off-the-shelf items, and the installation of wells and trenches can be done by reputable environmental firms. However, the design, operation, and monitoring of soil-venting systems are not trivial. In fact, choosing whether or not venting should be applied at a given site is a difficult decision in itself. If one decides to utilize venting, design criteria involving the number of wells, well spacing, well location, well construction, and vapor treatment systems must be addressed. A series of questions must be addressed to decide if venting is appropriate at a given site and to design cost-effective in situ soil-venting systems. This series of steps and questions forms a “decision tree” process. The development of this approach is an attempt to identify the limitations of in situ soil venting, and subjects or behavior that are currently difficult to quantify and for which future study is needed.

A Practical Approach to the Design, Operation, and Monitoring of In Situ Soil‐Venting Systems

Ionic and isotopic ratios for identification of salinity sources and missing data in the Gaza aquifer

[1] This study presents a methodology for designing long-term groundwater head monitoring networks in order to reduce spatial redundancy. A spatially redundant well does not change the potentiometric surface estimation error appreciably, if not sampled. This methodology, based on Support Vector Machines, makes use of a uniquely solvable quadratic optimization problem that minimizes the bound on generalized risk, rather than just the mean square error of differences between measured and “predicted” groundwater head values. The nature of the optimization problem results in sparse approximation of the function defining the potentiometric surface that was utilized to select the number and locations of long-term monitoring wells and guide future data collection efforts, which is a prerequisite in building and calibrating regional flow and transport models. The methodology is applied to the design of regional groundwater monitoring networks in the Water Resources Inventory Area (WRIA) 1, Whatcom County, northern Washington State, USA.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2004WR003304

Mariush Kemblowski

Papers

Multi-time scale stream flow predictions: The support vector machines approach

Soil Moisture Prediction Using Support Vector Machines

A Practical Approach to the Design, Operation, and Monitoring of In Situ Soil‐Venting Systems

Ionic and isotopic ratios for identification of salinity sources and missing data in the Gaza aquifer

Support vectors–based groundwater head observation networks design