Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

Statistics for Spatial Data.

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 erosion, transport and redeposition of sediments shape the Earth's surface, and affect the structure and function of ecosystems and society(1,2). The Yellow River was once the world's largest carrier of fluvial sediment, but its sediment load has decreased by approximately 90% over the past 60 years(3). The decline in sediment load is due to changes in water discharge and sediment concentration, which are both influenced by regional climate change and human activities. Here we use an attribution approach to analyse 60 years of runoff and sediment load observations from the traverse of the Yellow River over China's Loess Plateau - the source of nearly 90% of its sediment load. We find that landscape engineering, terracing and the construction of check dams and reservoirs were the primary factors driving reduction in sediment load from the 1970s to 1990s, but large-scale vegetation restoration projects have also reduced soil erosion from the 1990s onwards. We suggest that, as the ability of existing dams and reservoirs to trap sediments declines in the future, erosion rates on the Loess Plateau will increasingly control the Yellow River's sediment load.

Reduced sediment transport in the Yellow River due to anthropogenic changes

Drought is a complex natural hazard that impacts ecosystems and society in many ways. Many of these impacts are associated with hydrological drought (drought in rivers, lakes, and groundwater). It is, therefore, crucial to understand the development and recovery of hydrological drought. In this review an overview is given of the current state of scientific knowledge of definitions, processes, and quantification of hydrological drought. Special attention is given to the influence of climate and terrestrial properties (geology, land use) on hydrological drought characteristics and the role of storage. Furthermore, the current debate about the use and usefulness of different drought indicators is highlighted and recent advances in drought monitoring and prediction are mentioned. Research on projections of hydrological drought for the future is summarized. This review also briefly touches upon the link of hydrological drought characteristics with impacts and the issues related to drought management. Finally, four challenges for future research on hydrological drought are defined that relate international initiatives such as the Intergovernmental Panel on Climate Change (IPCC) and the ‘Panta Rhei’ decade of the International Association of Hydrological Sciences (IAHS). WIREs Water 2015, 2:359–392. doi: 10.1002/wat2.1085

For further resources related to this article, please visit the WIREs website.

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Hydrological drought explained

State estimation of tidal hydrodynamics using ensemble Kalman filter

The flow duration curve (FDC) is effectively the cumulative distribution function of streamflow. For a long time, hydrologists have sought deeper understanding of the process controls on the shape of FDC, which has been a challenge due to contrasting processes controlling the fast flow and slow flow components of streamflow and their interactions. In this paper, we outline a new framework for exploring the process controls of the FDC, which involves studying fast and slow flow components of FDC separately and combining them statistically, explicitly accounting for their dependence. We illustrate the potential of the framework by constructing empirical fast flow duration (FFDC) and slow flow duration (SFDC) curves from the flow components obtained by traditional baseflow separation. Streamflow time series data from 245 MOPEX catchments across the continental United States are used. The dependence of FFDC and SFDC components is captured by the Gumbel copula, the strength of which varies regionally. In catchments where FFDC and SFDC are independent, FDC can be approximated by a simple convolution of FFDC and SFDC. The proposed conceptual framework opens the way for future modeling studies to explore process controls of fast and slow components of streamflow separately, their dependence, and their relative contributions to the shape of the FDC.

Dingbao Wang

Papers

State estimation of tidal hydrodynamics using ensemble Kalman filter

A New Framework for Exploring Process Controls of Flow Duration Curves

Climatic and Landscape Controls on Long-Term Baseflow

Urbanization Impacts on Evapotranspiration Across Various Spatio-Temporal Scales

Modeling seasonal surface runoff and base flow based on the generalized proportionality hypothesis