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Hydrometeorological prediction involves the forecasting of the state and variation of hydrometeorological elements -- including precipitation, temperature, humidity, soil moisture, river discharge, groundwater, etc.-- at different space and time scales. Such forecasts form an important scientific basis for informing public of natural hazards such as cyclones, heat waves, frosts, droughts and floods. Traditionally, and at most currently operational centers, hydrometeorological forecasts are deterministic, “single-valued” outlooks: i.e., the weather and hydrological models provide a single best guess of the magnitude and timing of the impending events. These forecasts suffer the obvious drawback of lacking uncertainty information that would help decision-makers assess the risks of forecast use. Recently, hydrometeorological ensemble forecast approaches have begun to be developed and used by operational collection of hydrometeorological services. In contrast to deterministic forecasts, ensemble forecasts are a multiple forecasts of the same events. The ensemble forecasts are generated by perturbing uncertain factors such as model forcings, initial conditions, and/or model physics. Ensemble techniques are attractive because they not only offer an estimate of the most probable future state of the hydrometeorological system, but also quantify the predictive uncertainty of a catastrophic hydrometeorological event occurring. The Hydrological Ensemble Prediction Experiment (HEPEX), initiated in 2004, has signaled a new era of collaboration toward the development of hydrometeorological ensemble forecasts. By bringing meteorologists, hydrologists and hydrometeorological forecast users together, HEPEX aims to improve operational hydrometeorological forecast approaches to a standard that can be used with confidence by emergencies and water resources managers. HEPEX advocates a hydrometeorological ensemble prediction system (HEPS) framework that consists of several basic building blocks. These components include:(a) an approach (typically statistical) for addressing uncertainty in meteorological inputs and generating statistically consistent space/time meteorological inputs for hydrological applications; (b) a land data assimilation approach for leveraging observation to reduce uncertainties in the initial and boundary conditions of the hydrological system; (c) approaches that address uncertainty in model parameters (also called ‘calibration’); (d) a hydrologic model or other approach for converting meteorological inputs into hydrological outputs; and finally (e) approaches for characterizing hydrological model output uncertainty. Also integral to HEPS is a verification system that can be used to evaluate the performance of all of its components. HEPS frameworks are being increasingly adopted by operational hydrometeorological agencies around the world to support risk management related to flash flooding, river and coastal flooding, drought, and water management. Real benefits of ensemble forecasts have been demonstrated in water emergence management decision making, optimization of reservoir operation, and other applications.





Hydrological Predictability, Scales, and Uncertainty Issues

The survival and well-being of human civilization depends on water. Human civilization is especially vulnerable to large variations in the water cycle such as flood and drought that disrupts food supplies and can cause havoc to day-to-day operations. Many of these extreme events have occurred in recent years including large droughts and extreme floods in many parts of the world. The looming threat of climate change has the additional potential to make the impacts of extreme water cycle events an even greater threat to society. The ability to have foreknowledge of these extremes in the water cycle can provide time for preparations to reduce the negative impacts of these extremes on society. Predictions of these extreme events require models of the hydrometeorological system, including all its associated uncertainties, and appropriate observations systems to provide input data to these models. Ensemble forecasts using statistical and physically based models that also account for forecast uncertainties have great potential to make the needed predictions of future hydrometeorological events.This chapter discusses the basis for predictability, predictive scales, and uncertainty associated with hydrometeorological prediction. Although much uncertainty may be associated with some hydrometeorological predictions, ensemble forecasting techniques offer a way to quantify this uncertainty making it possible to have more useful predictions for decision makers and for the ultimate benefit to society.

Joshua K. Roundy, Qingyun Duan, John C. Schaake

Overview of Meteorological Ensemble Forecasting


Overview of Weather and Climate Systems

Weather and climate phenomena develop as part of the coupled ocean-atmosphere-land-ice system. To understand the nature of the coupled system and its constituent processes, as well as the basis for and the limits of their predictability, some important concepts are reviewed, including determinism, chaotic error growth, and linear as well as nonlinear perturbation dynamics. It is shown that weather is predictable but only for finite times. Initial and model errors amplify, eventually rendering weather and climate forecasts useless. First, skill is lost in forecasts of fine-scale features while larger-scale phenomena remain predictable for longer periods of time. Processes and other characteristics associated with different scales of motion are discussed next, proceeding from the finest to the largest, coupled global-scale ocean-atmosphere phenomena. The potential use of ensemble forecast techniques to quantify scale and case-dependent predictability in the context of hydrologic forecasting is emphasized throughout.

Huiling Yuan, Zoltan Toth, Malaquias Peña, Eugenia Kalnay

Numerical Weather Prediction Basics: Models, Numerical Methods, and Data Assimilation

Numerical weather prediction has become the most important tool for weather forecasting around the world. This chapter provides an overview of the fundamental principles of numerical weather prediction, including the numerical framework of models, numerical methods, physical parameterization, and data assimilation. Historical revolution, the recent development, and future direction are introduced and discussed.

Zhaoxia Pu, Eugenia Kalnay

Ensemble Methods for Meteorological Predictions

Since the atmospheric system is a nonlinear chaotic system, its numerical prediction is bound by a predictability limit due to imperfect initial conditions and models. Ensemble forecasting is a dynamical approach to quantify the predictability of weather, climate, and water forecasts. This chapter introduces various methods to create an ensemble of forecasts based on three aspects: perturbing initial conditions (IC), perturbing a model, and building a virtual ensemble. For generating IC perturbations, methods include (1) random, (2) time-lagged, (3) bred vector, (4) ensemble transform (ET), (5) singular vector (SV), (6) conditional nonlinear optimal perturbation (CNOP), (7) ensemble transform Kalman filter (ETKF), (8) ensemble Kalman filter (EnKF), and (9) perturbations in boundaries including land surface and topography. For generating model perturbations, methods include (1) multi-model and multi-physics, (2) stochastically perturbed parametrization tendency (SPPT), (3) stochastically kinetic energy backscatter (SKEB), (4) convection triggering, (5) stochastic boundary-layer humidity (SHUM), (6) stochastic total tendency perturbation (STTP), and (7) vorticity confinement. A method to create a spatially correlated random pattern (mask) needed by SPPT, SKEB, etc. is introduced based on the Markov process; a factor separation method is introduced to estimate the relative impact of various physics schemes and their interactions. A method of perturbing a dynamic core to create an ensemble is also mentioned. Quantitative forecast uncertainty information and ensemble products can also be generated from “virtual ensembles” based on existing deterministic forecasts through at least five different approaches including (1) time-lagged, (2) poor-man’s, (3) hybrid, (4) neighborhood, and (5) analog ensembles. Generally speaking, the selection of perturbation methods in constructing an EPS is more important for smaller-scale and shorter-range forecasts and less critical for larger-scale and longer-range forecasts. Finally, the frequently asked question about the trade-off between ensemble size and model resolution is discussed. By introducing these methods, we hope to help readers who are interested in ensemble forecasting but not familiar with these approaches to build their own EPS or produce ensemble products as well as for students to learn the subject of ensemble forecasting.

Jun Du, Judith Berner, Roberto Buizza, Martin Charron, Peter Houtekamer, Dingchen Hou, Isidora Jankov, Mu Mu, Xuguang Wang, Mozheng Wei, Huiling Yuan

Major Operational Ensemble Prediction Systems (EPS) and the Future of EPS

Since the early 1990s, ensemble methods have been increasingly used to address predictability issues, and provide estimates of forecast uncertainties, e.g., in the form of a range of forecast scenarii or of probabilities of occurrence of weather events. Although there is an overall agreement on the main objectives of ensemble-based, probabilistic prediction, different methods have been followed to develop ensemble systems. In this chapter, we will review the methods followed at the major weather prediction centres to develop global ensembles, and we will highlight the links between the method followed and the ensemble forecast performance. The material presented in this chapter is based on the operational, global, medium-range ensembles operational at the time of writing (2014).

Roberto Buizza, Jun Du, Zoltan Toth, Dingchen Hou

Intraseasonal to Interannual Climate Variability and Prediction

This chapter outlines a set of topics essential to become aware of the science, methods, and procedures for operational prediction in the intraseasonal to interannual (ISI) time range. The quality of ISI predictions rely on three basic capabilities: observing networks to sample the Earth’s climate system, an analysis scheme to summarize past and present observations into physically consistent time series of spatial fields, and a prediction method to project a present state of the climate system into the future. Observing networks provide essential data to estimate the true state of the climate system at regular time intervals and to measure physical climate processes and climate variability. Conventional observing networks are designed to sample the most relevant scales of variability and processes occurring in the climate system. Numerical analysis schemes generate physically consistent estimates of the state of the climate system based on observations; they vary in complexity from simple interpolation methods to modern data assimilation schemes. The dynamical approach to carry out ISI predictions use numerical schemes that couple atmosphere, land, ocean and cryosphere models. ISI predictions are also carried out using statistical methods or a combination of the two approaches. The computer burden associated with carrying out dynamical forecasts with comprehensive coupled models is high. Thus, operational centers perform those coupled model runs routinely out to a few seasons only.Current prediction practices include running the coupled models in ensemble mode to account for the uncertainty in the forecasts and to filter out unpredictable signals through ensemble averaging. Furthermore, recognizing the difficulty for a single model to measure its own forecast limitations, it is common to combine ensembles from multiple independent models in a scheme called multi-model ensemble. The practice of incorporating reanalysis and hindcast data sets as tools to post-process raw forecast outputs considerably reduces forecast systematic errors, improves reliability, and enhances the estimation of potential skill and the detection of extreme events. The outputs of coupled global models often serve as input to downstream models such as limited-area high-resolution climate models, river routing, crop growth, and expanding the applicability of ISI forecasts to the regional and local level. Graphical interfaces that permit data analysis and smart decision support systems are becoming necessary to assist forecasters and decision-makers in their real-time endeavors.As models become more skillful and reliable, the methods to generate climate numerical guidance have evolved from subjective approaches to increasingly objective and unsupervised numerical procedures. Nonetheless, human intervention typically increases the skill and value of the final products and is essential for product interpretation and communication to final users. Challenges to realistically model the climate system are many, but those highlighted by the scientific community include better model representation of fine-scale processes in clouds, ocean eddies, and surface interactions and feedbacks and better coupled integration of model climate components. More skillful ISI forecasts are also conditioned to greater computer resources, more extensive and strategic observing systems, and effective data assimilation and model initialization schemes for the coupled climate prediction systems.

Malaquias Peña, L. Gwen Chen, Huug van den Dool

Post-processing of Meteorological Ensemble Forecasting for Hydrological Applications


Hydrological Challenges in Meteorological Post-processing

Uncertainties in the hydrometeorological forecasting chain derive from a large number of sources and are inherent to any system. One source of uncertainty is the discrepancy between the meteorological forecasts and the weather which subsequently occurs. Post-processing meteorological forecasts can reduce this discrepancy by removing systematic errors and produce more reliable, corrected forecasts. However, when the corrected NWP output is used in hydrological applications, problems may occur where consistency and correlation between meteorological variables have not been maintained. Therefore a correction that improves the forecast performance of one or more NWP outputs does not necessarily have a positive influence on the hydrological model forecasts. In this chapter the most important needs of the hydrological community in terms of meteorological post-processing are presented. The most commonly used techniques for post-processing are presented along with the pros, cons, and pitfalls in terms of their usage in hydrological applications. Finally, a few important areas of future research are identified.

Fredrik Wetterhall, Paul Smith

Application to Post-processing of Meteorological Seasonal Forecasting

Seasonal hydrological forecasting relies on accurate and reliable ensemble climate forecasts. A calibration, bridging, and merging (CBaM) method has been developed to statistically postprocess seasonal climate forecasts from general circulation models (GCMs). Postprocessing corrects conditional biases in raw GCM outputs and produces forecasts that are reliable in ensemble spread. The CBaM method is designed to extract as much skill as possible from the GCM. This is achieved by firstly producing multiple forecasts using different GCM output fields, such as rainfall, temperature, and sea surface temperatures, as predictors. These forecasts are then combined based on evidence of skill in hindcasts. Calibration refers to direct postprocessing of the target variable – rainfall for example. Bridging refers to indirect forecasting of the target variable – forecasting rainfall with the GCM’s Nino3.4 forecast for example. Merging is designed to optimally combine calibration and bridging forecasts. Merging includes connecting forecast ensemble members across forecast time periods by using the “Schaake Shuffle,” which creates time series forecasts with appropriate temporal correlation structure. CBaM incorporates parameter and model uncertainty, leading to reliable forecasts in most applications. Here, CBaM is applied to produce monthly catchment rainfall forecasts out to 12 months for a catchment in northeastern Australia. Bridging is shown to improve forecast skill in several seasons, and the ensemble time series forecasts are shown to be reliable for both monthly and seasonal totals.

Andrew Schepen, Q. J. Wang, David E. Robertson

Multi-model Combination and Seamless Prediction

(Hydro-) Meteorological predictions are inherently uncertain. Forecasters are trying to estimate and to ultimately also reduce predictive uncertainty. Atmospheric ensemble prediction systems (EPS) provide forecast ensembles that give a first idea of forecast uncertainty. Combining EPS forecasts, issued by different weather services, to multi-model ensembles gives an even better understanding of forecast uncertainty. This article reviews state of the art statistical post-processing methods that allow for sound combinations of multi-model ensemble forecasts. The aim of statistical post-processing is to maximize the sharpness of the predictive distribution subject to calibration. This article focuses on the well-established parametric approaches: Bayesian model averaging (BMA) and ensemble model output statistics (EMOS). Both are readily available and can be used for straightforward implementation of methods for multi-model ensemble combination. Furthermore, methods to ensure seamless predictions in the context of statistical post-processing are summarized. These methods are mainly based on different types of copula approaches. Since skill of (statistically post-processed) ensemble forecasts is generally assessed using particular verification methods, an overview over such methods to verify probabilistic forecasts is provided as well.

Stephan Hemri

Hydrological Models


Hydrological Cycles, Models, and Applications to Forecasting

This chapter presents an overview of hydrology, water cycle, land surface processes (e.g., precipitation, snow, glaciers and frozen soils, evapotranspiration, surface and subsurface runoff, overland and river flow routing), and hydrologic modeling and its history. The chapter is concluded with an outlook for future.

Sharad K. Jain, Vijay P. Singh

Black-Box Hydrological Models

This chapter discusses different types of black-box hydrological models that are based on input-output relationships rather than physical principles. They include antecedent precipitation index (API) models, regression models, time series models, artificial neural network (ANN) models, fuzzy logic models, and frequency analysis models. The purpose of this chapter is neither to provide a complete discussion of the theory of hydrological systems nor to offer a complete coverage of the studies published in the literature. Rather, the chapter is focused on presenting general theories and methods of different types of black-box models, basic model forms, and related applications in hydrology and water resources engineering.

Chong-Yu Xu, Lihua Xiong, Vijay P. Singh

Conceptual Hydrological Models

Conceptual hydrological models, sometimes also called gray-box models, are precipitation-runoff models built based on observed or assumed empirical relationships among different hydrological variables. They are different from black-box models which consider precipitation-runoff relationship only statistically. They are also different from the physically based distributed hydrological models which are based on solving differential equations describing the physical laws of mass, energy, and momentum conservations. This chapter describes how conceptual hydrological models represent the different hydrological processes involved in converting precipitation to runoff over land, and then to streamflow discharge at the basin outlet, including precipitation, snow accumulation and ablation, infiltration, soil moisture storage, evapotranspiration, runoff generation, baseflow, and river routing. Some of the well-known models are also used for illustration.

Zhaofei Liu, Yamei Wang, Zongxue Xu, Qingyun Duan

Distributed Hydrological Models

Physically based distributed hydrological models (PBDHMs), the development of which has been facilitated by advancements in GIS and remote sensing, meteorology, computer science and engineering, and other related science and engineering disciplines, divide the terrain of a basin into fine-resolution cells and calculate the hydrological processes at both the cell and basin scales. Numerous PBDHMs have been proposed. Because PBDHMs can model hydrological processes at a fine resolution and physically derive model parameters from the properties of the terrain, they have the potential to simulate/predict hydrologic processes more effectively, and they can be employed within ungauged basins. Following a brief review of the development of PBDHMs, this chapter introduces the general structures and methodologies of currently utilized PBDHMs. The basin division method, the sources of terrain property data used to construct PBDHMs, and the flow network delineation method are summarized, and the hydrological processes within watersheds, including interception, evapotranspiration, runoff formation and movement, and runoff routing, are discussed. The methodologies most commonly employed by PBDHMs are then introduced, including those used to calculate the interception, evaporation, runoff formation, and runoff routing. Parameter determination methods are discussed, three of which are introduced in detail: the physically based method, the scalar method, and the automated optimization method. Finally, a case study is presented that demonstrates the entire procedure of constructing a Liuxihe model for a river basin flood simulation/prediction to provide the reader with a complete example of the application of a PBDHM to a real-world problem.

Yangbo Chen

Land Surface Hydrological Models

The details of land-surface models (LSMs) are presented here from the perspective of providing the proper boundary condition to and interaction with a “parent” atmospheric model. Topics include atmospheric forcing to LSMs, land data sets, surface-layer turbulence, surface fluxes and energy and water budgets, land-surface physics, and the role of the land states and surface fluxes in local land-atmosphere interaction. Connections of LSMs with hydrological models (e.g., saturated zone or groundwater, and streamflow or river-routing) and land data assimilation are outside the scope of this chapter.

Michael B. Ek

Model Parameter Estimation and Uncertainty Analysis


Parameter Estimation and Predictive Uncertainty Quantification in Hydrological Modelling

The majority of hydrological and environmental models contain parameters that must be specified before the model can be used. Parameter estimation is hence a very common problem in environmental sciences and has received tremendous amount of research and industry attention. This chapter reviews some of the key principles of parameter estimation, with a focus on calibration approaches and uncertainty quantification. The distinct approaches of manual calibration, optimization, multi-objective optimization, and probabilistic approaches are described in terms of key theory and representative applications. Advantages and limitations of these strategies are listed and discussed, with a focus on their ability to represent parametric and predictive uncertainties. The role of posterior diagnostics to check calibration and model assumptions that impact on parameter estimation is emphasized. Auxiliary tricks and techniques are described to simplify the process of parameter estimation in practical applications. The chapter concludes with an outline of directions for ongoing and future research. It is hoped that this chapter will help hydrologists and environmental modellers get to the current state of research and practice in model calibration, parameter estimation, and uncertainty quantification.

Dmitri Kavetski

Methods to Estimate Optimal Parameters

Model, data, and parameter estimation are three fundamental elements in hydrologic process modeling and forecasting. Recent progresses in hydrologic modeling have been made toward more efficient and effective estimation of model parameters. In this chapter, classical and recently developed parameter optimization methods and their applications in hydrological model calibration are reviewed. Those methods include gradient-based optimization methods, direct search methods, and recently developed stochastic global optimization methods. A recently developed surrogate model approach, with the purpose to reduce computational burden of model which runs through replacing the hydrologic process model with a cheaper-to-run surrogate model, is also discussed. Extending from a single objective function parameter optimization, multiobjective optimization methods and their core concept in deriving trade-offs are also summarized. Examples are provided to demonstrate the strengths and limitations of optimization algorithms summarized in this chapter.

Tiantian Yang, Kuolin Hsu, Qingyun Duan, Soroosh Sorooshian, Chen Wang

Uncertainty Quantification of Complex System Models: Bayesian Analysis

This chapter summarizes the main elements of Bayesian probability theory to help reconcile dynamic environmental system models with observations, including prediction in space (interpolation), prediction in time (forecasting), assimilation of data, and inference of the model parameters. Special attention is given to the treatment of parameter uncertainty (first-order approximations and Bayesian intervals), the prior distribution, the formulation of the likelihood function (using first-principles), the marginal likelihood, and sampling techniques used to estimate the posterior target distribution. This includes rejection sampling, importance sampling, and recent developments in Markov chain Monte Carlo simulation to sample efficiently complex and/or high-dimensional target distributions, including limits of acceptability. We illustrate the application of Bayes’ theorem and inference using three illustrative examples involving the flow and storage of water in the surface and subsurface. At least some level of calibration of these models is required to match their output with observations of system behavior and response. Algorithmic recipes of the different methods are provided to simplify implementation and use of Bayesian analysis.

Jasper A. Vrugt, Elias C. Massoud

Sensitivity Analysis Methods

Sensitivity analysis (SA) is an important tool for assessing and reducing uncertainties in computer-based models. This chapter presents a comprehensive review of some commonly used SA methods, including gradient-based, variance-based, and regression-based methods. Features and applicability of those methods are described and illustrated with some examples. Merits and limitations of different methods are explained, and the criteria of choosing appropriate SA methods for different applications are suggested.

Yanjun Gan, Qingyun Duan

Observation and Data Assimilation


Fundamentals of Data Assimilation and Theoretical Advances

Hydrometeorological predictions are not perfect as models often suffer either from inadequate conceptualization of underlying physics or non-uniqueness of model parameters or inaccurate initialization. During the past two decades, Data Assimilation (DA) has received increased prominence among researchers and practitioners as an effective and reliable method to integrate the hydrometeorological observations from in situ measure and remotely-sensed sensors into predictive models for enhancing the forecast skills while taking into account all sources of uncertainties. The successful application of DA in different disciplines has resulted in an ever-increasing publications. This chapter provides a progressive essay covering fundamental and theoretical underpinnings of DA techniques and their applications in a variety of scientific fields. More detailed examples of applications are presented in following chapters in this section.

Hamid Moradkhani, Grey S. Nearing, Peyman Abbaszadeh, Sahani Pathiraja

Soil Moisture Data Assimilation

Accurate knowledge of soil moisture at the continental scale is important for improving predictions of weather, agricultural productivity, and natural hazards, but observations of soil moisture at such scales are limited to indirect measurements, either obtained through satellite remote sensing or from meteorological networks. Land surface models simulate soil moisture processes, using observation-based meteorological forcing data, and auxiliary information about soil, terrain, and vegetation characteristics. Enhanced estimates of soil moisture and other land surface variables, along with their uncertainty, can be obtained by assimilating observations of soil moisture into land surface models. These assimilation results are of direct relevance for the initialization of hydrometeorological ensemble forecasting systems. The success of the assimilation depends on the choice of the assimilation technique, the nature of the model and the assimilated observations, and, most importantly, the characterization of model and observation error. Systematic differences between satellite-based microwave observations or satellite-retrieved soil moisture and their simulated counterparts require special attention. Other challenges include inferring root-zone soil moisture information from observations that pertain to a shallow surface soil layer, propagating information to unobserved areas and downscaling of coarse information to finer-scale soil moisture estimates. This chapter summarizes state-of-the-art solutions to these issues with conceptual data assimilation examples, using techniques ranging from simplified optimal interpolation to spatial ensemble Kalman filtering. In addition, operational soil moisture assimilation systems are discussed that support numerical weather prediction at ECMWF and provide value-added soil moisture products for the NASA Soil Moisture Active Passive mission.

Gabrielle Jacinthe Maria De Lannoy, Patricia de Rosnay, Rolf Helmut Reichle

Assimilation of Streamflow Observations

Streamflow is arguably the most important predictor in operational hydrologic forecasting and water resources management. Assimilation of streamflow observations into hydrologic models has received growing attention in recent decades as a cost-effective means to improve prediction accuracy. Whereas the methods used for streamflow data assimilation (DA) originated and were popularized in atmospheric and ocean sciences, the nature of streamflow DA is significantly different from that of atmospheric or oceanic DA. Compared to the atmospheric processes modeled in weather forecasting, the hydrologic processes for surface and groundwater flow operate over a much wider range of time scales. Also, most hydrologic systems are severely under-observed. The purpose of this chapter is to provide a review on streamflow measurements and associated uncertainty and to share the latest advances, experiences gained, and science issues and challenges in streamflow DA. Toward this end, we discuss the following aspects of streamflow observations and assimilation methods: (1) measurement methods and uncertainty of streamflow observations, (2) streamflow assimilation applications, and (3) benefits and challenges streamflow DA with regard to large-scale DA, multi-data assimilation, and dealing with timing errors.

Seong Jin Noh, Albrecht H. Weerts, Oldrich Rakovec, Haksu Lee, Dong-Jun Seo

Post-processing of Hydrological Ensemble Forecasts


Motivation and Overview of Hydrological Ensemble Post-processing

In this introduction to this chapter on hydrologic post-processing, we discuss the different but complementary directives that the “art” of post-processing must satisfy: the particular directive defined by specific applications and user needs; versus the general directive of making any ensemble member indistinguishable from the observations. Also discussed are the features of hydrologic post-processing that are similar and separate from meteorological post-processing, providing a tie-in to early chapters in this handbook. We also provide an overview of the different aspects the practitioner should keep in mind when developing and implementing algorithms to adequately “correct and calibrate” ensemble forecasts: when forecast uncertainties should be characterized separately versus maintaining a “lumped” approach; additional aspects of hydrological ensembles that need to be maintained to satisfy additional user requirements, such as temporal covariability in the ensemble time series, an overview of the different post-processing approaches being used in practice and in the literature, and concluding with a brief overview of more specific requirements and challenges implicit in the “art” of post-processing.

Thomas M. Hopson, Andy Wood, Albrecht H. Weerts

Short-Range Ensemble Forecast Post-processing

Short-term hydrological ensemble forecasts do not usually account for the uncertainty in the initial conditions. Consequently, raw forecasts are often biased and under-dispersed and must be post-processed. Both precipitation and streamflow forecasts for short lead-time depart from the Gaussian distribution, and this important characteristic limits the choice of possible post-processing approaches. Post-processing is performed by calibrating a statistical model using a training dataset containing past forecasts and the corresponding observations. This chapter covers the most common post-processing approaches for short-term hydrological forecasts. They are divided into four categories: analog methods, regressions, kernel dressing, and Bayesian Model Averaging. The vast majority of post-processing methods can be categorized as regression-based. A selection of the most commonly encountered ones in hydrology is presented: quantile regression, nonhomogeneous regression, and logistic regression. Any post-processing approach brings benefits and drawbacks, which are discussed at the end of this chapter. However, according to the few existing comparative studies, no single method is appropriate for all forecasting situation. Therefore, the reader should make his or her own mind regarding which one to choose, according to his or her own specific needs and limitations.

Marie-Amélie Boucher, Emmanuel Roulin, Vincent Fortin

Seasonal Ensemble Forecast Post-processing

In many parts of the world, water resources systems manage sub-seasonal to seasonal (S2S) variability in climate and runoff in part through the use of operational streamflow forecasts, supplemented by predictions of climate and other hydrologic variables. S2S hydrologic forecasts are produced through both statistical and dynamical (model-based) approaches, and separate S2S forecasts may be combined in multi-model frameworks to increase their skill. Statistical post-processing can be used to enhance the skill and reliability of model-based S2S predictions, and to reduce bias, as well as to merge forecasts from multiple approaches. This chapter describes seasonal hydrologic forecast approaches and products, and presents common techniques used in both the post-processing of single ensemble forecast series as well as the combination of multiple forecasts. Also discussed are the sources of S2S hydrological predictability and particular challenges and opportunities related to post-processing seasonal hydrologic predictions, for which the sample sizes of past simulations, observations and predictions are relatively more limited than in the context of short to medium range prediction.

Andy Wood, A. Sankarasubramanian, Pablo Mendoza

Verification of Hydrometeorological Ensemble Forecasts


Attributes of Forecast Quality

Forecast verification is a process used to assess the quality of hydrometeorological ensemble forecasts. This chapter describes the many aspects of forecast quality using a distributions-oriented approach. Using the joint distribution of forecasts and observations, or one of its factorizations into a conditional and marginal distribution, the aspects of forecast quality are defined. Hypothetical ensemble forecasts are then used to illustrate aspects of forecast quality. The hypothetical ensemble forecasts are used to construct single-valued forecasts, probability forecasts for an event, and ensemble probability distribution forecasts. Their forecast quality is then diagnosed using visual comparisons and numerical comparisons of forecast quality measures. The examples illustrate that a single aspect of forecast quality is insufficient and that many aspects are needed to understand the nature of the forecasts. Some practical considerations in the application of the framework to ensemble forecast verification are discussed.

A. Allen Bradley, Julie Demargne, Kristie J. Franz

Verification Metrics for Hydrological Ensemble Forecasts

This chapter reviews the most commonly used verification metrics for measuring the performance of hydrological ensemble forecasts. It links metrics to the different attributes of forecast quality and discusses the links between verification variables, metrics, and applications in a broad perspective. It provides an overview of the use of these metrics in forecast evaluation studies and general insights into what forecasters, practitioners, and end-users should consider when applying verification measures in the practice of hydrological ensemble forecasting.

François Anctil, Maria-Helena Ramos

Verification of Meteorological Forecasts for Hydrological Applications

This chapter illustrates how verification is conducted with operational meteorological ensemble forecasts. It focuses on the main aspects of importance to hydrological applications, such as verification of point and spatial precipitation forecasts, verification of temperature forecasts, verification of extreme meteorological events, and feature-based verification.

Eric Gilleland, Florian Pappenberger, Barbara Brown, Elizabeth Ebert, David Richardson

Verification of Short-Range Hydrological Forecasts

For the mitigation of floods and flashfloods, operational nowcast and forecast systems are crucial. This chapter provides practical illustrations of the verification of hydrological ensemble prediction systems with a temporal horizon of up to 5 days.Section 2 shows the application of two ensemble approaches for discharge nowcasts. The results show that both ensemble approaches have added value compared to deterministic nowcasts.Section 3 presents the evaluation of an operational flood forecasting system. The system is run with the two deterministic COSMO-2 and COSMO-7 weather forecasts and with the probabilistic COSMO-LEPS weather forecast. The evaluation with several skill scores suggests that decisions that need to be taken with a lead time of 1 day and more should be based on the ensemble forecast.Ensemble forecasts can be difficult to interpret. Section 4 provides a helpful tool for the estimation of flood peak timing and magnitude based on probabilistic forecasts.

Katharina Liechti, Massimiliano Zappa

Verification of Medium- to Long-Range Hydrological Forecasts

Hydrological forecasting is crucial for hydropower production and risk management related to extreme events. Since uncertainty cannot be eliminated from such a process, forecasts should be probabilistic in nature, taking the form of probability distributions over future events. However, verification tools adapted to probabilistic hydrological forecasting have only been recently considered. How can such forecasts be verified accurately? In this chapter a simple theoretical framework proposed by Gneiting et al. (2007) is employed to provide a formal guidance to verify probabilistic forecasts. Some strategies and scoring rules used to measure the performance of hydrological forecasting systems, namely, Hydro-Québec, are presented. Monte Carlo simulation experiments and applications to a real archive of operational medium-range forecasts are also presented. An experiment is finally performed to evaluate long-range hydrological forecasts in a decisional perspective, by employing hydrological forecasts in a stochastic midterm planning model designed for optimizing electricity production. Future research perspectives and operational challenges on diagnostic approaches for hydrological probabilistic forecasts are given.

Luc Perreault, Jocelyn Gaudet, Louis Delorme, Simon Chatelain

Application of Hydrological Forecast Verification Information

Verification studies and systems often focus solely on the exercise of verifying forecasts and not on the application of verification information. This chapter discusses the potential for application of hydrological forecast verification information to improve decision-making in and around the forecast process. Decision-makers include model developers and system designers, forecasters, forecast consumers, and forecast administrators. Each of these has an important role in decisions about forecasts and/or the application of forecasts that may be improved through use of forecast verification. For each, we describe the role, the actions that could be taken to improve forecasts or their application, the context and constraints of those actions, and needs for verification information. Consistent with other studies and assessments on forecast verification, we identify the need for a routine forecast verification system to archive data, plan for operations, measure forecast performance, and group forecasts according to application. Further, we call on forecast agencies and forecast consumers to use forecast verification as a routine part of their operations in order to continually improve services and to engage others to use forecast verification to improve decision-making.

Kevin Werner, Jan S. Verkade, Thomas C. Pagano

Communication and Use of Ensemble Forecasts for Decision Making


Overview of Forecast Communication and Use of Ensemble Hydrometeorological Forecasts

Over the last few decades, hydrometeorological forecasting, warning and decision making has benefited greatly from advances in the natural, physical, computing and social sciences. A fast developing computing capability has enabled meteorologists to produce ensemble prediction systems (EPS) that quantify the uncertainty in forecasting and simulating floods, droughts, and in water management decision making. At the same time, the social sciences have helped to understand the human perceptions of risk information and how different actors communicate hazard, risk and uncertainty information. Ultimately hydrometeorological forecasts are used in making decisions. However, to be effective, such decisions must be communicated to the hazard response organisations and to the general public. For this, the communication must be simple and clear, it must be relevant and should come from a trusted source. This overview summarises how such communication is organised for a variety of applications in different countries. It is the effectiveness of the entire system which must be considered and assessed. As ensembles are increasingly used in increasingly longer term management and policy decisions, the range of end-users and their differing requirements can only expand and flexibility and adaptability to individual circumstances will be required from both the natural and social scientists involved.

Jutta Thielen-del Pozo, Michael Bruen

Present and Future Requirements for Using and Communicating Hydrometeorological Ensemble Prediction Systems for Short-, Medium-, and Long-Term Applications

This chapter provides representative examples for using and communicating hydrometeorological ensemble prediction systems (HEPS) for short-, medium-, and long-term applications. The needs of the specific end users in disaster management, flood forecasting centers, and water management are highlighted.In the first section, the requirements are presented for a nowcasting system based on radar data designed to provide sufficient lead time for decision makers responsible for urban areas. The generation of rainfall ensembles from radar measurements is described using the so-called string of beads methodology. The aspects required by decision makers for flood management are followed by the technical set-up and constraints.The second section illustrates how short-term HEPS can contribute to increasing the predictability of flash flood events on a regional scale with complementary indicators to higher-resolution local information systems based on short-term forecasts and observations.In the third section, the benefits of hydrological ensembles are elaborated for flood forecasting and shipping for a well-controlled, trans-national river basin such as the river Rhine. For several years, medium-range ensemble prediction systems have been explored for flood forecasting in medium to large river basins such as the Rhine.The last section describes the requirements of HEPS for water management and how they are used at the example of hydropower in Sweden. In snow-dominated hydrological regimes such as in Scandinavia, reservoirs need to be carefully managed in order to have enough capacity for storing spring flood volume, while keeping enough water for securing the required power generation. The chapter concludes with the strengths and the limitations of HEPS for various applications.

Geoff Pegram, Damien Raynaud, Eric Sprokkereef, Martin Ebel, Silke Rademacher, Jonas Olsson, Cristina Alionte-Eklund, Barbro Johansson, Göran Lindström, Henrik Spångmyr

Best Practice in Communicating Uncertainties in Flood Management in the USA

Ensemble forecasting has gained a great deal of popularity for addressing and estimating uncertainty associated with both meteorologic and hydrologic forecasts over the past decade. While ensemble-based hydrologic forecasts have been in routine operations for longer-term forecasts for many years, the notion of short- and medium-term probabilistic forecasts in support of water and flood management efforts is relatively new and is a developing science and service. Approaches to effectively conveying and communicating hydrologic forecast uncertainty are being actively developed and vetted with potential user communities. Important experience and insight will be gained over the next few years as the community of developers, forecasters, and end users work to leverage probabilistic forecasts in a risk-based decision environment. With proper focus and support, these efforts have the potential to significantly improve flood, ecosystems, and water management with benefits to multiple sectors of our society.

Robert K. Hartman

Saving Lives: Ensemble-Based Early Warnings in Developing Nations

Natural disasters disproportionately affect the developing nations due to the lack of effective early warning systems. In this chapter, we present the need, challenges, and opportunities of early warning systems in developing nations for decision making in disaster risk management and demonstrate the added value of ensemble forecasting in particular in data- and infrastructure-scarce regions. First, we review the global extent of flood and drought disaster damages in the last few decades on human lives and the economy and demonstrate that a disproportionately high rate of death (per event) occurred in developing regions, where there is no (or ineffective) operational early disaster warning systems. Next, we present the everyday needs and challenges of preparing for and responding to natural disasters in Nigeria, a typical developing country with fragmented data infrastructure and limited national early warning system capability. Particularly, we share experiences from the most recent major flood disaster and demonstrate a potential value of ensemble-based flood early warnings, using streamflow forecasts from the Global Flood Awareness System (GloFAS).However, forecasting of disasters alone is not sufficient if the information is not translated into actionable advice at a local community level. This is particularly important for ensemble forecasting which requires training for the forecasters as well as the receiving authorities. In order to achieve this, technical knowledge and communication infrastructure are needed to deliver the early warning information to the relevant communities and concerned authorities. Multi-stakeholder partnerships bringing together scientific community, policy, and decision makers and end users from international to local level could facilitate humanitarian aid organizations, and decision makers understand and use the ensemble predictions on timely basis before, during, and after disaster strikes. The chapter concludes with highlighting the multi-stakeholder partnership initiatives on floods (Global Flood Partnership (GFP)) and droughts (Integrated Drought Management Programme (IDPM)), established with the common goal of reducing flood and drought risk across the globe.

Feyera A. Hirpa, Kayode Fagbemi, Ernest Afiesimam, Hassan Shuaib, Peter Salamon

Communicating and Using Ensemble Flood Forecasts in Flood Incident Management: Lessons from Social Science

This chapter explores the practical challenges of communicating and using ensemble forecasts in operational flood incident management. It reviews recent social science research on the variety and effectiveness of hydrological ensemble prediction systems (HEPS) visualization methods and on the cognitive and other challenges experienced by forecast recipients in understanding probabilistic forecasts correctly. To explore how those generic findings from the research literature work out in actual operational practice, the chapter then discusses a series of case studies detailing the development, communication, and use of HEPS products in various institutional contexts in France, Britain, and internationally at the EU and global levels. The chapter concludes by drawing out some broader lessons from those experiences about how to communicate and use HEPS more effectively.

David Demeritt, Elisabeth M. Stephens, Laurence Créton-Cazanave, Céline Lutoff, Isabelle Ruin, Sébastien Nobert

Overview of Communication Strategies for Uncertainty in Hydrological Forecasting in Australia

With a Focus on “Assessing Forecast Quality of the National Seasonal Streamflow Forecast Service”

The National Seasonal Streamflow Forecasting Service operated by the Bureau of Meteorology since 2010 delivers monthly updates of 3 month ensemble forecasts at 147 locations across 75 river basins using the statistical Bayesian joint probability (BJP). Seasonal forecasts are communicated to the public using statistical concepts such as “chances,” “ensembles,” “lower/higher than median,” etc. However, these concepts require advanced competencies in statistics, and they cannot be conveyed to a general audience easily. This chapter focuses on the challenge of communicating forecast skill to a wide range of users more effectively. A simple forecast performance measure called the “Aggregated Forecast Performance Index (AFPI)” was introduced which captures key attributes such as forecast reliability and accuracy and combines them into a single easy-to-understand and well-informed aggregated measure. Based on this index, it was demonstrated that bureau’s seasonal streamflow forecasts are reliable. They also offer improved accuracy by narrowing down the forecast uncertainty (up to 25%) with respect to reference climatology and hence offer a value proposition for water managers to improve their decision-making.

Narendra Kumar Tuteja, Senlin Zhou, Julien Lerat, Q. J. Wang, Daehyok Shin, David E. Robertson

Ensemble Forecast Application and Showcases


Introduction to Ensemble Forecast Applications and Showcases

Hydrometeorological ensemble forecasting has gradually entered the offices of operational water managers changing forecasting practice across a wide range of applications. This section illustrates the range of applications available today, with the following showcases: Where in the world have hydrological ensemble prediction systems (HEPS) found practical application and are increasingly yielding added value in hazard mitigation? Can I anticipate flash floods? Can I anticipate and cope with floods? Do I really need to draw down my reservoir and make room for a flood that might not occur? Can I optimize the production of hydropower reservoir operations? Is there any chance that my municipality might be affected by critical water shortages in the coming weeks? What do we learn from the operation of a continental-scale prediction system addressing users in different countries? How does communication between forecast centers and end users work in real-life operations? These showcases illustrate some of the numerous HEPS that have been implemented around the world. We hope that the success stories and pitfalls discussed in these examples will inspire and support successful development of further new applications.

Massimiliano Zappa, S. J. van Andel, Hannah L. Cloke

Hydrological Ensemble Prediction Systems Around the Globe

A large number of hydrological forecasting systems exist across the globe. Recent advances have pushed the limits of predictability of discharge and other hydrological variables from a few hours to several days or even months. In this chapter, we aim to give an overview of Hydrological Ensemble Prediction Systems across the globe. It provides brief descriptions of existing or preoperational systems as background, and discusses the challenges ahead. This overview shows that there is at least one system per continent, though their geographic domain varies considerably among very small catchments, countries national and interregional basins, transnational basins, continents, or even the entire globe. It highlights common challenges and differences.

Florian Pappenberger, Thomas C. Pagano, J. D. Brown, Lorenzo Alfieri, D. A. Lavers, L. Berthet, F. Bressand, Hannah L. Cloke, M. Cranston, J. Danhelka, J. Demargne, N. Demuth, C. de Saint-Aubin, P. M. Feikema, M. A. Fresch, R. Garçon, A. Gelfan, Y. He, Y. -Z. Hu, B. Janet, N. Jurdy, P. Javelle, L. Kuchment, Y. Laborda, E. Langsholt, M. Le Lay, Z. J. Li, F. Mannessiez, A. Marchandise, R. Marty, D. Meißner, D. Manful, D. Organde, V. Pourret, Silke Rademacher, Maria-Helena Ramos, D. Reinbold, S. Tibaldi, P. Silvano, Peter Salamon, D. Shin, C. Sorbet, Eric Sprokkereef, V. Thiemig, Narendra Kumar Tuteja, S. J. van Andel, Jan S. Verkade, B. Vehviläinen, A. Vogelbacher, Fredrik Wetterhall, Massimiliano Zappa, R. E. Van der Zwan, Jutta Thielen-del Pozo

Flash Flood Forecasting Based on Rainfall Thresholds

Extreme rainstorms often trigger catastrophic flash floods in Europe and in several areas of the world. Despite notable advances in weather forecasting, most operational early warning systems for extreme rainstorms and flash floods are based on rainfall observations derived from rain gauge networks and weather radars, rather than on forecasts. As a result, warning lead times are bounded to few hours, and warnings are usually issued when the event is already taking place.This chapter illustrates three recently developed systems that use information on observed and forecasted precipitation to issue flash flood warnings. The first approach is an indicator for heavy precipitation events, developed to complement the flood early warning of the European Flood Awareness System (EFAS) and targeted to short and intense events, possibly leading to flash flooding in small catchments. The system is based on the European Precipitation Index Based on Simulated Climatology (EPIC), which in EFAS is computed using COSMO-LEPS ensemble weather forecasts and a 20-year consistent reforecast dataset.The second system is a flash flood early warning tool developed based on precipitation statistics. A total of 759 sub-catchments in southern Switzerland is considered. Intensity-duration-frequency (IDF) curves for each catchment have been calculated based on gridded precipitation products for the period 1961–2012 and gridded reforecast of the COSMO-LEPS for the period 1971–2000. The different IDF curves at the catchment level in combination with precipitation forecasts are the basis for the flash flood early warning tool. The forecast models used are COSMO-2 (deterministic, updated every 3 h and with a lead time of 24 h) and COSMO-LEPS (probabilistic, 16-member and with a lead time of 5 days).The third system (FF-EWS) uses probabilistic high-resolution precipitation products generated from the observations of the weather radar network to monitor situations prone to trigger flash floods in Catalonia (NE Spain). These ensemble precipitation estimates and nowcasts are used to calculate the basin-aggregated rainfall (that is, the rainfall accumulated upstream of each point of the drainage network), which is the variable used to characterize the potential flash flood hazard.Examples of successful and less skilful forecasts for all three systems are shown and commented to highlight pros and cons.

Lorenzo Alfieri, Marc Berenguer, Valentin Knechtl, Katharina Liechti, Daniel Sempere-Torres, Massimiliano Zappa

Medium Range Flood Forecasting Example EFAS

Europe repeatedly observes flood events that affect several countries at the same time and which require the coordination of assistance at the European level. The European Flood Awareness System (EFAS) has been developed specifically to respond to the need for forecasting transnational floods with sufficient lead time to allow coordination of aid at the European level in case the national capacities for emergency management are exceeded. In order to achieve robust and reliable flood forecasting at the continental scale with lead times up to 10 days, EFAS promotes probabilistic forecasting techniques based on multiple numerical weather prediction inputs including ensemble prediction systems. Its aim is to complement existing national flood forecasting services with added value information and to provide European decision makers with coherent overviews on ongoing and upcoming floods in Europe for better planning and coordination of aid. To date, EFAS is a unique system providing daily, probabilistic flood forecast information for the entire of Europe on a single platform. Being a complementary system to national ones, EFAS predicts the probabilities for exceeding critical flood thresholds rather than quantitative information on stream flows. By maintaining a dedicated, multinational partner network of EFAS users, novel research could be transferred directly to the operational flood forecasting centers in Europe. EFAS development started in 2003, and the system has become fully operational under the umbrella of Emergency Management Service of the European Copernicus Space Program in 2011.

Jutta Thielen-del Pozo, Peter Salamon, Peter Burek, Florian Pappenberger, C. Alionte Eklund, Eric Sprokkereef, M. Hazlinger, M. Padilla Garcia, R. Garcia-Sanchez

Seasonal Drought Forecasting on the Example of the USA

Drought is a slowly developing process and usually begins to impact a region without much warning once the water deficit reaches a certain threshold. Predicting the drought a few months in advance will benefit a variety of sectors for drought planning and preparedness. In response to the National Integrated Drought Information System (NIDIS), the Princeton land surface hydrology group has been working on drought monitoring and forecasting for over 10 years and has developed a seasonal drought forecasting system based on global climate forecast models and a large-scale land surface hydrology model. This chapter will showcase the performances of the system in predicting soil moisture drought area, frequency, and severity over the Conterminous United States (CONUS) at seasonal scales; discuss about the challenges in forecasting streamflow for hydrologic drought; and provide an outlook for future developments and applications.

Eric F. Wood, Xing Yuan, Joshua K. Roundy, Ming Pan, Lifeng Luo

Ensemble Streamflow Forecasts for Hydropower Systems

Decision-making Hydropower operation and planning requires streamflow forecasts at both short (typically, the first 4–5 days) and long ranges (a few months or a season ahead) over different spatial scales. Operational streamflow forecasting services a variety of decisions, made under conditions of risk and uncertainty, e.g., flood protection, dam safety, system’s operation, optimization, and planning of power production. In areas where snow falls in significant quantities during winter, spring freshet poses additional challenges given the uncertainties related to the timing and volume of melt water flowing into hydropower reservoirs. Reservoir levels need to be gradually lowered over the winter to make it possible to store snowmelt water in spring. Reservoirs are thus important regulators of streamflow natural variability. They act as a storage place to water that can be used later to meet periods of higher electricity demands or to sell surplus electricity to the power distribution grid. They also usually are multipurpose, and their operation must take into account the different water uses, which can, in some cases, be conflictual. The importance of accurate and reliable streamflow forecasts is therefore unquestionable. The hydropower sector has long recognized that streamflow forecasting is intrinsically uncertain and the use of ensemble forecasts is progressing fast. Key challenges today are related to the integration of state-of-the-art weather services, the implementation of systematic, advanced data assimilation schemes, to the assessment of the links between forecast quality and value, and to the enhancement of risk-based decision-making.

Marie-Amélie Boucher, Maria-Helena Ramos

Hydropower Forecasting in Brazil

Most of the electric power in Brazil comes from hydropower, and the short-term power production at each of the major power plants in Brazil is optimized using streamflow forecasts of lead times up to 14 days. These forecasts were usually obtained using stochastic models based only on the last observed streamflow values. During the last few years, rainfall–runoff models that use predicted rainfall as the main input start to replace the stochastic models. However, this new model generation still uses deterministic precipitation forecasts and does not take advantage of the ensemble precipitation forecasts that are already available in Brazil from regional and global meteorological models. Based on recent research results, it is likely that ensemble streamflow forecasts outperform deterministic forecasts in application to short-term reservoir management for objectives such as energy generation and flood mitigation. This chapter presents an assessment of 4 years of ensemble inflow forecasts to a major hydropower reservoir in Brazil, the Três Marias dam, on the São Francisco River. A 14 member ensemble obtained from a global numerical weather prediction model of the Brazilian Center for Weather Prediction is used, and results are evaluated in terms of ensemble applicability for a period between 2008 and 2012. Results are encouraging, and due to this it is believed that ensemble inflow forecasts to major reservoirs in Brazil will be used in a near future as input to the optimization of the national electric power producing system.

Carlos E. M. Tucci, Walter Collischonn, Fernando Mainardi Fan, Dirk Schwanenberg

New York City’s Operations Support Tool: Utilizing Hydrologic Forecasts for Water Supply Management

The New York City Department of Environmental Protection (DEP) supplies over one billion gallons per day (BGD) of water to more than nine million people in the New York City metropolitan area, making it one of the largest suppliers of surface water in the United States. DEP’s water supply system is as complex as it is large; it draws water from three distinct watersheds and features a number of interconnections and redundancies allowing for a large number of potential operating conditions. The system has a wide range of objectives – from supplying clean, reliable water for municipal demand to meeting environmental flow requirements for downstream stakeholders. Combined with the existing system complexity, these disparate objectives can make operational decision making a challenge.In 2013, DEP launched the Operations Support Tool (OST) – a state-of-the-art model built to assist the utility in water supply operation decisions. OST consists of a system model (OASIS) to simulate water supply operation decisions and a linked hydrodynamic two-dimensional water quality model (CE-QUAL-W2). The model is initialized using current system conditions (e.g., reservoir elevations, water quality conditions) and is driven forward in time using ensemble hydrologic forecasts. This setup gives DEP the ability to simulate a wide variety of operational strategies in near real-time, allowing for objective alternative analysis prior to making operational decisions. Ensemble hydrologic forecasts are a critical part of the success of this approach, as they enable DEP to evaluate decisions probabilistically by explicitly considering hydrologic uncertainty.This chapter provides an overview of the New York City water supply system, details the hydrologic forecasts used in OST, and reviews a handful of real operational applications of OST and the hydrologic forecast system.

James Porter, Gerald Day, John C. Schaake, Lucien Wang

Probabilistic Shipping Forecast

Inland waterway transport is an important even though often neglected economic sector relying on hydrological forecasts in order to increase its operating efficiency. Besides river ice and floods, low stream flow is the main hydrological impact for shipping along the European inland waterways as it sustainably affects the load capacity of vessels and thus transportation costs several times a year. For this reason, inland waterway transport benefits from water-level forecasts in order to take preventive action and adjust the draft, especially during stream flow droughts.Although most navigation-related water-level forecasts are still deterministic, the waterway transport sector is a well-suited customer of probabilistic forecast products for several reasons: The number of decisions to be taken is quite high, especially in comparison to the operation of protection measures against rare flood events. Furthermore, in waterway transport, the user’s costs and losses associated with possible forecast-based decisions are well known and monetary valuation of losses, like nonoperation times or additional effort due to lighterage, is more feasible as it is for example with regard to human lives or environmental pollution. Last but not least shipping is an inhomogeneous stakeholder as different vessel types and routes cause different cost structures and sensitivities due to navigation conditions. Selecting one “best-guess” forecast, being optimal for all users, is impossible.In this chapter, hydrological forecasts as one component to support inland waterway transport are presented and the added value of probabilistic forecasts is demonstrated applying a simulation based cost model for the River Rhine, being one of the world’s most frequented inland waterways.

Dennis Meißner, Bastian Klein

Probabilistic Inundation Forecasting

Many existing operational hydrological ensemble forecasting systems only produce forecasts of river discharge. It is possible to convert discharge forecasts into inundation extents, in particular because there are well-established tools for the estimation of inundation hazard. The basic components of the modeling framework from which to produce inundation forecasts are: (1) meteorological forcing; (2) a hydrological model; (3) a hydraulic model; and; (4) a methodology to derive probabilistic inundation maps. We perform all those steps using the example of the 2013 River Elbe event. We validate the maps of flooding probability against the observations. We stress the importance of the spatial discretization of the digital elevation maps (DEM) and the influence of the resolution of the flood defense topographic features. This study shows that up to 80% of the flooded area along the Elbe in 2013 could have been forecasted to inundate 7 days in advance, using the probabilistic modeling framework proposed.

A. Mueller, C. Baugh, P. Bates, Florian Pappenberger

Challenges of Decision Making in the Context of Uncertain Forecasts in France

Flood is a major risk in France and an operational hydrometeorological organization (a team of 450 employees for national coordination and local services) is in place since 2003 for surveying the main river courses, about 22,000 km which can be damaged by flash flood, fluvial flood, and coastal flood hazard. Besides the building of a national network of hydrometric station, with real-time access of data on the Internet, the services are responsible for flood vigilance, over the next 24 h, and for more detailed forecasts at shorter lead-time. The information is disseminated since 2006 on the website. Hydrological and hydraulic deterministic models are used to increase the forecast lead-time for some 500 hydrometric stations located close to vulnerable flood areas. Within the set of information integrated into the operational procedure, ensemble meteorological forecasts are used by the hydro-forecasters to evaluate rainfall distribution in the following days. Besides those routine activities, the European Flood Awareness System (EFAS) platform, the ensemble based forecasting system, has been tested since 2009 for some 60 flood events to study how the system can be best used within the French flood vigilance and warning procedure. During the first years of the evaluation, the results stayed quite difficult to be accounted for in the operational activities, as the number of false alarms and missed events was too high. Since 2013, the tendency is completely different, with the production of Flash Flood reports for watersheds smaller than 3,000 km2. The localization of the impacted area and the timing is better foreseen; this tendency should be even improved when real-time discharges of main gauging stations will be transferred to EFAS.

Caroline Wittwer, C. de Saint-Aubin, C. Ardilouze

Hydrological Ensemble Prediction Applied in China

In China, to prolong lead-time prediction in order to meet with the requirement of flood defense, short range ensemble stream flow prediction is implemented. Based on the forecasting and the historical storm model, a group of precipitation data is generated as input of rainfall-runoff model. Furthermore, to meet with the requirement of water resources management, in the humid regions rainfall-runoff ensemble prediction has been applied for monthly runoff prediction, in large basins conditional probability method has also been applied to assess the next monthly runoff probability under a fixed runoff initial condition.

Guangsheng Wang, Zhijie Yin, Jianqing Yang, Yuhong Yan

Mathematical and Statistical Fundamentals for Hydrometeorological Ensemble Forecasting


Probability and Statistical Theory for Hydrometeorology

The hydrometeorological forecasting plays an important role in water resources planning and management. The fundamentals of probability and statistics in hydrometeorology are reviewed in this chapter to aid the forecasting practices. We first introduce the elements of probability theory in the classical statistics, including random variables, probability distribution, joint probability, and total probability theorem. The probability estimation is among the key topics in hydrometeorology for statistical inferences, such as uncertainty analysis and statistical forecasting. The probability inference in the univariate case is first introduced with different methods, including parametric distribution, nonparametric distribution, and mixed distribution. Many hydroclimatic variables are mutually correlated, and the dependence modeling of multivariate random variables through the construction of the joint distribution is then introduced. Most of the context is introduced from the view of classical statistics, while a preliminary introduction of the Bayesian approach is also provided. At last, some commonly used methods for hydrometeorological forecasting are introduced, along with a short summary of this chapter.

Zengchao Hao, Vijay P. Singh, Wei Gong

Estimation of Probability Distributions for Hydrometeorological Applications

Hydrometeorologists use imperfect (i.e., incomplete and/or partially erroneous) measurements and imperfect models to make predictions, both for forecasting and to support scientific inference. Because no models or data are ever perfect, forecasting and hypothesis testing must account for uncertainty. The probability calculus is unarguably the most common quantitative framework used for this purpose. This article presents probabilistic methods for estimating and reducing uncertainty that are common in hydrometeorological applications. The major focus is on Bayesian methods and approximations of those methods based on ensembles (i.e., Monte Carlo methods). The article includes a brief overview of both parametric and nonparametric methods, a brief introduction to inverse methods, and a brief introduction to data assimilation from a Bayesian perspective. It is important to caution that although the probability calculus can be used to estimate predictive uncertainty and to aid scientific reasoning, all applications of probabilistic reasoning necessarily contain some amount of subjectivity.

Grey S. Nearing

Regression Techniques Used in Hydrometeorology

Regression methods play an important role in ensemble forecasting. The atmosphere-land-ocean system is complex and dynamical, which makes it difficult to predict the state of hydrometeorological variables deterministically. Consequently, stochastic approaches become useful for hydrometeorological forecasting. As forecast uncertainty is inevitable, it is of key importance to use regression approaches to extract useful information from raw observational data and forecasts from dynamical models while providing an appropriate estimation of the confidence level of the forecasts. Regression methods are usually used in two ways in ensemble forecasting. One is used as a statistical forecasting model, which accounts for the relationships between predictors and historical observation data. Another is used as a post-processor for the forecasts from dynamical models in order to correct various biases in them and to improve their reliability and skill scores. If the statistical relationships between the dynamical forecasts and the observation data exist, the systematic bias and ensemble distribution errors can be corrected, and associated uncertainty can be reduced. The two means of applying regression approaches share a common statistical foundation. This chapter will give a brief introduction to various common linear/nonlinear regression approaches that have been used or can be potentially applicable in ensemble forecasting.

Wei Gong


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