Assessing the reliability of probabilistic flood inundation model predictions

An ability to quantify the reliability of probabilistic flood inundation predictions is a requirement not only for guiding model development but also for their successful application. Probabilistic flood inundation predictions are usually produced by choosing a method of weighting the model parameter space, but previous study suggests that this choice leads to clear differences in inundation probabilities. This study aims to address the evaluation of the reliability of these probabilistic predictions. However, a lack of an adequate number of observations of flood inundation for a catchment limits the application of conventional methods of evaluating predictive reliability. Consequently, attempts have been made to assess the reliability of probabilistic predictions using multiple observations from a single flood event. Here, a LISFLOOD-FP hydraulic model of an extreme (>1 in 1000 years) flood event in Cockermouth, UK, is constructed and calibrated using multiple performance measures from both peak flood wrack mark data and aerial photography captured post-peak. These measures are used in weighting the parameter space to produce multiple probabilistic predictions for the event. Two methods of assessing the reliability of these probabilistic predictions using limited observations are utilized; an existing method assessing the binary pattern of flooding, and a method developed in this paper to assess predictions of water surface elevation. This study finds that the water surface elevation method has both a better diagnostic and discriminatory ability, but this result is likely to be sensitive to the unknown uncertainties in the upstream boundary condition

Probabilistic wind power forecasts with an inverse power curve transformation and censored regression

Forecasting wind power is an important part of a successful integration of wind power into the power grid. Forecasts with lead times longer than 6 h are generally made by using statistical methods to post-process forecasts from numerical weather prediction systems. Two major problems that complicate this approach are the non-linear relationship between wind speed and power production and the limited range of power production between zero and nominal power of the turbine. In practice, these problems are often tackled by using non-linear non-parametric regression models. However, such an approach ignores valuable and readily available information: the power curve of the turbine's manufacturer. Much of the non-linearity can be directly accounted for by transforming the observed power production into wind speed via the inverse power curve so that simpler linear regression models can be used. Furthermore, the fact that the transformed power production has a limited range can be taken care of by employing censored regression models. In this study, we evaluate quantile forecasts from a range of methods: (i) using parametric and non-parametric models, (ii) with and without the proposed inverse power curve transformation and (iii) with and without censoring. The results show that with our inverse (power-to-wind) transformation, simpler linear regression models with censoring perform equally or better than non-linear models with or without the frequently used wind-to-power transformation.

A global empirical system for probabilistic seasonal climate prediction

Preparing for episodes with risks of anomalous weather a month to a year ahead is an important challenge for governments, non-governmental organisations, and private companies and is dependent on the availability of reliable forecasts. The majority of operational seasonal forecasts are made using process-based dynamical models, which are complex, computationally challenging and prone to biases. Empirical forecast approaches built on statistical models to represent physical processes offer an alternative to dynamical systems and can provide either a benchmark for comparison or independent supplementary forecasts. Here, we present a simple empirical system based on multiple linear regression for producing probabilistic forecasts of seasonal surface air temperature and precipitation across the globe. The global CO2-equivalent concentration is taken as the primary predictor; subsequent predictors, including large-scale modes of variability in the climate system and local-scale information, are selected on the basis of their physical relationship with the predictand. The focus given to the climate change signal as a source of skill and the probabilistic nature of the forecasts produced constitute a novel approach to global empirical prediction. Hindcasts for the period 1961–2013 are validated against observations using deterministic (correlation of seasonal means) and probabilistic (continuous rank probability skill scores) metrics. Good skill is found in many regions, particularly for surface air temperature and most notably in much of Europe during the spring and summer seasons. For precipitation, skill is generally limited to regions with known El Niño–Southern Oscillation (ENSO) teleconnections. The system is used in a quasi-operational framework to generate empirical seasonal forecasts on a monthly basis.

Data Assimilation and Inverse Methods in Terms of a Probabilistic Formulation

The weak-constraint inverse for nonlinear dynamical models is discussed and derived in terms of a probabilistic formulation. The well-known result that for Gaussian error statistics the minimum of the weak-constraint inverse is equal to the maximum-likelihood estimate is rederived. Then several methods based on ensemble statistics that can be used to find the smoother (as opposed to the filter) solution are introduced and compared to traditional methods. A strong point of the new methods is that they avoid the integration of adjoint equations, which is a complex task for real oceanographic or atmospheric applications. they also avoid iterative searches in a Hilbert space, and error estimates can be obtained without much additional computational effort. the feasibility of the new methods is illustrated in a two-layer quasigeostrophic model.

Willingness-to-pay for a probabilistic flood forecast: a risk-based decision-making game

Probabilistic hydro-meteorological forecasts have over the last decades been used more frequently to communicate forecastuncertainty. This uncertainty is twofold, as it constitutes both an added value and a challenge for the forecaster and the user of the forecasts. Many authors have demonstrated the added (economic) value of probabilistic over deterministic forecasts across the water sector (e.g. flood protection, hydroelectric power management and navigation). However, the richness of the information is also a source of challenges for operational uses, due partially to the difficulty to transform the probability of occurrence of an event into a binary decision. This paper presents the results of a risk-based decision-making game on the topic of flood protection mitigation, called “How much are you prepared to pay for a forecast?”. The game was played at several workshops in 2015, which were attended by operational forecasters and academics working in the field of hydrometeorology. The aim of this game was to better understand the role of probabilistic forecasts in decision-making processes and their perceived value by decision-makers. Based on the participants’ willingness-to-pay for a forecast, the results of the game show that the value (or the usefulness) of a forecast depends on several factors, including the way users perceive the quality of their forecasts and link it to the perception of their own performances as decision-makers.