Thordis L. Thorarinsdottir

Uncertainty Quantification in Complex Simulation Models Using Ensemble Copula Coupling

Critical decisions frequently rely on high-dimensional output from complex computer simulation models that show intricate cross-variable, spatial and temporal dependence structures, with weather and climate predictions being key examples. There is a strongly increasing recognition of the need for uncertainty quantification in such settings, for which we propose and review a general multi-stage procedure called ensemble copula coupling (ECC), proceeding as follows: 1. Generate a raw ensemble, consisting of multiple runs of the computer model that differ in the inputs or model parameters in suitable ways. 2. Apply statistical postprocessing techniques, such as Bayesian model averaging or nonhomogeneous regression, to correct for systematic errors in the raw ensemble, to obtain calibrated and sharp predictive distributions for each univariate output variable individually. 3. Draw a sample from each postprocessed predictive distribution. 4. Rearrange the sampled values in the rank order structure of the raw ensemble to obtain the ECC postprocessed ensemble. The use of ensembles and statistical postprocessing have become routine in weather forecasting over the past decade. We show that seemingly unrelated, recent advances can be interpreted, fused and consolidated within the framework of ECC, the common thread being the adoption of the empirical copula of the raw ensemble. Depending on the use of Quantiles, Random draws or Transformations at the sampling stage, we distinguish the ECC-Q, ECC-R and ECC-T variants, respectively. We also describe relations to the Schaake shuffle and extant copula-based techniques. In a case study, the ECC approach is applied to predictions of temperature, pressure, precipitation and wind over Germany, based on the 50-member European Centre for Medium-Range Weather Forecasts (ECMWF) ensemble.

Forecast verification for extreme value distributions with an application to probabilistic peak wind prediction

Predictions of the uncertainty associated with extreme events are a vital component of any prediction system for such events. Consequently, the prediction system ought to be probabilistic in nature, with the predictions taking the form of probability distributions. This paper concerns probabilistic prediction systems where the data are assumed to follow either a generalized extreme value (GEV) distribution or a generalized Pareto distribution. In this setting, the properties of proper scoring rules that facilitate the assessment of the prediction uncertainty are investigated, and closed form expressions for the continuous ranked probability score (CRPS) are provided. In an application to peak wind prediction, the predictive performance of a GEV model under maximum likelihood estimation, optimum score estimation with the CRPS, and a Bayesian framework are compared. The Bayesian inference yields the highest overall prediction skill and is shown to be a valuable tool for covariate selection, while the predictions obtained under optimum CRPS estimation are the sharpest and give the best performance for high thresholds and quantiles. Copyright

Ensemble Model Output Statistics for Wind Vectors

AbstractA bivariate ensemble model output statistics (EMOS) technique for the postprocessing of ensemble forecasts of two-dimensional wind vectors is proposed, where the postprocessed probabilistic forecast takes the form of a bivariate normal probability density function. The postprocessed means and variances of the wind vector components are linearly bias-corrected versions of the ensemble means and ensemble variances, respectively, and the conditional correlation between the wind components is represented by a trigonometric function of the ensemble mean wind direction. In a case study on 48-h forecasts of wind vectors over the North American Pacific Northwest with the University of Washington Mesoscale Ensemble, the bivariate EMOS density forecasts were calibrated and sharp, and showed considerable improvement over the raw ensemble and reference forecasts, including ensemble copula coupling.

Comparison of non-homogeneous regression models for probabilistic wind speed forecasting

In weather forecasting, non-homogeneous regression (NR) is used to statistically post-process forecast ensembles in order to obtain calibrated predictive distributions. For wind speed forecasts, the regression model is given by a truncated normal (TN) distribution, where location and spread derive from the ensemble. This article proposes two alternative approaches which utilise the generalised extreme value (GEV) distribution. A direct alternative to the TN regression is to apply a predictive distribution from the GEV family, while a regime-switching approach based on the median of the forecast ensemble incorporates both distributions. In a case study on daily maximum wind speed over Germany with the forecast ensemble from the European Centre for Medium-Range Weather Forecasts (ECMWF), all three approaches significantly improve the calibration as well as the overall skill of the raw ensemble with the regime-switching approach showing the highest skill in the upper tail.

Forecaster's dilemma: Extreme events and forecast evaluation

In public discussions of the quality of forecasts, attention typically focuses on the predictive performance in cases of extreme events. However, the restriction of conventional forecast evaluation methods to subsets of extreme observations has unexpected and undesired effects, and is bound to discredit skillful forecasts when the signal-to-noise ratio in the data generating process is low. Conditioning on outcomes is incompatible with the theoretical assumptions of established forecast evaluation methods, thereby confronting forecasters with what we refer to as the forecasters dilemma. For probabilistic forecasts, proper weighted scoring rules have been proposed as decision theoretically justifiable alternatives for forecast evaluation with an emphasis on extreme events. Using theoretical arguments, simulation experiments, and a real data study on probabilistic forecasts of U.S. inflation and gross domestic product growth, we illustrate and discuss the forecasters dilemma along with potential remedies.

Propagation of rating curve uncertainty in design flood estimation

Statistical flood frequency analysis is commonly performed based on a set of annual maximum discharge values which are derived from stage measurements via a stage-discharge rating curve model. Such design flood estimation techniques often ignore the uncertainty in the underlying rating curve model. Using data from eight gauging stations in Norway, we investigate the effect of curve and sample uncertainty on design flood estimation by combining results from a Bayesian multi-segment rating curve model and a Bayesian flood frequency analysis. We find that sample uncertainty is the main contributor to the design flood estimation uncertainty. However, under extrapolation of the rating curve, the uncertainty bounds for both the rating curve model and the flood frequency analysis are highly skewed and ignoring these features may underestimate the potential risk of flooding. We expect this effect to be even more pronounced in arid and semi-arid climates with a higher variability in floods. This article is protected by copyright. All rights reserved.

Sea level adaptation decisions under uncertainty

Sea level rise has serious consequences for harbor infrastructure, storm drains and sewer systems, and many other issues. Adapting to sea level rise requires comparing different possible adaptation strategies, comparing the cost of different actions (including no action), and assessing where and at what point in time the chosen strategy should be implemented. All these decisions must be made under considerable uncertainty—in the amount of sea level rise, in the cost and prioritization of adaptation actions, and in the implications of no action. Here we develop two illustrative examples: for Bergen on Norways west coast and for Esbjerg on the west coast of Denmark, to highlight how technical efforts to understand and quantify uncertainties in hydrologic projections can be coupled with concrete decision-problems framed by the needs of the end-users using statistical formulations. Different components of uncertainty are visualized. We demonstrate the value of uncertainties and show for example that failing to take uncertainty into account can result in the median-projected damage costs being an order of magnitude smaller.

GAUSSIAN RANDOM PARTICLES WITH FLEXIBLE HAUSDORFF DIMENSION

Gaussian particles provide a flexible framework for modelling and simulating three-dimensional star-shaped random sets. In our framework, the radial function of the particle arises from a kernel smoothing, and is associated with an isotropic random field on the sphere. If the kernel is a von Mises-Fisher density, or uniform on a spherical cap, the correlation function of the associated random field admits a closed form expression. The Hausdorff dimension of the surface of the Gaussian particle reflects the decay of the correlation function at the origin, as quantified by the fractal index. Under power kernels we obtain particles with boundaries of any Hausdorff dimension between 2 and 3.

Verification: Assessment of Calibration and Accuracy

Abstract In ensemble forecasting, forecast verification methods are needed to diagnose both the need for statistical postprocessing and the effectiveness of the postprocessing methods in producing calibrated and accurate forecasts. This chapter discusses an array of techniques that can be used in this context, making the distinction between verification tools that are useful for ranking competing forecasters and those that are more appropriate for improving our understanding of the performance of a single method. With a focus on continuous variables, verification methods for both univariate and multivariate forecasts are discussed, including approaches that are specifically tailored to the evaluation of extreme events.

Bayesian motion estimation for dust aerosols

Dust storms in the earth’s major desert regions significantly influence microphysical weather processes, the CO2-cycle and the global climate in general. Recent increases in the spatio-temporal resolution of remote sensing instruments have created new opportunities to understand these phenomena. However, the scale of the data collected and the inherent stochasticity of the underlying process pose significant challenges, requiring a careful combination of image processing and statistical techniques. Using satellite imagery data, we develop a statistical model of atmospheric transport that relies on a latent Gaussian Markov random field (GMRF) for inference. In doing so, we make a link between the optical flow method of Horn and Schunck and the formulation of the transport process as a latent field in a generalized linear model. We critically extend this framework to satisfy the integrated continuity equation, thereby incorporating a flow field with nonzero divergence, and show that such an approach dramatically improves performance while remaining computationally feasible. Effects such as air compressibility and satellite column projection hence become intrinsic parts of this model. We conclude with a study of the dynamics of dust storms formed over Saharan Africa and show that our methodology is able to accurately and coherently track storm movement, a critical problem in this field.