Michael Scheuerer

Probabilistic quantitative precipitation forecasting using Ensemble Model Output Statistics

Statistical post-processing of dynamical forecast ensembles is an essential component of weather forecasting. In this article, we present a post-processing method that generates full predictive probability distributions for precipitation accumulations based on ensemble model output statistics (EMOS). We model precipitation amounts by a generalized extreme value distribution that is left-censored at zero. This distribution permits modelling precipitation on the original scale without prior transformation of the data. A closed form expression for its continuous rank probability score can be derived and permits computationally efficient model fitting. We discuss an extension of our approach that incorporates further statistics characterizing the spatial variability of precipitation amounts in the vicinity of the location of interest. The proposed EMOS method is applied to daily 18-h forecasts of 6-h accumulated precipitation over Germany in 2011 using the COSMO-DE ensemble prediction system operated by the German Meteorological Service. It yields calibrated and sharp predictive distributions and compares favourably with extended logistic regression and Bayesian model averaging which are state of the art approaches for precipitation post-processing. The incorporation of neighbourhood information further improves predictive performance and turns out to be a useful strategy to account for displacement errors of the dynamical forecasts in a probabilistic forecasting framework.

The TIGGE Project and Its Achievements

AbstractThe International Grand Global Ensemble (TIGGE) was a major component of The Observing System Research and Predictability Experiment (THORPEX) research program, whose aim is to accelerate improvements in forecasting high-impact weather. By providing ensemble prediction data from leading operational forecast centers, TIGGE has enhanced collaboration between the research and operational meteorological communities and enabled research studies on a wide range of topics.The paper covers the objective evaluation of the TIGGE data. For a range of forecast parameters, it is shown to be beneficial to combine ensembles from several data providers in a multimodel grand ensemble. Alternative methods to correct systematic errors, including the use of reforecast data, are also discussed.TIGGE data have been used for a range of research studies on predictability and dynamical processes. Tropical cyclones are the most destructive weather systems in the world and are a focus of multimodel ensemble research. Their ...

Statistical Postprocessing of Ensemble Precipitation Forecasts by Fitting Censored, Shifted Gamma Distributions*

AbstractA parametric statistical postprocessing method is presented that transforms raw (and frequently biased) ensemble forecasts from the Global Ensemble Forecast System (GEFS) into reliable predictive probability distributions for precipitation accumulations. Exploratory analysis based on 12 years of reforecast data and ⅛° climatology-calibrated precipitation analyses shows that censored, shifted gamma distributions can well approximate the conditional distribution of observed precipitation accumulations given the ensemble forecasts. A nonhomogeneous regression model is set up to link the parameters of this distribution to ensemble statistics that summarize the mean and spread of predicted precipitation amounts within a certain neighborhood of the location of interest, and in addition the predicted mean of precipitable water. The proposed method is demonstrated with precipitation reforecasts over the conterminous United States using common metrics such as Brier skill scores and reliability diagrams. It...

Interpolation of spatial data – A stochastic or a deterministic problem?

Interpolation of spatial data is a very general mathematical problem with various applications. In geostatistics, it is assumed that the underlying structure of the data is a stochastic process which leads to an interpolation procedure known as kriging. This method is mathematically equivalent to kernel interpolation, a method used in numerical analysis for the same problem, but derived under completely different modelling assumptions. In this paper we present the two approaches and discuss their modelling assumptions, notions of optimality and different concepts to quantify the interpolation accuracy. Their relation is much closer than has been appreciated so far, and even results on convergence rates of kernel interpolants can be translated to the geostatistical framework. We sketch different answers obtained in the two fields concerning the issue of kernel misspecification, present some methods for kernel selection and discuss the scope of these methods with a data example from the computer experiments literature.

Variogram-Based Proper Scoring Rules for Probabilistic Forecasts of Multivariate Quantities*

AbstractProper scoring rules provide a theoretically principled framework for the quantitative assessment of the predictive performance of probabilistic forecasts. While a wide selection of such scoring rules for univariate quantities exists, there are only few scoring rules for multivariate quantities, and many of them require that forecasts are given in the form of a probability density function. The energy score, a multivariate generalization of the continuous ranked probability score, is the only commonly used score that is applicable in the important case of ensemble forecasts, where the multivariate predictive distribution is represented by a finite sample. Unfortunately, its ability to detect incorrectly specified correlations between the components of the multivariate quantity is somewhat limited. In this paper the authors present an alternative class of proper scoring rules based on the geostatistical concept of variograms. The sensitivity of these variogram-based scoring rules to incorrectly pre...

An alternative procedure for selecting a good value for the parameter c in RBF-interpolation

The impact of the scaling parameter c on the accuracy of interpolation schemes using radial basis functions (RBFs) has been pointed out by several authors. Rippa (Adv Comput Math 11:193–210, 1999) proposes an algorithm based on the idea of cross validation for selecting a good such parameter value. In this paper we present an alternative procedure, that can be interpreted as a refinement of Rippa’s algorithm for a cost function based on the euclidean norm. We point out how this method is related to the procedure of maximum likelihood estimation, which is used for identifying covariance parameters of stochastic processes in spatial statistics. Using the same test functions as Rippa we show that our algorithm compares favorably with cross validation in many cases and discuss its limitations. Finally we present some computational aspects of our algorithm.

Assessing the Calibration of High-Dimensional Ensemble Forecasts Using Rank Histograms

Any decision-making process that relies on a probabilistic forecast of future events necessarily requires a calibrated forecast. This article proposes new methods for empirically assessing forecast calibration in a multivariate setting where the probabilistic forecast is given by an ensemble of equally probable forecast scenarios. Multivariate properties are mapped to a single dimension through a prerank function and the calibration is subsequently assessed visually through a histogram of the ranks of the observation’s preranks. Average ranking assigns a prerank based on the average univariate rank while band depth ranking employs the concept of functional band depth where the centrality of the observation within the forecast ensemble is assessed. Several simulation examples and a case study of temperature forecast trajectories at Berlin Tegel Airport in Germany demonstrate that both multivariate ranking methods can successfully detect various sources of miscalibration and scale efficiently to high-dimensional settings. Supplemental material in form of computer code is available online.

Spatial Postprocessing of Ensemble Forecasts for Temperature Using Nonhomogeneous Gaussian Regression

AbstractStatistical postprocessing techniques are commonly used to improve the skill of ensembles from numerical weather forecasts. This paper considers spatial extensions of the well-established nonhomogeneous Gaussian regression (NGR) postprocessing technique for surface temperature and a recent modification thereof in which the local climatology is included in the regression model to permit locally adaptive postprocessing. In a comparative study employing 21-h forecasts from the Consortium for Small Scale Modelling ensemble predictive system over Germany (COSMO-DE), two approaches for modeling spatial forecast error correlations are considered: a parametric Gaussian random field model and the ensemble copula coupling (ECC) approach, which utilizes the spatial rank correlation structure of the raw ensemble. Additionally, the NGR methods are compared to both univariate and spatial versions of the ensemble Bayesian model averaging (BMA) postprocessing technique.

Trends in the predictive performance of raw ensemble weather forecasts

This study applies statistical postprocessing to ensemble forecasts of near-surface temperature, 24 h precipitation totals, and near-surface wind speed from the global model of the European Centre for Medium-Range Weather Forecasts (ECMWF). The main objective is to evaluate the evolution of the difference in skill between the raw ensemble and the postprocessed forecasts. Reliability and sharpness, and hence skill, of the former is expected to improve over time. Thus, the gain by postprocessing is expected to decrease. Based on ECMWF forecasts from January 2002 to March 2014 and corresponding observations from globally distributed stations, we generate postprocessed forecasts by ensemble model output statistics (EMOS) for each station and variable. Given the higher average skill of the postprocessed forecasts, we analyze the evolution of the difference in skill between raw ensemble and EMOS. This skill gap remains almost constant over time indicating that postprocessing will keep adding skill in the foreseeable future.

Analog Probabilistic Precipitation Forecasts Using GEFS Reforecasts and Climatology-Calibrated Precipitation Analyses*

AbstractAnalog postprocessing methods have previously been applied using precipitation reforecasts and analyses to improve probabilistic forecast skill and reliability. A modification to a previously documented analog procedure is described here that produces highly skillful, statistically reliable precipitation forecast guidance at ° grid spacing. These experimental probabilistic forecast products are available via the web in near–real time.The main changes to the previously documented analog algorithm were as follows: (i) use of a shorter duration (2002–13), but smaller grid spacing, higher-quality time series of precipitation analyses for training and forecast verification (i.e., the Climatology-Calibrated Precipitation Analysis); (ii) increased training sample size using data from 19 supplemental locations, chosen for their similar precipitation analysis climatologies and terrain characteristics; (iii) selection of analog dates for a particular grid point based on the similarity of forecast characteri...