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Forecast skill of numerical weather prediction (NWP) models for precipitation accumulations over California is rather limited at subseasonal time scales, and the low signal-to-noise ratio makes it challenging to extract information that provides reliable probabilistic forecasts. A statistical postprocessing framework is proposed that uses an artificial neural network (ANN) to establish relationships between NWP ensemble forecast and gridded observed 7-day precipitation accumulations, and to model the increase or decrease of the probabilities for different precipitation categories relative to their climatological frequencies. Adding predictors with geographic information and location-specific normalization of forecast information permits the use of a single ANN for the entire forecast domain and thus reduces the risk of overfitting. In addition, a convolutional neural network (CNN) framework is proposed that extends the basic ANN and takes images of large-scale predictors as inputs that inform local increase or decrease of precipitation probabilities relative to climatology. Both methods are demonstrated with ECMWF ensemble reforecasts over California for lead times up to 4 weeks. They compare favorably with a state-of-the-art postprocessing technique developed for medium-range ensemble precipitation forecasts, and their forecast skill relative to climatology is positive everywhere within the domain. The magnitude of skill, however, is low for week-3 and week-4, and suggests that additional sources of predictability need to be explored.

The 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 extratropical transition also has a major impact on the skill of midlatitude forecasts. We also review how TIGGE has added to our understanding of the dynamics of extratropical cyclones and storm tracks. Although TIGGE is a research project, it has proved invaluable for the development of products for future operational forecasting. Examples include the forecasting of tropical cyclone tracks, heavy rainfall, strong winds, and flood prediction through coupling hydrological models to ensembles. Finally, the paper considers the legacy of TIGGE. We discuss the priorities and key issues in predictability and ensemble forecasting, including the new opportunities of convective-scale ensembles, links with ensemble data assimilation methods, and extension of the range of useful forecast skill.

The U.S. National Blend of Models provides statistically postprocessed, high-resolution multimodel ensemble guidance, providing National Weather Service forecasters with a calibrated, downscaled starting point for producing digital forecasts. Forecasts of 12-hourly probability of precipitation (POP12) over the contiguous United States are produced as follows: 1) Populate the forecast and analyze cumulative distribution functions (CDFs) to be used later in quantile mapping. Were every grid point processed without benefit of data from other points, 60 days of training data would likely be insufficient for estimating CDFs and adjusting the errors in the forecast. Accordingly, “supplemental” locations were identified for each grid point, and data from the supplemental locations were used to populate the forecast and analyzed CDFs used in the quantile mapping. 2) Load the real-time U.S. and Environment Canada (now known as Environment and Climate Change Canada) global deterministic and ensemble forecasts, interpolated to ⅛°. 3) Using CDFs from the past 60 days of data, apply a deterministic quantile mapping to the ensemble forecasts. 4) Dress the resulting ensemble with random noise. 5) Generate probabilities from the ensemble relative frequency. 6) Spatially smooth the forecast using a Savitzky–Golay smoother, applying more smoothing in flatter areas. Forecasts of 6-hourly quantitative precipitation (QPF06) are more simply produced as follows: 1) Form a grand ensemble mean, again interpolated to ⅛°. 2) Quantile map the mean forecast using CDFs of the ensemble mean and analyzed distributions. 3) Spatially smooth the field, similar to POP12. Results for spring 2016 are provided, demonstrating that the postprocessing improves POP12 reliability and skill, as well as the deterministic forecast bias, while maintaining sharpness and spatial detail.

We propose a statistical post-processing method that yields locally calibrated probabilistic forecasts of temperature, based on the output of an ensemble prediction system. It represents the mean of the predictive distributions as a sum of short-term averages of local temperatures and ensemble prediction system driven terms. For the spatial interpolation of temperature averages and local forecast uncertainty parameters we use an intrinsic Gaussian random-field model with a location-dependent nugget effect that accounts for small-scale variability. Applied to the COSMO-DE ensemble, our method yields locally calibrated and sharp probabilistic forecasts and compares favourably with other approaches.

Tropical cyclones are extreme events with enormous and devastating consequences to life, property, and our economies. As a result, large-scale efforts have been devoted to improving tropical cyclone forecasts with lead times ranging from a few days to months. More recently, subseasonal forecasts (e.g., 2–6-week lead time) of tropical cyclones have received greater attention. Here, we study whether bias-corrected, subseasonal tropical cyclone reforecasts of the GEFS and ECMWF models are skillful in the Atlantic basin. We focus on the peak hurricane season, July–November, using the reforecast years 2000–19. Model reforecasts of accumulated cyclone energy (ACE) are produced, and validated, for lead times of 1–2 and 3–4 weeks. Week-1–2 forecasts are substantially more skillful than a 31-day moving-window climatology, while week-3–4 forecasts still exhibit positive skill throughout much of the hurricane season. Furthermore, the skill of the combination of the two models is found to be an improvement with respect to either individual model. In addition to the GEFS and ECMWF model reforecasts, we develop a statistical modeling framework that solely relies on daily sea surface temperatures. The reforecasts of ACE from this statistical model are capable of producing better skill than the GEFS or ECMWF model, individually, and it can be leveraged to further enhance the model combination reforecast skill for the 3–4-week lead time.

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.

A 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 yields probabilistic forecasts that are reliable, highly skillful, and sharper than the previously demonstrated analog procedure. In situations with limited predictability, increasing the size of the neighborhood within which ensemble forecasts are considered as predictors can further improve forecast skill. It is found, however, that even a parametric postprocessing approach crucially relies on the availability of a sufficiently large training dataset.

Proper 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 predicted means, variances, and correlations is studied in a number of examples with simulated observations and forecasts; they are shown to be distinctly more discriminative with respect to the correlation structure. This conclusion is confirmed in a case study with postprocessed wind speed forecasts at five wind park locations in Colorado.

Hamill et al. described a multimodel ensemble precipitation postprocessing algorithm that is used operationally by the U.S. National Weather Service (NWS). This article describes further changes that produce improved, reliable, and skillful probabilistic quantitative precipitation forecasts (PQPFs) for single or multimodel prediction systems. For multimodel systems, final probabilities are produced through the linear combination of PQPFs from the constituent models. The new methodology is applied to each prediction system. Prior to adjustment of the forecasts, parametric cumulative distribution functions (CDFs) of model and analyzed climatologies are generated using the previous 60 days’ forecasts and analyses and supplemental locations. The CDFs, which can be stored with minimal disk space, are then used for quantile mapping to correct state-dependent bias for each member. In this stage, the ensemble is also enlarged using a stencil of forecast values from the 5 × 5 surrounding grid points. Different weights and dressing distributions are assigned to the sorted, quantile-mapped members, with generally larger weights for outlying members and broader dressing distributions for members with heavier precipitation. Probability distributions are generated from the weighted sum of the dressing distributions. The NWS Global Ensemble Forecast System (GEFS), the Canadian Meteorological Centre (CMC) global ensemble, and the European Centre for Medium-Range Weather Forecasts (ECMWF) ensemble forecast data are postprocessed for April–June 2016. Single prediction system postprocessed forecasts are generally reliable and skillful. Multimodel PQPFs are roughly as skillful as the ECMWF system alone. Postprocessed guidance was generally more skillful than guidance using the Gamma distribution approach of Scheuerer and Hamill, with coefficients generated from data pooled across the United States.

Probabilistic forecasts of wind speed are important for a wide range of applications, ranging from operational decision making in connection with wind power generation to storm warnings, ship routing and aviation. We present a statistical method that provides locally calibrated, probabilistic wind speed forecasts at any desired place within the forecast domain based on the output of a numerical weather prediction (NWP) model. Three approaches for wind speed post-processing are proposed, which use either truncated normal, gamma or truncated logistic distributions to make probabilistic predictions about future observations conditional on the forecasts of an ensemble prediction system (EPS). In order to provide probabilistic forecasts on a grid, predictive distributions that were calibrated with local wind speed observations need to be interpolated. We study several interpolation schemes that combine geostatistical methods with local information on annual mean wind speeds, and evaluate the proposed methodology with surface wind speed forecasts over Germany from the COSMO-DE (Consortium for Small-scale Modelling) ensemble prediction system.