Weather 21206

[Toney Talbot]

Scatteredsevere thunderstorms are expected across portions of the central/northern Plains Sunday while heavy to excessive rainfall may bring flooding to northern Minnesota and the Tennessee Valley. Dry and windy conditions will bring elevated to critical fire weather across parts of the Great Basin while dry thunderstorms may lead to new wildfire starts in the northern Rockies. Read More >

Schematic of (left) an FCN and (right) an NN with one hidden layer. In both cases, data flow from left to right. Orange nodes and connections illustrate station embeddings, and blue nodes are for auxiliary input variables. Mathematical operations are to be understood as elementwise operations for vector objects.

Boxplots of stationwise mean CRPSS of all postprocessing models using the (top) raw ensemble and (bottom) EMOS-loc as the reference forecast. A dot within each box represents the mean CRPSS at one of the observation stations. The CRPSS is computed so that positive values indicate an improvement of the model specified on the horizontal axis over the reference. Similar plots with different reference models are provided in the supplemental material.

Ensemble weather predictions require statistical postprocessing of systematic errors to obtain reliable and accurate probabilistic forecasts. Traditionally, this is accomplished with distributional regression models in which the parameters of a predictive distribution are estimated from a training period. We propose a flexible alternative based on neural networks that can incorporate nonlinear relationships between arbitrary predictor variables and forecast distribution parameters that are automatically learned in a data-driven way rather than requiring prespecified link functions. In a case study of 2-m temperature forecasts at surface stations in Germany, the neural network approach significantly outperforms benchmark postprocessing methods while being computationally more affordable. Key components to this improvement are the use of auxiliary predictor variables and station-specific information with the help of embeddings. Furthermore, the trained neural network can be used to gain insight into the importance of meteorological variables, thereby challenging the notion of neural networks as uninterpretable black boxes. Our approach can easily be extended to other statistical postprocessing and forecasting problems. We anticipate that recent advances in deep learning combined with the ever-increasing amounts of model and observation data will transform the postprocessing of numerical weather forecasts in the coming decade.

Most postprocessing methods correct systematic errors in the raw ensemble forecast by learning a function that relates the response variable of interest to predictors. From a machine learning perspective, postprocessing can be viewed as a supervised learning task. For the purpose of this study we will consider postprocessing in a narrower distributional regression framework where the aim is to model the conditional distribution of the weather variable of interest given a set of predictors. The two most prominent approaches for probabilistic forecasts, Bayesian model averaging (BMA; Raftery et al. 2005) and nonhomogeneous regression, also referred to as ensemble model output statistics (EMOS; Gneiting et al. 2005), rely on parametric forecast distributions. This means one has to specify a predictive distribution and estimate its parameters, for example, the mean and the standard deviation in the case of a Gaussian distribution. Within the EMOS framework the distribution parameters are connected to summary statistics of the ensemble predictions through suitable link functions that are estimated by minimizing a probabilistic loss function over a training dataset. Including additional predictors, such as forecasts of cloud cover or humidity, is not straightforward within this framework and requires elaborate approaches to avoid overfitting (Messner et al. 2017), a term that describes the inability of a model to generalize to data outside the training dataset. We propose an alternative approach based on modern machine learning methods, which is capable of including arbitrary predictors and learns nonlinear dependencies in a data-driven way.

Much work over the past years has been spent on flexible machine learning techniques for statistical modeling and forecasting (McGovern et al. 2017). Random forests (Breiman 2001), for instance, can model nonlinear relationships including arbitrary predictors while being robust to overfitting. They have been used for the classification and prediction of precipitation (Gagne et al. 2014), severe wind (Lagerquist et al. 2017), and hail (Gagne et al. 2017). Within a postprocessing context, quantile regression forest models have been proposed by Taillardat et al. (2016).

Neural networks are a flexible and user-friendly machine learning algorithm that can model arbitrary nonlinear functions (Nielsen 2015). They consist of several layers of interconnected nodes that are modulated with simple nonlinearities (Fig. 1; section 4). Over the past decade many fields, most notably computer vision and natural language processing (LeCun et al. 2015), but also biology, physics, and chemistry (Angermueller et al. 2016; Goh et al. 2017), have been transformed by neural networks. In the atmospheric sciences, neural networks have been used to detect extreme weather in climate datasets (Liu et al. 2016) and parameterize subgrid processes in general circulation models (Gentine et al. 2018; Rasp et al. 2018). Neural networks have also been used for forecasting solar irradiances (Wang et al. 2012; Chu et al. 2013) and damaging winds (Lagerquist et al. 2017). However, the complexity of the neural networks used in these studies was limited.

The remainder of the paper is structured as follows. Section 2 describes the forecast and observation data as well as the notation used throughout the study. In section 3 we describe the benchmark postprocessing models, followed by a description of the neural network techniques in section 4. The main results are presented in section 5. In section 6 we explore the relative importance of the predictor variables. A discussion of possible extensions follows in section 7 before our conclusions are presented in section 8.

For this study, we focus on 2-m temperature forecasts at surface stations in Germany at a forecast lead time of 48 h. The forecasts are taken from the THORPEX Interactive Grand Global Ensemble (TIGGE) dataset1 (Bougeault et al. 2010). In particular, we use the global European Centre for Medium-Range Weather Forecasts (ECMWF) 50-member ensemble forecasts initialized at 0000 UTC every day. The data in the TIGGE archive are upscaled onto a 0.5 0.5 grid, which corresponds to a horizontal grid spacing of around 35/55 km (zonal/meridional). For comparison with the station observations, the gridded data were bilinearly interpolated to the observation locations. In addition to the target variable, we retrieved several auxiliary predictor variables (Table 12). These were chosen broadly based on meteorological intuition.3 For each variable, we reduced the 50-member ensemble to its mean and standard deviation.

The forecasts are evaluated at 537 weather stations in Germany (see Fig. 24). The 2-m temperature data are available from the Climate Data Center of the German Weather Service [Deutscher Wetterdienst (DWD)5]. Several stations have periods of missing data, which are omitted from the analysis. During the evaluation period in calendar year 2016, observations are available at 499 stations.

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