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Statistical postprocessing techniques are nowadays key components of the forecasting suites in many national meteorological services (NMS), with, for most of them, the objective of correcting the impact of different types of errors on the forecasts. The final aim is to provide optimal, automated, seamless forecasts for end users. Many techniques are now flourishing in the statistical, meteorological, climatological, hydrological, and engineering communities. The methods range in complexity from simple bias corrections to very sophisticated distribution-adjusting techniques that incorporate correlations among the prognostic variables. The paper is an attempt to summarize the main activities going on in this area from theoretical developments to operational applications, with a focus on the current challenges and potential avenues in the field. Among these challenges is the shift in NMS toward running ensemble numerical weather prediction (NWP) systems at the kilometer scale that produce very large datasets and require high-density high-quality observations, the necessity to preserve space-time correlation of high-dimensional corrected fields, the need to reduce the impact of model changes affecting the parameters of the corrections, the necessity for techniques to merge different types of forecasts and ensembles with different behaviors, and finally the ability to transfer research on statistical postprocessing to operations. Potential new avenues are also discussed.

Most bias correction algorithms used in climatology, for example quantile mapping, are applied to univariate time series. They neglect the dependence between different variables. Those that are multivariate often correct only limited measures of joint dependence, such as Pearson or Spearman rank correlation. Here, an image processing technique designed to transfer colour information from one image to another—the N-dimensional probability density function transform—is adapted for use as a multivariate bias correction algorithm (MBCn) for climate model projections/predictions of multiple climate variables. MBCn is a multivariate generalization of quantile mapping that transfers all aspects of an observed continuous multivariate distribution to the corresponding multivariate distribution of variables from a climate model. When applied to climate model projections, changes in quantiles of each variable between the historical and projection period are also preserved. The MBCn algorithm is demonstrated on three case studies. First, the method is applied to an image processing example with characteristics that mimic a climate projection problem. Second, MBCn is used to correct a suite of 3-hourly surface meteorological variables from the Canadian Centre for Climate Modelling and Analysis Regional Climate Model (CanRCM4) across a North American domain. Components of the Canadian Forest Fire Weather Index (FWI) System, a complicated set of multivariate indices that characterizes the risk of wildfire, are then calculated and verified against observed values. Third, MBCn is used to correct biases in the spatial dependence structure of CanRCM4 precipitation fields. Results are compared against a univariate quantile mapping algorithm, which neglects the dependence between variables, and two multivariate bias correction algorithms, each of which corrects a different form of inter-variable correlation structure. MBCn outperforms these alternatives, often by a large margin, particularly for annual maxima of the FWI distribution and spatiotemporal autocorrelation of precipitation fields.

Univariate bias correction algorithms, such as quantile mapping, are used to address systematic biases in climate model output. Intervariable dependence structure (e.g., between different quantities like temperature and precipitation or between sites) is typically ignored, which can have an impact on subsequent calculations that depend on multiple climate variables. A novel multivariate bias correction (MBC) algorithm is introduced as a multidimensional analog of univariate quantile mapping. Two variants are presented. MBCp and MBCr respectively correct Pearson correlation and Spearman rank correlation dependence structure, with marginal distributions in both constrained to match observed distributions via quantile mapping. MBC is demonstrated on two case studies: 1) bivariate bias correction of monthly temperature and precipitation output from a large ensemble of climate models and 2) multivariate correction of vertical humidity and wind profiles, including subsequent calculation of vertically integrated water vapor transport and detection of atmospheric rivers. The energy distance is recommended as an omnibus measure of performance for model selection. As expected, substantial improvements in performance relative to quantile mapping are found in each case. For reference, characteristics of the MBC algorithm are compared against existing bivariate and multivariate bias correction techniques. MBC performs competitively and fills a role as a flexible, general purpose multivariate bias correction algorithm.

Current statistical postprocessing methods for probabilistic weather forecasting are not capable of using full spatial patterns from the numerical weather prediction (NWP) model. In this paper, we incorporate spatial wind speed information by using convolutional neural networks (CNNs) and obtain probabilistic wind speed forecasts in the Netherlands for 48 h ahead, based on KNMI’s deterministic HARMONIE-AROME NWP model. The probabilistic forecasts from the CNNs are shown to have higher Brier skill scores for medium to higher wind speeds, as well as a better continuous ranked probability score (CRPS) and logarithmic score, than the forecasts from fully connected neural networks and quantile regression forests. As a secondary result, we have compared the CNNs using three different density estimation methods [quantized softmax (QS), kernel mixture networks, and fitting a truncated normal distribution], and found the probabilistic forecasts based on the QS method to be best.

Statistical downscaling (SD) derives localized information from larger-scale numerical models. Convolutional neural networks (CNNs) have learning and generalization abilities that can enhance the downscaling of gridded data (Part I of this study experimented with 2-m temperature). In this research, we adapt a semantic-segmentation CNN, called UNet, to the downscaling of daily precipitation in western North America, from the low resolution (LR) of 0.25° to the high resolution (HR) of 4-km grid spacings. We select LR precipitation, HR precipitation climatology, and elevation as inputs; train UNet over the subset of the south- and central-western United States using Parameter–Elevation Regressions on Independent Slopes Model (PRISM) data from 2015 to 2018, and test it independently in all available domains from 2018 to 2019. We proposed an improved version of UNet, which we call Nest-UNet, by adding deep-layer aggregation and nested skip connections. Both the original UNet and Nest-UNet show generalization ability across different regions and outperform the SD baseline (bias-correction spatial disaggregation), with lower downscaling error and more accurate fine-grained textures. Nest-UNet also shares the highest amount of information with station observations and PRISM, indicating good ability to reduce the uncertainty of HR downscaling targets.

Climate models are our major source of knowledge about climate change. The impacts of climate change are often quantified by impact models. Whereas impact models typically require high resolution unbiased input data, global and regional climate models are in general biased, their resolution is often lower than desired. Thus, many users of climate model data apply some form of bias correction and downscaling. A fundamental assumption of bias correction is that the considered climate model produces skillful input for a bias correction, including a plausible representation of climate change. Current bias correction methods cannot plausibly correct climate change trends, and have limited ability to downscale. Cross validation of marginal aspects is not sufficient to evaluate bias correction and needs to be complemented by further analyses. Future research should address the development of stochastic models for downscaling and approaches to explicitly incorporate process understanding.

Many statistical downscaling methods require observational inputs and expert knowledge and thus cannot be generalized well across different regions. Convolutional neural networks (CNNs) are deep-learning models that have generalization abilities for various applications. In this research, we modify UNet, a semantic-segmentation CNN, and apply it to the downscaling of daily maximum/minimum 2-m temperature (TMAX/TMIN) over the western continental United States from 0.25° to 4-km grid spacings. We select high-resolution (HR) elevation, low-resolution (LR) elevation, and LR TMAX/TMIN as inputs; train UNet using Parameter–Elevation Regressions on Independent Slopes Model (PRISM) data over the south- and central-western United States from 2015 to 2018; and test it independently over both the training domains and the northwestern United States from 2018 to 2019. We found that the original UNet cannot generate enough fine-grained spatial details when transferred to the new northwestern U.S. domain. In response, we modified the original UNet by assigning an extra HR elevation output branch/loss function and training the modified UNet to reproduce both the supervised HR TMAX/TMIN and the unsupervised HR elevation. This improvement is named “UNet-Autoencoder (AE).” UNet-AE supports semisupervised model fine-tuning for unseen domains and showed better gridpoint-level performance with more than 10% mean absolute error (MAE) reduction relative to the original UNet. On the basis of its performance relative to the 4-km PRISM, UNet-AE is a good option to provide generalizable downscaling for regions that are underrepresented by observations.

This study addresses the need to provide comprehensive historical climate data and climate change projections at a scale suitable for, and readily accessible to, researchers and resource managers. This database for western North America (WNA) includes over 20 000 surfaces of monthly, seasonal, and annual climate variables from 1901 to 2009; several climate normal periods; and multimodel climate projections for the 2020s, 2050s, and 2080s. A software package, ClimateWNA, allows users to access the database and query point locations, obtain time series, or generate custom climate surfaces at any resolution. The software uses partial derivative functions of temperature change along elevation gradients to improve medium-resolution baseline climate estimates and calculates biologically relevant climate variables such as growing degree-days, number of frost-free days, extreme temperatures, and dryness indices. Historical and projected future climates are obtained by using monthly temperature and precipitation anomalies to adjust the interpolated baseline data for the location of interest. All algorithms used in the software package are described and evaluated against observations from weather stations across WNA. The downscaling algorithms substantially improve the accuracy of temperature variables over the medium-resolution baseline climate surfaces. Climate variables that are usually calculated from daily data are estimated from monthly climate variables with high statistical accuracy.

It is argued that anthropogenic global warming may decrease the global occurrence of cold waves. However, a historical record-extreme cold wave, popularly called the “boss level” cold wave, attacked East Asia in January 2016, which gives rise to the discussion of why this boss-level cold wave occurred during the winter with the warmest recorded global mean surface air temperature (SAT). To explore the impacts of human-induced global warming and natural internal atmosphere variability, we investigated the cold-wave-related circulation regime (i.e., the large-scale atmospheric circulation pattern) and compared the observation with the large ensemble simulations of the MIROC5 model. Our results showed that this East Asian extreme cold-wave-related atmospheric circulation regime mainly exhibited an extremely strong anomaly of the Ural blocking high (UBH) and a record-breaking anomaly of the surface Siberian high (SH), and it largely originated from the natural internal atmosphere variability. However, because of the dynamic effect of Arctic amplification, anthropogenic global warming may increase the likelihood of extreme cold waves through shifting the responsible natural atmospheric circulation regime toward a stronger amplitude. The probability of occurrence of extreme anomalies of UBH, SH, and the East Asia area mean SAT have been increased by 58%, 57%, and 32%, respectively, as a consequence of anthropogenic global warming. Therefore, extreme cold waves in East Asia, such as the one in January 2016, may be an enhanced response to the larger internal atmospheric variability modulated by human-induced global warming.

Climate model outputs are commonly corrected using statistical univariate bias correction methods. Most of the time, those 1d-corrections do not modify the ranks of the time series to be corrected. This implies that biases in the spatial or inter-variable dependences of the simulated variables are not adjusted. Hence, over the last few years, some multivariate bias correction (MBC) methods have been developed to account for inter-variable structures, inter-site ones, or both. As proof-of-concept, we propose to adapt a computer vision technique used for Image-to-Image translation tasks (CycleGAN) for the adjustment of spatial dependence structures of climate model projections. The proposed algorithm, named MBC-CycleGAN, aims to transfer simulated maps (seen as images) with inappropriate spatial dependence structure from climate model outputs to more realistic images with spatial properties similar to the observed ones. For evaluation purposes, the method is applied to adjust maps of temperature and precipitation from climate simulations through two cross-validation approaches. The first one is designed to assess two different post-processing schemes (Perfect Prognosis and Model Output Statistics). The second one assesses the influence of nonstationary properties of climate simulations on the performance of MBC-CycleGAN to adjust spatial dependences. Results are compared against a popular univariate bias correction method, a “quantile-mapping” method, which ignores inter-site dependencies in the correction procedure, and two state-of-the-art multivariate bias correction algorithms aiming to adjust spatial correlation structure. In comparison with these alternatives, the MBC-CycleGAN algorithm reasonably corrects spatial correlations of climate simulations for both temperature and precipitation, encouraging further research on the improvement of this approach for multivariate bias correction of climate model projections.