Post-Processing Ensemble Weather Forecasts for Introducing Multisite and Multivariable Correlations using Rank Shuffle and Copula Theory

Statistical methods have been widely used to post-process ensemble weather forecasts for hydrological predictions. However, most of the statistical post-processing methods apply to a single weather variable at a single location, thus neglecting the inter-site and inter-variable dependence structures of forecast variables. This study synthesized a multisite and multivariate (MSMV) post-processing framework that extends the univariate method to the MSMV version by directly rearranging the post-processed ensemble members (post-reordering strategy) or by rearranging the latent variables used in univariate method (pre-reordering strategy). Based on the univariate Generator-based Post-Processing (GPP) method, the two reordering strategies and three dependence reconstruction methods (Rank shuffle (RS), Gaussian Copula (GC), and Empirical Copula (EC)) totaling 6 MSMV methods (RS-Pre, GC-Pre, EC-Pre, RS-Post, GC-Post, and EC-Post) were evaluated in post-processing ensemble precipitation and temperature forecasts for the Xiangjiang Basin in China using the 11-member ensemble forecasts from the Global Ensemble Forecasting System (GEFS). The results showed that raw GEFS forecasts tend to be biased for both the forecast ensembles and the inter-site and inter-variable dependencies. Univariate method can improve the univariate performance of ensemble mean and spread but misrepresent the inter-site and inter-variable dependence among the forecast variables. The MSMV framework can well utilize the advantages of the univariate method and also reconstruct the inter-site and inter-variable dependencies. Among the six methods, RS-Pre, RS-Post, GC-Post, and EC-Post perform better than the others with respect to reproducing the univariate statistics and multivariable dependences. The post-reordering strategy is recommended to combine the univariate method (i.e. GPP) and reconstruction methods.

Bimodality in ensemble forecasts of 2 m temperature: identification

Bimodality and other types of non-Gaussianity arise in ensemble forecasts of the atmosphere as a result of nonlinear spread across ensemble members. In this paper, bimodality in 50-member ECMWF ENS-extended ensemble forecasts is identified and characterized. Forecasts of 2 m temperature are found to exhibit widespread bimodality well over a derived false-positive rate. In some regions bimodality occurs in excess of 30 % of forecasts, with the largest rates occurring during lead times of 2 to 3 weeks. Bimodality occurs more frequently in the winter hemisphere with indications of baroclinicity being a factor to its development. Additionally, bimodality is more common over the ocean, especially the polar oceans, which may indicate development caused by boundary conditions (such as sea ice). Near the equatorial region, bimodality remains common during either season and follows similar patterns to the Intertropical Convergence Zone (ITCZ), suggesting convection as a possible source for its development. Over some continental regions the modes of the forecasts are separated by up to 15 °C. The probability density for the modes can be up to 4 times greater than at the minimum between the modes, which lies near the ensemble mean. The widespread presence of such bimodality has potentially important implications for decision makers acting on these forecasts. Bimodality also has implications for assessing forecast skill and for statistical postprocessing: several commonly used skill-scoring methods and ensemble dressing methods are found to perform poorly in the presence of bimodality, suggesting the need for improvements in how non-Gaussian ensemble forecasts are evaluated.

Assessing the Impact of Dropsonde Data on Rain Forecasts in Taiwan with Observing System Simulation Experiments

This paper presents an observing system simulation experiment (OSSE) study to examine the impact of dropsonde data assimilation (DA) on rainfall forecasts for a heavy rain event in Taiwan. The rain event was associated with strong southwesterly flows over the northern South China Sea (SCS) after a weakening tropical cyclone (TC) made landfall over southeastern China. With DA of synthetic dropsonde data over the northern SCS, the model reproduces more realistic initial fields and a better simulated TC track that can help in producing improved low-level southwesterly flows and rainfall forecasts in Taiwan. Dropsonde DA can also aid the model in reducing the ensemble spread, thereby producing more converged ensemble forecasts. The sensitivity studies suggest that dropsonde DA with a 12-h cycling interval is the best strategy for deriving skillful rainfall forecasts in Taiwan. Increasing the DA interval to 6 h is not beneficial. However, if the flight time is limited, a 24-h interval of DA cycling is acceptable, because rainfall forecasts in Taiwan appear to be satisfactory. It is also suggested that 12 dropsondes with a 225-km separation distance over the northern SCS set a minimum requirement for enhancing the model regarding rainfall forecasts. Although more dropsonde data can help the model to obtain better initial fields over the northern SCS, they do not provide more assistance to the forecasts of the TC track and rainfall in Taiwan. These findings can be applied to the future field campaigns and model simulations in the nearby regions.

A Conformal Predictive System for Distribution Regression with Random Features

Distribution regression is the regression case where the input objects are distributions. Many machine learning problems can be analysed in this framework, such as multi-instance learning and learning from noisy data. This paper attempts to build a conformal predictive system(CPS) for distribution regression, where the prediction of the system for a test input is a cumulative distribution function(CDF) of the corresponding test label. The CDF output by a CPS provides useful information about the test label, as it can estimate the probability of any event related to the label and be transformed to prediction interval and prediction point with the help of the corresponding quantiles. Furthermore, a CPS has the property of validity as the prediction CDFs and the prediction intervals are statistically compatible with the realizations. This property is desired for many risk-sensitive applications, such as weather forecast. To the best of our knowledge, this is the first work to extend the learning framework of CPS to distribution regression problems. We first embed the input distributions to a reproducing kernel Hilbert space using kernel mean embedding approximated by random Fourier features, and then build a fast CPS on the top of the embeddings. While inheriting the property of validity from the learning framework of CPS, our algorithm is simple, easy to implement and fast. The proposed approach is tested on synthetic data sets and can be used to tackle the problem of statistical postprocessing of ensemble forecasts, which demonstrates the effectiveness of our algorithm for distribution regression problems.

Stratospheric Modulation of Arctic Oscillation Extremes as Represented by Extended-Range Ensemble Forecasts

The Arctic Oscillation (AO) describes a seesaw pattern of variations in atmospheric mass over the polar cap. It is by now well established that the AO pattern is in part determined by the state of the stratosphere. In particular, sudden stratospheric warmings (SSWs) are known to nudge the tropospheric circulation toward a more negative phase of the AO, which is associated with a more equatorward shifted jet and enhanced likelihood for blocking and cold air outbreaks in mid-latitudes. SSWs are also thought to contribute to the occurrence of extreme AO events. However, statistically robust results about such extremes are difficult to obtain from observations or meteorological (re-)analyses due to the limited sample size of SSW events in the observational record (roughly 6 SSWs per decade). Here we exploit a large set of extended-range ensemble forecasts within the subseasonal-to-seasonal (S2S) framework to obtain an improved characterization of the modulation of AO extremes due to stratosphere-troposphere coupling. Specifically, we greatly boost the sample size of stratospheric events by using potential SSWs (p-SSWs), i.e., SSWs that are predicted to occur in individual forecast ensemble members regardless of whether they actually occurred in the real atmosphere. For example, for the ECMWF S2S ensemble this gives us a total of 6101 p-SSW events for the period 1997–2021. A standard lag-composite analysis around these p-SSWs validates our approach, i.e., the associated composite evolution of stratosphere-troposphere coupling matches the known evolution based on reanalyses data around real SSW events. Our statistical analyses further reveal that following p-SSWs, relative to climatology: 1) persistently negative AO states (> 1 week duration) are 16 % more likely, 2) the likelihood for extremely negative AO states (< −3σ) is enhanced by at least 35 %, while that for extremely positive AO states (> +3σ) is reduced to almost zero, 3) a p-SSW preceding an extremely negative AO state within 4 weeks is causal for this AO extreme (in a statistical sense) up to a degree of 27 %. A corresponding analysis relative to strong stratospheric vortex events reveals similar insights into the stratospheric modulation of positive AO extremes.

On the ROC Area of Ensemble Forecasts for Rare Events

The relative operating characteristic (ROC) curve is a popular diagnostic tool in forecast verification, with the area under the ROC curve (AUC) used as a verification metric measuring the discrimination ability of a forecast. Along with calibration, discrimination is deemed as a fundamental probabilistic forecast attribute. In particular, in ensemble forecast verification, AUC provides a basis for the comparison of potential predictive skill of competing forecasts. While this approach is straightforward when dealing with forecasts of common events (e.g. probability of precipitation), the AUC interpretation can turn out to be oversimplistic or misleading when focusing on rare events (e.g. precipitation exceeding some warning criterion). How should we interpret AUC of ensemble forecasts when focusing on rare events? How can changes in the way probability forecasts are derived from the ensemble forecast affect AUC results? How can we detect a genuine improvement in terms of predictive skill? Based on verification experiments, a critical eye is cast on the AUC interpretation to answer these questions. As well as the traditional trapezoidal approximation and the well-known bi-normal fitting model, we discuss a new approach which embraces the concept of imprecise probabilities and relies on the subdivision of the lowest ensemble probability category.

Process-Based Evaluation of Stochastic Perturbed Microphysics Parameterization Tendencies on Ensemble Forecasts of Heavy Rainfall Events

Stochastic model error schemes, such as the stochastic perturbed parameterization tendencies (SPPT) and independent SPPT (iSPPT) schemes, have become an increasingly accepted method to represent model error associated with uncertain subgrid-scale processes in ensemble prediction systems (EPSs). While much of the current literature focuses on the effects of these schemes on forecast skill, this research examines the physical processes by which iSPPT perturbations to the microphysics parameterization scheme yield variability in ensemble rainfall forecasts. Members of three 120-member Weather Research and Forecasting (WRF) model ensemble case studies, including two distinct heavy rain events over Taiwan and one over the northeastern United States, are ranked according to an area-averaged accumulated rainfall metric in order to highlight differences between high- and low-precipitation forecasts. In each case, high-precipitation members are characterized by a damping of the microphysics water vapor and temperature tendencies over the region of heaviest rainfall, while the opposite is true for low-precipitation members. Physically, the perturbations to microphysics tendencies have the greatest impact at the cloud-level and act to modify precipitation efficiency. To this end, the damping of tendencies in high-precipitation forecasts suppresses both the loss of water vapor due to condensation and the corresponding latent heat release, leading to grid-scale supersaturation. Conversely, amplified tendencies in low-precipitation forecasts yield both drying and increased positive buoyancy within clouds.