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.

A Class of Copula-Based Bivariate Poisson Time Series Models with Applications

A class of bivariate integer-valued time series models was constructed via copula theory. Each series follows a Markov chain with the serial dependence captured using copula-based transition probabilities from the Poisson and the zero-inflated Poisson (ZIP) margins. The copula theory was also used again to capture the dependence between the two series using either the bivariate Gaussian or “t-copula” functions. Such a method provides a flexible dependence structure that allows for positive and negative correlation, as well. In addition, the use of a copula permits applying different margins with a complicated structure such as the ZIP distribution. Likelihood-based inference was used to estimate the models’ parameters with the bivariate integrals of the Gaussian or t-copula functions being evaluated using standard randomized Monte Carlo methods. To evaluate the proposed class of models, a comprehensive simulated study was conducted. Then, two sets of real-life examples were analyzed assuming the Poisson and the ZIP marginals, respectively. The results showed the superiority of the proposed class of models.

Optimization of Electric Vehicles Based on Frank-Copula-GlueCVaR Combined Wind and Photovoltaic Output Scheduling Research

Improving the efficiency of renewable energy and electricity utilization is an urgent problem for China under the objectives of carbon peaking and carbon neutralization. This paper proposes an optimization scheduling method of electric vehicles (EV) combined with wind and photovoltaic power based on the Frank-Copula-GlueCVaR. First, a joint output model based on copula theory was built to describe the correlation between wind and photovoltaic power output. Second, the Frank-Copula-GlueCVaR index was introduced in a novel way. Operators can now predetermine the future wind–photovoltaic joint output range based on this index and according to their risk preferences. Third, an optimal scheduling model aimed at reducing the group charging cost of EVs was proposed, thereby encouraging EV owners to participate in the demand response. Fourth, this paper: proposes the application of a Variant Roth–Serve algorithm; regards the EV group as a multi-intelligent group; and finds the Pareto optimal strategy of the EV group through continuous learning. Finally, case study results are shown to effectively absorb more renewable energy, reduce the consumption cost of the EV group, and suppress the load fluctuation of the whole EV group, which has a practical significance and theoretical value.

Meteorological drought analysis using copula theory for the case of upper Tekeze river basin, Northern Ethiopia

Meteorological drought is a climate-related natural disaster. It indicates a shortage of precipitation over a long period, usually for a season or a year. This study was initiated to analyze meteorological drought using copula theory. Long-year (1982–2020) rainfall and soil moisture data were used to analyze standardized precipitation index (SPI) and standardized soil moisture index (SSI), respectively. The best-fit copula family was selected to construct the joint probability distribution (JPD) of SPI and SSI. Multivariate standardized drought index (MSDI) at 3-, 6-, and 12-month timescales were analyzed using the MSDI toolbox. The non-parametric Mann-Kendall (M-K) statistical test was used for trend detection. The result shows the newly developed MSDI captured all extreme drought events with the highest severity (-3.21) that occurred during the observation period compared to SPI and SSI. MSDI shows the famine caused by the drought of 1984 and 1985 remains well known to the world, with the drought duration and severity of 10 months and 18.7 years, respectively and its joint return period was 33.0 years. The result of the M-K and Sen’s Slope estimator statistical tests shows a positive trend for all drought timescales in the basin. The extreme drought captured by the MSDI most frequently occurred in the basin. This implicated that meteorological drought analysis using multiple indices is better than a single index. The results of this study will help devise drought adaptation and mitigation strategies in the basin and beyond.

Exploring the Highway Icing Risk: Considering the Dynamic Dependence of Icing-Inducing Factors

In terms of the dynamic dependence between icing-inducing factors, this study is to explore the risk distribution of highways when icing events occur in the study area. A joint distribution considering the dynamic correlation of inducing factors was first constructed employing the Copula theory, which then yielded the possibility of icing events. Meanwhile, hazard zones and intensities of icing were proposed under different exceeding probabilities. After finishing the vulnerability analysis of highways, the risk matrix was used to conduct the icing risk for the highway, which was then applied to the construction of the risk zoning map. The results showed that there was an upper-tail dependence between extreme precipitation and temperature in the study area in winter, which could be well captured by the Gumbel Copula function. Indeed, the constructed joint distribution can express the possibility of icing under different intensities of precipitation and temperature. Besides, the highway with the tallest vulnerability in the study area was the Hegang-Yichun line. The case application showed that during March 2020, the traffic lines with a high icing risk were distributed around Fujin, Jiamusi, Hegang, and Qitaihe cities, and the Hegang section of the Hegang-Yichun line was at the highest icing risk. The low-risk lines were concentrated in the western part of the study area. This study is of great significance for the prevention and control of ice-snow disasters on the highway in cold regions.