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 Sample Generation of Scenario Earthquake Shaking Maps via a Combination of Modal Decomposition and Empirical Copula toward Seismic Hazard Assessment

ABSTRACT To quantify variations in seismic hazard assessment, a large number of scenario earthquake shaking maps (hereafter referred to as s-EQ maps for short) are required. In this article, we propose a method to easily generate a large number of s-EQ maps by combining modal decomposition and empirical copula. First, by applying modal decomposition to a set of existing s-EQ maps, we identify a scenario set with a parameter space to reduce the dimensionality of models. Next, we model a probability distribution of the modal coordinates, which we regard as random variables to allow us to induce a probability measure on the parameter space. By applying an empirical copula for modeling the probability distributions, the dependence structure between modal coordinates and the probability distribution of an individual modal coordinate can be discussed independently. Some simulations show that the dependence structure between modal coordinates is important to not distort the seismic hazard assessment. The proposed method can be applied to actual existing s-EQ maps to easily generate a large number of new s-EQ maps that follow the original probability distribution. We also show that variations can be added to the newly generated s-EQ maps by adjusting the empirical copula. Furthermore, we give a generalization of the proposed method to cases with nonequal probabilities of occurrence of existing scenarios.

Research on Revenue Insurance Premium Ratemaking of Jujube Based on Copula-Stochastic Optimization Model

During the process of jujube planting, there are not only natural risks caused by natural disasters but also market risks caused by price factors. In the study, firstly, wavelet analysis method was used to stabilize the jujube yield per unit area and the jujube price from 1997 to 2018 in Aksu region, Xinjiang, China. Secondly, EasyFit software was used to fit the distribution functions of yield per unit area and price, respectively. Thirdly, the optimal Copula function which connects the marginal distribution functions and its joint distribution function was selected with the principle of “the minimum square distance from the empirical Copula function.” Finally, taking the premium rate and the insurance amount as two decision variables, the farmer’s risk minimization as the objective function, around the four constraints of functions and role of insurance, the nonspeculative nature of insurance, the sustainability of insurance, and the moral hazard factors and the farmers’ willing to participate in insurance, the Copula-stochastic optimization model was set up to determine the premium rate of jujube revenue insurance in Aksu region.

A generalized approach to generate synthetic short-to-medium range hydro-meteorological forecasts

<p>Forecast informed operations hold great promise as a soft pathway to improve water resources system performance. Generating synthetic forecasts of hydro-meteorological variables is crucial for robust validation of this approach, as advanced numerical weather prediction hindcasts have a limited timespan (10-40 years) that is insufficient for assessing risk related to forecast-informed operations during extreme events. We develop a generalized error model for synthetic forecast generation that is applicable to a range of forecasted variables used in water resources management. The approach samples from the distribution of forecast errors over the available hindcast period and adds them to long records of observed data to generate synthetic forecasts. The approach utilizes the flexible Skew Generalized Error Distribution (SGED) to model marginal distributions of forecast errors that can exhibit heteroskedastic, auto-correlated, and non-Gaussian behavior. An empirical copula is used to capture covariance between variables and forecast lead times and across space. We demonstrate the method for medium-range forecasts across Northern California in two case studies for 1) streamflow and 2) temperature and precipitation, which are based on hindcasts from operational CONUS hydrologic and meteorological forecast models. The case studies highlight the flexibility of the model and its ability to emulate space-time structures in forecasts at scales critical for flood management. The proposed method is generalizable to other locations and computationally efficient, enabling fast generation of long synthetic forecast ensembles that are appropriate for the design and testing of forecast informed policy or characterization of forecast uncertainty for water resources risk analysis.</p>

Using Phase Annealing to generate surrogate discharge time series

<p>Phase randomization and its variants such as the Amplitude-adjusted (AAFT) and the Iterative amplitude adjusted (IAAFT) Fourier transform are used to check statistical significance of a given hypothesis and/or to generate time series that are similar to a reference in some statistical sense. These methods have the drawback of producing incorrect dependence structures e.g. empirical copula density, asymmetries and entropies. Recently, another form of such methods, “Phase Annealing”, was introduced, giving a possibility to generate n-dimensional realizations of a process under given constraint(s). The main concern using this method is the selection of correct objective function(s).</p><p>Here we show discharge time series generation using Phase Annealing with new objective functions. This allowed us to generate time series that are much longer than the reference, which in turn was helpful in establishing better distributions of floods.</p><p>We also show the generation of discharge time series at multiple locations that have the correct spatio-temporal dependences among all the series. Using the results, we generated full distributions of simultaneous extremes at observation locations.</p><p>Further uses may include clustering catchments that are likely to bring floods together and reliability analysis i.e. simulating distributions of failures for a system with many dependent/independent components. Drawbacks using this method are also shown.</p>

On the asymptotic covariance of the multivariate empirical copula process

Genest and Segers (2010) gave conditions under which the empirical copula process associated with a random sample from a bivariate continuous distribution has a smaller asymptotic covariance than the standard empirical process based on a random sample from the underlying copula. An extension of this result to the multivariate case is provided.

New copulas based on general partitions-of-unity (part III) — the continuous case

In this paper we discuss a natural extension of infinite discrete partition-of-unity copulas which were recently introduced in the literature to continuous partition of copulas with possible applications in risk management and other fields. We present a general simple algorithm to generate such copulas on the basis of the empirical copula from high-dimensional data sets. In particular, our constructions also allow for an implementation of positive tail dependence which sometimes is a desirable property of copula modelling, in particular for internal models under Solvency II.