Flexible Modeling of Variable Asymmetries in Cross-Covariance Functions for Multivariate Random Fields

The geostatistical analysis of multivariate spatial data for inference as well as joint predictions (co-kriging) ordinarily relies on modeling of the marginal and cross-covariance functions. While the former quantifies the spatial dependence within variables, the latter quantifies the spatial dependence across distinct variables. The marginal covariance functions are always symmetric; however, the cross-covariance functions often exhibit asymmetries in the real data. Asymmetric cross-covariance implies change in the value of cross-covariance for interchanged locations on fixed order of variables. Such change of cross-covariance values is often caused due to the spatial delay in effect of the response of one variable on another variable. These spatial delays are common in environmental processes, especially when dynamic phenomena such as prevailing wind and ocean currents are involved. Here, we propose a novel approach to introduce flexible asymmetries in the cross-covariances of stationary multivariate covariance functions. The proposed approach involves modeling the phase component of the constrained cross-spectral features to allow for asymmetric cross-covariances. We show the capability of our proposed model to recover the cross-dependence structure and improve spatial predictions against traditionally used models through multiple simulation studies. Additionally, we illustrate our approach on a real trivariate dataset of particulate matter concentration ($$PM_2.5$$PM2.5), wind speed and relative humidity. The real data example shows that our approach outperforms the traditionally used models, in terms of model fit and spatial predictions

Identifying high-wind features within extratropical cyclones using a probabilistic random forest

&amp;lt;p&amp;gt;Strong winds associated with extratropical cyclones are one of the most dangerous natural hazards in Europe. These high winds are mostly connected with five mesoscale dynamical features, namely the warm (conveyor belt) jet (WJ), the cold (conveyor belt) jet (CJ), (post) cold-frontal convective gusts (CFC), strong cold sector winds (CS) and &amp;amp;#8211; at least in some storms &amp;amp;#8211; the sting jet (SJ). While all these have strong winds in common, the timing, location and some further characteristics tend to differ and hence likely also the forecast errors occurring in association with them.&amp;lt;/p&amp;gt;&amp;lt;p&amp;gt;Here we present a novel objective identification approach for the features listed above, based on a probabilistic random forest using each feature&amp;amp;#8217;s most important characteristics in wind, rainfall, pressure and temperature evolution. However, as CJ and SJ turn out to be difficult to distinguish in surface observations alone, we decided to consider the two features together. This identification can then be used to generate a climatology for Central Europe, to analyse forecast errors specific to individual features, and to ultimately improve forecasts of high wind events through feature-dependent statistical post-processing. To achieve this, we strive to identify the features in irregularly spaced surface observations and in gridded analyses and forecasts in a consistent way, thus making it independent of spatial dependencies and gradients.&amp;lt;/p&amp;gt;&amp;lt;p&amp;gt;To train the probabilistic random forest, we subjectively identify the four storm features in twelve winter storm cases between 2015 and 2020 in both hourly surface observations and high-resolution reanalyses of the German COSMO model over Europe, using an interactive data analysis and visualisation tool. Results show that mean sea-level pressure (tendency), potential temperature, precipitation amount and wind direction are most important for the distinction between the features. From the random forest we get occurrence probabilities for each feature at every station, which can be converted into areal information using Kriging.&amp;lt;/p&amp;gt;&amp;lt;p&amp;gt;The results show a satisfactory identification for all features, especially for WJ and CFC. We encounter, however, some difficulties to clearly distinguish the CJ and CS, which are dynamically similar. A climatology is currently being compiled for both surface observations and the reanalyses over a period of around 20 years using the trained probabilistic random forests and further for high-resolution COSMO ensemble forecasts, for which we want to analyse forecast errors and develop feature-dependent postprocessing procedures.&amp;lt;/p&amp;gt;</jats:p