Spatial Mixture Copula Model For Multiple Correlated Responses With An Environmental Application

In environmental monitoring, multiple measurements are often collected at many locations and these measurements depend on each other in complex ways, such as nonlinear dependence. In this research, a novel copula-based geostatistical modelling approach was developed to model multivariate continuous spatial random fields using mixture copulas that captures both spatial and joint dependence of multiple responses over two-dimensional locations. In a bivariate context, the mixture copulas were used to capture the joint spatial dependence of a bivariate random field and the spatial copula of the bivariate random field was constructed as the convex combination of mixture copulas. The proposed model was applied to real forest data and simulated nonlinear data. The performance of the novel method was compared with existing spatial methods, which included a univariate spatial pair-copula model, a multivariate spatial pair-copula model that utilises nonlinear principal component analysis (NLPCA), and conventional kriging. The results show that the proposed model outperforms the existing methods in the interpolation of individual responses and reproduction of their bivariate dependence.

Clustering dependence structures of environmental extremes

<p>Identifying hidden spatial patterns that define sub-regions characterized by a similar behaviour is a central topic in statistical climatology. This task, often called regionalization in hydrology, is helpful for recognizing areas in which the variables under consideration have a similar stochastic distribution and thus, potentially, in reducing the dimensionality of the data. Many examples are available in this context, spanning from hydrology to weather and climate science. However, the majority of regionalization techniques focuses on the spatial clustering of a single variable of interest. Given the often severe impacts of climate extremes at the regional scale, here we develop an algorithm that identifies homogeneous spatial sub-regions that are characterized by a common bivariate dependence structure in the tails of a bivariate distribution.  In particular, we use a novel nonparametric distance able to capture the similarities and differences in the tail behaviour of bivariate distributions as the core of our clustering procedure. We apply the approach to identify homogeneous regions with varying coherence in the co-occurrence of sea level pressure and precipitation extremes in Great Britain and Ireland.</p>

Measuring compound flood potential from river discharge and storm surge extremes at the global scale

The interaction between physical drivers from oceanographic, hydrological, and meteorological processes in coastal areas can result in compound flooding. Compound flood events, like Cyclone Idai and Hurricane Harvey, have revealed the devastating consequences of the co-occurrence of coastal and river floods. A number of studies have recently investigated the likelihood of compound flooding at the continental scale based on simulated variables of flood drivers, such as storm surge, precipitation, and river discharges. At the global scale, this has only been performed based on observations, thereby excluding a large extent of the global coastline. The purpose of this study is to fill this gap and identify regions with a high compound flooding potential from river discharge and storm surge extremes in river mouths globally. To do so, we use daily time series of river discharge and storm surge from state-of-the-art global models driven with consistent meteorological forcing from reanalysis datasets. We measure the compound flood potential by analysing both variables with respect to their timing, joint statistical dependence, and joint return period. Our analysis indicates many regions that deviate from statistical independence and could not be identified in previous global studies based on observations alone, such as Madagascar, northern Morocco, Vietnam, and Taiwan. We report possible causal mechanisms for the observed spatial patterns based on existing literature. Finally, we provide preliminary insights on the implications of the bivariate dependence behaviour on the flood hazard characterisation using Madagascar as a case study. Our global and local analyses show that the dependence structure between flood drivers can be complex and can significantly impact the joint probability of discharge and storm surge extremes. These emphasise the need to refine global flood risk assessments and emergency planning to account for these potential interactions.

Measuring compound flood potential from river discharge and storm surge extremes at the global scale and its implications for flood hazard

The interaction between physical drivers from oceanographic, hydrological, and meteorological processes in coastal areas can result in compound flooding. Compound flood events, like Cyclone Idai and Hurricane Harvey, have revealed the devastating consequences of the co-occurrence of coastal and river floods. A number of studies have recently investigated the likelihood of compound flooding at the continental scale based on simulated variables of flood drivers such as storm surge, precipitation, and river discharges. At the global scale, this has only been performed based on observations, thereby excluding a large extent of the global coastline. The purpose of this study is to fill this gap and identify potential hotspots of compound flooding from river discharge and storm surge extremes in river mouths globally. To do so, we use daily time-series of river discharge and storm surge from state-of-the-art global models driven with consistent meteorological forcing from reanalysis datasets. We measure the compound flood potential by analysing both variables with respect to their timing, joint statistical dependence, and joint return period. We find many hotspot regions of compound flooding that could not be identified in previous global studies based on observations alone, such as: Madagascar, Northern Morocco, Vietnam, and Taiwan. We report possible causal mechanisms for the observed spatial patterns based on existing literature. Finally, we provide preliminary insights on the implications of the bivariate dependence behaviour on the flood hazard characterisation using Madagascar as a case study. Our global and local analyses show that the dependence structure between flood drivers can be complex and can significantly impact the joint probability of discharge and storm surge extremes. These emphasise the need to refine global flood risk assessments and emergency planning to account for these potential interactions.

Inverting the dynamical evolution of globular clusters: clues to their origin

Scaling relations for globular clusters (GC) differ from the scaling relations for pressure supported (elliptical) galaxies. In this contribution we discuss the relative importance of nature and nurture in the establishment of the scaling between cluster density (or radius), mass and Galactocentric distance for the Milky Way GCs. We show that energy diffusion by stellar encounters (i.e. two-body relaxation) is the dominant mechanism in shaping the bivariate dependence of density on mass and Galactocentric distance for GCs with masses ≲ 106M⊙, and it can not be excluded that GCs formed with similar scaling relations as the more massive ultra-compact dwarf galaxies (UCDs). To explore the initial properties that give rise to the distributions of these quantities, we developed a fast cluster evolution model (Evolve Me A Cluster of StarS, emacss) and use it in a hierarchical Bayesian framework to fit a parameterised model for the initial properties of Milky Way GCs to the observed present-day properties. The best-fit cluster initial mass function is substantially flatter (power-law with index − 0.6 ± 0.2) than what is observed for young massive clusters (YMCs) forming in the nearby Universe (power-law with index − 2). This result is driven by the metal-poor GCs, a slightly steeper CIMF is allowed when considering the metal-rich GCs separately (α ≃ −1.2 ± 0.4). If stellar mass loss and two-body relaxation in the Milky Way tidal field are the dominant disruption mechanisms, then GCs formed differently from YMCs.

A continuous rainfall model based on vine copulas

Copulas have already proven their flexibility in rainfall modelling. Yet, their use is generally restricted to the description of bivariate dependence. Recently, vine copulas have been introduced, allowing multi-dimensional dependence structures to be described on the basis of a stage by stage mixing of 2-dimensional copulas. This paper explores the use of such vine copulas in order to incorporate all relevant dependences between the storm variables of interest. On the basis of such fitted vine copulas, an external storm structure is modelled. An internal storm structure is superimposed based on Huff curves, such that a continuous time series of rainfall is generated. The performance of the rainfall model is evaluated through a statistical comparison between an ensemble of synthetical rainfall series and the observed rainfall series and through the comparison of the annual maxima.

A continuous rainfall model based on vine copulas

Copulas have already proven their flexibility in rainfall modelling. Yet, their use is generally restricted to the description of bivariate dependence. Recently, vine copulas have been introduced, allowing multi-dimensional dependence structures to be described on the basis of a stage by stage mixing of two-dimensional copulas. This paper explores the use of such vine copulas in order to incorporate all relevant dependencies between the storm variables of interest. On the basis of such fitted vine copulas, an external storm structure is modeled. An internal storm structure is superimposed based on Huff curves, such that a continuous time series of rainfall is generated. The performance of the rainfall model is evaluated through a statistical comparison between an ensemble of synthetical rainfall series and the observed rainfall series and through the comparison of the annual maxima.