Probabilistic modeling of flood characterizations with parametric and minimum information pair-copula model

This paper highlights the usefulness of the minimum information and parametric pair-copula construction (PCC) to model the joint distribution of flood event properties. Both of these models outperform other standard multivariate copula in modeling multivariate flood data that exhibiting complex patterns of dependence, particularly in the tails. In particular, the minimum information pair-copula model shows greater flexibility and produces better approximation of the joint probability density and corresponding measures have capability for effective hazard assessments. The study demonstrates that any multivariate density can be approximated to any degree of desired precision using minimum information pair-copula model and can be practically used for probabilistic flood hazard assessment

How well do regional climate models simulate the spatial dependence of precipitation? An application of pair-copula constructions

We investigate how well a suite of regional climate models (RCMs) from the ENSEMBLES project represents the residual spatial dependence of daily precipitation. The study area we consider is a 200 km×200 km region in south central Norway, with RCMs driven by ERA-40 boundary conditions at a horizontal resolution of approximately 25 km×25 km. We model the residual spatial dependence with pair-copula constructions, which allows us to assess both the overall and tail dependence in precipitation, including uncertainty estimates. The selected RCMs reproduce the overall dependence rather well, though the discrepancies compared to observations are substantial. All models overestimate the overall dependence in the west-east direction. They also overestimate the upper tail dependence in the north-south direction during winter, and in the west-east direction during summer, whereas they tend to underestimate this dependence in the north-south direction in summer. Moreover, many of the climate models do not simulate the small-scale dependence patterns caused by the pronounced orography well. However, the misrepresented residual spatial dependence does not seem to affect estimates of high quantiles of extreme precipitation aggregated over a few grid boxes. The underestimation of the area-aggregated extreme precipitation is due mainly to the well-known underestimation of the univariate margins for individual grid boxes, suggesting that the correction of RCM biases in precipitation might be feasibl

Inference on extremal dependence in the domain of attraction of a structured H\"usler-Reiss distribution motivated by a Markov tree with latent variables

A Markov tree is a probabilistic graphical model for a random vector indexed by the nodes of an undirected tree encoding conditional independence relations between variables. One possible limit distribution of partial maxima of samples from such a Markov tree is a max-stable H\"usler-Reiss distribution whose parameter matrix inherits its structure from the tree, each edge contributing one free dependence parameter. Our central assumption is that, upon marginal standardization, the data-generating distribution is in the max-domain of attraction of the said H\"usler-Reiss distribution, an assumption much weaker than the one that data are generated according to a graphical model. Even if some of the variables are unobservable (latent), we show that the underlying model parameters are still identifiable if and only if every node corresponding to a latent variable has degree at least three. Three estimation procedures, based on the method of moments, maximum composite likelihood, and pairwise extremal coefficients, are proposed for usage on multivariate peaks over thresholds data when some variables are latent. A typical application is a river network in the form of a tree where, on some locations, no data are available. We illustrate the model and the identifiability criterion on a data set of high water levels on the Seine, France, with two latent variables. The structured H\"usler-Reiss distribution is found to fit the observed extremal dependence patterns well. The parameters being identifiable we are able to quantify tail dependence between locations for which there are no data.Comment: 31 pages, 17 figure

Spatial wildfire risk modeling using mixtures of tree-based multivariate Pareto distributions

Wildfires pose a severe threat to the ecosystem and economy, and risk assessment is typically based on fire danger indices such as the McArthur Forest Fire Danger Index (FFDI) used in Australia. Studying the joint tail dependence structure of high-resolution spatial FFDI data is thus crucial for estimating current and future extreme wildfire risk. However, existing likelihood-based inference approaches are computationally prohibitive in high dimensions due to the need to censor observations in the bulk of the distribution. To address this, we construct models for spatial FFDI extremes by leveraging the sparse conditional independence structure of H\"usler--Reiss-type generalized Pareto processes defined on trees. These models allow for a simplified likelihood function that is computationally efficient. Our framework involves a mixture of tree-based multivariate Pareto distributions with randomly generated tree structures, resulting in a flexible model that can capture nonstationary spatial dependence structures. We fit the model to summer FFDI data from different spatial clusters in Mainland Australia and 14 decadal windows between 1999--2022 to study local spatiotemporal variability with respect to the magnitude and extent of extreme wildfires. Our results demonstrate that our proposed method fits the margins and spatial tail dependence structure adequately, and is helpful to provide extreme wildfire risk measures

Copula-based stochastic modelling of evapotranspiration time series conditioned on rainfall as design tool in water resources management

In the last few decades, the frequency and intensity of water-related disasters, also called climate-related disasters, e.g. floods, storms, heat waves and droughts, has gone up considerably at both global and regional scales, causing significant damage to many societies and ecosystems. Understanding the behavior and frequency of these disasters is extremely important, not only for reducing their damages but also for the management of water resources. These disasters can often be characterized by multiple dependent variables and therefore require a flexible multivariate approach for studying such phenomena. In this study, we focus on copulas, which are multivariate functions that describe the dependence structure between stochastic variables, independently of their marginal behaviors. The study aimed at different potential applications of copulas in hydrology, such as a multivariate frequency analysis and a copula-based approach for assessing a rainfall model. And further, a stochastic copula-based evapotranspiration generator was developed. As an application, the potential impacts of climate change on river discharge was investigated partly based the latter generator

Copula-based statistical modelling of synoptic-scale climate indices for quantifying and managing agricultural risks in australia

Australia is an agricultural nation characterised by one of the most naturally diverse climates in the world, which translates into significant sources of risk for agricultural production and subsequent farm revenues. Extreme climatic events have been significantly affecting large parts of Australia in recent decades, contributing to an increase in the vulnerability of crops, and leading to subsequent higher risk to a large number of agricultural producers. However, attempts at better managing climate related risks in the agricultural sector have confronted many challenges. First, crop insurance products, including classical claim-based and index-based insurance, are among the financial implements that allow exposed individuals to pool resources to spread their risk. The classical claim-based insurance indemnifies according to a claim of crop loss from the insured customer, and so can easily manage idiosyncratic risk, which is the case where the loss occurs independently.Nevertheless, the existence of systemic weather risk (covariate risk), which is the spread of extreme events over locations and times (e.g., droughts and floods), has been identified as the main reason for the failure of private insurance markets, such as the classical multi-peril crop insurance, for agricultural crops. The index-based insurance is appropriate to handle systemic but not idiosyncratic risk. The indemnity payments of the index-based insurance are triggered by a predefined threshold of an index (e.g., rainfall), which is related to such losses. Since the covariate nature of a climatic event, it sanctions the insurers to predict losses and ascertain indemnifications for a huge number of insured customers across a wide geographical area. However, basis risk, which is related to the strength of the relationship between the predefined indices used to estimate the average loss by the insured community and the actual loss of insured assets by an individual, is a major barrier that hinders uptake of the index-based insurance. Clearly, the high basis risk, which is a weak relationship between the index and loss, destroys the willingness of potential customers to purchase this insurance product. Second, the impact of multiple synoptic-scale climate mode indices (e.g., Southern Oscillation Index (SOI) and Indian Ocean Index (IOD)) on precipitation and crop yield is not identical in different spatial locations and at different times or seasons across the Australian continent since the influence of large-scale climate heterogeneous over the different regions. The occurrence, role, and amplitude of synoptic-scale climate modes contributing to the variability of seasonal crop production have shifted in recent decades. These variables generally complicate the climate and crop yield relationship that cannot be captured by traditional modelling and analysis approaches commonly found in published agronomic literature such as linear regression. In addition, the traditional linear analysis is not able to model the nonlinear and asymmetric interdependence between extreme insurance losses, which may occur in the case of systemic risk. Relying on the linear method may lead to the problem that different behaviour may be observed from joint distributions, particularly in the upper and lower regions, with the same correlation coefficient. As a result, the likelihood of extreme insurance losses can be underestimated or overestimated that lead to inaccuracies in the pricing of insurance policies. Another alternative is the use of the multivariate normal distribution, where the joint distribution is uniquely defined using the marginal distributions of variables and their correlation matrix. However, phenomena are not always normally distributed in practice. It is therefore important to develop new, scientifically verified, strategic measures to solve the challenges as mentioned above in order to support mitigating the influences of the climate-related risk in the agricultural sector. Copulas provide an advanced statistical approach to model the joint distribution of multivariate random variables. This technique allows estimating the marginal distributions of individual variables independently with their dependence structures. It is clear that the copula method is superior to the conventional linear regression since it does not require variables have to be normally distributed and their correlation can be either linear or non-linear. This doctoral thesis therefore adopts the advanced copula technique within a statistical modelling framework that aims to model: (1) The compound influence of synoptic-scale climate indices (i.e., SOI and IOD) and climate variables (i.e., precipitation) to develop a probabilistic precipitation forecasting system where the integrated role of different factors that govern precipitation dynamics are considered; (2) The compound influence of synoptic-scale climate indices on wheat yield; (3) The scholastic interdependencies of systemic weather risks where potential adaptation strategies are evaluated accordingly; and (4) The risk-reduction efficiencies of geographical diversifications in wheat farming portfolio optimisation. The study areas are Australia’s agro-ecological (i.e., wheat belt) zones where major seasonal wheat and other cereal crops are grown. The results from the first and second objectives can be used for not only forecasting purposes but also understanding the basis risk in the case of pricing climate index-based insurance products. The third and fourth objectives assess the interactions of drought events across different locations and in different seasons and feasible adaptation tools. The findings of these studies can provide useful information for decision-makers in the agricultural sector. The first study found the significant relationship between SOI, IOD, and precipitation. The results suggest that spring precipitation in Australia, except for the western part, can be probabilistically forecasted three months ahead. It is more interesting that the combination of SOI and IOD as the predictors will improve the performance of the forecast model. Similarly, the second study indicated that the largescale climate indices could provide knowledge of wheat crops up to six months in advance. However, it is noted that the influence of different climate indices varies over locations and times. Furthermore, the findings derived from the third study demonstrated the spatio-temporally stochastic dependence of the drought events. The results also prove that time diversification is potentially more effective in reducing the systemic weather risk compared to spatially diversifying strategy. Finally, the fourth objective revealed that wheat-farming portfolio could be effectively optimised through the geographical diversification. The outcomes of this study will lead to the new application of advanced statistical tools that provide a better understanding of the compound influence of synoptic-scale climatic conditions on seasonal precipitation, and therefore on wheat crops in key regions over the Australian continent. Furthermore, a comprehensive analysis of systemic weather risks performed through advanced copula-statistical models can help improve and develop novel agricultural adaptation strategies in not only the selected study region but also globally, where climate extreme events pose a serious threat to the sustainability and survival of the agricultural industry. Finally, the evaluation of the effectiveness of diversification strategies implemented in this study reveals new evidence on whether the risk pooling methods could potentially mitigate climate risks for the agricultural sector and subsequently, help farmers in prior preparation for uncertain climatic events

A hazard model of sub-freezing temperatures in the United Kingdom using vine copulas

Extreme cold weather events, such as the winter of 1962/63, the third coldest winter ever recorded in the Central England Temperature record, or more recently the winter of 2010/11, have significant consequences for the society and economy. This paper assesses the probability of such extreme cold weather across the United Kingdom (UK), as part of a probabilistic catastrophe model for insured losses caused by the bursting of pipes. A statistical model is developed in order to model the extremes of the Air Freezing Index (AFI), which is a common measure of the magnitude and duration of freezing temperatures. A novel approach in the modelling of the spatial dependence of the hazard has been followed which takes advantage of the vine copula methodology. The method allows complex dependencies to be modelled, especially between the tails of the AFI distributions, which is important to assess the extreme behaviour of such events. The influence of the North Atlantic Oscillation and of anthropogenic climate change on the frequency of UK cold winters has also been taken into account. According to the model, the occurrence of extreme cold events, such as the 1962/63 winter, has decreased approximately 2 times during the course of the 20th century as a result of anthropogenic climate change. Furthermore, the model predicts that such an event is expected to become more uncommon, about 2 times less frequent, by the year 2030. Extreme cold spells in the UK have been found to be heavily modulated by the North Atlantic Oscillation (NAO) as well. A cold event is estimated to be ≈3–4 times more likely to occur during its negative phase than its positive phase. However, considerable uncertainty exists in these results, owing mainly to the short record length and the large interannual variability of the AFI.</p