A new method is proposed for modelling the yearly maxima of sub-daily precipitation, with the aim of producing spatial maps of return level estimates. Yearly precipitation maxima are modelled using a Bayesian hierarchical model with a latent Gaussian field, with the blended generalised extreme value (bGEV) distribution used as a substitute for the more standard generalised extreme value (GEV) distribution. Inference is made less wasteful with a novel two-step procedure that performs separate modelling of the scale parameter of the bGEV distribution using peaks over threshold data. Fast inference is performed using integrated nested Laplace approximations (INLA) together with the stochastic partial differential equation approach, both implemented in . Heuristics for improving the numerical stability of with the GEV and bGEV distributions are also presented. The model is fitted to yearly maxima of sub-daily precipitation from the south of Norway and is able to quickly produce high-resolution return level maps with uncertainty. The proposed two-step procedure provides an improved model fit over standard inference techniques when modelling the yearly maxima of sub-daily precipitation with the bGEV distribution. Supplementary materials accompanying this paper appear on-line.

Diurnal temperature range is an important variable in climate science that can provide information regarding climate variability and climate change. Changes in diurnal temperature range can have implications for hydrology, human health and ecology, among others. Yet, the statistical literature on modeling diurnal temperature range is lacking. In this article we propose to model the distribution of diurnal temperature range using the five-parameter lambda (FPL) distribution. Additionally, in order to model diurnal temperature range with explanatory variables, we propose a distributional quantile regression model that combines quantile regression with marginal modeling using the FPL distribution. Inference is performed using the method of quantiles. The models are fitted to 30 years of daily observations of diurnal temperature range from 112 weather stations in the southern part of Norway. The flexible FPL distribution shows great promise as a model for diurnal temperature range, and performs well against competing models. The distributional quantile regression model is fitted to diurnal temperature range data using geographic, orographic, and climatological explanatory variables. It performs well and captures much of the spatial variation in the distribution of diurnal temperature range in Norway.

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<p>Extreme precipitation can lead to great floods and landslides and cause severe damage and economical losses. It is therefore of great importance that we manage to assess the risk of future extremes. Furthermore, natural hazards are spatiotemporal phenomena that require extensive modelling in both space and time. Extreme value theory (EVT) can be used for statistical modelling of spatial extremes, such as extreme precipitation over a catchment. An important concept when modelling a natural hazard is the degree of extremal dependence for the given phenomenon. Extremal dependence describes the possibility of multiple extremes occurring at the same time. For the stochastic variables X and Y, with distribution functions F<sub>X </sub>and F<sub>Y</sub>, the measure</p><p>χ = lim<sub>u</sub><sub>→1 </sub>P(F<sub>X</sub>(X) > u Ι F<sub>Y</sub>(Y) > u)</p><p>describes the pairwise extremal dependence between X and Y. If χ = 0, then the variables are <em>asymptotically independent</em>. If χ > 0, they are<br><em>asymptotically dependent</em>. Thus, extremes tend to occur simultaneously in space for processes that are asymptotically dependent, while this seldom occurs for asymptotically independent processes. It is a general belief that extreme precipitation tends to be asymptotically independent. However, to our knowledge, not much work has been put into analysing the extremal dependence structure of precipitation. Different statistical models have been developed, which can be applied for modelling spatial extremes. The most popular model is the <em>max-stable process</em>. Unfortunately, this model does not provide a good fit to asymptotically independent processes. Other models have been developed for better incorporating asymptotic independence, but most have not been extensively applied yet. We aim to examine the extremal dependence structure of precipitation in Norway, with the ultimate goal of modelling and simulating extreme precipitation. This is achieved by examining multiple popular statistics for extremal dependence, as well as comparing different spatial EVT models. This analysis is performed on hourly, gridded precipitation data from the MetCoOp Ensemble Prediction System (MEPS), which is publicly available from the internet: http://thredds.met.no/thredds/catalog/meps25epsarchive/catalog.html.</p>