Modelling the occurrence of heat waves in maximum and minimum temperatures over Spain and projections for the period 2031-60.

The occurrence of extreme heat events in maximum and minimum daily temperatures is modelled using a non-homogeneous common Poisson shock process. It is applied to five Spanish locations, representative of the most common climates over the Iberian Peninsula. The model is based on an excess over threshold approach and distinguishes three types of extreme events: only in maximum temperature, only in minimum temperature and in both of them (simultaneous events). It takes into account the dependence between the occurrence of extreme events in both temperatures and its parameters are expressed as functions of time and temperature related covariates. The fitted models allow us to characterize the occurrence of extreme heat events and to compare their evolution in the different climates during the observed period. This model is also a useful tool for obtaining local projections of the occurrence rate of extreme heat events under climate change conditions, using the future downscaled temperature trajectories generated by Earth System Models. The projections for 2031-60 under scenarios RCP4.5, RCP6.0 and RCP8.5 are obtained and analysed using the trajectories from four earth system models which have successfully passed a preliminary control analysis. Different graphical tools and summary measures of the projected daily intensities are used to quantify the climate change on a local scale. A high increase in the occurrence of extreme heat events, mainly in July and August, is projected in all the locations, all types of event and in the three scenarios, although in 2051-60 the increase is higher under RCP8.5. However, relevant differences are found between the evolution in the different climates and the types of event, with a specially high increase in the simultaneous ones

Testing independence between two nonhomogeneous point processes in time

Point processes are often used to model the occurrence times of different phenomena, such as heatwaves or spike trains. Many of those problems require to study the independence between nonhommogeneous point processes in time, and this work develops three families of tests to assess that hypothesis. They can be applied to different types of processes, and all together they cover a wide range of situations appearing in real problems. The first family includes two tests for Poisson processes. The second family is based on the close point distance, and the third one on cross dependence functions. An extensive simulation study of the size and power of the tests is carried out and some practical rules to select the most appropriate test in different cases, are provided. The proposed tests are demonstrated on a real data application about the occurrence of extreme heat events in three Spanish locations

Modelos para la precipitación diaria en el marco de los modelos lineales generalizados

En la memoria se desarrollan modelos estadísticos que permiten caracterizar, en un grado adecuado, el comportamiento de la precipitación diaria en un observatorio. La modelización elegida representa el proceso de lluvia mediante dos componentes, la ocurrencia de precipitación, representada por una variable binaria, y la cantidad medida en los días lluviosos, cada una de las cuales requiere construir un submodelo. En ambos casos, la distribución de la variable de interés no es Gaussiana y su valor esperado depende de covariables atmosféricas; por esto, el marco de los modelos lineales generalizados (GLM) y sus extensiones que permiten considerar la dependencia entre respuesta sucesivas, resulta un esquema de modelización adecuado. En el capítulo 1 se hace una revisión bibliográfica de los modelos de precipitación y una presentación de la familia de modelos a utilizar. El capítulo 2 de la memoria se dedica al análisis de las herramientas de crítica de los modelos y a hacer una propuesta de valoración de los mismos. Se propone una metodología que tiene en cuenta, además de las medidas habituales, la capacidad de los modelos para clasificar correctamente las observaciones, reproducir el ciclo estacional, la evolución interanual de la lluvia o la distribución de la longitud de las rachas seca y húmeda. El capítulo 3 se dedica a la construcción de modelos y al análisis de su capacidad para ajustar las series de precipitación de cuatro observatorios de la cuenca del Ebro con diferentes características climáticas e información atmosférica dispar. Los modelos de ocurrencia considerados son cadenas de Markov cuyas probabilidades de transición se estiman mediante regresión logística. La estrategia de construcción estudia, en pasos sucesivos, la significación de diferentes convariables: indicadores de ocurrencia en los días previos, armónicos para representar el ciclo anual y covariables climática. El objetivo del capítulo 4 es construir un modelo que predsiga la precipitación de un observatorio. En el capítulo 5 se desarrolla un "downscaling" de las precipitaciones en un escenario de cambio climático

Bayesian variable selection in generalized extreme value regression: modeling annual maximum temperature

In many applications, interest focuses on assessing relationships between covariates and the extremes of the distribution of a continuous response. For example, in climate studies, a usual approach to assess climate change has been based on the analysis of annual maximum data. Using the generalized extreme value (GEV) distribution, we can model trends in the annual maximum temperature using the high number of available atmospheric covariates. However, there is typically uncertainty in which of the many candidate covariates should be included. Bayesian methods for variable selection are very useful to identify important covariates. However, such methods are currently very limited for moderately high dimensional variable selection in GEV regression. We propose a Bayesian method for variable selection based on a stochastic search variable selection (SSVS) algorithm proposed for posterior computation. The method is applied to the selection of atmospheric covariates in annual maximum temperature series in three Spanish stations

Caracterización espacio-temporal de la evolución de la precipitación anual en la cuenca del Ebro

Ponencia presentada en: III Congreso de la Asociación Española de Climatología “El agua y el clima”, celebrado en Palma de Mallorca del 16 al 19 de junio de 2002.[ES]El objetivo de este trabajo es realizar una caracterización espacio-temporal de la evolución de la precipitación en la cuenca del Ebro. Para ello se construye una base de datos con 29 series con información mensual del periodo 1916-2000. Por estaciones, y posteriormente con las series anuales, se realiza un proceso de homogeneización. Mediante un análisis de conglomerados, complementado con un análisis de las tendencias en la lluvia anual, se efectúa una regionalización de la cuenca. Para cada una de las regiones definidas se construye una serie temporal que describe la evolución de la lluvia en ese territorio. Sobre esas series regionales se realiza un análisis de tendencias.[EN]The aim of this work is the spatial-time characterisation of the rainfall evolution in the Ebro river basin. A database for a network of 29 meteorological stations throughout the basin with monthly rainfall information for the period 1916-2000 has been built. The corresponding seasonal and annual series were subjected to a homogenization process. A cluster analysis complemented with a trend analysis of annual rainfall allows us to classify the basin in eight homogeneous areas. Finally, regional time series describing the rainfall evolution in each defined region have been built and analysed to study their trend behaviour.Este trabajo ha sido financiado por la Oficina de Planificación Hidrológica de la Confederación Hidrográfica del Ebro (asistencia técnica 2001-PH-14-I)

Distribución de la sequía más severa en un intervalo de tiempo dado

Ponencia presentada en: III Congreso de la Asociación Española de Climatología “El agua y el clima”, celebrado en Palma de Mallorca del 16 al 19 de junio de 2002.[ES]El objetivo de este trabajo es caracterizar la máxima sequía que cabe esperar en un determinado periodo de tiempo. Para ello es necesario disponer de un modelo estocástico que describa el proceso de sequias (proponemos un proceso Poisson cluster para describir la ocurrencia y tres series de variables aleatorias, Longitud, Déficit e Intensidad Máxima, para describir la severidad) y desarrollar los resultados teóricos necesarios sobre la distribución del máximo en una muestra de tamaño Poisson.[EN]This work aims to characterize the largest drought event to occur in a given period of time. A Poisson cluster process is used to model drought occurrence and three series of random variables (Length, Deficit and Maximum Intensity) to describe their severity. Some theoretical results on the distribution of the maximum in a random Poisson size sample are developed for describing the largest drought events

Assessing space and time changes in daily maximum temperature in the Ebro basin (Spain) using model-based statistical tools

There is continuing interest in the investigation of change in temperature over space and time. For this analysis, we offer statistical tools to illuminate changes temporally, at desired temporal resolution, and spatially, using data generated from suitable space–time models. The proposed tools can be used with the output from any suitable model fitted to any set of spatially referenced time series data. The tools to assess space and time changes include spatial surfaces of probabilities and spatial extents for events defined by exceeding a threshold. The spatial surfaces capture the spatial variation in the probability or risk of an exceedance event, while the spatial extents capture the expected proportion of incidence of an event for a region of interest. This approach is used analyse the changes in daily maximum temperature in an inland Mediterranean region (NE of Spain) in the period 1956–2015. The area is very heterogeneous in orography and climate, including the central Ebro valley and part of the Pyrenees. We use a collection of daily temperature series obtained from simulation under a Bayesian daily temperature model fitted to 18 stations in that area. The results for the summer period show that, although there is an increasing risk in all the events used to quantify the effects of climate change, it is not spatially homogeneous, with the largest increase arising in the centre of the Ebro valley and the Eastern Pyrenees area. The risk of an increase in the average daily maximum temperature from 1966–1975 to 2006–2015 higher than 1°C is higher than 0.5 over all of the region, and close to 1 in the previous areas. The extent of daily maximum temperature higher than the reference mean has increased 3.5% per decade. The mean of the extent indicates that 95% of the area under study has suffered a positive increment of the average temperature, and almost 70% an increment higher than 1°C

Model-based tools for assessing space and time change in daily maximum temperature: an application to the Ebro basin in Spain

There is continuing interest in the investigation of change in temperature over space and time. We offer a set of tools to illuminate such change temporally, at desired temporal resolution, and spatially, according to region of interest, using data generated from suitable space-time models. These tools include predictive spatial probability surfaces and spatial extents for an event. Working with exceedance events around the center of the temperature distribution, the probability surfaces capture the spatial variation in the risk of an exceedance event, while the spatial extents capture the expected proportion of incidence of a given exceedance event for a region of interest. Importantly, the proposed tools can be used with the output from any suitable model fitted to any set of spatially referenced time series data. As an illustration, we employ a dataset from 1956 to 2015 collected at 18 stations over Arag\'{o}n in Spain, and a collection of daily maximum temperature series obtained from posterior predictive simulation of a Bayesian hierarchical daily temperature model. The results for the summer period show that although there is an increasing risk in all the events used to quantify the effects of climate change, it is not spatially homogeneous, with the largest increase arising in the center of Ebro valley and Eastern Pyrenees area. The risk of an increase of the average temperature between 1966-1975 and 2006-2015 higher than $1^\circ$C is higher than 0.5 all over the region, and close to 1 in the previous areas. The extent of daily temperature higher than the reference mean has increased 3.5% per decade. The mean of the extent indicates that 95% of the area under study has suffered a positive increment of the average temperature, and almost 70% higher than $1^{\circ}$C.Comment: 23 pages main manuscript and 7 pages supplemen

Spatial quantile autoregression for season within year daily maximum temperature data

Regression is the most widely used modeling tool in statistics. Quantile regression offers a strategy for enhancing the regression picture beyond customary mean regression. With time-series data, we move to quantile autoregression and, finally, with spatially referenced time series, we move to space-time quantile regression. Here, we are concerned with the spatiotemporal evolution of daily maximum temperature, particularly with regard to extreme heat. Our motivating data set is 60 years of daily summer maximum temperature data over Aragón in Spain. Hence, we work with time on two scales—days within summer season across years—collected at geocoded station locations. For a specified quantile, we fit a very flexible, mixed-effects autoregressive model, introducing four spatial processes. We work with asymmetric Laplace errors to take advantage of the available conditional Gaussian representation for these distributions. Further, while the autoregressive model yields conditional quantiles, we demonstrate how to extract marginal quantiles with the asymmetric Laplace specification. Thus, we are able to interpolate quantiles for any days within years across our study region

Bayesian joint quantile autoregression

Quantile regression continues to increase in usage, providing a useful alternative to customary mean regression. Primary implementation takes the form of so-called multiple quantile regression, creating a separate regression for each quantile of interest. However, recently, advances have been made in joint quantile regression, supplying a quantile function which avoids crossing of the regression across quantiles. Here, we turn to quantile autoregression (QAR), offering a fully Bayesian version. We extend the initial quantile regression work of Koenker and Xiao (2006) in the spirit of Tokdar and Kadane (2012). We offer a directly interpretable parametric model specification for QAR. Further, we offer a p-th order QAR(p) version, a multivariate QAR(1) version, and a spatial QAR(1) version. We illustrate with simulation as well as a temperature dataset collected in Arag\'on, Spain.Comment: 21 pages (+18 pages supplement), 8 figures (+15 figures supplement), 1 table (+6 tables supplement