Jesús Abaurrea

Drought Analysis Based on a Marked Cluster Poisson Model

Abstract This paper presents an operational definition of drought events based on an “excess over threshold” approach applied on rainfall series and develops a stochastic model for describing droughts defined in that way. The model consists of a Poisson cluster process to represent drought occurrence and a marked process composed of three series of random variables (duration, deficit, and maximum intensity) to describe drought severity; it is theoretically justified, and adequate procedures to check its validity are suggested and applied on five Spanish rainfall series. Useful parameters for the design and planning of water resource systems, together with their confidence intervals, are estimated from the model.

Risk measures for events with a stochastic duration: an application to drought analysis

Droughts, as many climatic and environmental phenomena, are events with a random duration. In the monitoring and risk management of this type of phenomena, it is important the development of measures of the risk that an ongoing event ends. This work develops a risk measure conditional on the current state of the event, that can be easily updated in real time. The measure is based on the hazard function of the duration of an event, that is modeled as a parametric function of covariates describing the current state of the process. The use of (time-dependent) internal covariates is often required to describe that state, and maximum likelihood methods cannot be used to estimate the model. Therefore, an approach based on partial likelihood functions that permit the inclusion of both external and internal covariates is suggested. This approach is very general but it has the drawback of requiring some programming to be implemented. However, it is proved that for durations with a geometric distribution, an equivalent and easily implemented approach based on generalized linear models can be used to estimate the hazard function. This methodology is applied to develop a risk measure in drought analysis. The approach is exemplified using the drought series from a Spanish location (Huesca) and internal covariates derived from the rainfall series. The whole modeling process is thoroughly described, including the covariate selection procedure and some new validation tools.

Modeling and projecting the occurrence of bivariate extreme heat events using a non-homogeneous common Poisson shock process

A joint model is proposed for analyzing and predicting the occurrence of extreme heat events in two temperature series, these being daily maximum and minimum temperatures. Extreme heat events are defined using a threshold approach and the suggested model, a non-homogeneous common Poisson shock process, accounts for the mutual dependence between the extreme events in the two series. This model is used to study the time evolution of the occurrence of extreme events and its relationship with temperature predictors. A wide range of tools for validating the model is provided, including influence analysis. The main application of this model is to obtain medium-term local projections of the occurrence of extreme heat events in a climate change scenario. Future temperature trajectories from general circulation models, conveniently downscaled, are used as predictors of the model. These trajectories show a generalized increase in temperatures, which may lead to extrapolation errors when the model is used to obtain projections. Various solutions for dealing with this problem are suggested. The results of the fitted model for the temperature series in Barcelona in 1951–2005 and future projections of extreme heat events for the period 2031–2060 are discussed, using three global circulation model trajectories under the SRES A1B scenario.

A bootstrap test of independence between three temporal nonhomogeneous Poisson processes and its application to heat wave modeling

The main contribution of this work is a bootstrap test to check the independence between temporal nonhomogeneous Poisson processes. The test statistic is based on the close point relation, which adapts the crossed nearest neighbour distance ideas of spatial point processes to the case of nonhomogeneous time point processes. Since it is complicated to obtain the probability distribution of the test statistic under the null hypothesis and the parameters of the processes are usually unknown, the

Dynamic Regression Model for Hourly River Level Forecasting Under Risk Situations: an Application to the Ebro River

p

Trend analysis of water quality series based on regression models with correlated errors

p value is obtained using a parametric bootstrap approach. A simulation study shows that the size of the test is close to the nominal one. The power is analyzed considering three approaches for generating dependent nonhomogeneous processes and different levels of dependence, and satisfactory results are obtained in all cases. Although the test was initially intended for Poisson processes, it can be applied to any type of point process in one dimension which can be simulated. This test is a valuable tool in the validation analysis of common Poisson shock models. For the bivariate case, the process can be decomposed into three independent Poisson processes, and the assumption of independence between them has to be checked. As an application, the joint modeling of the occurrence process of extreme heat events in daily maximum and minimum temperatures is described.

Modeling and forecasting extreme hot events in the central Ebro valley, a continental-Mediterranean area

Rainfall series and their corresponding extreme event processes are analysed in order to study the evolution of their mean value and variability. Two statistical approaches are used, one based on the analysis of the entire time series and the other on modelling the extreme event process. The performance of two precipitation indices, SPI and percentiles, has been compared using long, medium and short time scales. We present the results corresponding to Huesca and Murcia rainfall records, two markedly different locations in Spain.

Drought analysis based on a cluster Poisson model: distribution of the most severe drought

This work proposes a new statistical modelling approach to forecast the hourly river level at a gauging station, under potential flood risk situations and over a medium-term prediction horizon (around three days). For that aim we introduce a new model, the switching regression model with ARMA errors, which takes into account the serial correlation structure of the hourly level series, and the changing time delay between them. A whole modelling approach is developed, including a two-step estimation, which improves the medium-term prediction performance of the model, and uncertainty measures of the predictions. The proposed model not only provides predictions for longer periods than other statistical models, but also helps to understand the physics of the river, by characterizing the relationship between the river level in a gauging station and its influential factors. This approach is applied to forecast the Ebro River level at Zaragoza (Spain), using as input the series at Tudela. The approach has shown to be useful and the resulting model provides satisfactory hourly predictions, which can be fast and easily updated, together with their confidence intervals. The fitted model outperforms the predictions from other statistical and numerical models, specially in long prediction horizons.