Kamil Feridun Turkman

Spatial and temporal extremes of wildfire sizes in Portugal (1984–2004)

Spatial and temporal patterns of large fire (>100 ha) incidence in Portugal over the period 1984–2004 were modeled using extreme value statistics, namely the Peaks Over Threshold approach, which uses the Generalized Pareto Distribution (GPD) as a model. The original dataset includes all fires larger than 5 ha (30 616 fires) that were observed in Portugal during the study period, mapped from Landsat satellite imagery. The country was divided into eight regions, considered internally homogeneous from the perspective of their fire regimes and respective environmental correlates. The temporal analysis showed that there does not appear to be any trend in the incidence of very large fires, but revealed a cyclical behavior in the values of the GPD shape parameter, with a period in the range of 3 to 5 years. Spatial analysis highlighted strong regional differences in the incidence of large fires, and allowed the calculation of return levels for a range of fire sizes. This analysis was affected by the presence of a few outlying observations, which may correspond to clusters of contiguous fire scars, resulting in artificially large burned areas. We discuss some of the implications of our findings in terms of consequences for fire management aimed at preventing the occurrence of extremely large fires, and present ideas for extending the present study.

Spatial extremes of wildfire sizes: Bayesian hierarchical models for extremes

In Portugal, due to the combination of climatological and ecological factors, large wildfires are a constant threat and due to their economic impact, a big policy issue. In order to organize efficient fire fighting capacity and resource management, correct quantification of the risk of large wildfires are needed. In this paper, we quantify the regional risk of large wildfire sizes, by fitting a Generalized Pareto distribution to excesses over a suitably chosen high threshold. Spatio-temporal variations are introduced into the model through model parameters with suitably chosen link functions. The inference on these models are carried using Bayesian Hierarchical Models and Markov chain Monte Carlo methods.

A predictive approach to tail probability estimation

One of the issues contributing to the success of any extreme value modeling is the choice of the number of upper order statistics used for inference, or equivalently, the selection of an appropriate threshold. In this paper we propose a Bayesian predictive approach to the peaks over threshold method with the purpose of estimating extreme quantiles beyond the range of the data. In the peaks over threshold (POT) method, we assume that the threshold identifies a model with a specified prior probability, from a set of possible models. For each model, the predictive distribution of a future excess over the corresponding threshold is computed, as well as a conditional estimate for the corresponding tail probability. The unconditional tail probability for a given future extreme observation from the unknown distribution is then obtained as an average of the conditional tail estimates with weights given by the posterior probability of each model.

Periodic Autoregressive Model Identification Using Genetic Algorithms

Periodic autoregressive (PAR) models extend the classical autoregressive models by allowing the parameters to vary with seasons. Selecting PAR time‐series models can be computationally expensive, and the results are not always satisfactory. In this article, we propose a new automatic procedure to the model selection problem by using the genetic algorithm. The Bayesian information criterion is used as a tool to identify the order of the PAR model. The success of the proposed procedure is illustrated in a small simulation study, and an application with monthly data is presented.

Extremes of bilinear time series models

The class of bilinear time series models is an obvious generalization of linear ARMA models and has found many applications in time series modeling. It is known that the sample paths of even the simplest bilinear process may have sudden bursts of large negative and positive values that vary in form and amplitude depending on the model parameters. Yet, little is known about the extremal properties of this class. In this paper, we look at the extremal properties of bilinear processes and explain how model parameters affect the extremal behavior.

Calibration of the Fire Weather Index over Mediterranean Europe based on fire activity retrieved from MSG satellite imagery

Here we present a procedure that allows the operational generation of daily maps of fire danger over Mediterranean Europe. These are based on integrated use of vegetation cover maps, weather data and fire activity as detected by remote sensing from space. The study covers the period of July–August 2007 to 2009. It is demonstrated that statistical models based on two-parameter generalised Pareto (GP) distributions adequately fit the observed samples of fire duration and that these models are significantly improved when the Fire Weather Index (FWI), which rates fire danger, is integrated as a covariate of scale parameters of GP distributions. Probabilities of fire duration exceeding specified thresholds are then used to calibrate FWI leading to the definition of five classes of fire danger. Fire duration is estimated on the basis of 15-min data provided by Meteosat Second Generation (MSG) satellites and corresponds to the total number of hours in which fire activity is detected in a single MSG pixel during one day. Considering all observed fire events with duration above 1h, the relative number of events steeply increases with classes of increasing fire danger and no fire activity was recorded in the class of low danger. Defined classes of fire danger provide useful information for wildfire management and are based on the Fire Risk Mapping product that is being disseminated on a daily basis by the EUMETSAT Satellite Application Facility on Land Surface Analysis.

Nonlinear Time Series Models

Assume that for \(t \in \mathbb{Z}\), (Z t ) and \((Z_{t}^{{\ast}})\) are respectively uncorrelated and independent sequences of r.v’s having identical marginal distribution F(⋅ ), with zero mean and variance \(\sigma _{Z}^{2} <\infty\).

Optimal alarm systems for autoregressive processes

Abstract Let { X n } be a stationary sequence. The optimal alarm policy for detecting future upcrossings of the sequence is studied in a Bayesian predictive context and particular calculations are carried for an autoregressive process of order 1.

Generating Annual Fire Risk Maps Using Bayesian Hierarchical Models

Vegetation fires are an important environmental and socioeconomic problem, and large budgets are spent in fire prevention and fire fighting. Detailed knowledge of spatiotemporal patterns of fire occurrence is required for effective and efficient fire management, and annual fire risk maps can be an important tool to support strategic decisions relating to location-allocation of equipment and human resources. Here, we define risk of fire in the narrow sense as the probability of its occurrence, without addressing the loss component. We propose and evaluate two alternative approaches to the development of annual fire risk maps, using an atlas of annual burned area maps of Portugal (1975–2009), derived from the classification of satellite imagery, and a set of environmental maps representing vegetation, climatic, and topographic covariates. We look at current approaches for producing annual fire risk maps, and suggest improvements by incorporating the strong spatial and temporal dependence that exists in the data. This is accomplished using two different modeling strategies. The first strategy consists of modeling interarrival times between fires using a discrete version of the Weibull model. The second strategy consists of modeling annual fire occurrences using a first-order nonhomogeneous Markov model. These two distinct strategies accommodate different possibilities to introduce time-dependent covariates and make complementary probabilistic statements.

Extremes of Nonlinear Time Series

We have seen in Sect. 2.1.4 that nonlinear processes, due to their dependence on initial conditions, often magnify error causing unstable behavior. Even when stationary solutions exist, this noise magnification and dependence on initial conditions reflects on the tails of the stationary distribution, as well as on how large values cluster.