Calibration of the Bulk and Extremes of Spatial Data

Abstract

In an environmental framework, extreme values of certain spatio-temporal processes, for example wind speeds, are the main cause of severe damage in property, such as electrical networks, transport and agricultural infrastructures. Typically, as is the case of wind speeds, data are available at few stations with many missing observations and consequently simulators are often used to augment information. However, simulated data often mismatch observed data, particularly at tails, therefore calibrating and bringing it in line with observed data may offer practitioners more reliable and richer data sources. In this work we will concentrate on calibrating the bulk and the extremes of data, simultaneously, avoiding methods that rely on the choice of a threshold. We propose and describe in detail a specific conditional quantile matching calibration method and exemplify it with wind speed data. We also briefly suggest how calibration should be extended specifically to data coming from the tails of simulated and observed data, using asymptotic models and methods suggested by extreme value theory.