Alexa A. Sochaniwsky and Paul D. McNicholas’s contribution to the Discussion of ‘Inference for extreme spatial temperature events in a changing climate with application to Ireland’ by Healy et al.

We congratulate the authors on an interesting and timely contribution. In addition to being a valuable contribution to an important conversation, the use of the generalized Pareto distribution (GPD) in this manner sparks ideas about extensions. In addition to a couple of straightforward questions, our comments focus on a possible extension of this work using hidden Markov models (HMMs) to identify extreme spatial temperature events for climate data analysis. The notion of an ‘extreme temperature’, whilst important, is both subjective and location specific. The United Nations gives some examples of how one may characterize an extreme temperature.1 Can the authors please clarify what exactly they consider an extreme temperature in Ireland during the period in question and to what extent, if any, the threshold varies over time? Presumably, the station data would allow for more significant discovery when used altogether rather than using individual weather station data alone. If so, a longitudinal HMM with a GPD may be effective for the identification of extreme temperature events. HMMs with a GPD have been developed for various time series datasets, including work by Kordnoori et al. (2019), Pender et al. (2016), and Deidda (2010). In fact, Pender et al. (2016) and Deidda (2010) have developed HMMs to capture extreme streamflow and rainfall events, respectively. Gaussian longitudinal HMMs have been developed (e.g. Maruotti, 2011) and other advances have been made but, as far as we know, a longitudinal HMM with the GPD has not yet been developed. Additionally, findings from this work could inform the degree of parameter pooling and parameter initializations in such a model. Regarding the latter, occurrence rates of high threshold exceedances in temperature could inform the initialization of the transition matrix and the initial state probability distribution. Regarding pooling, the number of parameters that need to be estimated in a longitudinal HMM varies vastly depending on subject dependence or, in the context of these data, the spatial dependence. Complete independence or dependence of the weather stations would most likely be an unreasonable assumption for these data; however, partial pooling, where weather stations share parameter estimates—potentially, by region—might balance error and accuracy with computational cost. Conflicts of interest: none declared. Not applicable. The author replied later in writing as follows:

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