Authors’ reply to the Discussion of ‘Inference for extreme spatial temperature events in a changing climate with application to Ireland’
Year: 2024
Type: article
Abstract: Firstly, we would like to sincerely thank all the discussants, particularly the proposer and seconder, for their interest in our paper, the variety of questions they have asked, and their suggestions for enhancements to the methods we use. We are especially pleased that the points that the discussants raise are across the entire spectrum of the paper. Below we separate our response into the main themes that were raised, specifically, fundamental modelling of extremes, the use of climate models, the analysis of missing data, marginal modelling choices, dependence modelling choices, accounting for uncertainty, and potential future extensions. We made the explicit decision for the paper to focus exclusively on the spatial behaviour of temperature data over Ireland and how this changed over time. We achieved this by working ostensibly with parametric models for independent spatial random fields and accounting for the effects of short-term, weather-driven temporal dependence using a novel block bootstrapping scheme. Clearly, a number of potential questions involving dependence within individual extreme events, the effect of clustering of events over time, and any form of accumulation of past behaviour of the process on future events are therefore ruled out in our strategy. We are, therefore, pleased that Opitz’s discussion contribution presents a variety of examples from agriculture, ecology, and epidemiology and that we could add examples of storm sequencing effects on beach management for coastal flood defence or fluvial flooding, for which the temporal behaviour of the process over a much longer time-scale than that of individual extreme events is critical for applications. Even within the context of independent and identically distributed replicates of a spatial process, Sochaniwsky et al. raise fundamental questions about what an extreme event is. The separation of natural hazards from the subsequent risk to society is key to our definition of an extreme event. Here, the natural hazard is simply the spatial temperature field on a hot day in summer somewhere in Ireland, while the risk is the combination of the natural hazard and the impact caused by exposure to that hazard (e.g. heat stress, loss of crops, etc.). Our focus is on modelling the natural hazard temperature exclusively. So we do not account for how people, agriculture etc. across the world have different capacities to withstand the same temperature. To answer the point of Sochaniwsky et al. more directly, at each site it is natural to describe an extreme as an exceedance of a high quantile (the threshold) by the natural hazard at that location, with the quantile used being selected objectively so that exceedances are well modelled by a generalized Pareto distribution (GPD). We additionally must account for the spatial continuity of the natural hazard. As we do not want to restrict the type of extreme spatial event being modelled, we describe a methodology to statistically model spatial fields which exceed the marginal threshold at least in one site in the region of interest. By design, for any pertinent question about temperature hazards, the probability associated with that event can be derived in a self-consistent way from our single statistical spatial extreme value model. In this way, we avoid the need for different modelling assumptions for any extreme event of interest and need not be concerned with any physical inconsistencies such an approach might produce. Our focus was to derive a method to produce replicate simulations of potential extreme spatial fields in order to estimate probabilistic properties of any measure of interest in these events, whilst accounting for all marginal and dependence parameters’ uncertainties. As highlighted by Huser, it is possible to use simulations of an extremal process to derive results about hot spots of the process, which are particularly helpful for identifying where the hazard is at its most extreme for non-stationary processes (Hazra & Huser, 2021). Another useful spatial hazard measure which helps quantify how concentrated a spatial extreme event is, at different levels of extremity, is the severity area frequency curve used by Winter et al. (2016). The flexibility in our approach means that all these measures of extreme spatial events can be derived from our framework. Our view is that one important contribution our paper makes is tackling the issue of how best to present the evidence of, and the uncertainty in, the spatial characteristics of natural hazards to policymakers. Here, the role of the statistician is vital as it requires a critical combination of simplicity of presentation and for the complexity of the various types of extreme events to be captured. Hence, we are particularly pleased that Smith asks about what the paper provides for policymakers. What is certainly true is that although policymakers have a good handle on extremes of univariate natural hazards, they struggle to account for dependence in their thinking about multivariate or spatial dependence and its implications for risk assessment or even its effect on the frequency of certain types of spatial events. A particular example is illustrated by Figure 10 in Tawn et al. (2018), where the estimate of the probability of a 1 in 100-year event at a site occurring for at least one site (in a river network over England and Wales) in a year is shown to be 0.9, whereas the policymakers had expected the answer to be much closer to 0.01—the case of perfect dependence. So to develop a framework which carries over the marginal and dependence estimation uncertainties into such probability estimates and provide a single framework under which probabilities of extreme spatial events can be estimated self-consistently we see it as a major step to help policy makers make reliable and coherent decisions in a critical aspect of risk assessment that has so far been much understudied. In answer to Smith’s query about the contribution of the paper more generally, we hope it will be seen as a call for a much stronger combination of skill sets from the climate science and statistical communities. Realistically neither community can sufficiently address issues of natural hazard modelling without taking a collaborative approach which bridges the efforts and knowledge of the two communities. Clearly, there is much to be done in this field, with potential lines of evolution of our proposed methods having been already raised in the discussion. We are excited if our study has raised more questions than it has answered and so it is a trigger point for new collaborative research on this important topic of spatial extreme events. Our paper relies on climate model output to capture the spatial patterns of the temperature field. However, our choice of a single climate model and our use of it as a covariate has yielded some useful suggestions from the discussants. Similarly, the use of Numerical Weather Prediction Models (NWP), which are constantly ‘nudged’ by observations to match the geophysical model state of the weather state, was also raised. Common themes included how our approach might transfer to other regions or to future time periods; the use of (statistical) down-scaling to obtain higher resolution records; and the construction of the covariates themselves. Porcu et al. point out that many regions in the world do not have an observational record of similar quantity or quality to Ireland, and so our approach may not translate. This is of course correct, but we do point readers to the considerable efforts being made by NOAA and the to and So in our approach may be much more many regions which have observations also have climate model with the we have means to A useful future would be to the of where our approach We point the discussants to et al. to a discussion on the of observational et al. that our approach has much in with we that this is far more to any approach that observations and models to provide on However, in to we do not on the spatial dependence of the climate model Porcu et al. that our approach is critical of climate models, and we other methods to down-scaling for extremes, such as from We that is different from the climate model we use models are constantly to with as is this aspect that makes our approach the two of are the of our approach being used for in time, that we have considerable in the climate model at extreme This was not an approach we in our paper, as we within the time of the We that it would be to use future from a climate using our observational and produce future estimates of of the discussants about our of missing that in our observational data Common themes included the potential of missing the of the missing data, and the use of we to using the to help with event to help the we with missing data from our study of observational data, extremal spatial and to extreme temperature events. 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behaviour of the of the distribution could to in the which was the region of most for and Tawn although there is an number of parametric models, we were not that a single model form would be over the of Ireland, and such an would to modelling for such that the of covariates in the model must be across the which may not be However, we are by the and to evidence of the of the models in there are potential issues with our quantile where we avoid the by the at with et al. an by using quantile modelling for the entire would be to see if this approach made in our questions about the of into the particularly on of about the at each site of the marginal in different fields raise similar at the least to the on the in any that the has a that the this can be in by the for the is as in and one can the a of the and of the However, it is more to such knowledge the is In our have a knowledge about the of high of the and this is as in and Tawn We are for the that provides on and how they are to to 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a on the and with the the more evidence and with for the and to our not account for or associated spatial but the and their spatial that there is a need for some spatial to be for in the climate and data modelling of the in these coastal The are and so we do not that from the climate model to would have made any to our However, we see that there is potential for such an as by to be important modelling more regions than of over Ireland with associated with a of a over of are with the evidence from the other points the not being at a of In univariate extreme value there are two to and model extreme the block using the extreme value distribution and the threshold exceedance using the is helpful to see that these methods can be derived from a process as shown by Smith the of the two Smith questions we would be using the of the block for the as the are independent of the threshold choice a high threshold is selected for the to be the model for of the in our choice where the with the threshold We were to our on a combination of the approach of and which that with our approach the threshold exceedance can be estimated from the threshold and the evidence in and Tawn where it is shown that the choice of the block to the of the block has as a effect on the with the choice being to to our Porcu et al. raise a query about the of our of more temporal in extreme than and in particular that we do not provide a analysis of and distribution We are in our as the that extremes than the has been well in the and is in we are not modelling the data for a in the but modelling of the and of the distribution as a and capture as well as the extremes, this was to be to the threshold exceedance and the The results we about in the 100-year all these temporal the value of and their associated uncertainties. Our modelling of the spatial dependence of extreme temperature events processes the estimation of probabilities of a of of spatial temperature the paper a of to the assumptions we a number of discussants have about our which to the univariate on which to an process, the of the process, and on of our spatial of the process of the points out that and two of the process, the form that we use in of the paper, and one on the which the to over but not the The key the two is the of what the of extreme events. the approach a focus on a of events of interest and a physical the modelling our approach is with the of the on modelling and in multivariate extremes, of dependence and it a dependence threshold for a single presents some on our observational and climate model data, issues of the of the In that of processes requires the process to a as which in the of the paper to the being the process can be than its marginal quantile at site in the region that the process at one site is than its marginal as to In the process is to be independent In Figure of the paper, we evidence that a extremal probability over different to be a for the data for and climate model our to Pareto data, properties of these data, analysis some on the evidence for dependence. Figure 1 that for the observational data in the and regions of Ireland regions 1 and dependence is not a the of estimates to as the other regions in Figure the estimates are not to the estimates to be as the is will be by missing data as In these where there is using to separate dependence and is of dependence are to be more helpful in in such see et al. for a discussion of this in the context and and Tawn for measures of that are higher et al. that it may be possible to more key from the climate model data in our spatial the paper, we the of the climate model data to capture physical properties of the data and any analysis of data to that we are to see that Figure similar for the climate model data, has already the analysis we would have done to the evidence from Figure In the results that it is the two regions 1 and that to a from as it the for all regions for where the that of and form a of these there is some evidence that our modelling in the paper could be to for of Ireland to be which that models of the form and flexibility of and Tawn are We are not that for some regions of Ireland to be while the is will make much to our spatial hazard but we to future research which the to this The discussion that the extremal spatial dependence over Ireland is a not our modelling choice of an process process with and Porcu et al. also raise the issue of by our choice of the different using a of using the approach of and or a form of parametric we such are we are not they will have a effect on our we have about the of climate models to capture the of the spatial of the observational data, we to the physical properties that the of spatial extremal dependence. we it is best to the climate model data for evidence of other than or coastal which may these the in of these data and their of missing data or spatial in data if evidence is present from such an analysis is it in the observational In of the we a possible way to model dependence which in a more way than simply with we an which also from the which to be the to dependence over Ireland, the for regions 1 and by other need to be uncertainty in extremes was a that in a number of useful suggestions to focus on the role of models in our data the they with to the data, or the uncertainty of that they might A was the use of particularly that of Porcu et al. on the resolution the climate model data 10 and our This is of course of the spatial et We we have this by using the data as taking the point to each in each generally, we that climate model data are not even at a single being more using However, this is far more in other than with being the A number of discussants Huser, and et raised points about the use of of climate models, many of which are and point to of future We used one model combination and so have not to quantify what might had we used models that might on the temperature field over Ireland, as Smith which climate models capture extreme climate behaviour would be of not for our model but much more are to be made in of that may for on a of such as climate location, etc. A possible point for such a data might the & raised the point that we use the data as and so are the uncertainty in these This could be included in our model using an with a parametric uncertainty these could be used to a uncertainty for use as the in However, it is how much it would make to our output the of data we the uncertainty in and the of the temperature field. We that many to have the of our analysis (e.g. the many of these also uncertainty and et al. point to methods for the uncertainty our bootstrapping The most is that of where a model would capture and spatial patterns in a model. We on such an approach on in our but the of such models using far an for future We the paper by particularly as it for the We how this would match with our that temperature data had that were than the However, their is and so points to an of future the most of our approach is its to the analysis of independent spatial random the temporal dependence within events and the effects of of the spatial process on the risk and and even on the of the events. This was we were explicit about in the of our paper but is an area of much for future we were not to see a of from across the discussants, for of the to in this We certainly see our as a a analysis of extremes, which is a area for et & and an focus on events and event sequencing from the statistical extreme value We with Opitz’s that it important to how temporal dependence of weather extremes is into especially the of and extreme and we with Porcu et al. this more is in how is modelled in a non-stationary and raise some important points about using models to account for climate such as or in the or using covariates for and asks about the effects of and to weather Porcu et al. questions climate may be useful are, of covariates in the physical which to extreme weather events. The covariates on the physical Ireland, the covariates are the of a and the associated of heat and of from the by and Our view is that for our analysis at such covariates would to a in modelling to temporal dependence and could be and it issues with complexity as to of the potential for in by such physical our from analysis was that even taking the as a covariate was not particularly helpful for our for Ireland as it was to the extreme events of interest. The covariate or which and and Porcu et al. raise can the marginal a site the covariates or and the spatial dependence The paper by et al. the of this type of approach with fields with different and The that the use of climate models a covariate to be such covariate from observational data at a number of is not Even if are this presents two Firstly, to derive results there is a need to over the & which requires the estimation of the and how the properties of each and the probabilities each under climate and more is the question of how best to this knowledge into about spatial hazards for policymakers. We do that having a coherent modelling for with in extreme value is an important and missing from the extreme value which we hope will be As in the of the of our paper, in the context of climate extremes, we do that from climate models will a in this We thank et al. for our to the paper of et al. which results from the of model output to observational data within a We that this paper is tackling a issue to However, we see of that to our as in that case our climate model data has not been using the same weather events as for the data, so other than and the processes are independent of each their focus is on univariate with of the spatial dependence of the processes and use of a process to help in the is a we could our we have used simply the site on the climate model to as a covariate for but it may be more to use of these A in our approach to the in et al. is that they have a parametric marginal distribution (the which for the we on in of this in to point about models, we have about using for our et al. about using an approach in and to derive the distribution of the in a could be helpful for our of the probability of In that paper, they use a of for the distribution of the over a region of a random field. are two of this approach which we do not is best to our Firstly, using is most for as in and and we have value in the distribution of the over as our climate model is already on a to the spatial in the temperature process over to derive of the process at a than this using statistical methods than any physical properties in the We thank for some helpful as an to the area of and their to extreme events which we hope to be to like are new to this Clearly, it is to evidence the value of these to of extreme value and climate science in climate We struggle to see that any can provide at levels that are more extreme than any event in new climate than from some combination of extreme value methods in with of climate as the climate models capture physical and can future the of the data and extreme value methods have a of a method for will and we to future
Language: English
Subfield: Global and Planetary Change
Field: Environmental Science
Domain: Physical Sciences
SDG: Climate action
Open Access status: hybrid
Estimated APC paid: $3,518
OpenAlex ID: W4405318633