Downward counterfactual insights into weather extremes
Authors: Woo Gordon 
Published: March 2022

&lt;p&gt;There are many regions where the duration of reliable scientific observations of key weather hazard variables, such as rainfall and wind speed, is of the order of just a few decades.&amp;#160; This length of dataset is often inadequate for the application of extreme value theory to rare events. Theoretical analysis of chaotic dynamical systems shows that extremes should be distributed according to the classical Pareto distribution, with explicit expressions for the scaling and shape parameter[1]. Discrepant results may be interpreted as indicating the need for a longer data time series.&lt;/p&gt;&lt;p&gt;Physicists acknowledge that history is just one realisation of what could have happened. One way of supplementing a brief duration observational dataset is to generate an ensemble of alternative realisations of history. Of special practical interest within this counterfactual ensemble are downward counterfactuals - where the outcome turned for the worse.&amp;#160; Extreme hazard events often cause surprise, which reflects an underlying degree of outcome cognitive bias. Downward counterfactual is a term originating in the cognitive psychological literature, which has been applied by Woo[2] to the search for extreme hazard events.&amp;#160; Most human counterfactual thoughts are upward, focusing on risk mitigation or prevention, rather than downward, focusing on potential rare Black Swan events.&amp;#160;&lt;/p&gt;&lt;p&gt;The insight gained from downward counterfactual analysis is illustrated with the example of rainfall and flooding in Cumbria, Northwest England.&amp;#160; Daily rainfall records at Honister Pass, Cumbria, from 1970 to 2004, were statistically analysed to estimate the return period for the rainfall of 301.4mm oberved on 20 November 2009.&amp;#160; This return period was estimated to be 396 years[3].&amp;#160; But six years later, on 5 December 2015, this was substantially exceeded by 341.4mm rainfall.&lt;/p&gt;&lt;p&gt;In 2009, there was only a moderate El Ni&amp;#328;o.&amp;#160; Counterfactually, there might have been a strong El Ni&amp;#328;o.&amp;#160; Indeed, in 2015 there was a very strong El Ni&amp;#328;o. A downward counterfactual analysis of the heavy rainfall on 20 November 2009 would have included the possibility of a very strong El Ni&amp;#328;o.&amp;#160; This is one of a number of exacerbating dynamical meteorological factors that might have elevated the rainfall.&lt;/p&gt;&lt;p&gt;Where the data duration is much shorter than the return period of extreme events, a downward counterfactual stochastic simulation of factors raising the hazard will provide important additional insight for geophysical hazard assessment.&lt;/p&gt;&lt;p&gt;&amp;#160;&lt;/p&gt;&lt;div&gt;&lt;br&gt;&lt;div&gt;
&lt;p&gt;[1] Lucarini V., Faranda D., Wouters J., Kuna T. (2014) Towards a general theory of extremes for observables of chaotic dynamical systems. J.Stat.Phys., 154, 723-750.&lt;/p&gt;
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&lt;p&gt;[2] Woo G. (2019) Downward counterfactual search for extreme events.&amp;#160; Front. Earth. Sci. doi:10.3389/feart.2019.00340.&lt;/p&gt;
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&lt;p&gt;[3] Stewart L., Morris D., Jones D., Spencer P. (2010) Extreme rainfall in Cumbria, November 2009 &amp;#8211; an assessment of storm rarity. BHS Third Int. Symp., Newcastle.&lt;/p&gt;
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