For the given event date the closest N dynamical analogues are identified for each of two periods (past period and present period), over the given region. When available, ERA5 data is used. As ERA5 data is only available around a week behind real time, if it is not yet available data from the ECMWF forecast data is used instead. The analogues are identified from one of two variables: Mean Sea Level Pressure (MSL) or 500 hPa Geopotential Height (Z500). Only the season in which the event day occurs is assessed (DJF, MAM, JJA, or SON). Similar methods have been used in Thompson et al., 2024 and Thompson et al., preprint.
The methods used have evolved from those presented in Faranda et al., 2022.Analogues are identified using Euclidean distance. For this Euclidean distance between the event day and every day within the time period and event season, over the given region, is calculated. For each of the periods, we take the N days with the smallest Euclidean distances compared to the event as the analogue set.
We impose a gap of 5 days between the analogues, resulting in N unique events. If within the time period, the event itself is excluded from analogues.
Figure 1: The first figure shows the fields of the given event and composites of the analogue sets. The upper row shows the field from which the analogues are defined, with (a) the event field; (b) composite of the past period analogues; (c) composite of the present period analogues; and (d) the difference between present and past analogues. Rainfall, temperature, and wind[1] of the given date and analogue sets are presented in the rows below.
Figure 2: To assess analogue similarity between periods we calculate analogue quality, Q. Qevent is calculated for each analogue set as the inverse of the sum of the N Euclidean distances. Qanalogue is also calculated for each of the analogues, by identifying their N closest analogues within the same period and calculating the inverse sum of the Euclidean distances of those. Thus, we get a value of Qevent and a Qanalogue distribution (N values) for each period. Higher Qevent indicates that analogues are more similar to the event. Comparing Qevent for different periods allows an assessment of whether the atmospheric circulation enters the phase space of the event more or less frequently in each period — a higher Qevent indicates the pattern is more typical and lower more unusual.
Analogue quality is presented as violin plots showing the distribution of Qanalogue (violin) and Qevent (point) for the two periods, past in pink and present in green. Horizontal lines indicate the mean and range of the Qanalogue distributions.
Figure 3: Finally, timeseries of frequency of events of different similarity levels are produced. For this a similarity value is calculated for every day (within the event season) of every year between the start of the early period to the end of the later period. The Euclidean distance values (where a smaller value indicates a more similar field) are transformed into measure of similarity (where a larger value indicates greater similarity) using the equation: S = 1 – ED/EDmax (Where S is the new Similarity measure, ED is the Euclidean Distance of the each date (within the season) to the event date, and EDmax is the maximum Euclidean distance over the whole period assessed. Three thresholds are identified – the upper 5%, 10% and 20% of events in terms of similarity. The number of events above each of the thresholds for each year are plotted as three timeseries. The absolute values of quality and similarity are dependent on region size, and so not easily comparable between events.
Latitude/Longitude: It is recommended to use a region which is chosen based on the analogue field (SLP/Z500) of the event day (not a region based on the event impacts such as rainfall), ensuring the analogues are attempting to capture the key dynamical features of the event.
Period length: Longer time periods will give a better measure of long term changes in events, taking short time periods the results will be bias by interannual variability. Equal period length is recommended.N analogues to find: It is recommended to use N of ~number of years in the period, this will result in the analogues selected equating to the closest ∼1% of days. For less unusual event types higher N may be appropriate as there will be more events in the dataset with similar dynamical characteristics, the analogue quality plot can help determine an optimum value.
Choose Field (MSL/Z500): For slow-moving, persistent, weather systems (such as cut-off low pressure systems over Europe) it is recommended that Z500 be used. For faster moving systems (such as extratropical cyclones) SLP is more appropriate.
Thompson, V., Coumou, D., Galfi, V.M., Happé, T., Kew, S., Pinto, I., Philip, S., de Vries, H. and van der Wiel, K., 2024. Changing dynamics of Western European summertime cut-off lows: A case study of the July 2021 flood event. Atmospheric Science Letters, 25(10), p.e1260.
Thompson, V., Philip, S.Y., Pinto, I. and Kew, S.F., 2024. The influence of the Atlantic Multidecadal Variability on Storm Babet-like events. preprint in EGUsphere, pp.1-15.
Faranda, D., Bourdin, S., Ginesta, M., Krouma, M., Messori, G., Noyelle, R., Pons, F., and Yiou, P., 2022. A climate-change attribution retrospective of some impactful weather extremes of 2021, Weather Clim. Dynam., 3, pp.1311-1340
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[1] Wind is not included if the data is taken from the ECWMF forecast (for near real time assessments).