Using UNSEEN approach to attribute regional UK winter rainfall extremes

Three out of the five highest daily winter rainfall totals on record over Northern England have occurred from 2015 onwards. Heavy rainfall events in the winters of 2013–2014, 2015–2016 and 2019–2020 led to more than 2.8‐billion‐pounds of insurance losses from flooding in the UK. Has the frequency of these events been influenced by human‐induced climate change? Winter rainfall in the UK is extremely variable year‐to‐year, which makes the attribution of rainfall extremes particularly challenging. To tackle this problem, we introduce an UNprecedented Simulated Extreme Ensemble (UNSEEN) approach for the attribution of such extremes, thereby increasing the data available, and apply this approach to five recent flooding events on a regional scale. Using this method, for all five events we found a significant climate signal in the extreme regional rainfall totals immediately preceding the flooding. Results were fairly similar for each—with the events being found to become from 1.4 to 2.6 times more likely. An alternative attribution method that uses a different model with substantially less data did not find significant increases, reinforcing the need for very large amounts of data to detect significant changes in extreme rainfall against a noisy background of natural variability. We also examine how extreme rainfall is changing more broadly across English regions in winter, finding that 1‐in‐10 to 1‐in‐90‐year winter rainfall totals have changed significantly in Northern England. The high volume of data using UNSEEN has enabled us to examine the dynamics of these events, showing that daily extremes in winter are likely to have increased across all the circulation patterns responsible for high rainfall in English regions.

et al., 2022), which correlates with higher rainfall for most parts of the UK, especially the North-West (West et al., 2019).Northern England saw the highest winter daily rainfall total on record in February 2020, with three out of the top five winter totals occurring from 2015 onwards (Hollis et al., 2019).Rainfall extremes worldwide are increasing in intensity on hourly to daily timescales because of climate change (Fowler et al., 2021).The rates of intensification of rainfall extremes for timescales greater than 1 day are generally consistent with the increase projected by the Clausius-Clapeyron relation, which implies that each degree of warming at the Earth's surface, allows the atmosphere to hold around 7% more moisture (Fowler et al., 2021).The thermodynamic effect from the Clausius-Clapeyron relation may not be the only factor changing rainfall extremes.Kahraman et al. (2021) finds that climate change may make storms over Europe slower moving, allowing for more precipitation to fall over a given region in a shorter period of time.Dynamic changes, such as circulation changes over winter, may lead to a higher frequency of westerly and cyclonic weather patterns over the UK in the future (Pope et al., 2022).Schaller et al. (2016) similarly finds an attributable atmospheric circulation signal, with it responsible for 1/3rd of the anthropogenic increase in a 1-in-100-year January precipitation event for the UK.
Extreme wet days annually in the UK have seen a 17% increase in intensity when comparing 2008-2017 with the 1961-1990 baseline period (Kendon et al., 2018, suppl. 2).Observations for UK winters also show that mean precipitation between 2011 and 2020 was 19% higher on average compared to the same baseline period (Kendon et al., 2021).This follows a number of very wet winters between 2013-2014 and 2019-2020 over the UK.The Winter of 2013-2014 brought severe flooding to parts of England through a succession of low-pressure storms from December 5th to January the 3rd, with the storm on the 23rd-24th December bringing very extreme rainfall totals, causing severe inland flooding to Southern England (Kendon, 2014).Flooding in England and Wales during that winter resulted in £1.3 billion in damages for England and Wales, with over 10,000 properties flooded (Chatterton et al., 2016).
December of 2015 was also extremely wet for the UK, with Storm Desmond in early December producing large rainfall totals, especially in Cumbria where over 6500 homes and business were flooded as well as significant damage to transport infrastructure (HD Research, 2018;Kendon, 2015).Current flood defences are estimated to have protected 20,000 homes from flooding; however, December 2015 alone still saw over 16,000 properties flooded in England and overall insurance losses in excess of 1.3 billion (Marsh et al., 2016).Storm Eva arriving in the UK on Christmas Eve brought more extreme rainfall to already saturated ground, causing further flooding in North West England, parts of Scotland and West Yorkshire (Kendon, 2016).The winter of 2019-2020 then saw the third UK winter in 7 years with large flood impacts, with the UK experiencing its wettest February on record with Storms Ciara, Dennis and Jorge bringing very heavy rainfall (Davies et al., 2021).The insurance costs from the February 2020 flooding are estimated to be around £297 million, which could have been a lot more if the 36,725 properties protected from flooding had not been defended (FloodList, 2020;FloodList, 2020).
Attribution studies on extreme winter flooding events over the UK have shown mixed results so far.Christidis & Stott (2015), examining the UK winter of 2013-2014, found no clear anthropogenic signal over large temporal scales such as seasonal rainfall extremes, but did see an anthropogenic signal for a shorter temporal extreme, the 10-day max rainfall.An analysis on the wet stormy winter of 2019-2020 with the wettest UK February on record found that although the dominant factor was climate variability and a strong positive NAO, climate change made the event more likely (Davies et al., 2021).This study found the event to be 3 times more likely now and 9 times more likely by the end of the century compared to simulations with pre-industrial greenhouse gas emissions.A revisited real-time attribution study by Otto et al. (2018) for Storm Desmond in 2015 found an increase in likelihood of the event by 59% due to anthropogenic climate change, with an uncertainty range including no change.
Examining extreme winter rainfall events requires significantly more data than in the observations to detect any significant climate signal over the noise from natural variability, with the same applying to climate models with only a small number of ensemble members.In this paper we therefore use the UNprecedented Simulated Extreme ENsemble (UNSEEN) method (Thompson et al., 2017) and apply it to attribution of winter rainfall extremes.For this the latest upgraded Met Office Decadal Prediction System v4 (DePreSys4) dataset is used, which contains approximately 6490 Winter years between 1960 and 2029 (Hermanson, 2020).The UNSEEN approach has been used in a number of other studies.Thompson et al. (2017) uses DePreSys3 to examine the probability of breaking monthly winter rainfall records in the UK, finding that there is 34% chance of breaking a monthly winter regional rainfall record somewhere in England and Wales each winter.Kelder et al. (2020) use the ECMWF seasonal prediction system SEAS5 to examine changes in 3-day 100-year autumn rainfall extremes in Scandinavia, showing a significant increase in extremes for Svalbard, but an insignificant trend for Western Norway.The other advantage of using the UNSEEN approach is that there is sufficient data to examine changes in rainfall extremes within specific circulation patterns.Here, we use the Met Office weather patterns created by Neal et al. (2016), which are used as both a forecasting tool and now in a number of studies to analyse the changes in and within atmospheric circulation over the North Atlantic-European (NAE) domain (Cotterill et al., 2022;Kendon et al., 2020;Pope et al., 2022).
Comparing the results from the UNSEEN methodology to a more traditional attribution approach can give us an indication of confidence in the results.The additional approach used in this paper uses atmosphere-only climate model runs with boundary conditions for the year of the event, to compare the probability of exceeding the event in question for both factual and counterfactual runs.
In this work we use the UNSEEN approach as well the more classic attribution approach described above to attribute five recent extreme winter rainfall events between 2015 and 2021 on a regional scale.We address the following questions: • Has climate change influenced the likelihood of these five recent extreme rainfall events at a regional scale and are there differences between these UK regions?• What is the relationship between the return level for winter rainfall extremes and how much their likelihood is changing for 1-3-day timescales?• Are there any regional or timescale differences in this relationship?• Are winter rainfall extremes changing more in specific atmospheric circulation types?
This paper first looks at how the winter extreme rainfall totals prior to the flooding have changed between 1965 and the year of the event for each event, using the UNSEEN methodology.Then again using the UNSEEN approach we examine how the likelihood of 1-in-10 to 1-in-90-year winter rainfall extremes have changed between 1975 and 2015 for six different UK regions.We then compare the results using the two attribution methodologies.Finally, we examine any changes in extremes over that period for atmospheric circulation patterns individually, to see how changes vary across circulation types.

| Choice of events
The five events chosen for the attribution study had to satisfy the following criteria; there were significant flood impacts, the region of the event needed to be simulated well by the climate models used, and the event needed to be less extreme than a 1-in-100-year event based on the observation record.More extreme rainfall events were not considered in order for there to be enough datapoints to adequately constrain our statistical inferences.The return period of the event was calculated by taking annual maxima of the rainfall totals between 1900 and 2021 in the HadUK-gridded observations (Hollis et al., 2019), and fitting the points to a generalized extreme value (GEV) distribution to calculate the return period of the observed event.Once that criterion was used, the events were chosen to include the widest range of regions, return periods and timescales.The length of the event leading to flood impacts was defined by the most extreme return period, that is, if a 3-day event had a 50-year return period and a 2-day event had a 40-year return period, we chose the length of the extreme rainfall event to be 3-days.In almost all cases the event length was an obvious choice, where the worst impacts of the event occurred on the last day of the rainfall event and/or following day.For example, Storm Desmond that produced extreme rainfall over North East England between 3rd and 5th of December 2015 lead to flood impacts on the 5th-6th of December.In the calculation of the return period, we assume a stationary climate for rainfall extremes, in order that a longer timeseries of observed values could be used.The return period values are therefore likely to be conservative.We use the 16 administrative regions used in the UK climate projections (Met Office Hadley Centre, 2020) to define each region (Figure 1).

| Model data
We use two different modelling systems, DePreSys4 and HadGEM3, for the respective methodologies.

DePreSys4 dataset
The UNSEEN methodology uses simulations from the Met Office Decadal Prediction System v4 (Hermanson, 2020), which is a set of hindcasts run between 1960 and 2018 using the HadGEM3-GC3.1-MMmodel with 60 km resolution at mid latitudes and 85 atmospheric levels (Sellar et al., 2020).This is an updated version of DePreSys3 (Dunstone et al., 2016), and contains 10 ensemble members initialised using observations every November using analyses of both atmosphere and ocean variables (Kay et al., 2022).These are run each year for 10.4 years starting in November 1960 until November 2018 with RCP 4.5 used from 2005 onwards.These runs are publicly available on the Earth System Grid Federation (ESGF) website (https://esgf-index1.ceda.ac.uk).The first month in each of the runs is not used, as too much predictability is contained resulting in the ensemble members not being independent.

HadGEM3-A
HadGEM3-A is a global atmosphere only model with 85 atmospheric levels and 60 km horizontal resolution at the mid latitudes, with attribution runs from 1960 to present.The most recent runs designed for operational attribution, starting in 2016, contain 525 ensemble members for both runs that contain only Natural Forcings (NAT) and runs that contain All Forcings (ALL) (Ciavarella et al., 2018).Up-to-date Forcings, ENDGame dynamics with GA6.0 science (Hadley Centre Atmosphere Model) and JULES (Hadley Centre Land-Surface model) are used to create these latest attribution runs (Ciavarella et al., 2018).The boundary conditions for the runs come from sea surface temperatures (SSTs) and sea ice conditions (SICs) and stochastic physics is used to produce the ensemble members (more details given in Ciavarella et al., 2018).For the NAT runs, where greenhouse gas emissions are held at 1850 levels, the estimated contribution of anthropogenic forcings is subtracted from SSTs and SICs (Ciavarella et al., 2018).There are also historical runs for both ALL and NAT between 1960 and 2013 containing 15 ensemble members, which will be used for model validation in this work.

HadUK-Gridded observations
The HadUK-Gridded dataset over the UK contains 130 years of gridded daily rainfall data from 1891 to present.This dataset uses land surface observations either from in situ land surface or station data, along with an interpolation scheme, with recovered observations constantly being added to the dataset (Hollis et al., 2019).For this work we use the regional dataset containing the 16 administrative UK regions, whose averages are calculated using 1 km resolution gridded data over the desired region.

ERA5 re-analyses
To validate the Weather Pattern data created for DePreSys4, the ERA5 reanalysis dataset is used (Hersbach et al., 2020).The method in Neal et al. (2016) uses daily mean sea level pressure data from ERA5 and assigns daily weather patterns to the data.The frequency of weather patterns in ERA5 reanalysis is used to examine how well atmospheric circulation over North-Western Europe is captured in DePreSys4, where the same method of assigning weather patterns is applied.

| Attribution
Climate change attribution examines the impact of specific drivers on climate within a confidence interval using statistics (Stott et al., 2013).Multiple methods are used in attribution and the particular framing of the attribution question can lead to different results, however confidence in the results can be enhanced if there is agreement between different attribution methods (Stott et al., 2016).In this paper we use two different attribution methods to look at recent extreme rainfall events preceding flood impacts and are framed as follows.The first method using the UNSEEN dataset looks at how much the probability of exceeding the extreme rainfall event has increased since 1965.The second method using the HadGEM3-A attribution runs looks at how much the probability of exceeding the extreme rainfall event has increased for the year of the event due to anthropogenic emissions.The first method will be referred to as "unconditional attribution" where we do not sub-select any circulation type or SST patterns.Whereas the second method will be referred to as "conditional attribution" as we select ensemble members for the year of the event only, which are constrained to the SSTs and SICs for the year of the event.
Method 1: Unconditional attribution using UNSEEN approach In the UNSEEN unconditional attribution method, we use the DePreSys4 dataset containing 6490 winters between 1960 and 2029.The large size of the dataset over this time period allows us to analyse the long-term trend for very extreme events.Given that this comes from a coupled model, we are also not restricted to fixed SST boundary conditions and the ensemble will contain atmosphere-ocean processes.The main result shows how the likelihood of the extreme event has changed since 1960 with 95% confidence intervals based off the longterm trend.We carry out the following methodology for each of the flood events in Table 1, based off the extreme rainfall total associated with the event, each covering a different combination of event lengths, regions and return periods.
• Step 1: For the event (event = x mm) in a given region, lasting for number of days, n.A generalized extreme value distribution (GEV) over 100 years of observations is fitted to n-day annual maxima for winters from 1900 to 2021.From this the return period of the specific event in the region can be calculated.• Step 2: Over the baseline period  for the DePreSys4 data the corresponding extreme rainfall total in the model is calculated from the return period of the event.These first two steps act as a bias correction for the n-day totals seen in the observations and gives a bias corrected event total (bc_event).
T A B L E 1 The extreme rainfall events examined in the attribution study, including their main impacts, return period calculated based off regional observations with their 95% confidence intervals, antecedent conditions and length of the extreme rainfall event.
Event • Step 3: The DePreSys4 data is divided into six timeslices all containing 990 winter values and hence 990 n-day maxima (for details see Table S3, Supporting Information).For each timeslice, n-day annual maxima are calculated for the region, the GEV is fitted to them and the return period of bc_event in mm is calculated.
Step 5: To calculate confidence intervals on the change in likelihood, the 990 n-day annual maxima values are bootstrapped with replacement 10,000 times for each timeslice.Linear regressions are fitted producing 10,000 parameters and the 2.5 and 97.5 percentiles of the gradient are selected to represent the confidence intervals (CI) and the parameters are used to calculate the upper and lower bounds of change in likelihood for the event.
Using this timeslice GEV approach with DePreSys4 has the benefit that for each timeslice there are 990 annual maxima, meaning there are likely to be around 10 events exceeding a 1-in-99-year event for each GEV and enough timeslices to fit a meaningful regression to examine the long-term trend.The alternative approach is to use a peaks-over-threshold approach with a general Pareto distribution (GPD) rather than annual maxima using GEVs, which has the advantage that it wastes less of the data, that is, the second most extreme value in some years may be higher than annual maxima in other years (Coles, 2001).However, it is more complex and would require a number of adjustments especially when looking at 2-or 3-day totals where the data would be reused and hence not be independent.The GEV method, however, is the same regardless of the length of the event and works well given the ensemble members for annual maxima are independent when fitting GEVs to them.This is checked in the model validation section.
Method 2: Conditional attribution using HadGEM3-A The conditional attribution approach uses HadGEM3-A which compares the probability of the event, in both a world with all forcings (ALL) and a world where anthropogenic greenhouse gas emissions are held at 1850 levels (NAT).This method is conditional as we only compare ensembles for the year of the event looked at, which has fixed SST and SIC conditions.This technique has been used in many attribution studies, including Dalagnol et al. (2022) and Wang et al. (2023), which use the HadGEM3-A model runs.The following methodology is used for events in winters in or after 2016-2017 as there are only enough ensembles for the analysis after this point.
• Step 1: Using data over the baseline period  in the HadGEM3-A ALL runs, a GEV is fitted for n-day winter annual maxima for event length n.The return period of the event in question is translated into the corresponding extreme rainfall total in the model and is used as the event threshold.• Step 2: Using data only for the year of the event create GEVs for both the NAT ensemble members and ALL ensemble members for n-day annual maxima in DJF.
Using the common attribution approach of comparing the probability of exceeding the event threshold (Stott et al., 2013)  This approach has the advantage of both examining how much more likely the event was during the conditions in the event year and isolating anthropogenic emissions as a driver of climate.This was carried out for three of the events as two of them occurred before the winter of 2016-2017, where there were significantly fewer ensemble members than the 525 after 2016-2017.

| Met Office weather patterns
The Met Office weather patterns were created by Neal et al. ( 2016) by applying a k-means clustering method (Philipp et al., 2007) to EMULATE (European and North Atlantic daily to multidecadal climate variability) reanalysis data between 1850 and 2003 (Ansell et al., 2006) for sea level pressure (psl) over the North Atlantic European Domain (NAE).The 30 weather patterns resulting from this process have been verified by UK Meteorologists and were created to simulate a large range of circulation patterns covering this domain, with each pattern bringing a different climatology to the UK (Neal et al., 2016).The 30 weather patterns come in the form of daily psl anomalies on a 5 × 5 grid covering the NAE domain (30 W-20 E; 35 -70 N).Once created, these 30 weather patterns can be further grouped into eight consolidated patterns (Figure 2), such as NAO−, NAO+, Northwesterly, and others (Neal et al., 2016).These consolidated patterns represent the broadscale circulation type and are what we use in this study, noting that they will have significant variation within them.An example of this is the NAO− category (Figure 2) which will contain days that correspond to one of 6, 9, 11, 19, 25, 27, 28 from the 30 patterns (Figure S5).The synoptic setup for this composite is high pressure over a significant part of the UK similar to patterns 6, 9, 25, 27, but also contains days from patterns 11 and 28 where there is low pressure over the UK.There may also be cases where within a day there are contrasting pressure anomalies over the region, which may be averaged out during pattern assignment.

Creating weather pattern data for DePreSys4
The steps used to create the daily weather patterns for DePreSys4 are described below.The steps are carried out individually for each of the 10 ensemble members which are labelled r1i1p1f2-r10i1p1f2.The general method of assignment is the same one used in Pope et al. (2022) and Cotterill et al. (2022).
First, we create mean daily psl values for each day of the year over a baseline period.These data were re-gridded to the 5 × 5 EMULATE grid over the NAE domain using a baseline period of 1971-2015.Each ensemble member has 10.4 year-long sub-runs which start each year, meaning extracting the baseline period required is not trivial.Details of how this was done is given in Tables S1 and S2, where the baseline period for each ensemble member contains 450 years of data between 1971 and 2015 with an equal number of realizations for each year calendar year.This mean daily sea level pressure pattern over the baseline period for each day of the year is referred to as the climatology.
Second, all the DePreSys4 daily sea level pressure data were re-gridded to the 5 × 5 EMULATE grid over the NAE domain.For each 10.4 sub run individually, these daily data are compared to the climatology for each day to produce an anomaly.The anomaly from the climate model data is then compared to the anomalies of the 30 weather patterns and the closest distance becomes the weather pattern assigned to the day in question.See Figures S3 and S4 for model validation on the frequency of weather patterns for the DePreSys4 dataset.2016) are used to examine if there are any changes in winter daily precipitation extremes within particular circulation types on a regional scale over the UK.This is done by examining how the percentage of extreme rainfall days within each of the 8 patterns has changed between 1960 and 2020 for each pattern.An extreme rainfall day in this case is defined as the 99th percentile of winter daily rainfall for the region of choice.The 99th percentile is calculated over all the winter daily precipitation data in the DePreSys4 dataset covering 1960-2029 regardless of the weather pattern.The index used to look at changes within weather pattern is the delta change in the percentage of weather patterns days that are extreme, Δ pat-tern_n99 for pattern n for each individual UK region.This is calculated using the following steps for each weather pattern (wp) individually: • Select only data from the specific wp and divide the data into the six timeslices used in the attribution calculation.• For each timeslice, calculate the percentage of the daily rainfall events that exceed the 99th percentile.• Using a linear fit calculate the trend over the six timeslice values, using the parameters from the fit to calculate theoretical values for 1965 and 2020.• Calculate the percentage increase between 1965 and 2020 for that wp, Δ pattern_n99.• To get the 95% confidence intervals for Δ pattern_n99, bootstrap with replacement the data at the start of step 2 for each timeslice individually and repeat steps 2 and 3.This is done 10,000 times to produce that number of Δ pattern_n99 values.This is done for the four regions used in the attribution study cases, with the addition of South West England and North West England.Model validation for daily precipitation in these regions is in Figure S2.

| Extreme rainfall
To examine the ability of the two models used; DePreSys4 and HadGEM3-A to capture winter rainfall extremes in different UK regions, GEV distributions of daily annual maxima in DJF are compared for the model and observations.The baseline period used for the models is 1981-2010 and contains all ensemble members, with a slightly longer period  for the HadUKgridded observation to allow for more data points.For DePreSys4 these years were extracted from the baseline period used from the weather patterns in section 2.3.2. Figure 3 shows this for the four regions examined in the five Attribution events, both climate models show strong agreement with the observations.Using the p-values from a two-sample Kolmogorov-Smirnov test to compare model and observation data for each region, all have pvalues equal or exceeding the 0.05 level.This means they have not been shown to be from significantly different distributions and therefore we can be confident that the two models are adequate at representing DJF daily rainfall extremes in those regions.This was not the case for many other UK regions including Wales and North-West England, which is why these regions were not chosen for the attribution studies.The disparity between the observations and models in these regions has also been found in other UNSEEN studies for the UK.These include Thompson et al. (2017), which examines monthly rainfall in winter and Kent et al. (2022), which looks at daily summer rainfall extremes.These studies conclude that the regions with higher ground and complex topography tend to have the largest model biases, with orographic effects not being well simulated in climate models due to their relatively coarse resolution.This also appears true for the datasets used in this study.There is the odd exception, however, such as the East of England, which has less complex topography but still has a relatively big model bias.

| DePreSys4 fidelity
We further evaluate the performance of DePreSys4 via the commonly used fidelity tests for the UNSEEN approach (Kelder et al., 2020;Thompson et al., 2017).These tests are carried out on the different moments of the distribution (mean/standard deviation/skewness/kurtosis) for the annual maxima metrics used in each of the five attribution studies (Figure 4), comparing 10,000 proxy timeseries from DePreSy4 to the HadUK-gridded observations between 1971 and 2018.Good agreement between DePreSys4 and the observations is seen, measured as the observed value falling within 95% of the model proxy timeseries data for all metrics.The proxy timeseries were created by randomly sampling values from the DePreSys4 runs for each year between 1971 and 2018 creating 10,000 proxy time series, each 48 years long.In addition to this, we also analysed the realism of the model trends by comparing the trend (mmÁyear −1 ) of the proxy timeseries, to the observed trend, showing very good agreement between DePreSys4 and HadUK-grid (Figure S1).
The unconditional approach using DePreSys4 requires a few additional validation tests in order to confirm that the method is reliable (Figure 5).First, given each of the 10 ensemble members are initialised at the same time, tests were carried out to examine the independence of each member.Second, each run is a 10.4-year long hindcast and hence we check in case there is any model drift in terms of rainfall over the 10.4 years.Third, to check that the year-to-year natural variability in the frequency of days with settled/unsettled conditions has been sufficiently reduced when averaged over all ensemble members, by examining weather pattern data over this time.Member independence is examined using the Spearman rank coefficient, using the same method as in Kelder et al. (2020), with some small differences.This involves checking whether pairs of ensemble member Rx1d values for the same year are closer to each other for each lead time, compared to randomly choosing two Rx1d values from the dataset (more details in sect.5, Supporting Information).The results (Figure 5a) shows that there is no significant correlation between ensemble members of the same year and lead time for rainfall extremes, compared to the correlation between rainfall extremes for randomly chosen year and lead-times.Neal et al. (2016) shows that forecast skill in the UK weather patterns is present till around Day 15.Given the members are all initialised at the start of November for their 10.4 year-long runs-the patterns will have diverged enough in their atmospheric state by the start of the first winter.Figure 5b where GEV distributions of Rx1d in winter are compared for each lead time (year 1-11) over the time period 1975-2014 shows no clear model drift over lead times in the four regions.
To examine the natural variability over the UK through its main driver, the NAO, we examine the eight weather patterns, grouping them into two categories.The two categories are; Unsettled conditions (NAO+, Southwesterly, Northwesterly and Low near UK) which are pre-dominantly cyclonic, and settled conditions (NAO−, Scandinavian High, High over UK, Azores high) that are predominantly anticyclonic (Neal et al., 2016).Figure 5c compares the average frequency of patterns with unsettled conditions over the UK for both the DePreSys4 data and ERA5.The results show that the year-year variance in the frequency of days with unsettled conditions is very small when averaging over all ensemble member runs over this time period and hence should have negligible impact on the trend.The variance in natural variability in similar to the observations/ERA5 when comparing individual model runs (Figure 5d).There is a slightly higher incidence of days with unsettled weather conditions in ERA5 compared to DePreSys4; however, this should not impact the results of the trend analysis significantly given the bias correction.

| Unconditional attribution using UNSEEN
The results from the unconditional attribution approach described in section 2.2 shows a statistically significant increase in likelihood since 1965 of the winter rainfall extremes associated with all five events examined (Figure 6).The three extreme 1-3-day rainfall totals seen in northern England regions, Yorkshire and Humber from Storm Eva and Storm Ciara and Northeast England from Storm Desmond varied between 2.1 and 2.6 times more likely since 1965, and at least 30%-50% more likely based off the lower confidence bounds.Rainfall totals from Storm Dennis were examined individually for two different regions, the East-Midlands and Southeast England, as the impacts, event length and extremity were different for both.Despite these differences the 2-day rainfall total over Southeast England and the 1-day total over the East Midlands showed similar changes in frequency since 1965, 1.5 (CI: 1.2-1.8)and 1.4 (CI: 1.1-1.9)times more likely in the winter of 2019/2020, respectively.There does appear to be a relationship between the return time of the event and its increase in likelihood, with more extreme events showing larger increases.The more extreme events also have larger confidence intervals as they sit further within the tail of the distribution as can be seen in Figure 6.This is investigated further in section 3.2.

| Conditional attribution using HadGEM3-A
The results from the conditional attribution approach (Figure 7) described in section 2.2 shows no significant changes in likelihood for the extreme rainfall totals seen in the winter of 2019-2020 for Storm Ciara in Yorkshire and Humber or Storm Dennis in the East Midlands or Southeast England.This approach compared natural and historic simulations of HadGEM3-A conditioned on SSTs and SICs for that year.The results of this attribution approach do not agree with the unconditional UNSEEN approach, which uses a range of different perturbed Ocean states over a long period.
The DePreSys4 dataset shows a very clear signal in rainfall extremes, not replicated by HadGEM3-A using the conditional method, despite both being on the same resolution grid and from a HadGEM3 model.There could be multiple reasons for this.First, the unconditional method uses around 5-6 times more data over a long time period, which reduces the noise in extremes from natural variability.There are 525 years of data fitted to GEVs using the conditional method and 990 years of data being fitted to each distribution for the unconditional method.Second, as any climate signal is still very weak, not all models may show this change.Otto et al. (2018) found that when studying extreme rainfall over October-February (ONDJF) over the UK the HadGEM3-A showed a weak/no trend in rainfall extremes compared to other models which use a coupled ocean-atmosphere.
F I G U R E 6 Unconditional attribution results using the UNSEEN dataset DePreSys4, using long-term trends in the timeslice-GEV approach.For each event (a-e) the subplot of the left shows the change in likelihood of the event in that year compared to 1965 with 95% confidence intervals.The subplots to the right shows the long-term trend in the return period for the event of interest, with the baseline used  to calculate the event return period in the model.Each of the six timeslices contains 990 winters of data and a GEV fitted with the vertical bars representing the 95% confidence intervals after bootstrapping with replacement.[Colour figure can be viewed at wileyonlinelibrary.com]HadGEM3-A is also conditioned for the year of examination and all ensemble members use the same SST patterns as boundary conditions.This experiment therefore answers a somewhat different question to the UNSEEN approach and this underlines the importance of the framing of the attribution question.

| Relationship between climate signal and return periods
Using the UNSEEN methodology used for the unconditional attribution, the change in likelihood in 1-in-10 up to 1-in-90-year events were calculated for different combinations of regions and event-lengths (Figure 8).The changes are calculated over the last 40 years (between 1975 and 2015), for six different English regions.These include the four used in the attribution section, with the addition of North-west England and South-west England, which are validated in Figure S2.For regions in northern and central England these changes are significant across all return levels and event lengths, with larger increases in likelihood for rainfall totals with higher return periods (1.4/2.2 times more likely for 1-in-10/90-year events, respectively).This is not replicated for southern regions of England for return periods of 50-90 years, where there is no significant change, and even a decrease in likelihood of the 1-in-90-year rainfall total in South-west England.There is also much higher confidence in the results for smaller return periods.
F I G U R E 7 Conditional attribution results using HadGEM3-A for three events later than 2017.For each event (a-c) the subplot of the left shows the change in likelihood of the event in that year with 95% confidence intervals.The subplot to the right compares the GEV distribution of the ALL and NAT only forcings runs for the year in question using 525 ensemble members for each from the HadGEM3-A, with their 95% confidence intervals.This is a 2-day annual maxima for event (a, c), and a 1-day annual maxima for (b).[Colour figure can be viewed at wileyonlinelibrary.com]

| Climate signal changes within different circulation types
To examine the dynamics of the changes in winter rainfall extremes the 8 Met Office weather patterns are used.Figure 9b shows the breakdown of weather patterns for the 1000 most extreme daily rainfall totals occurring in each region.This shows that different circulation types impact some regions of England more than others in terms of extreme totals.The change in the percentage of weather pattern days that are extreme (99th percentile), Δ pattern_n99 for each region, is increasing across all circulation types (Figure 9a), with increases seen equally across the board for all regions with no outliers.This suggests that a thermodynamic change is at least partly responsible for the changes in regional daily extremes seen in section 3.2.The two weather patterns that do not bring extreme rainfall to the UK were not included (high over the UK and Azores high).The biggest increases in frequency of extreme rainfall totals comes from within the NAO+ weather pattern, where there is a significant increase across all six regions.

| DISCUSSION
This study shows that using datasets containing a significant amount of data (more than 100 simulations for each The change in likelihood in 1-3 day winter rainfall extremes between 1975 and 2015, for return periods of 10, 50 and 90 years.This uses DePreSys4 data using the same method as that used for the unconditional attribution.This is done for six English regions with the range corresponding to the 95% confidence intervals.[Colour figure can be viewed at wileyonlinelibrary.com] calendar year) there is a detectable climate signal in winter rainfall extremes in northern and central regions across England.The UNSEEN approach shows that for these regions, 1-in-90-year winter precipitation extremes on a 1-3 day timescale have increased in frequency significantly by about 2.2 times on average in the last The increase in the probability of getting an extreme event for that regime between 1965 and 2020 in winter based off the DePreSys4 dataset.The result is based off fitting a linear regression across six timeslices over this time period and uses the eight weather regime classifications, however, does not include the two patterns with high pressures over the UK due to lack of extreme events to fit trend to.The 95% confidence intervals are calculated using bootstrapping with replacement with the method described in Examining changes within the weather patterns section.(b) Takes the 1000 most extreme events for each region and shows the percentage of them that correspond to each of the eight regimes.[Colour figure can be viewed at wileyonlinelibrary.com] 40 years.With current observational records showing that three out of the five highest daily winter rainfall totals over the Northern England domain on record have occurred from 2015 onwards, this suggests that this is not purely down to natural variability and that climate change has already played a role.
Furthermore, analysis of recent extreme rainfall totals preceding the five impactful flooding events examined in the winters of 2015-2016 and 2019-2020 were found to be significantly more likely compared to half a century ago (1.4-2.6 times).These events had a wide range of return periods from 7 to 81 years, timescales (1-3 days) and regions.Higher return periods in winter rainfall extremes saw larger changes in frequency; however, the climate signal was similar across all the timescales examined.Regions in northern and central England saw similar climate signals, with weaker signals in southern England.
The second attribution method comparing factual simulations for the year 2020 with counterfactual simulations did not show significant differences in extreme rainfall totals for the events examined.This method used significantly fewer years of data, and the atmosphere only model used has been shown in other studies to have weaker trends in winter rainfall in comparison to other (coupled ocean-atmosphere) models and observations (Otto et al., 2018;Vautard et al., 2019).In this work we take the NAO to be the main mode of natural variability, but other factors on a global scale may cause natural variability in rainfall over the UK that may have impacted this trend.The assumption is made that natural variability from the NAO has not changed significantly with climate change before 2020.
Using the eight Met Office weather patterns over the UK we also showed that the increase in winter rainfall extremes using the UNSEEN approach is occurring across all the weather patterns that bring heavy rainfall.This suggests that thermodynamic effects are contributing towards these current increases, as well as any dynamical changes that may be occurring.Changes in the frequency of weather patterns over the UK in winter is predicted in the future with Pope et al. (2022) showing that cyclonic/westerly wind patterns are likely to increase.Schaller et al. (2016) shows that atmospheric circulation in winter may already be changing as a result of climate change contributing to the increased likelihood of UK Winter flooding in 2013-2014.This work shows that the attribution results are both sensitive to the type of model and framing used.It is also likely to be sensitive to the model choice, where the methodologies used in this paper rely entirely on datasets from the HadGEM family of models, unlike some of the mainstream attribution methods such as that for rapid attribution (Philip et al., 2020) which uses multi-model analysis.There are also alternatives to how the UNSEEN methodology is carried out in the context of attribution, Kelder et al. (2020) look at events of similar length (3 days) over Western Norway with a focus on 1-in-100-year events, where the main methodology implements a nonstationary GEV approach with a time covariate.By contrast the UNSEEN methodology in this work uses a stationary GEV timeslice approach to detect the trend, which is possible given that the DePreSys4 dataset provides a longer timeseries.
In this paper we only examine the winter rainfall extremes on a 1-3 day scale and not land use or antecedent conditions.UKCP Climate projections show a prediction towards warmer wetter winters (Lowe et al., 2019) due to climate change.This combined with the changes in likelihood we found for short-term winter rainfall extremes may increase the risk of winter flooding beyond the 1-3 day extremes examined in this paper.Examining this along with changes in potential evapotranspiration and land use using flood inundation modelling would provide valuable insight into how flood risk is changing overall.Furthermore, the climate signal in rainfall extremes is shown to be stronger and more consistent with observations in higher resolution runs from the same driving model (Cotterill et al., 2021).This underlines the need for more ensembles at high resolution, covering at least part of a time period close to a climate with limited anthropogenic influence.

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I G U R E 1 Map of the 16 administrative regions for the UK used for the UKCP climate projections (Met Office Hadley Centre, 2020).The regions used in the attribution studies are highlighted in bold.[Colour figure can be viewed at wileyonlinelibrary.com] in both ALL and NAT (Pall and Pnat, respectively), are calculated from the fitted GEVs.The change in likelihood of the event that year due to anthropogenic climate change is Pall/Pnat.• Step 3: To calculate confidence intervals on the change in likelihood, the n-day annual maxima values are bootstrapped with replacement 10,000 times for both ALL and NAT with 10,000 corresponding Pall/Pnat values to calculate the 95% confidence intervals.

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I G U R E 2 Maps of the eight weather patterns from Neal et al. (2016) used in this study.The 30 weather patterns created are grouped into these eight patterns above.The maps represent mean sea level pressure (mslp) values plotted in foreground in 2 hPa intervals and the anomalies plotted as filled contours in hPa.The eight circulation patterns are representative of (NAO−, NAO+, Northwesterly, Southwesterly, Scandinavian high, High pressure over the UK, Low close to the UK, Azores high) for patterns 1-8, respectively.Source: Neal et al. (2016).[Colour figure can be viewed at wileyonlinelibrary.com]Examining changes within the weather patterns The eight weather patterns from Neal et al. (

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I G U R E 3 Comparison of winter 1-day annual maxima (Rx1d) in the models and observations for the four UK regions examined in the attribution studies.The p-value represents the results from a two-sided K-S test, where the GEV for both the model data (DePreSys4/ HadGEM3-A) and observational data are compared to show they are not from significantly different distributions.HadGEM3-A contains 15 years of data for each year and DePreSys4 contains 110 years of data for each year.[Colour figure can be viewed at wileyonlinelibrary.com] 3 | ANALYSIS AND RESULTS

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I G U R E 4 Plot showing the fidelity tests comparing the mean/standard deviation/skewness/kurtosis in the DePreSys4 runs to the observed timeseries from HadUK-grid between 1971 and 2018.Each row represents the region and corresponding timescale for each of the five events examined in the form of winter annual maxima.The histogram data represents the statistics for 10,000 proxy series between 1971 and 2018 for the DePreSys4 runs and the black line represents the equivalent statistics for the observations over the same time period.[Colour figure can be viewed at wileyonlinelibrary.com]

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I G U R E 5 Validation of DePreSys4 dataset.(a) A boxplot of Spearman rank coefficients for lead times of 1-11 years for each region in DJF for 1 year annual maxima.The boxplots contain the correlation between Rx1d and time for each combination of the 10 ensembles over a 40 year period.The grey shaded areas are the 95% CI intervals for the whiskers and the median, when sampling random members, lead times and values using the same method.(b) DJF daily precip annual maxima GEV curves for each lead time for four chosen regions in attribution study to examine if any model drift is occurring.(c) This shows the frequency of unsettled weather patterns for the UK in DJF (NAO+, Southwesterly, Northwesterly and Low near UK) for each year in both ERA5 and the mean over all DePreSys4 data.(d) The same but uses sampled 66-year timeslices for DePreSys4 instead of the mean, for a direct comparison of yearly variance in weather circulation.[Colour figure can be viewed at wileyonlinelibrary.com]