2.1 Weather@home 2

Weather@home (Massey et al., 2015) consists of an atmospheric global climate model, HadAM3P, and its regional counterpart, the regional climate model HadRM3P, which dynamically downscales the GCM to a higher resolution over a limited domain. As part of the climateprediction.net project (Allen, 1999), weather@home takes advantage of computing time donated by volunteers around the world to run very large numbers of climate model simulations, of the order of tens of thousands.

The data analysed in this study is based on version 2 of weather@home (hereafter, w@h2, see Guillod et al., 2017a), which uses the more recent land surface scheme MOSES 2. The regional model covers the European CORDEX domain at a horizontal resolution of 0.22^∘ (about 25×25 km) on a rotated longitude–latitude grid (e.g. Kotlarski et al., 2014). The model, including its setup for this domain, is described and validated in detail by Guillod et al. (2017a).

Table 1Observational datasets. For the mean climate validation the common overlapping period 1961–2006 is used, while for precipitation extremes validation the overlap period between the historical baseline and CEH-GEAR (1900–2006) is used.

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2.2 Observational data

The gridded datasets listed in Table 1 are used for comparison and validation. For temperature, the E-OBS dataset (Haylock et al., 2008) is selected, as it is conveniently available on the same rotated longitude–latitude grid as HadRM3P. For precipitation, we use the CEH-GEAR dataset (Keller et al., 2015), which provides rainfall on a 1 km grid from 1890 to 2015. Observational estimates of potential evaporation are taken from the CHESS-PE dataset (Robinson et al., 2015), available from 1961 to 2012 and derived with two formulations, with and without correction for interception evaporation. For both CEH-GEAR and CHESS-PE, data are aggregated onto the 0.22^∘ model grid prior to all analyses.

Table 2List of the climate time series for various scenarios. GM SST stands for global mean SST.

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3.1 Model simulations

A total of 11 large ensembles (“batches”) of w@h2 simulations are conducted, producing model output for three distinct time periods and a range of scenarios (see Table 2). The three time periods cover the past century (“historical baseline”; 1900–2006) and two 30-year future time slices (near and far future; 2020–2049 and 2070–2099, respectively) assuming the high greenhouse gas emission scenario RCP8.5 (Meinshausen et al., 2011). For each future time slice, uncertainty in transient climate response is taken into account by sampling a range of five sea surface temperature (SST) warming patterns derived from CMIP5 (Taylor et al., 2012), as detailed in Sect. 3.2, while for the historical baseline only one ensemble is generated, using the observed ocean state, leading to the total of 11 batches (1 batch for each time period and SST pattern).

All ensembles are generated using the same overarching design, described in Guillod et al. (2017a) for the historical baseline. Essentially, simulations are initialised on 1 December before each simulated year (e.g. 1 December from 2019 to 2048 for near future), using restart files from earlier 12-month spin-up simulations, and are run for 13 months. The aim is to produce 100 simulations for each year (for each time slice and scenario), but, due to the nature of volunteer distributed computing, not all model simulations are completed at the same time. Therefore, in this case, 200–400 simulations per year are sent out and, whenever 100 simulations have been returned for each simulated year within a batch, this batch is closed and no additional simulation output is added to it. In cases when the minimum number of simulation per year did not reach 100 after some time, the batch was closed anyway, leading to a minimum number of simulations per year ranging from 85 to 100 depending on the scenario (Table 2).

Months 2–13 of the simulations being returned from each year are analysed, providing around 100 single-year simulations of data for each year (January to December), or a total of 10 700 years of data for the historical baseline and 3000 years of data for each future time slice scenario.

For the historical baseline, the simulations are the same as those analysed by Guillod et al. (2017a). SSTs and sea ice are prescribed to observed values using version 2 of the HadISST dataset (Rayner et al., 2003; Titchner and Rayner, 2014). Similarly, other input variables such as greenhouse gas concentrations, volcanoes and solar activity, and SO₂ concentrations are prescribed to historical values as described in Guillod et al. (2017a).

The future scenarios are 30-year time slices that correspond to years 1975–2004 of the historical baseline but with added climate change. Therefore, natural forcings (volcano and solar activity) are taken from 1975 to 2004, while greenhouse gases are taken from RCP8.5 for the simulated years (2020–2049 and 2070–2099). For sea surface temperature and sea ice, a similar approach is taken as in attribution studies (e.g. Schaller et al., 2016), but the future (rather than past) SST warming is added to (rather than subtracted from) observations. More specifically, the climate change signal derived from CMIP5 models (i.e. SST warming and corresponding changes in sea ice) is added to the 1975–2004 observed values used in the historical baseline. The details on the creation of future SST and sea ice are given in Sect. 3.2.

Table 3Output variables available in the dataset at various temporal frequencies.

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A number of daily and monthly variables are saved in the regional model (Table 3). Of particular relevance to hydro-meteorology and extremes, the following variables are available at daily time steps from the regional model output: minimum and maximum temperature (tasmin and tasmax, respectively), precipitation, surface air humidity (mean dew-point temperature), mean sea level pressure, and additional variables required to compute potential evaporation (E_pot) (10 m wind speed, and incoming and net longwave and shortwave radiation fluxes at the land surface) as well as offline-computed E_pot estimates (see Sect. 3.3 for details on the computation). In addition, 5-day averages of soil moisture on the four model levels as well as surface latent and sensible heat fluxes are available. All these variables, plus cloud cover and individual components of precipitation (convective versus large scale and snowfall versus rainfall) are available as monthly averages. Finally, weather@home is based on a calendar containing 360 days per year (i.e. 30 days per month), like many GCMs.

Table 4Monthly surface resistance values (r_s, in s m⁻¹) used in the computation of E_pot. The baseline values are shown under pepm and are kept constant in future time slices for variable pepm. pepm_adjrs denotes the future values accounting the changes in CO₂ concentration (see Sect. 3.3 for details).

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3.2 Sea surface temperature projections

To create the future SSTs and sea ice concentrations (SIC), two datasets are used: every available CMIP5 model simulation (Taylor et al., 2012), including all physics parameter and initial condition perturbations; and the HadISST2 observed SST and SIC (Rayner et al., 2003; Titchner and Rayner, 2014). The CMIP5 model data are used to produce the large-scale warming patterns of SST for the two future time slices (2020–2049 and 2070–2099), whereas the HadISST data are used to provide the small-scale variability of the SST (whereby “small scale” refers here to anomalies from 30-year averages).

For the AMIP (climate model simulations with prescribed SSTs) component of the CMIP5 project, the projected change in SST and SIC are obtained from a single (per modelling group) coupled ocean–atmosphere model, and the models are integrated for a single decade from 2026 to 2035. This approach has two disadvantages. Firstly, using a single model does not take into account the variation in the ensemble of CMIP5 models, both in the global mean SST (GMSST) and the pattern of warming produced. Secondly, the small-scale variability of the SST patterns do not match those in our observed dataset, which makes comparison between the historical scenario and the two future scenarios difficult. To get around these problems we construct a statistical model of SST warming patterns and impose the small-scale variability from the observed dataset, so as to match the historical scenario.

To construct the statistical model we use the SSTs for every model with data available for the RCP8.5 scenario. The below analysis is carried out for each month in the datasets, so as to reflect the greater warming in the December–February season (DJF) in the CMIP5 ensemble. Firstly the SSTs are converted to anomalies by subtracting the 1986–2005 mean obtained from the corresponding historical run with the same model, run, initialisation and perturbation number. This gives a time series of SST anomalies for each CMIP5 ensemble member from 2006 to 2100. Secondly, to remove the small-scale variability and generate the large-scale warming patterns, a 30-year running-gradient filter is applied to every grid box in the SST anomalies.

The statistical model of SST warming patterns is constructed from these smoothed SST anomalies by first performing an empirical orthogonal function (EOF, Wilks, 2011) analysis on the smoothed SST anomalies for the year 2050. This produces a set of patterns (the EOFs) and principal components (PCs) which explain the variation in the smoothed SST anomalies across the CMIP5 ensemble members. The number of EOFs and PCs was truncated at six as, during the analysis, it was determined that the first six accounted for 98  % of the variability. As we are interested in producing transient series of SSTs for two periods, the six EOFs were projected onto the smoothed SST anomalies for each year between 2020–2049 and 2070–2099 to produce time series of pseudo-PCs for each model and each year in the two scenarios. Next, a linear regression was performed on each set of pseudo-PCs for each year to derive a relationship between the pseudo-PCs in that year and the PCs in 2050. These PC relationships are used in the reconstruction of the SSTs later.

The core of the statistical model is a multi-variate distribution (MVD) of the truncated PCs in the year 2050, modelled by a Gaussian copula (Nelsen, 2007) with skew–normal marginals (Azzalini, 2005) using the “copula” and “sn” packages in the R statistical analysis software (R Core Team, 2016). A MVD is used as, although the EOFs are orthogonal to each other, the signs of the PCs within an ensemble member are not independent. Once the copula has been constructed it is sampled 10 000 times, which produces a set of six PCs for each sample. The SST warming pattern is then reconstructed from these PCs and the EOFs for the year 2050, and the GMSST of the warming pattern is calculated and recorded with the PCs. This allows the construction of a probabilistic distribution of the GMSST warming in the CMIP5 ensemble which also contains the information (PCs) of how to construct the GMSST. Note that, for a given percentile, there will be 100 different sets of PCs. This allows the construction of up to 100 different warming patterns for each GMSST value, where the contributions to the mean warming occur in different physical locations. For this experiment we choose the 10th, 50th and 90th percentile values of GMSST so as to incorporate CMIP5 models with both low and high sensitivity in their GMSST response to elevated greenhouse gas concentrations.

Weather in the UK is potentially sensitive to the North Atlantic (NA) SSTs and in particular to gradients thereof (e.g. Rodwell et al., 1999; Rodwell and Folland, 2002). To account for this we use a NA SST gradient index to select the two most different warming patterns, in relation to this metric, from the 100 potential warming patterns for each of the 10th and 90th percentiles. This gradient is defined as the difference between the area-weighted means of two areas in the North Atlantic, following Schaller et al. (2016): A southern area bounded by the longitude–latitude coordinates 30–50^∘ N, 40–0^∘ W and a northern area bounded by 50–70^∘ N, 40–0^∘ W.

From the sampling of the output of the copula we form five warming patterns for the year 2050, by combining the PCs with the EOFs: p10n corresponds to the pattern with a GMSST warming at the 10th percentile and the minimum NA SST gradient, p10x the 10th percentile GMSST and the maximum NA SST gradient, p90n the 90th percentile and the minimum NA SST gradient, and p90x the 90th percentile and maximum NA SST gradient, and MMM a median scenario with the median GMSST and middle NA SST gradient. Each of these patterns has an associated set of PCs for the year 2050. To generate a time series of SST anomalies the linear relationship between the original PCs in the year 2050 and the pseudo-PCs is used to construct time series of PCs for each of the 5 warming patterns above. These PCs (derived from the linear relationship) are then combined with the EOFs for the year 2050 to generate a time series of SST anomalies between the years 2020–2049 and 2070–2099 for each of the 5 warming patterns.

To generate absolute climatological SST values, the time series of SST anomalies are added to the 1986–2005 mean of the HadISST2 dataset (since the above procedure was applied to anomalies from those same years). Since the future time slices are to be compared to the reference time period 1975–2004 (baseline), the small-scale variability from these years is then also added onto the sum of the SST anomalies and HadISST mean. This small-scale variability is also derived from the HadISST2 data by applying the 30-year smoother and then subtracting the smoothed data from the original HadISST2 data. This calculates the residuals of the smoother for 1975–2004 when compared to the original data source and removes the large-scale variability from HadISST, which was already added by the warming patterns.

To construct the sea ice we use the 10 best CMIP5 models at representing historical sea ice between 1979 and 2005, as ranked by Shu et al. (2015). For each future period (2020–2049 and 2070–2099), for every grid box we pool the SST anomalies for the RCP8.5 scenario and the corresponding SIC anomalies. We then derive a linear relationship, for each grid box, between the SST anomaly and the SIC anomaly by using a linear regression. Time series of SIC absolute values are then constructed for each grid box by calculating the SIC anomaly from the time series of SST anomalies computed above and the linear relationship between the SST anomaly and SIC anomaly. The 1986 to 2005 mean of the HadISST2 SIC is then added to the time series of SIC anomalies and then some post-processing is performed. Firstly, ice holes, which occur where a grid box with no ice is surrounded by eight grid boxes with ice, are filled with the mean value of the eight surrounding grid boxes. Secondly, isolated ice, where a grid box with ice is surrounded by grid boxes with no ice, is removed by setting the SIC in the grid box to 0. Thirdly, a longitudinal smoother is applied to the resulting data field.

As a result of this procedure, five SST time series are obtained for each future time slice (near and far future), which have the same small-scale variability as the 1975–2004 HadISST SSTs and sample the inter-model variability in SST warming from CMIP5 both in terms of the GMSST and NA SST gradient. These five patterns are hereafter referred to as scenarios and are summarised in Table 2. Supplement Figs. S1 and S2 display the resulting warming imposed on observed SSTs for near and far-future scenarios, by season and scenario.

3.3 Potential evaporation estimates

Potential evaporation (E_pot) is defined as the amount of water that would evaporate from the land surface (soil, vegetation) into the atmosphere if soil moisture supply was not limiting. Although a form of E_pot is computed in the code of the land surface model MOSES 2, it cannot be directly saved as an output and must therefore be computed offline from the meteorological model output. Since E_pot is an important variable that is used as an input to some impact models (e.g. hydrological models), this computation is done and the estimated E_pot time series are included in the dataset along with the other variables. To do so, we estimate daily E_pot (in  mm day⁻¹) from the atmospheric model output based on the Penman–Monteith equation (Monteith, 1965) as follows (modified from Rudd and Kay, 2016):

where the following variables depend on the atmospheric variables: Δ is the rate of change of saturated vapour pressure with temperature ($\mathrm{kPa}{}^{\circ }{\mathrm{C}}^{-\mathrm{1}}$), R_n is net radiation at the surface (W m⁻²), e_s is the saturation vapour pressure at near-surface air temperature (kPa), e_d is the near-surface vapour pressure (kPa), r_a is the aerodynamic resistance to vapour transfer in the atmosphere (s m⁻¹) and r_s is the bulk surface (canopy or bare soil) resistance (s m⁻¹). The following are constants in Eq. (1): λ is the latent heat of evaporation (2.45×10⁶ J kg⁻¹), ρ_a is the near-surface air density (1 kg m³), c_a is the specific heat of air (1013  $\mathrm{J}{\mathrm{kg}}^{-\mathrm{1}}{}^{\circ }{\mathrm{C}}^{-\mathrm{1}}$) and γ is the psychrometric constant (0.066 $\mathrm{kPa}{}^{\circ }{\mathrm{C}}^{-\mathrm{1}}$).

The saturation vapour pressure e_s can generally be computed from temperature T (in ^∘C) as

Therefore, we can derive

where T is approximated by the average of daily minimum and daily maximum temperature ($T=(\mathrm{tasmin}+\mathrm{tasmax})/\mathrm{2}$). For the computation of e_s itself from daily data, however, we use a more accurate approach consisting of averaging e_s values estimated from daily minimum and maximum temperature (tasmin and tasmax), i.e.

The near-surface vapour pressure can be directly estimated from daily averaged dew-point temperature (tdps, in ^∘C) based on Eq. (2),

and the aerodynamic resistance is computed from the daily mean 10 m wind speed (wss, in m s⁻¹) using

hence including a logarithmic correction for wind height.

Finally, surface resistance r_s is computed as in Rudd and Kay (2016), consistently with MORECS E_pot estimates (Hough and Jones, 1997) and leading to the monthly surface resistance values shown in Table 4. E_pot is not only affected by meteorological conditions, but also by vegetation. In particular, for future projections an important driver for vegetation is the ambient CO₂ concentration: plant stomata may need to open less widely with higher CO₂ concentrations, thereby conserving water (e.g. Keenan et al., 2013). Not accounting for this effect in offline E_pot estimations has been shown to lead to an overestimation of continental drying (Milly and Dunne, 2016), which is particularly relevant for drought analyses. Therefore, along with E_pot estimates for future time slices using the same r_s value as in the baseline (variable pepm), an additional variable (pepm_adjrs) is introduced, which accounts for the impact of CO₂ on stomatal resistance and, therefore, on E_pot. To do so, we follow Rudd and Kay (2016) and use the estimate of change in crop and grass conductance per 1 ppm CO₂ concentration increase of Kruijt et al. (2008) ($-\mathrm{9.3}\times {\mathrm{10}}^{-\mathrm{2}}$ %) and apply these to change in the 30-year averaged CO₂ concentration between each future time period (469.5 ppm in the near future and 798.6 ppm in the far future) and 1975–2004 values (352.7 ppm). The resulting monthly r_s values are displayed in Table 4 for pepm and pepm_adjrs for near and far future.

Both variables (pepm and pepm_adjrs) are computed for each day using the r_s value of the corresponding month, and monthly values are subsequently computed by averaging the daily values.

3.4 Generation of continuous time series from single years

Unlike other extreme events such as heat waves, heavy precipitation or cold spells, droughts often extend over months to years. While for short events (i.e. from a day to, say, 1 month) the direct use of single-year simulations can be suitable, longer, continuous time series are required to study droughts. However, a limitation of weather@home is that it can generate simulations of only relatively short durations owing to the relatively slow computation on volunteers' personal computers. Here, we develop a methodology to derive plausible long continuous time series from a large ensemble of single-year simulations, whereby simulations in a given year are “stitched” to those of the next year using an appropriate criterion.

The criterion based on which simulations are stitched ideally ensures that the weather history of a simulation is consistent with the conditions found at the beginning of the next year's simulation to which it is stitched to. Given the slow nature of the temporal evolution of droughts, emphasis is put on obtaining continuous time series not necessarily from one day to the next, but rather on a temporal scale of the order of a week. Additionally, given the use of a large ensemble of simulations to construct multiple time series, the objective is not to derive time series that are really continuous (a task that may be considered impossible given the chaotic nature of the atmosphere), but rather to derive a set of time series that can be considered as continuous in the sense that their statistics can hardly be distinguished from those of continuous simulations. Therefore, we focus on those components of the climate system that exhibit significant temporal memory (or autocorrelation) and that may impact the atmosphere. The ocean (i.e. sea surface temperature and sea ice) is a major component with these characteristics; however, being prescribed to observations in our simulations, it is continuous by definition and hence it does not need additional consideration for stitching purposes. Another such component is the land surface, in particular soil moisture. Soil moisture exhibits a few relevant characteristics: first, it exhibits memory of typically a few weeks to months (e.g. Koster and Suarez, 2001) and, therefore, one may want to ensure that this memory is not lost in the stitching process – this may be particularly critical in the case of droughts. Second, the temporal evolution of soil moisture is mainly driven by precipitation minus evapotranspiration (P−E), i.e. by the weather in previous weeks to months. In other words, soil moisture can be seen as an approximate integrator of P−E over time. Ensuring that soil moisture is continuous therefore also likely constrains the history of the weather, which in turn increases the temporal consistency in atmospheric conditions in the stitched time series (for example, simulations with wet soils at the end of a year are likely to have exhibited wet conditions in December, while simulations with dry soils at the end of the year likely display less rainfall and higher temperature in December). Finally, soil moisture has been shown to be involved in key feedbacks relevant to droughts and heat waves (Seneviratne et al., 2010), such as soil moisture–temperature (Hirschi et al., 2011; Miralles et al., 2014) and soil moisture–precipitation (Roundy et al., 2013; Guillod et al., 2015) feedbacks. Therefore, ensuring continuous soil moisture avoids biases in the statistics of the weather in the following few weeks. Note that this last characteristic is most relevant in transitional regions between wet and dry climate and is probably not critical in the UK in the winter season, when our simulations are stitched. Other variables that could have been considered include snow; however, given that snow is not very frequent at the end of December over the UK, it may be difficult to distinguish between the large number of simulations which do not exhibit any snow at all.

Figure 1Illustration of the simulation design and stitching, using soil moisture model data averaged over the Thames catchment. Each panel shows, for a given year (a: 1990; b: 1991), 5-day averages of soil moisture in the upper 1 m of the soil for 20 model simulations. The first month of the simulations (December of the previous year, part of the spin-up) is indicated by grey lines, followed by the 12 months (January to December) in colours. End-of-year values of 1990 simulations and the same time steps in the spin-up leading to 1991 values, highlighted by dark grey boxes, have to be compared to find the combination allowing the best match between  simulations. Light grey boxes indicate the same time steps that will be used to stitch to 1989 (a) and 1992 (b).

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Based on these considerations, we use soil moisture as a basis for stitching. Figure 1 displays an example of time series that are obtained with our simulation setup for two consecutive years, with the first month of the simulations (grey lines, implicitly part of a 13-month spin-up) leading to 12-month simulations (coloured). Stitching the 1990 simulations to the 1991 simulations is based on identifying the best match between the 1990 end-of-simulation values (last value for each simulation) and the value at the same time step in the 1991 simulations, i.e. the last value in the spin-up (in grey) leading to the 1991 simulations. Five-day averages (i.e. pentads) of soil moisture in the upper 1 m of the soil (three out of four model levels in this case) over the British Isles are used for this purpose.

While Fig. 1 is useful to understand the principle of the stitching methodology, the problem is more complex for gridded data as there are multiple locations (or grid cells) and, thus, multiple time series to consider for each set of simulations. An appropriate simplification of this problem is to ensure continuity of the main spatial patterns of soil moisture. To do this, we concentrate on the main modes of variability by computing the EOFs for the last pentad of December at the end of our  simulations (Fig. 2). The leading EOF pattern is homogeneous in sign and thus characterises the overall soil moisture conditions within the analysed domain, while the second EOF characterises a southeast–northwest contrast. Together, these two leading EOFs explain 60 % of the total variance, while further EOFs account for a much lower fraction of the variability (6 % and lower). Hence, we retain these two EOFs and use the reduced two-dimensional space of the principal components corresponding to these EOFs (hereafter, PC1–2 space) to compare soil moisture fields and find similar conditions, defined by the lowest possible distance in this two-dimensional space.

Figure 2Leading EOFs of upper 1m soil moisture over the British Isles in the last pentad in December. The fraction of explained variance is indicated on each panel.

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The procedure used for stitching is as follows.

1. Wait until a minimum of n simulations is available for each year, which will allow the creation of n time series (e.g. n=100 for historical baseline).

2. Compute the PCs of soil moisture at the last pentad of December in months 1 (“start of run”) and 13 (“end of run”) of each simulation, i.e. obtaining the starting and ending soil moisture conditions.

3. Starting with the year Y with the lowest number of simulations available (=n), all simulations are stitched forward as follows: the distance in the soil moisture PC1–2 space between each end-of-run value from simulations on year Y and each start-of-run value from simulations on year Y+1 is computed. The Hungarian algorithm (R function “solve_LSAP” in package “clue”, Kuhn, 1955, 1956; Papadimitriou and Steiglitz, 1982; Hornik, 2005, 2016) is then applied to find the combination that minimises the sum of the squared distances.

4. The year Y+1 simulations that have been selected are used and the previous step is repeated until the last year of the time series is reached.

5. The same procedure is applied backward, i.e. matching start-of-run values on year Y to end-of-run values on year Y−1. This is done repeatedly until the first year of the time series is reached.

The output of this procedure is a table which lists, for each time series, the simulation identifier for each year. The performance of the stitching methodology is evaluated from the historical baseline (1900–2006) by considering the soil moisture error obtained through stitching, using the comparison of stitched and continuous simulations.

Figure 3Temporal continuity of soil moisture in the stitched ensemble compared to continuous simulations in the historical baseline (1900–2006). (a) Bivariate distribution of soil moisture PCs 1 and 2 at the last December pentad. (b–d) Empirical cumulative distribution function (ecdf) of the changes in the PC1–2 space between the last pentad in December and the three subsequent pentads (colours) in continuous simulations (continuous lines), the stitched ensemble (thick lines) and a randomly stitched ensemble (points). The dashed black line shows the ecdf of the same distance at the time of stitching, i.e. between the same pentad in stitched simulations. (b) Absolute distance in the PC1–2 space, (c) change in PC1 and (d) change in PC2.

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Figure 3a shows the distribution of simulations in the PC1–2 space, for the last pentad in December. As detailed above, to create continuous time series, soil moisture at the end of the simulations on year Y (month 13 of the simulation; last December pentad) is compared to soil moisture at the same time step in month 1 of simulations leading to year Y+1. The distribution of the obtained distances in the PC1–2 space at the time of stitching is shown in black on Fig. 3b. To evaluate this in the context of a continuous simulation, we analyse changes between consecutive soil moisture pentads in continuous simulation (continuous lines on Fig. 3b–d), taken from the last pentad in December to any of the first three pentads in January (i.e. transition at the beginning of our simulations). We find that the difference at the time of stitching (dashed black line) is substantially smaller than typical changes with a lag of one pentad in continuous simulations (continuous green line), both in terms of distance in PC1–2 space (Fig. 3b) and changes in these PCs considered individually (Fig. 3c, d); i.e. the soil moisture error is smaller than a temporal lag of one pentad. Furthermore, changes between the last December and first January pentads (i.e. with a lag of one) are only slightly larger in the stitched ensemble (dashed lines) than in continuous simulations (continuous lines). For a lag of three pentads (purple), the changes in soil moisture PCs are very similar in stitched and continuous simulations. In these panels, these changes can also be compared to what would happen in a randomly stitched ensemble (dotted lines). The changes in such an ensemble are, as expected, independent of the lag (since no temporal correlation is retained) and are substantially larger than those found in both the soil-moisture-stitched and continuous ensembles (dotted lines, lying on top of each other for all lags). These results show that the presented methodology allows successfully stitching single-year simulations to each other, thereby ensuring consistency in weather statistics on timescales of weeks.

4.1 Mean climate and bias correction

4.1.2 Bias correction

With the biases in temperature being relatively small, they are not explicitly corrected. Although correcting the biases in E_pot might seem appealing owing to their significant amplitude, such a procedure is not attractive since it comes with strong assumptions that might not hold. First, the origin of E_pot biases may be multiple, from temperature biases to bias in the radiation (e.g. overestimated net radiation owing to underestimated cloud cover) and aerodynamic (wind) components of the E_pot computation. Hence, to properly bias-correct E_pot, variables used to compute it should be corrected individually before computing E_pot. However, the lack of long-term gridded observations at a suitable resolution for some of these variables hampers such a procedure. Second, E_pot is not observed directly but estimated from meteorological variables, leading to large discrepancies between observed estimates owing to various assumptions (formulation, parameters) and data used to compute them. This implies that a bias-corrected E_pot would be highly dependent on the chosen source of observed E_pot. Third, the assumption that the same bias correction can be applied to future scenarios would be even more questionable for E_pot than for precipitation because of the interdependence of the variables used to compute it. Based on these considerations, E_pot is not bias corrected in our dataset. However, users are recommended to investigate whether these biases have an impact on their results and to take these into account, especially when investigating summer drought. This recommendation also applies to users that compute E_pot themselves using an alternative formulation.

By contrast, the substantial precipitation biases may be particularly problematic for drought analysis and correcting for these is therefore necessary. To do so, a simple linear approach was chosen, using monthly bias-correction factors (e.g. Lafon et al., 2013). The choice of bias-correction algorithm depends on the nature of the biases present and the uncertainty with which properties of the observed and modelled precipitation distributions can be estimated (e.g. Teutschbein and Seibert, 2012; Lafon et al., 2013). For example, if biases are present in higher-order moments of the simulated precipitation distribution, then more sophisticated bias-correction techniques are warranted than if only the mean is biased. Nonetheless, the higher-order moments of the precipitation record can only be corrected if they can be estimated with confidence, which is not always possible for short-duration datasets. There is therefore a trade-off between reducing biases and introducing additional (often unconstrained) uncertainty. As recommended by Lafon et al. (2013), we use the simplest possible method which is able to correct significant biases in the data. In the present analysis we use a linear bias correction, which we calculate offers adequate correction of seasonal biases in the mean and which does not adversely affect higher-order moments of the rainfall distribution. It is also noted that for drought studies using climate model outputs the distribution of dry days (i.e. days with precipitation <1 mm) can be important to preserve. In the present case we find that this distribution is maintained without further specific corrections (Fig. S4). These were defined based on the overlapping time period between all observational datasets (CEH-GEAR, CHESS-PE, E-OBS) and our baseline, i.e. years 1961–2006. The mean precipitation for each calendar month was computed from the 100 baseline time series, and their ratio to the corresponding values in CEH-GEAR were computed (Fig. S5). However, in order to avoid sudden discontinuities between grid cells, a spatial smoothing was applied to the ratio using a 3-by-3 grid cells moving box and taking weights of 1∕2 for the centre box and 1∕16 for the surrounding eight boxes, leading to the precipitation bias-correction factors shown in Fig. 5. Note that only the Great Britain coverage of CEH-GEAR data is used for bias correction, since CEH-GEAR data over Northern Ireland are available as a separate product and have not been processed.

Figure 5Bias-correction multiplicative factor applied to precipitation. A spatial smoothing was applied to the monthly ratios between observed (GEAR) and modelled (w@h2) 1961–2006 precipitation (see Fig. S5 for the unsmoothed ratio).

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Subsequently, daily and monthly precipitation values were multiplied by the factor for the corresponding month. The bias-corrected precipitation is also made available as part of the dataset as an additional variable (prbc, see Table 3). Unless explicitly mentioned, analyses in the rest of this study are based on bias-corrected precipitation data.

4.2 Hydro-meteorological extremes

In this section, the ability of the time series to represent the distribution of dry and wet extreme precipitation events is assessed, first on the scale of Great Britain averages for prolonged dry periods (Sect. 4.2.1) and then on the regional scale for prolonged dry periods and for shorter, high-precipitation events (Sect. 4.2.2). Comparison to CEH-GEAR is done based on the overlapping years, i.e. 1900–2006, and using only data over Great Britain.

Figure 6Return time plots of (a–d) low seasonal precipitation and (e–h) low precipitation accumulated in 1–4 consecutive hydrological years, for Great Britain averages from 1900 to 2006. (red) CEH-GEAR, (grey) individual w@h2 time series and (black) all w@h2 time series pooled together. For each time series, seasonal or (multi-)year averages of precipitation were computed and spatially aggregated over Great Britain prior to the computation of return values.

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4.2.2 Regional extremes

The analysis presented in the previous section was applied to regional averages of bias-corrected precipitation. To summarise the main findings, we focus on six selected UKCP09 river basin regions (Fig. 7; results for all 19 regions are shown in the Supplement) which are representative of various climate conditions within the country and include two regions particularly prone to droughts (Thames and Anglian). We focus on precipitation totals over multiple hydrological years and display, for each region, the distribution of 100 return values estimated from the individual time series as box plots, with the value estimated from the CEH-GEAR dataset overlaid as a white dot, for a number of return times (Fig. 8; see Fig. S10 for all regions). Overall, the observed values lie well within the range of modelled values, with a few exceptions: in some regions (e.g. North East Scotland) the time series slightly underestimate the values (i.e. overestimate drought intensity), while values are overestimated (i.e. dryness is underestimated) in the Western Highland region, probably due to the remaining bias after correction (see Sect. 4.1.3). For shorter durations, a similar plot for low seasonal precipitation is shown in Fig. S11 and allows dataset users to assess the performance of the dataset depending on their region and purpose.

Figure 7Subset of six river basin regions in Great Britain used in the analysis. All 19 UKCP09 river basin regions are shown in Fig. S3.

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Figure 8Return values of low precipitation accumulated over 1–4 hydrological years (x axis) in the 100 baseline time series (box plot) and in CEH-GEAR (white dot) for each region (panel), for return times of 5–50 years. See Fig. S10 for the plots for all regions and Fig. S11 for the same analysis on seasonal precipitation rather than hydrological years. Whiskers display the range from individual time series.

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Figure 9Return values of high-precipitation indices rx1day, rx5day and rx30day (x axis) in the 100 baseline time series (box plot) and in CEH-GEAR (white dot) for each region (panel), for return times of 5–50 years (colour). Bias-corrected precipitation data are boxed in white (raw precipitation data in black). Whiskers display the range from individual time series. Note that for these metrics, the raw precipitation data compares better to observations than bias-corrected values. See Fig. S12 for the plots for all regions.

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Figure 10Difference in near-surface air temperature between far future and baseline (years 1975–2004 therein) for each season (row) and scenario (column). Hatching indicates grid cells with statistically non-significant changes at the 95 % level according to a two-sided T test (almost all grid cells are significant here). The corresponding figure for the near-future time slices is shown in Fig. S13.

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Figure 11Comparison of temperature projections with UKCP09: for each region, boxes show changes (2070–2099 minus 1961–1990) in JJA (left boxes) and DJF (right boxes) in the five sets of MaRIUS time series and in UKCP09 (high emission scenario: SRES A1FI; 10 000 values available). Whiskers display the 10–90 % range from each group. See Fig. S14 for the plots for all regions.

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Although the dataset was created within a project focusing on droughts, it could be used for other hydro-meteorological extremes such as floods. Therefore, we provide validation of high-precipitation events at the regional level by focusing on total precipitation over a defined number N of consecutive days, rxNday for N=1, 5 and 30 days. Figure 9 shows the return values for these three indices in a similar way as Fig. 8, but showing the results for both raw (uncorrected) and bias-corrected precipitation (see also Fig. S12 for all regions). The observed estimates are found to mostly lie within the spread of values obtained from the climate time series for raw precipitation but less so for bias-corrected precipitation. This suggests that the simple linear monthly bias correction that has been applied may not be appropriate for such events. An alternative hypothesis is that the model represents the processes related to high-precipitation formation relatively well (e.g. representation of UK-scale dynamical systems and thermodynamic processes, Schaller et al., 2016) but has more difficulties in representing longer-term persistence – a common feature of climate models (e.g. Ault et al., 2012). Therefore, we recommend the application of another bias-correction technique (e.g. quantile–quantile mapping) for studies on high-precipitation events.

It should be noted that the analysis of short-term events should be done on individual years separately rather than on the whole time series; for example rx5day should not lie at the transition from one year to the next since the weather is not strictly continuous (Sect. 3.4). For example, for rx5day, for each year, the first value is from 1–5 January and the last values from 25–30 December (the 360 days in a year are split into 12 months of 30 days), but it may not be appropriate to use the five pentads that range from 26 December–1 January to 30 December–4 January, in order to exclude undesirable concatenation of inconsistent weather systems.

5.1 Changes in mean climate

Figure 10 shows the changes in mean temperature in all far-future scenarios with respect to the baseline (1975–2004) and for each season. All changes are statistically significant at the 95 % level according to a two-sided T test based on climatological values from individual time series for both time periods. Generally, temperature increases are highest in the scenarios with higher global mean SST increases (FF-p90x and FF-p90n) and lowest in the scenarios with low global mean SST increases (FF-p10n and FF-p10x). Consistently with UKCP09, temperature increases are largest in the southeast and in summer in all scenarios. Similar but lower increases in temperature are found in the near-future time slice (Fig. S13).

Figure 12Same as Fig. 10 but for precipitation (bias corrected, prbc). Hatching indicates grid cells with statistically non-significant changes at the 95 % level according to a two-sided T test. The corresponding figure for the near-future time slices is shown in Fig. S15.

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Figure 13Same as Fig. 11 but for precipitation, in %. Grey boxes indicate cases where 0 lies within the 5–95 % range. See Fig. S16 for the plots for all regions.

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Figure 11 shows the distribution of all possible changes in temperature (i.e. from all combinations of the future time series with the baseline time series) and in UKCP09 (high emission scenario A1FI), relative to the years 1961–1990 for consistency with the UKCP09 data. The spread of UKCP09 values accounts for a wider range of uncertainty than in our time series, as it includes various climate models and parameter uncertainty. However, our various future scenarios generally cover the range of mean changes projected by the latest UK climate change scenarios (see also Fig. S14 for all regions).

The patterns of changes in seasonal mean precipitation (Fig. 12) highlight that, while in winter precipitation changes seem mostly related to global mean SST increases (as for temperature), summer precipitation changes are most sensitive to the North Atlantic SST gradient: time series FF-p10n and FF-p90n induce the smallest precipitation decreases, while FF-p10x and FF-p90x lead to the largest precipitation decrease. Thus, large SST gradients in the North Atlantic (as defined by the metric described in Sect. 3.2) lead to drier summer conditions. Note that the median scenario (“FF”, called MMM in this figure for multi-model median) exhibits the CMIP5 median change in this feature, while the four other scenarios depict extreme cases in both direction and should hence be considered as sensitivity scenarios. The mechanisms through which SST influence precipitation may include the North Atlantic Oscillation (NAO), which has been shown to be influenced by SSTs in the Atlantic and to influence European weather (e.g. Woollings et al., 2015). It should be noted that changes in raw (without bias correction) precipitation are smaller in JJA, leading to an overall weaker drying in absolute terms. Most of the changes are statistically significant, apart from substantial areas in MAM and SON in individual cases and small areas in DJF. Similar patterns of change, but smaller in amplitude and thereby less robustly significant (especially in DJF), are identified in the near-future time slices (Fig. S15). By definition, relative changes are similar in both raw and bias-corrected precipitation as the same multiplicative factors are applied to both time periods.

Comparison of precipitation changes to UKCP09 (Fig. 13; see also Fig. S16 for all regions) reveals that the simulated time series lies on the dry end of the standard UK climate projections. The changes may thus be more similar to UKCP02, the previous UK climate scenarios, which were based on the same models that are used in w@h2. This feature is important to keep in mind, especially when analysing changes in drought. The dataset can thus be seen as an ideal test bed for dry conditions, but the actual future may potentially not be as dry as suggested by the climate time series presented in this paper. Note that in some cases, such as DJF in North East Scotland, changes are mostly not statistically significant in the sense that no change is included in the 5–95 % range.

Figure 14Same as Fig. 10 but for E_pot (with stomatal resistance adjusted to CO₂ concentration; see Fig. S17 for the changes when stomatal resistance is kept constant). Hatching indicates grid cells with statistically non-significant changes at the 95 % level according to a two-sided T test. The corresponding figures for the near-future time slices are shown in Figs. S18 and S19.

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Figure 15Distribution of return values of the 10-year event for low precipitation on two consecutive hydrological years (box plot) for each region (panel) and scenario (colour). Whiskers display the range from individual time series. Grey boxes for future scenarios indicate statistically non-significant change in mean return value with respect to the baseline at the 95 % level according to a two-sided T test. See Fig. S20 for the plots for all regions; the corresponding figure for the near-future time slices is shown in Fig. S21.

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Figure 16Distribution of return values of the 10-year event for rx5day (box plot) for each region (panel) and scenario (colour), using raw precipitation data (i.e. not bias corrected). Whiskers display the range from individual time series. Grey boxes for future scenarios indicate statistically non-significant change in mean return value with respect to the baseline at the 95 % level according to a two-sided T test. See Fig. S22 for the plots for all regions; the corresponding figure for the near-future time slices is shown in Fig. S23.

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Finally, projected changes in seasonal mean E_pot are displayed in Fig. 14, using the E_pot formulation where stomatal resistance is adjusted to CO₂ future concentrations. E_pot values substantially increase in summer and to a lower extent in autumn and spring. The changes are mostly driven by the global mean SST increase, similar to temperature and as one may expect due to the strong controls exerted by temperature on this variable. We note that not adjusting stomatal resistance to increased CO₂ concentrations in the future (Fig. S17) would result in a significantly stronger increase in E_pot and therefore recommend the use of pepm_adjrs for future analyses to prevent overestimating increases in drought. As for temperature and precipitation, the near-future time slice displays changes that are qualitatively similar to those of the far future but smaller in amplitude (Figs. S18 and S19).

5.2 Changes in hydro-meteorological extremes

As for the validation of extremes done in Sect. 4.2.2, we concentrate on extremes of low precipitation cumulated over a number of consecutive hydrological years and on high-precipitation extremes cumulated over a small number of consecutive years.

Figure 15 displays the 10-year return value (i.e. third highest value in each 30-year time series) of low precipitation accumulated over 2 hydrological years (see Fig. S20 for all regions). The distribution of the values estimated from each time series is shown for the baseline and for each far-future scenario, whereby boxes for future scenarios whose mean value does not significantly differ from the baseline according to a two-sided T test at the 95 % level are displayed in grey. Generally, a strong drying is found; i.e. 10-year dry events are getting more intense. In most regions, most of the difference between the individual future scenarios (i.e. SST warming patterns) appears to be related to the North Atlantic SST pattern, rather than to global mean SSTs. This suggests, given the findings of Fig. 12, that the summer response may drive the changes in longer droughts (2 hydrological years in this case).

Similarly, Fig. 16 displays the change in 10-year return value of rx5day, using uncorrected precipitation data since these perform better than bias corrected for high-precipitation events as highlighted in Sect. 4.2.2. High-precipitation extremes are expected to increase in intensity in most scenarios, except in those with low global mean sea surface temperature increase (FF-p10n and FF-p10x) in some regions, despite a smaller signal-to-noise ratio induced by the sampling of 10-year return values from 30-year time series. Unlike for drought, global mean SST increases appear to be the main factor leading to the response in extreme high precipitation, consistently with the Clausius–Clapeyron relationship (higher SST leading to higher evaporation and higher moisture content) and with the current understanding of atmospheric thermodynamics (e.g. Schaller et al., 2016). Results for all regions are shown in Fig. S21.

In the near-future time slice, similar but smaller changes are found for low precipitation (Fig. S22); i.e. an increase in drought severity may already be expected in this time period. However, for high-precipitation events (rx5day, Fig. S23), the increase is very small in this time period and is in most cases not statistically significant.