Climate change is affecting the frequency and intensity of extreme weather, with implications for infrastructure adaptation and human health . Over the 21st century, progress has been made in attributing the influence of climate change on individual extreme weather events . However, while much attention has focused on extreme weather, less focus has been given to how climate change will affect the experience of everyday, non extreme weather. Though extreme weather is impactful, and can contribute disproportionately to the mean , by definition it represents weather on only a small number of days. Previous work has considered how climate change has and will affect the occurrence of mild weather and the closely related concept of “outdoor days” , defined variously as days with comfortable near-surface temperature and/or clear skies and minimal precipitation. Model projections broadly show an increase in mild conditions in the mid-high latitudes and a decrease in the tropics , albeit with substantial regional variation. However, regional projections of temperature and precipitation depend on uncertain future changes in large-scale weather patterns .

A different approach is to consider how the thermodynamic aspects of climate change – those related to rising temperature and humidity – will affect day-to-day weather, given no change in weather patterns. Those effects represent the most robust aspects of regional climate change. We adopt a storyline approach to explore changes in the weather of a year from history. reconstructed an extreme event from 1903, Storm Ulysses, in an atmospheric reanalysis system, and translated its impacts into a warmer world. Using the same experiments, as well as an additional novel reanalysis experiment described below, we present a broader survey of changes across the 12 months of 1903. The weather from all 12 months of 1903 is first reconstructed using an atmospheric reanalysis system that assimilates observations of atmospheric pressure (including rescued pressure observations not available in the production version of the reanalysis) and uses observed SSTs and sea ice concentrations as lower boundary conditions . Then, the model and data assimilation system are completely re-run while assimilating the same pressure observations, but altering the SST boundary conditions and atmospheric CO2 in order to translate the historical weather into a warmer world. As the same pressure observations are assimilated in each experiment, the experiments experience the same weather patterns, minimising uncertainty due to projected changes in atmospheric circulation. We then explore how the thermodynamic impacts of day-to-day weather differ in a warmer and moister atmosphere. For example, in the absence of circulation changes, how does a given ocean warming affect the distribution of daily temperature? Do cold days and hot days warm by the same amount? Does rainfall become more or less frequent, and more or less variable from day to day?

Our approach is similar to other storyline attribution methods, such as nudging experiments where the large-scale winds are relaxed towards specified values , and the pseudo global warming (PGW) method, where the boundary conditions for regional climate models (RCMs) are adjusted to reflect the effects of climate change . These adjustments, often referred to as PGW “deltas”, are chosen such that the imposed dynamical driving at the RCM boundaries is unchanged in the warmer world simulation. Similarly to the reanalysis experiments, there is no change in intraannual variability between the control and “counterfactual” (nudged or PGW) simulations, which allows robust signals to be extracted from shorter simulations than are typically required with free-running climate models . The main differences between these two methods are in how the circulation is constrained: in PGW, typically the 3D dynamics are imposed only at the edge of the RCM domain, while large-scale nudging can be performed globally or across a smaller regional domain in the free troposphere ; in the reanalysis experiments, the synoptic circulation at the surface is constrained through the assimilation of surface pressure observations. Long historical records of surface pressure and SST observations allow the reanalysis approach to study periods that occurred before the advent of widespread upper-air observations in the mid-20th century. As in some nudged simulations, the reanalysis experiments are also global, allowing multiple locations to be studied in a single run. The reanalysis experiments in this paper thus offer an additional and computationally efficient line of evidence regarding the thermodynamic effects of warming on regional weather and climate.

We begin by describing the reanalysis system and assimilated pressure data before presenting a global overview of changes in the warmer world experiments. The available pressure observations from 1903 are not distributed evenly in space, which restricts the regions we can study in detail using this approach for this particular year. We therefore focus on four regions with a high density of pressure observations in 1903. Our results are summarised in the final section.

We reconstruct the weather of 1903 using the NOAA-CIRES-DOE 20th Century Reanalysis version 3 data assimilation system (20CRv3, ). Using an Ensemble Kalman Filter, 20CRv3 assimilates observed pressure values with a NOAA atmospheric model to provide a best estimate of the atmospheric state at each point in time. The atmospheric model used is the NOAA GFS v14.0.1. The atmospheric model is coupled to the Noah land surface model, which incorporates a 4-layer soil model and dynamic fractional snow cover . An 80-member ensemble of 3-hourly atmospheric fields is produced on a 0.7° Gaussian grid. SSTs and sea ice concentrations are prescribed from observed values. The system assimilates pressure observations taken over land and ocean as well as tropical cyclone central pressures from best-track datasets (see , for details of the boundary conditions and pressure observations).

We present results from three reanalysis experiments. The first experiment, denoted 20CRv3⁺, is identical to the improved reanalysis in . It consists of a reconstruction of 1903 using the same SST and radiative forcings as in the production version of 20CRv3, with two further changes: a refinement of the data assimilation scheme, and the inclusion of many additional rescued pressure observations over Europe. These changes sharpen features of the weather fields and improve the utility of the reconstructions; see the appendices of for details. Figure 1 shows the pressure observations used in the 20CRv3⁺ experiment. Some regions are much richer in historical pressure observations than others. We expect the atmospheric circulation to be better constrained in these regions than in regions with fewer pressure observations, and so we focus most of our analysis on four regions with a high density of observations in 1903, shown by the blue boxes in Fig. 1. These regions cover northwestern Europe (NW_Europe), the western Mediterranean (Western_Med), the East Coast of the US (US_East_Coast), and Southeastern Australia (SE_Aus).

In addition to 20CRv3⁺, two further experiments are performed to translate the weather of 1903 into a warmer world. The first, denoted +2 K, is as in : a uniform +2 K perturbation is added to the SSTs, with radiative forcings kept at 1903 values. In the second, denoted +2 K + CO2, in addition to the +2 K SST perturbation, global atmospheric CO2 concentration is increased to 530 ppm. Differences between the two warmer world experiments therefore indicate the direct role of the CO2 radiative forcing. Sea ice boundary conditions are unchanged in the warmer world experiments compared to 20CRv3⁺. Sensitivity tests suggest that this can cause spurious signals near the ice edge, but these effects do not extend far from the ice edge due to the strong constraint of prescribed SSTs and the assimilation of pressure observations (not shown). The SST, CO2, and sea ice conditions are idealised and do not reflect observed or projected patterns of change – they are chosen to illustrate the role of ocean warming and atmospheric composition on the weather of 1903 in a simple way. In both experiments, the same pressure observations are assimilated as in 20CRv3⁺, so that the atmospheric flow is similarly constrained in all three experiments; we thus isolate the thermodynamic impacts of the perturbations on the reconstructed weather of 1903. We analyse 12 months of data (from January to December 1903) in each experiment. Each warmer world experiment is spun up for 6 months prior to January 1903 to allow the atmosphere to adjust to the perturbed boundary conditions. The 20CRv3⁺ and +2 K experiments are as in and , while the +2 K + CO2 experiment is novel.

An example of everyday weather in a well-observed region is shown in Fig. 2, which shows 3-hourly time series of 2 m-temperature and precipitation in 20CRv3⁺ and the +2 K + CO2 experiment averaged over Central England (the boxed area in Fig. 8b–d) for January and July 1903. The equivalent plots for the +2 K experiment are shown in Fig. S1 in the Supplement. Temperatures in 20CRv3⁺ are in good agreement with observed daily values from the Central England Temperature series (CET) , which represents observed average temperatures over a similar region. As no temperature observations are assimilated, this comparison provides an independent verification of the reanalysis skill in reproducing observed weather in this region. The warmer world simulations show day-to-day fluctuations in temperature and precipitation in phase with those of 20CRv3⁺, which indicates that the synoptic circulation is well constrained by the assimilated observations (the experiments experience the “same” weather). Temperatures in the warmer world experiments are consistently warmer than in 20CRv3⁺, with little overlap between the 20CRv3⁺ and warmer world ensemble shading, especially in January. The grey dashed line in the top panel indicates the air frost threshold (0 °C). Eight nights in the 20CRv3⁺ ensemble-mean dip below this threshold, while only five do in the +2 K + CO2 experiment – a reduction of 60 % in this small sample. For comparison, the annual number of air frost days in the UK has declined by around a quarter since the 1980s . Precipitation peaks in the warmer world experiments generally line up with those in 20CRv3⁺, though rainfall is less well constrained by the assimilated pressure observations than is near-surface temperature.

In addition to Central England, we also show a version of Fig. 2 for a region over northern Patagonia with far fewer nearby land-based pressure stations (Fig. S2, the green boxed region in Fig. 1). Day-to-day variations in temperature and precipitation are surprisingly similar in both experiments, despite the much weaker observational constraint than over Central England (Fig. 1). Although we restrict most of the later analysis to well-observed regions, Fig. S2 suggests that even a small number of nearby observations (from ships in this case) can constrain the circulation relatively well in the reanalysis system. This is particularly noteworthy given that the markers in Fig. 1 represent observations across all of 1903; within a single assimilation window, the density of ship-based observations will be much lower than that shown in Fig. 1.

Focusing on the year 1903 allows us to exploit the existing reanalysis experiments of . Globally, 1903 was a cold year: it is the 3rd coldest in the 175-year HadCRUT5.1 dataset Fig. S3a, and it is in at least the coldest third of years in each of the four well-observed regions we analyse in later sections (the lowest rank is 57th/175 in NW_Europe, i.e. 32nd percentile; Fig. S3b–e). The eruption of the Santa Maria volcano in October 1902 – one of the largest tropical volcanic eruptions of the century – presumably contributed to the generally cool conditions . Note that the volcanic aerosol forcing is identical in all of our experiments. The cold baseline conditions in 1903 mean that the perturbed climates in the warmer world experiments are not much warmer than some of the later years in the original 20CRv3 dataset, for which the system's performance has been validated. This builds confidence in the ability of the reanalysis system to plausibly represent the warmer world climates in our experiments.

Before focusing on regional aspects, we first present a global overview of changes in the warmer world experiments. Figure 3 shows globally and annually averaged 2 m-temperature, precipitable water (PWAT) and precipitation rate in each experiment. The distributions show the spread of values across the 80 ensemble members. The spatial patterns of the ensemble-mean temperature and precipitation changes are shown in Fig. 4. As seen in Fig. 3a, globally, the +2 K experiments are 2.1 K warmer than 20CRv3⁺ in the ensemble-mean, with the additional 0.1 K of warming arising due to enhanced warming over land (Fig. 4a). This highlights the prominent role of oceanic warming in driving continental temperatures, even in the absence of changes in CO2 forcing, such as through the moistening of continental air and hence enhanced downwelling longwave (LW) radiation over land . Interestingly, however, we also find an important role for direct CO2-induced warming, with a further 0.2 K of global warming in the +2 K + CO2 experiment due to additional enhanced warming over extratropical land (Fig. 4b). This corresponds to a larger global land/ocean warming ratio (1.35 in +2 K + CO2, compared to 1.21 in +2 K). Both warming ratio values are notably smaller in the warmer world experiments than in climate models and observations e.g.; the warmer world experiments are idealised and differ from observed climate change in several ways, including the uniform SST increase and the lack of changes in other forcing agents such as tropospheric aerosols (which are constant at modern day levels in 20CRv3), so we would not expect the ratios to match the real world values precisely. Another idealised design choice is the unchanged sea ice fields in the warmer world experiments, which is likely the reason for the weak Arctic warming in Fig. 4a. Keeping sea ice fixed in the warmer world experiments will result in a smaller increase in global-mean temperatures than if more plausible reductions in sea ice concentration had been specified (Fig. 3a). Enhanced warming also occurs over regions of high elevation including the Andes and Himalayas (Fig. 4a–b), consistent with thermodynamic mechanisms such as a reduction in snow albedo and Planck feedbacks . The direct CO2-induced warming is small over tropical land (Fig. 4b–c), likely due to masking of its radiative forcing by high clouds and upper-tropospheric water vapour . It has a larger warming effect in the extratropics, particularly over arid regions such as the Sahara and the Western US. In the latter region, additional warming of 0.6 K or more is seen due to the higher CO2 levels, which is around a fifth of the total warming in the +2 K + CO2 runs. This is likely to be a purely radiative consequence of the CO2 forcing, as the high density of pressure observations in the Western US will strongly constrain the circulation in each experiment (Fig. 1). Thus, even in the absence of circulation changes, the direct warming effect of atmospheric CO2 varies regionally and can be large in the extratropics.

Higher surface temperatures are associated with increased atmospheric moisture content in the warmer world experiments, as seen in globally averaged precipitable water (PWAT, Fig. 3b). The PWAT increases follow the same ordering as the temperature distributions. Accounting for the additional warming in the +2 K + CO2 runs, the relative increase in PWAT is similar in both experiments and is broadly in line with Clausius-Clapeyron scaling at 8.5 % K⁻¹ and 8.2 % K⁻¹ respectively .

Global precipitation also increases in the warmer world simulations (Fig. 3c), but more slowly than atmospheric moisture. Latent heating from precipitation is balanced globally by LW cooling of the atmosphere, which increases as the surface and atmosphere warm. This explains why a smaller precipitation increase is seen in the +2 K + CO2 experiment than in +2 K, despite a larger increase in atmospheric moisture: additional CO2 reduces LW emission to space and thus a smaller increase in precipitation is required to balance it. Hence, in isolation, the higher CO2 concentration acts to blunt the precipitation increase that arises due to surface warming . The increase of 2.4 % K⁻¹ in the +2 K + CO2 experiment is notably similar to values seen in climate model experiments , despite the lack of strict energy conservation in the reanalysis system due to the inclusion of analysis increments.

The spatial pattern of precipitation change is shown in Fig. 4d–e. In many respects, the pattern of change in the warmer world simulations resembles the canonical projected response to greenhouse warming in comprehensive climate models , despite the specificity of the 1903 SST boundary conditions and atmospheric circulation. Precipitation increases over much of the extratropics, while drying is seen over the Mediterranean and subtropical ocean basins. Precipitation intensity over land increases everywhere, but land areas including Africa, the western US, and Mediterranean experience fewer wet days (Fig. S4). Much of the drying over subtropical oceans is due to the inclusion of CO2 (Fig. 4f), which may reflect a shift of convection from ocean to land in association with the enhanced land warming driven by increased CO2 . The sparse observations over much of the tropics mean that the atmospheric circulation is less constrained in these regions; in the following sections, we therefore focus on changes in the four well-observed regions identified in Fig. 1.

An advantage of the counterfactual reanalysis experiments is the ability to look at changes in climate impacts over a variety of timescales, as the assimilation process means weather patterns in the warmer world counterfactuals remain close to the original (factual) reanalysis. While short, intense weather events can lead to acute damages, extreme months or seasons, or even sequences of seasons, can also be significant for sectors such as agriculture . Here we present an example of an event falling between the annual timescales discussed in previous sections and the synoptic timescales that are typically the subject of storyline attribution studies.

October 1903 is the wettest recorded calendar month for the UK (220.0 mm, in a series back to 1836; ) and in the longer England and Wales Precipitation series (218.1 mm, in a series back to 1766 ). Figure 8a shows the October 1903 rainfall total in a gridded observational product that interpolates between in-situ measurements . Large parts of Wales, Southwest England, and western Scotland recorded rainfall totals exceeding 200 mm. These regions also receive the most rain in 20CRv3⁺ (Fig. 8b), though the magnitude is smaller in the reanalysis than in the observations. We would not expect perfect quantitative agreement with the observations as the reanalysis grid is too coarse to fully resolve the orography in these regions; similar underestimates are seen over western regions of Great Britain in the case of Storm Ulysses earlier in 1903 . Output from the reanalysis could be downscaled using regional atmospheric models to better represent rainfall over mountainous regions if desired. Historical daily gridded rainfall observations are rarer outside the UK, so we also validate 20CRv3⁺ rainfall against station observations from each of the well-observed regions in the Supplement (see Sect. S2 in the Supplement).

Over flatter terrain, the reanalysis is in better agreement with the observations, such as over a less mountainous region in Central England (Fig. 8e). As no rainfall data is assimilated, this represents an additional independent verification of the reanalysis. Daily rainfall is shown in Fig. 8e for comparison with the observations, but the higher frequency rainfall data in the reanalysis reveals several intense, sub-daily rainfall events during October that are obscured in the daily-mean (e.g. the 3 h-rain rate centred at 6 October, 15:00 UTC is 44 mm d⁻¹ in 20CRv3⁺, Fig. S10).

Both warmer world experiments see increased rainfall over the UK and Ireland (Fig. 8c and d). The increase of 17 % in the +2 K experiment is equivalent to 8.8 % per K of local warming, while the increase of 12 % in +2 K + CO2 is somewhat smaller (equivalent to 6.0 % K⁻¹). These values are substantially larger than the increase in annual-mean precipitation of 3.0 % K⁻¹ over the larger NW_Europe region in the +2 K + CO2 experiment (not shown). The increase in October rainfall over the UK and Ireland is closer to, or even above, the Clausius-Clapeyron scaling seen in extreme daily rainfall events (Fig. 7c). This likely reflects the unusually high occurrence of heavy rainfall events in this month, with 5 distinct events above the all-year 95th percentile of daily precipitation in 20CRv3⁺ (Fig. 8e). Rainfall totals in extreme months or seasons may therefore scale much more rapidly with warming than the annual-mean.

On sub-daily time scales, the largest changes in October rainfall occur on wet days, whereas rain rates on drier days are comparable in both experiments (Fig. S10). This supports the finding in the previous section that substantial increases in time-mean rainfall can result from increased rainfall in a small number of heavy events. Notably, the warmer world rainfall rate at 6 October, 15:00 UTC is 58 mm d⁻¹, an increase of 31 % over the value in 20CRv3⁺ or around 15 % K⁻¹ – much greater than Clausius-Clapeyron scaling, as has previously been found for sub-daily rainfall extremes .

How would the everyday weather of a year from history be experienced in a warmer world? The reanalysis experiments in this paper share the same weather patterns, but by perturbing the SSTs and atmospheric CO2 we can explore how the weather of 1903 would be experienced in a warmer world by residents of four well-observed regions (the boxed regions in Fig. 1). We focus on changes in two key meteorological variables which affect day-to-day perception of the weather: temperature and rainfall. Residents of these regions would experience warmer near-surface temperatures nearly every day, with 99 % of days becoming warmer than in the 20CRv3⁺ reconstruction of 1903. On a typical day, land areas would be warmer by around 2–2.5 °C for a 2 K ocean surface warming. However, increases of 2.5–3 °C are seen on hot days (temperatures around 20 °C or above), and larger increases of 4–5 °C on days below freezing. The cold day response appears to be due to enhanced absorption of solar radiation by the land surface due to a reduction in snow cover; the warmer world version of 1903 would also be one with substantially less snow and ice. Mechanisms for the hot day response are mixed: in the US_East_Coast region it is linked to reduced evaporative cooling on the hottest days, while changes in cloud cover appear to be more important in the SE_Aus region.

The everyday experience of rainfall would also be different in the warmer world. Even without substantial changes in large-scale weather patterns, annual rainfall would increase in NW_Europe and SE_Australia, decrease in Western_Med, and show little change in US_East_Coast – but in each region, daily rainfall would become more variable, meaning larger rainfall swings from day to day, with implications for infrastructure and adaptation. Even in regions where the total annual rainfall increases, the increase would occur on roughly 1 d in every 10 (that is, on days above the 90th percentile of rainfall). Instead, there would be fewer drizzly days, and in three of the four regions an overall reduction in the number of rainy days when the additional CO2 is included. Conversely, the number of days in the heavier rainfall bins grows exponentially with increasing rain rate.

We find that the October 1903 rainfall total over the UK and Ireland, already the wettest month on record in England and Wales, would be 12 %–17 % higher in a +2 K warmer world. The reanalysis experiments presented here are idealised experiments rather than best estimates of the current climate, however they can give an indication of how much more rain the weather conditions of October 1903 might produce today. If we assume that global temperatures have warmed by 1.5 °C since 1903 (as compared to 2.3 °C in the +2 K + CO2 experiment, Fig. 3a) then we estimate that the weather conditions of October 1903 would produce an extreme UK average rainfall of around 240 mm in the current climate. The next wettest observed month is December 2015 at 216.3 mm . Future planned work using patterned SST perturbations and consistent CO2 concentrations will provide better estimates of how the impacts of historical extreme weather events would be different in the current climate. We will also perform additional experiments to translate events into a warmer future climate to inform adaptation planning.

We also find evidence of a direct CO2 effect on everyday weather. Higher atmospheric CO2 leads to enhanced warming of extratropical land than from SST warming alone, contributing 19 % of the total warming over the Western US in the +2 K + CO2 experiment. Higher CO2 levels act to suppress global precipitation and reduce the number of rainy days over NW_Europe, Western_Med, and US_East_Coast.

Our approach shares some of the limitations of other storyline attribution methods. The method in this paper makes two implicit assumptions: (1) that the weather patterns that occurred in 1903 could in principle occur in a world that is 2 K warmer; and (2) that assimilating the 1903 pressure observations with the 20CRv3 system does not lead to inconsistencies when the system's boundary conditions (SST, sea ice, and CO2 levels) are perturbed. We can gain insight into both by comparing the reanalysis assimilation statistics from the 20CRv3⁺ and +2 K + CO2 experiments. We find that the innovation (i.e. observed value minus first guess) and localisation length scales do not change substantially in the +2 K + CO2 experiment (Figs. S11a–d and S12a–b). However, the assimilation system does reject more pressure observations in +2 K + CO2 than in 20CRv3⁺ (Figs. S11e–f and S12c). The relative increase is largest in NW_Europe, the region with proportionally the fewest rejections in 20CRv3⁺, and smallest in SE_Aus. An increase in the number of rejected observations may indicate that the model’s response to the warming causes some inconsistencies with the pressure observations, particularly where the density of observations is high and hence the observational constraint is strongest, as in NW_Europe. Note that tropical cyclone central pressures are assimilated without opportunity for rejection in both experiments.

However, the increased number of rejected observations does not in itself mean that the simulated weather events are necessarily implausible in a warmer world, even if they become slightly less compatible with the model’s own forced circulation response. The atmospheric circulation response to warming is both uncertain theoretically and variable among climate models , which suggests caution regarding how much weight we assign to the dynamical response in 20CRv3. Even if the particular weather patterns of 1903 were to become less likely in a warmer world, it is difficult to argue that they would be impossible a priori, notwithstanding certain features of the 1903 climate (e.g. the eruption of the Santa Maria volcano in 1902, Fig. S3).

If changes in the atmospheric circulation do occur in future, they could lead to much larger changes in extreme temperature and precipitation, for example if persistent weather patterns were to occur more frequently . The reanalysis experiments can thus be considered a strongly conditioned form of attribution, as we consider only the effects of warming that are not related to changes in the large-scale circulation . This also means that feedbacks from the warming onto the large-scale circulation are neglected. For example, some studies have suggested that in heat waves arising due to a persistent atmospheric block, soil moisture anomalies can, in certain circumstances, feed back onto the atmospheric circulation pattern itself . Temperature increases on the hottest days may thus be higher than estimated in Fig. 5 if the circulation were allowed to respond. On the other hand, assimilating observed surface pressure does not constrain the atmospheric circulation entirely at all time and length scales – for example, the super-CC scaling of short-duration rainfall extremes in October 1903 (Fig. S10) indicate that sub-daily updraft velocities can show large changes, even in well-observed regions. Changes in vertical motion will also affect cloud behaviour, and may contribute to the cloud-mediated amplification of hot days in the SE_Aus region (Fig. S5d). Future work will compare where and how strongly the circulation is constrained in the reanalysis experiments versus other established methods such as spectral nudging .

In reality, the dynamics and thermodynamics of the system cannot be cleanly separated, but in studies like ours it allows us to focus our investigation on processes that we think are better represented by the current generation of climate models (thermodynamic effects) than others (such as persistent weather regimes). This can offer insight into the robust physical processes behind regional climate signals. For example, Mediterranean precipitation declines in spring, summer, and autumn in the warmer world experiments, but increases in winter, presumably due to local changes in atmospheric stability and humidity. We also find that, in the absence of shifts in the Mediterranean storm track, seasonality in the Mediterranean precipitation response is driven entirely by SST warming, as the direct effect of increased atmospheric CO2 is to reduce Mediterranean rainfall regardless of season. Other Mediterranean climates are also projected to dry, with atmospheric circulation contributing to the recent Chilean “megadrought” . Forthcoming experiments will consider the modern period where there are more pressure observations over Chile and other Mediterranean-like climates outside Europe.

This study has presented an exploration of a single year's weather. Our conclusions are restricted to regions with a high density of historical pressure observations, and some may be sensitive to the reanalysis system used – for example, there are longstanding problems in the simulation of light rainfall in numerical models , which limits confidence in the reduction of light rainfall and overall rainfall occurrence seen in the warmer world experiments. However, it is notable that even in a single year, the reanalysis experiments support changes in rainfall characteristics that have been seen in multiple generations of coupled models .