Introduction

Extreme weather events have a large impact on population, economy, infrastructure, agriculture and ecosystems. The attribution of these events to climate change is a relatively new scientific field and only emerged during the last decades1. The reason for this is that in classical climate-change science, attribution of an observed phenomenon to anthropogenic climate change requires demonstrating that the phenomenon is both consistent with anthropogenic climate change and inconsistent with any other explanation2. This classical approach generally fails in the case of single extreme events, because of the large role of internal variability. Palmer and Räisänen3 therefore suggested replacing the strong form of classical climate attribution with a weaker form, where it is only required to demonstrate that anthropogenic climate change made the event more likely. In general terms4, this can be seen as replacing specific causation (the actual cause of a specific event) with general causation (the potential to cause the specific event). Thereby, the statistics of an event are compared as it was observed under present climate (so-called ‘factual’ conditions), including climate change, to its corresponding statistics in a ‘counterfactual world’ without anthropogenic climate change. If the event was made more likely, e.g., as estimated by a risk ratio, then it is attributed to anthropogenic climate change, in this weaker sense of general causation. This has now become the conventional approach to event attribution5.

There are at least two inherent limitations of this conventional, probabilistic approach. The first is that a statistical population must be constructed, whereby the specific event is replaced by a much broader ‘event class’, which is typically univariate. Yet the impacts of the event, which are normally the reason for the interest in the event, can be quite sensitive to the particular details of the event. That is why it is widely understood in statistics that inferences concerning statistical populations cannot be reliably applied to individual members of those populations6. The second limitation is that even this weaker form of attribution relies on a clear climate change signal, which is generally obtained from climate models, and which can be ambiguous because of the deep uncertainties in the dynamical response to climate change at the local scale7. To address both of these limitations, Trenberth et al.8 suggested that distinguishing between dynamic and thermodynamic factors could lead to less uncertainty in the attribution of extreme events. In particular, they proposed treating the dynamical conditions leading to the event as given, and asking how the thermodynamic consequences of the event (e.g., heavy precipitation) were affected by known aspects of climate change, such as warming of sea-surface temperatures (SSTs). It was argued that the inclusion of this established scientific knowledge on climate change increases the signal-to-noise ratio and thus leads to a more reliable attribution result (see also Shepherd9, who dubbed it the ‘storyline’ approach). Lloyd and Oreskes10 noted that the storyline approach could be seen as guarding against false negatives (i.e., failing to detect the consequences of climate change), whilst the conventional approach guarded against false positives. Thus, both had their scientific purposes.

To implement the storyline approach in a climate model, one needs to be able to re-simulate specific extreme weather events which happened in the recent past under different climate conditions. For that, some kind of constraint on the model’s dynamics is needed. This is essential, because initially similar dynamical states will diverge in time through chaos, a phenomenon known as the ‘butterfly effect’11. Therefore, to follow an extreme event through its entire evolution, the model needs some additional enforcement to stay close to observations, beyond the initial or lateral boundary conditions. A popular method to fulfil this task is spectral nudging. It constrains the large spatial scales of a climate model within the free atmosphere (i.e., outside of the boundary layer) so that it is ‘nudged’ towards, for instance, reanalysis data. The technique was first adapted and applied to regional climate models at the GKSS research centre12 (today Helmholtz-Zentrum Hereon) after the idea emerged in the 1990s for weather models13. At a storm workshop in Reading in 2017, the authors started to develop the idea to combine their methods, namely storylines and global spectral nudging, to a new extreme event attribution technique called spectrally nudged storylines.

This article provides a perspective on how the storyline and spectral nudging methods were combined to spectrally nudged storylines as a new method of attributing extreme weather events to anthropogenic climate change. We show how the spectral nudging technique was established and evolved over time, for a variety of different purposes. What these different purposes have in common is the need to constrain the butterfly effect in order to answer a particular, conditional scientific question, where the large-scale flow can be reasonably regarded as given. Then we elaborate on the development and details of spectrally nudged storylines and review studies that use these methods. Spectrally nudged storylines are discussed in comparison to other strongly conditioned attribution methods, and first approaches are presented that apply spectrally nudged storylines for impact studies. We conclude with an outlook on further applications of spectrally nudged storylines given current developments in climate science.

A list of frequently asked questions on the method, subjectively assembled by the authors, is provided in Table 1 below. Since this kind of storyline attribution is a recent innovation, only a limited number of studies exist so far. However, we believe that the new attribution method adds valuable information for extreme event attribution and will improve communication about climate change and its impacts. Instead of providing generalized probabilities based on abstract model ensembles, the method gives readily interpretable answers to practical questions such as ‘What if this same extreme event happened in a warmer or cooler climate and how large is the human impact?’.

Table 1 Frequently asked questions about Spectrally Nudged Storylines, based on the authors’ experience
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Spectral nudging for climate models

The term ‘spectral nudging’ was first introduced by Waldron et al.13 to describe the imposition, through an extended Newtonian relaxation approach, of the large-scale weather patterns of a global atmospheric model throughout the domain of a limited-area weather forecasting model. Independently of this work, von Storch et al.12 developed spectral nudging for regional climate model simulations. In both cases, the method was developed for technical reasons, as an add-on to the standard method of constraining the large scales of a regional weather or climate model only through the lateral boundary conditions, as constraining only the lateral boundary conditions can lead to internal states inconsistent with the driving fields. Spectral nudging is applied for only a very few variables, specifically horizontal wind components or divergence and vorticity, and in the free atmosphere, to allow the lower atmosphere, and smaller-scale features, to respond to perturbations in a dynamically consistent way. It is called spectral, as the nudging is applied only for large spatial scales, for instance just for the low wavenumbers of a spectral model. (For grid point models a Fourier transformation is applied, to connect grid point space to wavenumber space.) The rationale behind the method (which can be verified a posteriori) is that local meteorological conditions are determined by a combination of the large-scale flow (provided by the nudging) and the details of the surface physics (provided by the model). Weisse and Feser14 showed that for ensemble simulations for wind hindcasts with and without spectral nudging using slightly disturbed starting conditions, spectral nudging reduces the internal model variability and leads to smaller differences to observations on average, compared with solely constraining the regional model through the lateral boundary conditions. In other words, it constrains the butterfly effect.

Von Storch et al.12 noted that spectral nudging could be seen as a “poor person’s data assimilation technique,” and thus was also a way of producing regional reanalyses, even without regional observations, using the regional model to fill in the physical detail. A large number of studies subsequently applied spectral nudging for dynamical downscaling of large-scale reanalysis data to produce long-term regional hindcasts of climate variability15. Of course, there is nothing to prevent applying spectral nudging within a global model16; the rationale in that case has nothing to do with lateral boundary conditions but instead has to do with avoiding temporal inhomogeneities that can arise from the assimilation of varying numbers of measurement data in reanalyses over time. In a similar spirit, spectral nudging can be used to validate a model against sparse observations, by ensuring that the comparison is ‘like for like’17. Importantly, all of these studies emphasize that the nudging must be carefully adjusted for the purpose at hand, since too strong nudging can lead to a dampening of regional processes, whilst too weak nudging can fail to sufficiently constrain the large-scale flow. More details on choosing the nudging settings can be found in the Supplementary and in refs. 16,18.

Relevant to our purpose here, spectral nudging has also been used for the attribution of causal effects. Here, the global model is run twice, once with and once without the causal effect. If the model was run freely, then the butterfly effect would mean that differences between the two simulations would not necessarily reflect the causal effect, but could also reflect internal variability. Overcoming this ambiguity by performing a large ensemble of simulations would return us to the previously discussed problems associated with probabilistic event attribution. In contrast, spectral nudging provides a direct causal estimate that is conditional on the imposed atmospheric state. For example, Kooperman et al.19 used spectral nudging to estimate the aerosol indirect effect, although the nudging was to a climate model simulation rather than to reanalysis. A closer parallel to extreme event attribution is Shepherd et al.20, who applied spectral nudging within a chemistry-climate model to attribute the role of halogen-induced stratospheric ozone loss in the observed record of global ozone. Because the observed record includes a strong component of natural variability, the set-up was able to resolve a number of outstanding scientific puzzles, e.g., where anomalous dynamical variability had masked chemical ozone loss. The attribution relied on the assumption that the effect of halogen-induced ozone loss on stratospheric circulation could be neglected in the interpretation of the ozone record, which is a reasonable assumption outside of the Antarctic ozone hole region.

Spectrally nudged storylines

The method of spectrally nudged storylines was introduced independently by Refs. 18,21, applied to heat waves. The method uses a global atmospheric climate model wherein the large-scale atmospheric weather patterns are nudged towards reanalysis data so that observed extreme events can be simulated in different climate states. (A necessary first step for any attribution is to confirm that the factual simulation can closely follow the event in question.) Between the individual storylines only those external parameters are changed that were influenced by anthropogenic forcing with high certainty, notably SSTs and greenhouse gases. (Modifying sea-ice concentrations is tricky because of the need to ensure physical consistency with the modified SSTs, so is handled on a case-by-case basis and may not be necessary. Note that the same issue arises with probabilistic attribution using atmospheric models, where the sensitivity to the sea-ice counterfactual will be much more consequential because of the response of the atmospheric circulation to the sea-ice modification.) In this way, the method keeps the dynamical conditions similar between storylines, while a focus is put on the thermodynamic responses to the imposed forcings, such as warming and increased specific humidity, which are provided by the model physics and which are the robust aspects of climate change7. Van Garderen et al.18 used a small ensemble of three members for each storyline to show that such a conditional attribution can lead to high signal-to-noise ratios and thus a higher confidence in the attribution, compared to the conventional, probabilistic approach. Examples of the different kinds of attribution statements provided by the two approaches are given in Table 218. A variant on this approach is to allow the SSTs to respond interactively to the changed greenhouse gases, whilst maintaining the nudging of the atmospheric state22.

Table 2 Example of the complementary attribution statements that are possible using the probabilistic and storyline approaches, for the case of the 2010 Russian heat wave (Table from van Garderen et al.18)
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The summer heat wave of 2022 over Europe was analysed by Feser et al.23. The study combined spectrally nudged storylines and a statistical cluster analysis of a 2000-year paleo simulation and reanalysis data to attribute the heat wave and put the extreme event into historical context. The main result is that anthropogenic climate change increased the heat wave by 1.25 °C on average and locally by up to 5.7 °C (Fig. 1). Although the present-day storyline does not exactly match the reanalysis due to model biases, the day-to-day variations are highly correlated, and it is the difference between storylines that matters. This illustrates how the storyline approach quantifies the distributions of differences (conditional specific causation) rather than the differences of distributions (general causation) considered in the conventional approach. The statistical analysis of a multimillennial paleo climate simulation confirmed that it was one of the most extreme heatwaves of the last 2000 years. This article outlines a first comprehensive approach or common framework to combine both the conventional statistical climate attribution and storyline attribution. In this way, different questions such as ‘How would the heat wave have evolved under different climate conditions?’ and ‘How extreme was the heat wave within the last millennia?’ can be answered.

Fig. 1: Storyline attribution of the European heatwave 2022.
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Left: The upper panel shows the 2 m temperatures [°C] (shaded) and present-day storyline geopotential height at 500hPa [m] (black contours) for July 2022. The lower panel shows the differences in 2 m temperature [°C] between the present-day and preindustrial simulations as shaded fields. Stippling indicates where all present-day ensemble members are > 0.1 °C above all preindustrial members for that grid point. Right: Daily mean 2m-temperature [°C] averaged over Europe (35–55°N, 10°W–25°E) for summer 2022 for the preindustrial (blue), present-day (red) and +2 °C (yellow) simulations and ERA5 (black stippled line) and NCEP (black solid line) reanalysis data. The climatology (grey shaded area) is the 5th–95th percentile range between 1985-2015 calculated with the general circulation model ECHAM16. Figure adapted from Feser et al.23.

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The method of spectrally nudged storylines can be applied not just to medium-term events such as heat waves, but also to long-term events such as droughts and to short-term events such as heavy rainfall, all within a seamless modelling framework. Van Garderen and Mindlin24 examined the 2011/2012 drought in southeastern South America, which had devastating impacts. Climate change has already clearly led to higher temperatures and thus to increased evaporation/evapotranspiration of water from vegetation, soil and water surfaces. On the other hand, climate change is causing more precipitation in this region, albeit in the winter season. The study showed that so far, but also in a 2 °C warmer world, this additional winter precipitation more than compensates for the increased summer evaporation. Whether this will also be the case as temperatures continue to rise, or whether evaporation will then dominate, is still unclear. This article was particularly interesting as a showcase for the potential of spectrally nudged storylines, as the interplay between larger winter precipitation offsetting the increasing summer drought potential would not have been captured with a drought index based on summer meteorological conditions alone.

In terms of heavy rainfall, a near-real-time storyline set-up was used to examine the extreme rainfall and subsequent flooding from storm Boris over Central and Eastern Europe in September 202425. This study shows that a near-real-time attribution is feasible with spectrally nudged storylines, given the ease of their implementation. Recently, John et al.26 applied the approach in a global climate model at a kilometre-scale resolution. This study represents a new step in very high-resolution storyline attribution, reaching convection-permitting scales in a global setting. In this regard, spectrally nudged storylines could lead to improved attribution results for extreme events that are more heterogeneous or of smaller spatial extent such as extreme convective precipitation, mesoscale systems or intense cyclones. Such simulations have a massive demand in high performance computing power and storage space, making them completely infeasible for probabilistic attribution, but at least within reach for the storyline approach.

A very recent development are regional spectrally nudged storylines and only a few studies applying them so far exist. Ref. 27 examined the European summer heat wave of 2019, using global storylines spectrally nudged to reanalysis data which were dynamically downscaled using a regional climate model. The regional storylines showed a more intense, longer lasting and spatially extended heat wave for future climate states due to human-induced climate change. Another recent study28 used spectral nudging to conduct thermodynamic global warming simulations for the continental US with a regional climate model. The resulting multi-decadal data set for present-time conditions and several future warming trajectories is openly available and seems to be an interesting data base for attribution applications. This is a return to the origins of spectral nudging, which as noted earlier was first developed for downscaling of climate change via regional models, but now applied in a storyline context to focus on particular kinds of extreme events. This new attribution approach offers the possibility to attribute extreme events of smaller spatial scale than heat waves and droughts, such as storms or intense precipitation events, without having to run a global high-resolution model.

Strongly conditioned attribution methods

As discussed in Ref. 9, the key ingredient is constraining the large-scale atmospheric circulation so as to distinguish between the dynamic and thermodynamic contributions to an extreme event. Ref. 1 refers to this as ‘strongly conditioned attribution’, since probabilistic attribution often also involves some level of conditioning, e.g., on SST patterns. Importantly, in strongly conditioned attribution the dynamical component is not ignored, but is treated separately because of the different level of uncertainty associated with dynamical aspects of climate change. There are two basic ways of constraining the atmospheric circulation: passively, through statistical selection; and actively, through a physical model (as with spectrally nudged storylines). The most commonly used methods, together with their advantages and disadvantages compared to other strongly conditioned attribution methods, are summarized in Table 3 and are described in slightly more detail below. Of course, in any particular application more than one method can be used, as in the case of Ref. 23 discussed above.

Table 3 Overview of strongly conditioned (storyline) event attribution methods
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A statistical downscaling technique termed Analogues was introduced by ref. 29. The key idea is to represent regional climate variables as a function of the large-scale atmospheric conditions (which is the rationale behind downscaling). For that, large-scale weather patterns for a given day are compared to high-resolution observation or reanalysis data, and time periods with the most similar circulation patterns (analogues) are selected. The observed weather at these times then serves as input to estimate the high-resolution climate state, assuming statistical stationarity. The technique can, for instance, be useful for statistical downscaling purposes or for paleoclimate reconstructions, but also for attribution of extreme events30. In the latter case, the difference between the analogue-estimated state and the actual state represents the thermodynamic component of climate change, relative to the reference period. For example, ref. 31 used the method to demonstrate that the cold European winter of 2010 was less cold than it would otherwise have been, because of anthropogenic warming.

Another statistical method of event attribution is termed Dynamical Adjustment. The method removes dynamical variations in a time series of a target variable, for instance by using empirical orthogonal functions, weather pattern clustering or linear regression, so that the anthropogenic climate change signal becomes more distinct32,33. The implicit assumption, as with storyline attribution, is that long-term dynamical variations are best regarded as internal variability. Rather than targeting a particular extreme event (as with Analogues), long-term trends are adjusted, although the decomposition can of course be examined for a particular event to provide an event attribution. Ref. 34 demonstrate the potential of dynamical adjustment as an attribution method for extreme events using the European cold spell and the Russian heat wave of 2010 as examples.

In regional climate modelling, a technique called Pseudo Global Warming (PGW) to study climate change effects on extreme events was presented by Ref. 35. It calculates climate change differences between global model simulations of e.g., present-day and pre-industrial climate or between future and present-day climate for important meteorological variables such as temperature, pressure, wind and humidity. These differences are then added to reanalysis data and constitute the PGW input data as modified boundary data for the regional climate model so that high-resolution simulations for the extreme event can be simulated for different climate states. The method is quite similar to spectrally nudged storylines, the difference is in its application being limited to regional studies and in not applying spectral nudging throughout the model domain. Although mainly used to study changes in climate, some studies have used PGW for attributing extremes to anthropogenic climate change, for instance, precipitation events over Asia36 or typhoon-induced extreme precipitation37.

Another model-based event attribution method is to use short-term weather forecasts of the event, which are re-simulated under counter-factual conditions. Since the dynamical conditioning only occurs via the initial conditions, it weakens with forecast lead time because of the spread in the forecast ensembles through the butterfly effect. This leads to a temporal non-stationarity in the degree of conditioning as well as from spin-up of the climate response during the forecast, which complicates the statistical analysis38. Moreover, the dynamical conditioning is only effective for weather forecast timescales of a few days to a week, where the main anthropogenic effect comes from the counter-factual SSTs38. Hence the method has mainly been used for tropical cyclones39, showing in particular that the rainfall was increased by anthropogenic climate change. Since the probability of the initial conditions is not assessed, it is still a conditional attribution. Another conditional attribution using a regional-model ensemble weather-hindcasting approach analysed the Colorado floods of September 2013, showing that anthropogenic drivers increased the magnitude of heavy precipitation40.

Compared to the other model-based approaches, global spectrally nudged storylines have the key advantage of providing model fields that are both spatially and temporally statistically homogeneous, making the statistical analysis much simpler, at the cost of not necessarily being able to follow small-scale extreme events.

A new approach which is very similar in spirit to spectrally nudged storylines is to use a simple data assimilation system rather than spectral nudging to constrain the atmospheric state41. In this approach, the only atmospheric field assimilated is sea level pressure, which is combined with either factual or counter-factual SSTs. The method appears to be very effective for analysis of storms, and can be applied to historical storms in the distant past provided surface pressure observations are available. Thus, rather than asking how a recent extreme event would have been in the past, this method is able to ask how an extreme event from the distant past would be today. We do not include this method in Table 3 since there is not yet sufficient literature.

Impact-based studies applying spectrally nudged storylines

A new task for spectrally nudged storylines is to move forward from attribution of hazards to attribution of their impacts. So far, only a small number of such studies have been published. One of them is a storyline study on Hurricane Sandy’s impact on New York City42, which assessed how sea-level rise and changes in storm features affected coastal flooding impacts on critical infrastructure. To account for some degree of internal variability, the hurricane was altered in its landfall position, intensity and shape. It was found that even moderate increases in sea level and changes in storm tracks can affect flood impacts. A strength of this study is the simulation of the compound flooding effect of storm surge, high tide, sea level rise and extreme precipitation which caused the hurricane’s impact on critical infrastructure. Through their specificity, storylines can provide a more advanced insight into the interaction of these drivers under past and future climate conditions.

Heat waves can lead to droughts, wildfires or crop failures. Extremely dangerous is the impact of heat on human mortality. This impact was assessed by ref. 43 for Germany. The aim was to predict the heat-related mortality for different future climate states based on storylines using advanced machine learning techniques. The storylines’ factual and future climate data relies on observed extreme events and shows how their impact on mortality may change if these events would happen in a warmer world. This is one of the first studies to combine machine learning with spectrally nudged storylines to attribute extreme event impacts. Neural networks are well suited and often superior to conventional statistical analysis in finding complex nonlinear relationships between extremes and variables such as mortality, provided that the underlying data basis is sufficiently large and of high quality. However, the machine learning model assumes that the climate-mortality relationship is not changing due to external factors in different climates, which may not be realistic in the far future.

In 2012, a large crop loss for soybeans, which even affected global food markets, occurred in the three largest soybean producing regions in the United States, Brazil, and Argentina due to compound hot and dry weather conditions. Ref. 44 examined the impact of climate change on soybean production for this extreme drought year using a statistical crop model combined with global storyline data. The study found that drought intensity did not change between the storylines, but higher temperatures and an intensified temperature-moisture interaction will lead to larger crop losses in the future. Applying such crop models to climate storylines may improve adaptation to climate change and communication with decision makers by identifying regions that are most vulnerable to anthropogenic climate change, e.g., where more irrigation or a change in crop type is needed.

Ref. 45 investigated near-surface ozone pollution levels in warmer climates, which would have health implications for humans and ecosystems. Storyline scenarios of air pollution were developed using a global atmospheric chemistry model to assess ozone pollution extremes in a warmer climate. The results point to two competing processes, which are dependent on the level of warming: vegetation and local photochemistry increase ozone extremes, while a concurrent moistening of the atmosphere leads to lower ozone concentrations. Such highly complex interrelating processes could well have been missed in a purely probabilistic attribution study, emphasizing the value of adding the storyline method in a combined attribution approach.

Outlook

Spectrally nudged storylines bring together the concepts of global climate downscaling (spectral nudging) and conditional attribution (storylines) to provide a methodology to predict surface climate from large-scale atmospheric circulation together with thermodynamic forcings, with the details filled in by the climate model. The methodology is easy to implement and easy to interpret, whilst respecting the complexity of a local situation, and thus exemplifies the key principles of “Small is Beautiful”46. We conclude this piece by reflecting on how spectrally nudged storylines can contribute to the changing face of climate science.

Impact attribution

There is a rapidly growing demand for attribution of climate impacts, yet this inevitably involves multiple causal factors, not just climate change. It is highly misleading if disasters are attributed solely to climate change, even if climate change increased their likelihood. In order to go from hazards to impacts for particular events, specific causation is needed: general causation is not sufficient47. Spectrally nudged storylines have the potential to fill this gap, as the few existing studies already show. What is needed is the inclusion of impact models with realistic intervention points, so that counterfactuals in the decision space can be combined with climate counterfactuals. Digital twins48 offer promise in this respect.

Unseen events

Risk management requires examining things that might have happened (so-called ‘downward counterfactuals’) rather than just those that did happen. There is rapidly growing work in this space, either mining large ensemble simulations49, or boosting ensemble members to create extremes that are more extreme than those observed50. This is very much in the spirit of ‘tales of future weather’51, but for the present. Such unseen events could be used to spectrally nudge higher resolution climate models and propagate the events through to impacts.

Dynamical aspects of climate change

A long-recognized limitation of the storyline approach to event attribution is its inability to account for possible changes in atmospheric circulation. This has been justified by the importance of quantifying the robust aspects of climate change, given the ambiguity of predicted circulation changes from climate models at the regional scale. However, circulation changes are beginning to emerge in the ever-lengthening observed record, and very often, they lie outside the range of changes predicted by the climate models, even after accounting for internal variability52. This raises the question of whether storylines of circulation change based on observations might be more useful than those based on the climate models themselves53. Spectral nudging using these observed circulation trends could be used to expand the range of explanatory factors considered in event storylines.

Bridging between specific and general causation

Both specific (storyline) and general (probabilistic) attribution have their purposes, and their strengths and weaknesses. Given the widespread prevalence of probabilistic event attribution and its planned operationalization, it is important to be able to connect the two approaches, and connect them both to attribution of changes in the statistics of extreme events, as reflected in aggregations over many events (and as discussed, e.g., in IPCC Assessment Reports). Because global spectrally nudged storylines are not event-specific but include all events worldwide during the simulation period, collections of events can be analysed, as with the attribution of a single hurricane season by aggregating over all forecasted hurricanes using the short-term forecast method54. This would also help connect attribution of historical events to long-term trends and future risk.

Global km-scale modelling

There is a growing push for the use of km-scale atmospheric models in order to explicitly model atmospheric convection, which is important for extreme events such as heavy precipitation55. Such models are very computationally expensive to run, however, which effectively precludes their use in probabilistic attribution. Any short simulation is necessarily conditional on the large-scale conditions. As already mentioned, spectral nudging provides an interpretable conditionality so that the short simulations can be more effectively compared against observations, and used for event attribution.

Artificial Intelligence (AI)

AI could further enhance the potential of climate storylines. In their recent study, Ref. 56 assess an AI-based weather and climate model in simulating extreme heat waves. They show that the model can realistically reproduce such events in different climate states. However, the study also points to a limiting factor. In comparison to physics-based models the AI-model tends to underestimate future warming. As a reason for this the authors suggest the absence of land-atmosphere feedbacks in the AI-based model. Perturbing AI-based models (analogously to how spectrally nudged AGCMs are perturbed with SSTs) has been shown to produce physically realistic responses in some AI-based weather models57. For application to extreme event attribution, AI is very well suited not just for detection and attribution of extreme events, but also for the detection of nonlinear relationships and drivers of extremes58. New AI attribution methods are currently explored in the EU-funded projects Climate Intelligence (CLINT, https://climateintelligence.eu/) and eXtreme events: Artificial Intelligence for Detection and Attribution (XAIDA, https://xaida.eu/) which already show promising results into the direction of combining AI and storyline attribution to result in a common attribution framework.