A basis set for exploration of sensitivity to prescribed ocean conditions for estimating human contributions to extreme weather in CAM5.1-1degree

Abstract This paper presents two contributions for research into better understanding the role of anthropogenic warming in extreme weather. The first contribution is the generation of a large number of multi-decadal simulations using a medium-resolution atmospheric climate model, CAM5.1-1degree, under two scenarios of historical climate following the protocols of the C20C+ Detection and Attribution project: the one we have experienced (All-Hist), and one that might have been experienced in the absence of human interference with the climate system (Nat-Hist). These simulations are specifically designed for understanding extreme weather and atmospheric variability in the context of anthropogenic climate change. The second contribution takes advantage of the duration and size of these simulations in order to identify features of variability in the prescribed ocean conditions that may strongly influence calculated estimates of the role of anthropogenic emissions on extreme weather frequency (event attribution). There is a large amount of uncertainty in how much anthropogenic emissions should warm regional ocean surface temperatures, yet contributions to the C20C+ Detection and Attribution project and similar efforts so far use only one or a limited number of possible estimates of the ocean warming attributable to anthropogenic emissions when generating their Nat-Hist simulations. Thus, the importance of the uncertainty in regional attributable warming estimates to the results of event attribution studies is poorly understood. The identification of features of the anomalous ocean state that seem to strongly influence event attribution estimates should therefore be able to serve as a basis set for effective sampling of other plausible attributable warming patterns. The identification performed in this paper examines monthly temperature and precipitation output from the CAM5.1-1degree simulations averaged over 237 land regions, and compares interannual anomalous variations in the ratio between the frequencies of extremes in the All-Hist and Nat-Hist simulations against variations in ocean temperatures.

emissions when generating their Nat-Hist simulations. Thus, the importance of the uncertainty in regional attributable warming estimates to the results of event attribution studies is poorly understood. The identification of features of the anomalous ocean state that seem to strongly influence event attribution estimates should therefore be able to serve as a basis set for effective sampling of other plausible attributable warming patterns. The identification performed in this paper examines monthly temperature and precipitation output from the CAM5.1-1degree simulations averaged over 237 land regions, and compares interannual anomalous variations in the ratio between the frequencies of extremes in the All-Hist and Nat-Hist simulations against variations in ocean temperatures.
Keywords: C20C+ D&A, CAM5.1, extremes, event attribution, attributable warming 1. Toward tackling a major uncertainty in event attribution analysis The field of research investigating the role of anthropogenic emissions in specific extreme weather events (termed "event attribution" in the remainder of this paper) has gained interest in recent years but is still in an early stage of development (Stott et al., 2013; National Academies of Sciences, Engineer-5 ing, and Medicine, 2016). At this stage, there are a considerable (and growing) number of methods being used, some with rather different philosophical underpinnings (Shepherd, 2016). One of the most popular methods compares the frequency of exceedance of some threshold in simulations of a dynamical atmospheric model driven under a factual scenario of observed radiative and 10 surface boundary conditions against the frequency in simulations driven under a counterfactual scenario of what those boundary conditions might have been like in the absence of human interference with the climate system (Pall et al., 2011). Conclusions of studies using this atmospheric-modelling time-slice approach are usually expressed numerically in terms of the Risk Ratio or Fraction 15 Attributable Risk (Stone and Allen, 2005). This type of experiment is explic-itly supported by the design of the Climate of the 20th Century Plus Detection and Attribution (C20C+ D&A) Project, the topic of the special journal issue in which this paper appears (Stone et al., In preparation).
A consequence of the relative youthful stage of this research field, however, 20 is that a number of aspects of the experiment design remain poorly understood in terms of the potential generation of bias and quantification of uncertainty (National Academies of Sciences, Engineering, and Medicine, 2016).
For the atmospheric-modelling time-slice approach, possibly the biggest uncertainty involves generation of the estimate of ocean warming (and sea ice retreat) 25 attributable to anthropogenic emissions. There are a number of plausible approaches to estimating the attributable warming, including approaches based on observed trends (Christidis and Stott, 2014), approaches based on simulations of dynamical models of the coupled atmosphere-ocean system (Pall et al., 2011;Christidis et al., 2012;Shiogama et al., 2014;Wolski et al., 2014;Schaller et al., 30 2016; Stone and Pall, 2017), and approaches that combine climate models and observations (Bichet et al., 2015(Bichet et al., , 2016. Estimates based on observed trends suffer from poor sampling, and thus a large amount of the estimated pattern of attributable warming consists of random endogenously generated variability rather than a response signal to an external forcing; because extreme weather 35 tends to feed off of local temperature gradients, such "noise" may have an important influence on event attribution results. Estimates based on atmosphereocean climate models may be better sampled (Stone and Pall, 2017), but they depend on usage of accurate estimates of the drivers of climate change as well as on the capability of atmosphere-ocean climate models to accurately repre-40 sent the effect of those drivers on ocean surface conditions. Only a few of the many studies so far using the atmospheric-modelling time-slice approach have used multiple estimates of the counterfactual natural scenario based on various attributable ocean warming estimates (Pall et al., 2011;Kay et al., 2011;Christidis et al., 2012;Shiogama et al., 2014;Christidis and Stott, 2014;Schaller 45 et al., 2016), and even these have used a miniscule number in relation to the enormous size of the space of possible values.
Considering the computational cost of running the simulations, the viability of the atmospheric-modelling time-slice approach to event attribution depends on the ability to reduce the size of the space of attributable ocean warming 50 estimates to a manageable number. A first step toward this is the assumption of separability into a spatio-temporal pattern and scalar global amplitude (Pall et al., 2011). The linearity of event attribution results for extreme autumn seasonal precipitation over England-Wales (Pall et al., 2011) and extreme local daily precipitation within South Africa (Angélil et al., 2014) as a function of the 55 global amplitude parameter suggests that this may be a reasonable assumption.
The pattern-amplitude separation not only substantially reduces the total size of the attributable warming space, but it also effectively solves the bias and uncertainty estimation issues for the amplitude half of the attributable warming problem, because this is accurately constrained by long-term historical global 60 warming (Stott et al., 2006;Pall et al., 2011). Note that the separation considered here differs from that proposed in Bichet et al. (2015Bichet et al. ( , 2016, which instead separates in spatial and temporal components. The assumption of pattern-scalar separability thus transforms the problem of attributable warming estimation into a problem of spatio-temporal pattern 65 estimation. We are still left with an effectively infinite number of possible patterns, however, so some further efficiency is required. One option, labeled here as the "available pattern approach", is to sample whatever pattern estimates are available (e.g. Pall et al., 2011;Schaller et al., 2016). A more complete sampling of the same space of available estimates might be achieved through cluster 70 analysis (Mizuta et al., 2014). The advantage is that the patterns are plausible responses to anthropogenic forcing (notwithstanding errors in observational data and biases in climate models). The disadvantage however is that there is no obvious reason why the space spanned by the relatively few patterns should be strongly aligned with the directions of high sensitivity of event attribution re-75 sults; thus, these few patterns may provide a poor indication of the sensitivity to plausible patterns that have not been sampled. One might imagine for instance that a set of available attributable ocean warming patterns differs only in the equator-to-pole gradient, while for a tropical region uncertainty in the risk ratio depends only on uncertainty in the interhemispheric gradient. Thus a second 80 option, proposed here and labeled the "sensitivity-based approach", is to instead focus on sampling patterns corresponding to the directions of highest sensitivity of event attribution results. The disadvantage of this second approach is that is unclear whether such patterns are plausible responses to anthropogenic forcing.
The two approaches are thus complementary.

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This paper sets out to facilitate sampling of the uncertainty in the attributable ocean warming pattern by further reducing the space of useful patterns to a manageable number using the sensitivity-based approach. We identify the directions of attributable warming with the highest sensitivity in event attribution results, with these directions being perturbations from the baseline 90 attributable warming estimate (Stone and Pall, 2017) used by the C20C+ D&A project. To do so, we examine the year-to-year sensitivity of risk ratio estimates for monthly extremes to interannual variability in sea surface temperatures (Risser et al., 2017), using a set of large ensembles of multi-decadal simulations of an atmospheric climate model. We start by describing the simu-95 lations in detail, including specifics of the experiment setup. We then describe the method used to identify sensitivity to anomalous sea surface temperature variability, and develop its application here to the identification of a subspace of patterns to which risk ratio estimates for events around the world are generally most sensitive. In this section we describe the simulations of the CAM5.1-1degree model of the atmosphere/land system submitted to the C20C+ D&A Project. These simulations are unusual in the combination of their number and duration, properties required for the study described in this paper. Because the C20C+ D&A 105 experiment protocol permits some flexibility, it may be useful to spell out the specifics of these simulations here.
2.1. The CAM5.1-1degree model CAM5.1 is the atmospheric component of the CESM1.0.3 earth system model (Neale et al., 2012). Here it is run at 1.25 • ×0.9375 • resolution in longi-110 tude and latitude respectively (hence the "1degree" suffix in our label for the model), with 30 vertical hybrid height-pressure levels. The dynamical equations are solved using the finite volume (FV) dynamical core. In our configuration, we also use CLM4.0 (Oleson et al., 2010;Lawrence et al., 2011), the model of land surface properties in CESM1.0.3. Chemistry and ecosystem properties are 115 not simulated in either the atmosphere or land models, but rather prescribed for computational efficiency.

Scenarios
The model has been run under the two benchmark scenarios of the C20C+ D&A project: All-Hist/est1, and Nat-Hist/CMIP5-est1 (Stone et al., In preparation;120 Stone and Pall, 2017). The collection of simulations of CAM5.1-1degree described in this paper are labeled "All-Hist/est1/v2-0" and "Nat-Hist/CMIP5-est1/v2-0" respectively, with the "v2-0" distinguishing from some trial All-Hist/est1/v1-0 simulations which have some differences in the radiative forcing and are not considered in this paper. The All-Hist/est1/v2-0 simulations are in-  (Table 1). All simulations start from the same initial state, except for small uniform perturbations applied to the three-dimensional temperature field (note that some simulations listed as starting on 1 January 1959 actually start a year earlier). For this study we ignore the first year of each simulation in order 135 to ensure sufficient divergence from the common initial macrostate.

Experiment setup
The All-Hist/est1/v2-0 simulations have been driven with observed (or observationallyderived) changes in greenhouse gas concentrations, sulphate aerosol burden, organic aerosol burden, black carbon aerosol burden, dust aerosol burden, sea salt The Nat-Hist/CMIP5-est1/v2-0 simulations mimic the All-Hist/est1/v2-0 in many ways, but with adjustments to represent the effect of removing the historical influence of anthropogenic emissions (Table 2 and references therein).

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Solar and volcanic forcing is identical to All-Hist/est1/v2-0. However, values for greenhouse gas concentrations, aerosol burdens, and ozone concentrations are held at estimated year 1855 values. SSTs from All-Hist/est1/v2-0 are cooled according to the "Nat-Hist/CMIP5-est1" monthly estimate of attributable warming from Stone and Pall (2017). This estimate of the warming attributable to hu-155 man interference with the climate system is calculated as the difference between   (2017) the "historical" (drivern with historical changes in both anthropogenic and natural forcings) and "historicalNat" (driven with historical changes in natural forcings only) simulations from the Coupled Model Intercomparison Project Phase 5 (CMIP5, Taylor et al., 2012). Sea ice concentrations are adjusted for consis-160 tency with the cooler temperatures according to the observed temperature-ice relationship (Stone and Pall, 2017). Visuals illustrating the spatial and temporal properties of the resulting All-Hist/est1 and Nat-Hist/CMIP5-est1 SSTs and sea ice coverage are provided in Stone and Pall (2017). Additionally, the data is available for download at http://portal.nersc.gov/c20c/.

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The C20C+ D&A protocols are flexible in terms of whether land use/cover change is considered a global or local anthropogenic forcing, and thus whether it is a driver of change which the benchmark Nat-Hist/CMIP5-est1 scenario is intended to diagnose. For the CAM5.1-1degree Nat-Hist/CMIP5-est1/v2-0 simulations we have interpreted it as a local forcing for the purposes of extreme 170 weather, and thus not something to be diagnosed in this global experiment.
Therefore, the All-Hist/est1/v2-0 land use/cover change is retained for the Nat- including on planned continual updates as observed SSTs and SICs become available.

Method
The experimental design used in the C20C+ simulations involves some important assumptions relating to the ocean surface state and the way the atmo- For complete details of the statistical approach, we refer the reader to the methods section of Risser et al. (2017); however, a summary is as follows. Given the long term nature of the CAM5.1-1degree simulations, we are interested in estimating the risk ratio over time at a total of T years, i.e., where p At and p N t are the occurrence probabilities for a defined extreme event in year t for scenario All-Hist and Nat-Hist, respectively. Together with a nonparametric (or binomial) likelihood, the scenario-specific probabilities for each calendar month are modeled using mixed-effects logistic regression as able for the monthly mean data (admittedly notwithstanding some intra-annual variability that is not accounted for by the t index) examined in this paper but would not be for daily frequencies.
Using (1) for p At and p N t , the risk ratio in year t is approximately Thus, RR 0 = exp {β A0 − β N 0 } is the "baseline" risk ratio for the entire time interval, a scalar that centres the analysis on a particular climate era (and means 210 that the approximation is not valid for a period experiencing a large amount of climate change in either scenario). The exp{β A1 x At1 − β N 1 x N t1 } term, a multiplicative scaling due to the covariates, describes the long term trend in the risk ratio, where the trend is taken to have the form of the difference in the global mean temperature covariates of the two scenarios. Finally, the exp{δ t } term is 215 a scaling for the risk ratio in a particular year that describes the year-to-year variability in the p At above and beyond variability in the p N t (after accounting for long term trends in the probabilities due to atmospheric warming). Hence, the δ t effects also describe the year-to-year variability in the risk ratio beyond the long term trend, and are of particular interest to our analysis in the next 220 section. Together the first two terms describe the mean anthropogenic effect as measured by the risk ratio; the δ t term describes anomalous year-to-year variations in that anthropogenic effect that result from the anomalous ocean state modulating the way that the climate system interprets the anthropogenic forcing.

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In order to account for regional differences in the probabilities p At and p N t and hence the δ t , we fit the statistical model to area-averaged monthly output from the simulations for each of 237 diagnostic land regions (Stone, 2017, , see regions. The focus on monthly extremes is motivated in part because these may be expected to be more sensitive to prescribed ocean conditions than shorter-duration events. Given that risk ratios tend to scale straightforwardly as a function of duration and spatial scale , the results here should be qualitatively relevant for hot, cold, and wet extremes for different 235 durations and regions than are examined here.

Year-to-year variability in extreme weather probabilities
As an example, Figure 1 shows

Correlation of risk ratio with sea surface temperatures
In order to achieve the goal of this paper, we would like to diagnose what is strongly focused on the North Atlantic (reaching values as high as 0.91), a region that has been linked to the recovery of the Sahel rains .

Application for alternative natural ocean surface estimates
Uncertainty in what the ocean surface might have been like in the absence 360 of anthropogenic interference is probably the largest uncertainty in the popular time-slice atmospheric modelling approach to event attribution first presented by Pall et al. (2011) and adopted by the C20C+ D&A project Stone et al.
(In preparation). One can generate a plausible estimate, as for instance the Nat-Hist/CMIP5-est1 SSTs used as the benchmark natural-SST estimate for 365 the C20C+ D&A project (Stone and Pall, 2017), but there exists an essentially infinite number of perturbations to such a natural-world SST estimate that could be just as plausible. How can we effectively sample across that uncertainty?
In this paper we have developed and presented the maps in Figure 6 as possible anomalous patterns in attributable warming to which estimates of the risk 370 ratio of extreme weather may be highly sensitive. The idea has been that areas of particularly high amplitude correlation in the maps are areas to which the risk ratio (or a similar measure of attributable influence) is most sensitive. For instance, there appears to be a large number of regions for whom the estimate of the risk ratio of wet months is sensitive to SSTs in the North Atlantic Ocean, 375 because the correlation values are particularly high for the leading principal component shown in Figure 6. The sensitive land regions tend to be located in the northern subtropics, with a particular focus on the northern half of Africa with the sensitivity patterns, and that ranking could be used to provide prioritisation of the sampling of the multiple existing estimates. Indeed, using these patterns as a means to more efficiently sample between existing available esti-400 mates may represent the most effective use of both the available estimates and these sensitivity patterns.

Conclusions
This paper has described the generation of an unusually numerous and lengthy set of simulations designed for investigation of extreme weather and 405 climate variability within the context of climate change, following the protocols of the C20C+ D&A project. The C20C+ D&A project currently includes halfcentury-long simulations under both the All-Hist/est1 and Nat-Hist/CMIP5-est1 scenarios for two additional atmospheric climate models (HadAM3P-N96 and HadGEM3-A-N216), but the ensemble sizes for the CAM5.1-degree simula-410 tions described here are considerably larger (Stone et al., In preparation). The "d4PDF" experiment with the MRI-AGCM3.2 model is comparable, being run at a somewhat higher spatial resolution and involving ensemble sizes twice as large for the full multi-decadal period (Shiogama et al., 2016). Considering that the d4PDF "natural" world is estimated using a different, observationally-based, 415 attributable warming estimate than is used here for CAM5.1-1degree, repetition of the analysis conducted here with d4PDF simulations would provide an indication of the robustness of results to both climate model and attributable warming estimate.
Multi-decadal simulations with atmosphere-ocean models run under "histor-420 ical" and "natural historical" scenarios are also available, for instance through CMIP5 , and the relatively small ensemble sizes can be mitigated by use of multiple years in a given era. Coupled atmosphere-ocean models include long-time-scale variability generated by the ocean, which may be relevant in some regions (Risser et al., 2017), but they can also suffer from 425 substantial biases that can be reduced when observed ocean conditions are prescribed (notwithstanding observational errors). Coupled models also include short-time-scale coupling that may be important for tropical cyclone dynamics (Dong et al., 2017). However, in order to accurately simulate tropical cyclones, climate models need to be run at a spatial resolution that in CMIP5

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was well beyond what was feasible for a large ensemble of multi-decadal simulations (Wehner et al., 2015). Thus, experiments with atmospheric models such as those here provide a complementary, and in some cases likely more accurate, tool for understanding extreme weather in the context of anthropogenic climate change.

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When atmospheric models are used in factual-counterfactual experiments for diagnosing the effect of anthropogenic emissions, uncertainty in how the ocean might respond to anthropogenic emissions is separated from the dynamical modelling apparatus. Instead, the ocean warming to emissions is prescribed. Thus, the uncertainty that might be characterised by using multiple atmosphere-ocean 440 models is now split between using multiple atmospheric models and multiple es-timates of the attributable ocean warming. Sampling these ocean warming estimates can be undertaken in essentially the same method as when using multiple atmosphere-ocean models: simply sample directly from individual atmosphereocean models. However, once the attributable ocean warming has been sepa-445 rated from the dynamical modelling, other possible estimates become available, such as observed trends (e.g. Christidis and Stott, 2014;Bichet et al., 2015).
The capability to sample beyond estimates from the limited number of available atmosphere-ocean models and (very limited) observations would thus mean that in one respect atmosphere-only experiments may paradoxically provide im-450 provements over atmosphere-ocean models in terms of how the ocean response is represented.