1. Introduction
The future evolution of local climate in response to anthropogenic emissions is of both societal and scientific interest. Climate models serve as an important and primary tool for understanding climate change, but they can have large biases at local scales (Palmer and Stevens 2019), and the large spread across models in local temperature trends has not decreased with model generations (Knutti and Sedláček 2013; Seneviratne and Hauser 2020). Since we cannot run experiments on the true Earth system, our remaining source of information is analysis of observable or inferable climatic responses to naturally occurring changes in radiative forcing.
The seasonal cycle in temperature is a natural choice of analog for climate change in some ways. Both the forcing and the response are large compared to internal variability—for example, warming from winter to summer in the extratropics is comparable to that between glacial and interglacial periods (Huybers and Curry 2006; Stine et al. 2009)—and relatively well measured. Further, many of the physical processes that operate as climate change feedbacks are fast enough that they plausibly would manifest similarly for the seasonal cycle. Indeed, a roughly one-to-one scaling between feedback strength for the seasonal cycle and for climate change has been found for the Northern Hemisphere snow albedo feedback (Hall and Qu 2006), the sea ice albedo feedback (Thackeray and Hall 2019), and the response of marine boundary layer clouds to changes in sea surface temperatures (Zhai et al. 2015). Significant relationships across models between seasonality in water vapor (Wu et al. 2008; Dalton and Shell 2013) and Southern Hemisphere cloudiness (Brown and Caldeira 2017), and climate sensitivity have also been noted, although the analyses do not allow for comparison of feedback strength across the two time scales. Finally, the amplitude of the seasonal cycle in temperature has been used to predict climate sensitivity with some success (Knutti et al. 2006), consistent with similar feedbacks operating in response to seasonally varying solar forcing and greenhouse gas forcing.
Despite these findings, there has been limited work exploring whether the seasonal cycle can directly inform about the spatial structure and magnitude of the continental temperature response to greenhouse gas forcing. This response is otherwise challenging to infer from the observational record given the large contribution of internal variability to observed local temperature trends, which obscures the signal even on multidecadal time scales (e.g., Deser et al. 2012; McKinnon and Deser 2018). The local temperature response to forcing is a function of multiple processes whose roles can be time scale dependent. Specifically, in an energy balance framework, the response of local temperature to radiative forcing is a function of the local energy imbalance, the strength of local feedbacks, and changes in heat flux divergence (e.g., Armour et al. 2013). The local energy imbalance is nonzero when the system is out of equilibrium, and is generally expected to be larger for higher-frequency forcing like the seasonal cycle as compared to increasing greenhouse gases. This factor alone causes a large frequency dependence in global temperature responses to forcing (MacMynowski et al. 2011) and must be accounted for in order to learn local sensitivity from seasonality. Whether local radiative and dynamical feedbacks operate consistently in response to the seasonal cycle in solar forcing versus increasing greenhouse gas concentrations is unclear. While multiple aforementioned studies do find similar feedback strength between seasonality and climate change (Hall and Qu 2006; Zhai et al. 2015; Thackeray and Hall 2019), the lack of published results on other feedbacks suggests that similar relationships have not been found. More broadly, it is increasingly clear that (global) feedback strength is both time (Armour et al. 2013; Andrews et al. 2015; Dong et al. 2019) and frequency (Lutsko and Takahashi 2018) dependent, largely due to the cloud response to changing sea surface temperature patterns. Therefore, the potential to gain knowledge about climate change from the seasonal cycle remains uncertain.
Here, we first identify a relationship between the amplitude and phase of the seasonal cycle and future Northern Hemisphere continental warming simulated by seven CMIP5-era large ensembles of climate model simulations (section 3). To explain this structure, we develop a hierarchy of energy balance models whose parameters are largely determined by seasonality alone. The energy balance models suggest that, by using both amplitude and phase information, it is possible to separately infer a seasonal feedback factor that is distinct from heat capacity effects for the seasonal cycle (section 4). We then simulate future trends using the energy balance model with the seasonal feedback factor and compare them to trends in climate models. The energy balance model exhibits similar spatial structures to the climate models, but the total continental temperature change is substantially weaker, suggesting that continental climate sensitivity differs from seasonal sensitivity (section 5). After summarizing our results, we conclude with a discussion of potential future research directions (section 6).
2. Data and methods
We use the seven CMIP5-era large ensembles in the Multi-Model Large Ensemble Archive (MMLEA; Deser et al. 2020). The MMLEA includes simulations from CCCma-CanESM2 (50 members), CSIRO-Mk3.6 (30 members), GFDL-ESM2M (30 members), GFDL-CM3 (20 members), MPI-ESM-LR (100 members), NCAR-CESM1 (40 members), and SMHI-EC-Earth (16 members). The simulations are forced by the historical (1920–2005) and then RCP8.5 (2006–2100) scenarios (Lamarque et al. 2010; Meinshausen et al. 2011). The climate models are at various native resolutions [see Table 1 in Deser et al. (2020)], and we regrid all output to a 1° spatial resolution using two-dimensional linear interpolation.
Temperatures from 1950 to 2020 in the first ensemble member of each climate model are used for the calculation of the amplitude and phase of the seasonal cycle. Throughout the paper, temperature refers to 2-m air temperature. Only one member is required to calculate the climatological amplitude and phase because they are minimally affected by sampling of internal variability: the amplitude and phase of the first ensemble member are correlated across grid boxes at greater than 0.99 for amplitude and greater than 0.98 for phase with all other ensemble members in each of the models. The climate change signal is quantified as the ensemble-mean annual-mean temperature trend from 2021 to 2050; averaging across the ensemble reduces the contribution of internal variability to the 30-yr trends.
Land is defined as any 1° grid box that has an average land fraction of at least 50%. We focus our study on the Northern Hemisphere extratropical continents (23°–80°N), where the seasonal cycle in temperature can be understood as a direct response to solar forcing, outgoing longwave radiation is largely linear with temperature (Richards et al. 2021), and there are large spatial variations in seasonality (Figs. 1a,b).
The (a) gain and (b) lag of the seasonal cycle averaged across the seven models in the Multi-Model Large Ensemble Archive. (c) The fraction variance explained by a single annual harmonic of the climatological seasonal cycle. The variance fraction is averaged across models.
Citation: Journal of Climate 37, 2; 10.1175/JCLI-D-22-0773.1
Seasonal forcing is prescribed as net shortwave radiation at the surface. We consider net shortwave at the surface rather than at the top of the atmosphere as was done in McKinnon and Huybers (2014) in order to exclude radiation absorbed by the atmosphere, although the forcing will lack the heat that is turbulently diffused through the atmospheric column and reaches the surface (Donohoe and Battisti 2013). In contrast to prior work (McKinnon and Huybers 2014), the forcing also excludes the seasonal cycle in atmospheric total energy divergence. The seasonality of this quantity is relatively small (Fig. 2c of Fasullo and Trenberth 2008), and the energy does not necessarily manifest as heating at the surface. The amplitude and phase of the seasonal forcing are based on the zonal average of the net shortwave at the surface, including over both land and ocean, although all results are nearly identical if the land-only zonal average is used instead. This formulation of seasonal radiative forcing is chosen so that zonal variations in surface albedo are accounted for as a feedback, rather than a forcing. The seasonal cycle in forcing is estimated using data from 1950 to 2020 in the first ensemble member of each climate model. The exception is SMHI-EC-Earth, for which upward shortwave was not available; for this model, we approximate net surface shortwave forcing as the mean of that across the other six models.
The amplitude and phase of the seasonal cycles in forcing and temperature are calculated by projecting their empirical monthly climatologies, with the mean removed, onto a complex basis function with annual frequency,
3. The seasonal cycle in temperature and its link to continental temperature trends
The gain and lag of the annual component of the seasonal cycle have a characteristic spatial pattern that emerges due to atmospheric heat transport and the strength of local feedbacks (Stine et al. 2009; Stine and Huybers 2012; McKinnon et al. 2013). Across the Northern Hemisphere extratropical continents, there is a general south-to-north and west-to-east increase in gain that captures the typical pattern of “continentality,” with northeastern Russia showing the greatest values (Fig. 1a). The lag shows distinct spatial structure from the gain. High lags can occur in both maritime climates such as western Europe and continental climates such as eastern Canada; similarly, low lags occur in places as disparate as Alaska and the desert of the Tarim basin in western China (Fig. 1b). The Pearson’s correlation coefficient across grid boxes between the model-average gain and lag is −0.41. The overall negative relationship—high gains associated with small lags, and the converse—is consistent with effective heat capacity as a control on seasonality, but the relatively small magnitude of the correlation indicates that each of the two measures of seasonality provides some independent information. Very similar structures are evident in observed climatological temperatures (not shown).
To explore the extent to which the processes controlling seasonality may pertain to climate change, we plot future (2021–50) annual-mean ensemble-mean linear temperature trends in the gain–lag phase space (Fig. 2). Temperature trends at each grid box are normalized by the area-weighted average temperature trend for each model to allow for intercomparison across models with different total warming, and each bin shown contains an average across at least five climate model grid boxes. Across most models, excepting CSIRO-Mk3.6, there is a clear and coherent nonlinear relationship between gain and lag, and forced temperature trends. Interestingly, the lag—which summarizes the phasing of the seasonal cycle—appears to be an important predictor of the magnitude of forced temperature trends, in addition to gain. As is intuitive, for a given lag, temperature trends are larger when the gain is larger: regions with greater seasonal temperature sensitivity exhibit greater climate change sensitivity. The linkage between lag and temperature trends is less intuitive and will be derived in the next section. Here, we simply note that, for a given gain, temperature trends are generally greater at longer lags (i.e., when the seasonal cycle is more delayed). These observations largely hold when grouping all models together (Fig. 2a) and for individual models (Figs. 2b–h), except for CSIRO-Mk3.6, which shows a weaker link between seasonality and temperature change, and tends to be an outlier in terms of its spatial patterns of warming.
Future (2021–50) annual-mean, ensemble-mean temperature trends binned by gain and lag for (a) all seven models in the Multi-Model Large Ensemble Archive and (b)–(h) each model individually. For comparison across models, all temperature trends are normalized by the area-weighted average trend across the Northern Hemisphere continents (excluding Greenland; see maps in Fig. 1). Bins that contain fewer than five climate model grid boxes are not shown. Gray contours are isolines of temperature change simulated by the seasonal energy balance model discussed in section 5.
Citation: Journal of Climate 37, 2; 10.1175/JCLI-D-22-0773.1
4. Energy balance models for the seasonal cycle
The gain and lag of the seasonal cycle in temperature in the mixture model can be calculated analytically as a function of the land and ocean end members, as well as the mixing parameter. The solution can be visualized using Fig. 3, where the end members are defined by their gain (amplitude) and lag (phase); the gain and lag of temperature at any given location are the vector sum of the scaled land and ocean end members. The value of λ influences the location of the end members in the phase space: for a given heat capacity, a larger λ leads to a smaller gain and smaller lag.
Schematic for the seasonal mixture model. The seasonal cycle is modeled as a weighted mixture between a land and ocean end member. The land end member (pink dot) has a high amplitude and small phase; the ocean end member has a small amplitude and large phase that is nearly in quadrature with the forcing. We model the seasonal cycle at a given location as mTland + (1 − m)Tocean. The vector sum is shown as a black star, and the gain and phase can be calculated using the Pythagorean theorem based on the length of the triangle legs X and Y.
Citation: Journal of Climate 37, 2; 10.1175/JCLI-D-22-0773.1
The relationships in the mixture model between the mixing parameter and feedback factor, and gain and lag, are shown in Figs. 4a and 4b. Changes in the mixing parameter affect both gain and lag, with larger mixing parameters leading to larger gains and smaller lags, as expected (Fig. 4a). The behavior of the feedback factor is of greater interest. As can be seen in Fig. 4b, the relative importance of gain and lag in recording the feedback factor depends on the location in the gain–lag phase space. For maritime land locations with small gains and high lags, such as the United Kingdom, the lag exhibits minimal sensitivity to the feedback factor and is instead primarily controlled by oceanic heat capacity. In contrast, the lag becomes an increasingly important recorder of the feedback factor, and can be more direct than the gain, for more continental locations. This can be seen by comparing the contours in Figs. 4a and 4b: increasing the mixing parameter in Fig. 4a leads to large increases in gain and decreases in lag, whereas increasing the sensitivity (1/λ) in Fig. 4b is primarily associated with increasing lags. Thus, although prior work has primarily focused on amplitude as a metric for seasonality, we suggest that the phasing of the seasonal cycle is equally or more important in learning about local sensitivity.
The (a) mixing parameter and (b) inverse of the feedback parameter as a function of gain and lag. In an energy balance framework, equilibrium temperature change scales with 1/λ. The mixing parameter influences both gain and lag, whereas the inverse feedback parameter primarily influences the lag, particularly at larger values of gain. (c) The temperature trend over 2021–50 in the energy balance model with the deep ocean in response to linear forcing from 1971 to 2050 (see section 5). The isolines from (c) are reproduced in each panel in Fig. 2 and capture many of the features present in the climate models.
Citation: Journal of Climate 37, 2; 10.1175/JCLI-D-22-0773.1
5. Comparing the response to seasonal and greenhouse gas forcing
Thus far, we have identified a coherent relationship between gain, lag, and local temperature change in CMIP5 large ensembles and derived an energy balance model framework that suggests that gain and lag can be used jointly to parse local feedback strength from heat capacity effects for seasonal forcing. We next explore whether the processes encapsulated in the seasonal mixture energy balance model [Eq. (8)] can explain the behavior seen in the CMIP5 large ensembles.
Temperature at a given location is again calculated as a linear mixture between
Maps of energy balance model parameters and trend predictions. (a) The seasonal mixing parameter. (b) The inverse of the seasonal feedback parameter. The 2021–50 annual-mean temperature trends in (c) the energy balance model and (d) the seven climate models in the Multi-Model Large Ensemble Archive. All panels show the multimodel mean; in (c) and (d), trends are shown normalized by the area-weighted average trend to account for differences in sensitivity across models. Red indicates greater than average warming and blue indicates less than average. The masked grid boxes in (a)–(c) in the United Kingdom are highly maritime locations where the gain and lag did not constrain the seasonal sensitivity; see text for more details.
Citation: Journal of Climate 37, 2; 10.1175/JCLI-D-22-0773.1
The annual-mean temperature trends from 2021 to 2050 produced by the energy balance model as a function of the gain and lag of the seasonal cycle are shown in Fig. 4c. The structure of the temperature trends in gain–lag space is similar to the inverse feedback factor shown in Fig. 4b, although with a greater sensitivity to gain due to the nonzero influence of ocean heat uptake on the trends. As expected from the derivations above, temperature trends are greater at larger gains and longer lags. The isolines from the energy balance model solution are also shown superimposed over the CMIP5 temperature trends in gain–lag space in Fig. 2. The energy balance model captures many of the major structures in the climate models, including the particular nonlinear structure in gain–lag space: in addition to temperature trends being greatest at large gains and long lags, they are more sensitive to gain at long lags and more sensitive to lag at large gains. Thus, the coherent behavior of climate model-simulated local temperature trends in gain–lag space is consistent with the mixture energy balance model. However, we emphasize that all results shown so far use temperature trends normalized by the area-weighted spatial average in each model.
We now turn to evaluating the specific spatial patterns and magnitude of temperature change. All temperature trends are multimodel ensemble means. Highly maritime grid boxes, primarily in the United Kingdom, whose gain and lag values fall outside of the energy balance model solution shown in Fig. 4 are masked, given our finding that seasonality in these locations is primarily sensitive to heat capacity effects rather than the feedback factor. The patterns of warming calculated from the energy balance model and from comprehensive climate models are similar (Figs. 5c,d). Most notably, both the climate and energy balance models show polar-amplified warming that maximizes around Hudson Bay in North America and in north-central Russia in Eurasia. The correlation across grid boxes between the two sets of trends is 0.81 [p value < 0.01; the p value is based on an effective number of spatial degrees of freedom of
Despite the similarity in pattern, the magnitude of warming differs between the seasonally inferred and comprehensive climate models: the climate models simulate 1.8°C (30 yr)−1 average warming across the domain, whereas the seasonal energy balance model produces only 0.6°C (30 yr)−1. The difference in sensitivity alone is not necessarily surprising given prior work on the time and frequency dependence of feedbacks that can emerge due to differing surface temperature patterns (e.g., Armour et al. 2013; Andrews et al. 2015; Dong et al. 2019) and changing relationships between shortwave radiation and surface temperature (Lutsko and Takahashi 2018). However, it is notable that the energy balance model captures the pattern of warming while underestimating the overall sensitivity.
The spatial pattern of the temperature trends can be broken down into meridional (along-latitude) and zonal (along-longitude) components. The dominant meridional structure in both the energy balance and climate models is polar amplification, as noted above (Figs. 6a,b). Interestingly, the ratio of warming of the Arctic (60°–80°N) relative to that of lower latitudes (30°–50°N) in the energy balance model is comparable to that of the climate models (1.45 and 1.56, respectively), even though the total rate of warming at both the low and high latitudes is smaller. The polar amplification in the energy balance model can emerge due to poleward-amplified sensitivity 1/λ or a poleward-amplified mixing parameter m. Both parameters themselves exhibit polar amplification (Figs. 6c,d), and their contribution to the change in temperature in the energy balance model can be quantified by setting the other parameter to be spatially constant, revealing that the polar-amplified warming is almost entirely due to a polar-amplified sensitivity (Fig. 6a). Thus, the energy balance model suggests that some processes related to polar amplification are manifesting at seasonal time scales, likely including the snow and sea ice albedo feedbacks as identified in prior work (Hall and Qu 2006; Thackeray and Hall 2019).
The land-only zonal average of the 2021–50 annual-mean temperature trends in (a) the energy balance model and (b) the climate model large ensembles. In (a), the energy balance model trends are also shown for the case in which either m (purple) or λ (blue) is held constant at its spatial-average value, demonstrating that meridional variations in sensitivity are the dominant control on polar amplification in the energy balance model. Both (c) the mixing parameter and (d) the sensitivity (1/λ) show polar amplification.
Citation: Journal of Climate 37, 2; 10.1175/JCLI-D-22-0773.1
The zonal patterns of temperature trends are calculated by removing the land-only zonal mean at each latitude and therefore highlight the spatial structure of temperature trends after accounting for the dominant signal of polar amplification. The energy balance model again reproduces many of the structures of warming simulated in the climate models, including greater than average warming in the U.S. Southwest, around Hudson Bay, and in the Middle East, as well as less than average warming in western Canada, the U.S. Southeast, and across western Europe (Fig. 7). Similar to the finding for meridional temperature trends, the zonal structure is almost entirely explained by λ rather than m. There are also important deviations: the energy balance model does not capture above-average warming in western Alaska, generally underestimates the spatial variability in temperature trends in Asia, and predicts that Japan will warm more than the zonal average, whereas climate models suggest it will warm less. The correlation across grid boxes between the two maps is 0.70 (p value < 0.01;
The zonal structure of the 2021–50 annual-mean temperature trends from (a) the energy balance model and (b) the seven climate models in the Multi-Model Large Ensemble Archive. Unlike in Fig. 5, the trends are not normalized. The masked grid boxes in (a) in the United Kingdom are highly maritime locations where the gain and lag did not constrain the seasonal sensitivity; see text for more details.
Citation: Journal of Climate 37, 2; 10.1175/JCLI-D-22-0773.1
6. Discussion and conclusions
Prior work has aimed to use the seasonal cycle to constrain global values of individual feedbacks (Hall and Qu 2006; Wu et al. 2008; Dalton and Shell 2013; Zhai et al. 2015; Thackeray and Hall 2019) and climate sensitivity (Covey et al. 2000; Knutti et al. 2006; McKinnon and Huybers 2014; Brown and Caldeira 2017), but the potential for seasonality to directly inform about local temperature sensitivity to forcing has not previously been explored. Here, we first demonstrate a clear and coherent relationship between the seasonal cycle, as measured by gain and lag, and forced temperature trends across the Northern Hemisphere continents in seven CMIP5-era large ensembles. Importantly, both the phasing and the amplitude of the seasonal cycle are relevant predictors of the magnitude of the temperature trends, particularly for more continental regions. We then demonstrate that this structure can be reproduced by a simple mixture energy balance model parameterized in terms of a spatially variable feedback factor and mixing parameter. The two sets of parameters can be learned by accounting for both amplitude and phase information from the seasonal cycle. The seasonally constrained energy balance model produces polar-amplified temperature trends that are similar in spatial structure to those from comprehensive climate models. However, their overall magnitude is approximately 3 times smaller, indicating that local temperature sensitivity evident on seasonal time scales cannot be straightforwardly mapped to the climate change response. The difference in magnitude is primarily evident in the meridional direction; the zonal variability in trends is more comparable although still slightly damped compared to the climate models.
The use of both amplitude and phase information allows for separately inferring a mixing parameter and feedback factor at each grid box. These two parameters summarize distinct processes with different relevant time scales. As can be straightforwardly seen for the seasonal model with no deep ocean [Eq. (8)] [see also Eqs. (4) and (5) in McKinnon and Huybers (2014), for the case with an infinite deep ocean], local temperature is a function of a forcing, feedback, and horizontal heat flux divergence term, where the diverged heat is stored in the ocean. The mixing parameter is present only in the divergence term, which is scaled by a factor of (1 − m); regions that are more maritime (smaller m) exhibit a more damped and delayed seasonal cycle due to this divergence. The importance of this term is diminished for the climate change forcing (Fig. 6), since the system is closer to equilibrium with the forcing. Instead, the energy balance model’s temperature responses to ramped forcing are primarily controlled by the seasonal feedback parameter λ, which captures the spatial variability in the strength of net radiative and dynamical feedbacks across the land only. Given that λ is learned from seasonality, it will only include processes that operate on a subseasonal time scale.
In addition to these seasonally determined parameters, the results from the energy balance model are sensitive to the choice of the heat capacities. Increasing the ocean mixed layer heat capacity causes the feedback parameter to have a stronger control on the lag but a weaker influence on the gain of the seasonal cycle. As a result, the multidecadal trends in response to greenhouse gas forcing—which are primarily controlled by the feedback parameter—also exhibit a relatively greater dependence on lag than gain that is inconsistent with the climate model behavior. The value used here for the mixed layer heat capacity (20 mwe) is consistent with known seasonality in the mixed layer depth (Kantha and Clayson 2000) but was also influenced by our prior knowledge of the broad contours of the relationship between gain, lag, and future temperature trends simulated by the climate models. The choice of land heat capacity also influences the results. Using a larger but still realistic land heat capacity leads to slightly less warming overall, a smaller range of trends across the continents, and a relatively greater role of the mixing parameter compared to the feedback factor for multidecadal trends. While we did not perform formal sensitivity experiments across the land and mixed layer heat capacities in the energy balance model, there are likely other sets of parameter choices that are physically consistent with our understanding of the climate system yet modify some of the results shown here.
In contrast, our findings have minimal dependence on the diffusivity parameter linking the mixed and deep layers (γ) and the heat capacity of the deep ocean (Cdeep). This lack of sensitivity is important if the seasonal cycle is to be used as a source of information about medium-term climate change because our model of seasonality itself is independent of their values. However, these parameters do emerge as somewhat important for transient climate sensitivity, highlighting a challenge to using seasonality to learn about long-term climate changes. In addition, an important assumption and limitation of our model is that the feedback parameter for the ocean end member is set to the land end member value, despite the well-known greater sensitivity of land than ocean (Joshi et al. 2008; Byrne and O’Gorman 2013). This decision was made because the energy balance model derivations demonstrate that seasonality cannot provide a strong constraint on, and is minimally affected by, the ocean feedback factor. All else being equal, using a larger oceanic feedback factor would further damp the temperature trends from the energy balance model.
The domain of our study was limited to the Northern Hemisphere extratropics for a number of reasons. We a priori excluded the tropics (30°S–30°N) because tropical seasonality in temperature is influenced by monsoon dynamics and seasonal shifts in the intertropical convergence zone. As a result, it is not well described by a single annual-period sinusoid and there are important nonlinearities between temperature and outgoing longwave radiation due to different phasing of temperature and humidity (Richards et al. 2021). It would be interesting in future work to expand the model of seasonality in order to account for tropical processes. We additionally only considered land because ocean temperatures are strongly affected by ocean dynamics; further, after developing the energy balance model, we found that ocean seasonality is controlled almost entirely by heat capacity within the energy balance model framework. Finally, and relatedly, we identified that, for maritime land regions with small gains and large lags, such as the United Kingdom, lag is dominantly controlled by mixing with the ocean end member rather than the feedback factor. This behavior also holds for most of the Southern Hemisphere extratropical landmasses (30°–60°S), so we excluded the Southern Hemisphere from the analysis. However, inclusion of the more continental grid boxes in the Southern Hemisphere has little impact on our results.
How to explain the ability for the seasonal model to inform about the spatial patterns of warming, but not the overall magnitude? One plausible explanation is that the ocean sets the overall sensitivity, which differs between the seasonal cycle and climate change, but that land surface properties modulate the local warming. This line of argument has been advanced to explain why drier regions and days warm more in climate model simulations of the tropics (Byrne and O’Gorman 2018; Byrne 2021; Duan et al. 2023), and the important role of sea surface temperature patterns for the time dependence of climate sensitivity is increasingly well established (Armour et al. 2013; Andrews et al. 2015; Dong et al. 2019). This explanation is consistent with our finding that the spatial structure of temperature trends along bands of latitude—along which there are large variations in land properties but relatively smaller variations in feedback strength—is similar in pattern and magnitude to climate models.
In sum, we have identified empirically that there is a strong relationship between seasonality and future warming in climate models. A mixture energy balance model provides a plausible set of physics to explain the relationship and produces the unexpected result that the phasing of the seasonal cycle should be considered in tandem with amplitude information to constrain local sensitivity. Attempts to apply the seasonally constrained energy balance model to climate change are mixed: the energy balance model produces similar spatial patterns of warming, but its overall sensitivity is too small. Future work should further parse the processes encapsulated in the λ parameter, particularly separating radiative and dynamical feedbacks, and leverage climate model simulations to identify the origin of the reduced seasonal sensitivity.
Acknowledgments.
K. A. M. was supported by the Packard Foundation. Analysis was performed on the Casper cluster supported by NSF NCAR’s Computational and Information Systems Laboratory.
Data availability statement.
All observational and model data are publicly available. The climate model large ensembles are available at the NCAR Climate Data Gateway, https://www.earthsystemgrid.org/dataset/ucar.cgd.ccsm4.CLIVAR_LE.html. Climate model forcing data were accessed at http://www.pik-potsdam.de/∼mmalte/rcps/. All computer codes to fit the models and create the figures are publicly available at https://github.com/karenamckinnon/seasonal.
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