A Physical Explanation for Ocean Air–Water Warming Differences under CO2-Forced Warming

Mark T. Richardson aJet Propulsion Laboratory, California Institute of Technology, Pasadena, California

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Abstract

Modeled global warming is often quantified using global near-surface air temperature (Tas). Meanwhile, long-term temperature datasets combine observations of Tas over land with sea surface temperature (SST) over ocean. Modeled ocean Tas warms more than SST, which can bias model–observation comparisons. Skin temperature (Ts), which is typically warmer than Tas, follows SST changes so the ocean surface temperature discontinuity δTs = TsTas decreases with warming. Here I show that under CO2 forcing, decreased δTs is consistently simulated for nonpolar ocean within ±60°S/N, but not for other regions. I investigate the causes of oceanic δTs decrease using a LongRunMIP climate simulation, radiative kernels, and standard methods for diagnosing forcing and feedbacks from the CMIP5 ensemble. CO2 forcing establishes longwave heating of the lower atmosphere and subsequent adjustments that result in a small Tas increase, and therefore a δTs decrease. During the subsequent warming in response to CO2 forcing, the model-mean surface evaporation feedback is 3.6 W m−2 °C−1 over oceans, which reduces Ts warming relative to Tas and further shrinks δTs. Present-day forcing and feedback contributions are of similar magnitude, and both contribute to small differences in model–observation comparisons of global warming rates when these differences are not accounted for.

Significance Statement

Earth’s surface skin temperature is generally warmer than that of the air just above, and this discontinuity drives upward turbulent heat fluxes. Under global warming, climate models consistently show that over oceans, the air above warms more than the water below. This causes issues when comparing model output and observational temperature records, since observational records blend land air and ocean water temperature. It also affects understanding of how surface energy and moisture fluxes will change with warming. Observational data are currently too uncertain to confidently support or refute this model behavior, and the IPCC recently noted that “there is no simple explanation based on physical grounds alone for how this difference responds to climate change.” This study provides such an explanation for changes over ocean, and shows that this result applies only to nonpolar oceans.

© 2023 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Mark Richardson, markr@jpl.nasa.gov

Abstract

Modeled global warming is often quantified using global near-surface air temperature (Tas). Meanwhile, long-term temperature datasets combine observations of Tas over land with sea surface temperature (SST) over ocean. Modeled ocean Tas warms more than SST, which can bias model–observation comparisons. Skin temperature (Ts), which is typically warmer than Tas, follows SST changes so the ocean surface temperature discontinuity δTs = TsTas decreases with warming. Here I show that under CO2 forcing, decreased δTs is consistently simulated for nonpolar ocean within ±60°S/N, but not for other regions. I investigate the causes of oceanic δTs decrease using a LongRunMIP climate simulation, radiative kernels, and standard methods for diagnosing forcing and feedbacks from the CMIP5 ensemble. CO2 forcing establishes longwave heating of the lower atmosphere and subsequent adjustments that result in a small Tas increase, and therefore a δTs decrease. During the subsequent warming in response to CO2 forcing, the model-mean surface evaporation feedback is 3.6 W m−2 °C−1 over oceans, which reduces Ts warming relative to Tas and further shrinks δTs. Present-day forcing and feedback contributions are of similar magnitude, and both contribute to small differences in model–observation comparisons of global warming rates when these differences are not accounted for.

Significance Statement

Earth’s surface skin temperature is generally warmer than that of the air just above, and this discontinuity drives upward turbulent heat fluxes. Under global warming, climate models consistently show that over oceans, the air above warms more than the water below. This causes issues when comparing model output and observational temperature records, since observational records blend land air and ocean water temperature. It also affects understanding of how surface energy and moisture fluxes will change with warming. Observational data are currently too uncertain to confidently support or refute this model behavior, and the IPCC recently noted that “there is no simple explanation based on physical grounds alone for how this difference responds to climate change.” This study provides such an explanation for changes over ocean, and shows that this result applies only to nonpolar oceans.

© 2023 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Mark Richardson, markr@jpl.nasa.gov

1. Introduction

The surface temperature discontinuity δTs refers to the difference between the temperature of the skin layer Ts and of the overlying air Tas, typically at a height of 2 m. The standard convention is that δTs = TsTas and it is generally positive, driving turbulent heat and moisture fluxes from the surface to the atmosphere above. Changes in δTs are intricately coupled to the surface energy balance and, via the latent heat flux, to the hydrological cycle. Climate models simulate regionally varying changes in δTsδTs, henceforth Δ denotes a change) under global warming. Model–observation comparisons are then complicated, since global-mean surface temperature (GMST) records combine measurements of SST over ocean with Tas over land and sea ice. In situ data typically estimate SST from near-surface water samples rather than the ocean skin layer, but observed SST trends are very similar to those in Ts (Merchant et al. 2014; Hausfather et al. 2017). In models, changes in Ts and near-surface water temperatures are similar enough that they are interchangeable for the purposes of this study (e.g., Fig. S1 in the online supplemental material). The Coupled Model Intercomparison Project (CMIP) Tas diagnosis method is left to modeling groups, for an example see section 5 of Oleson et al. (2010), where it depends on properties including Ts and the temperature of the lowest atmospheric layer.

Historically, many comparisons used model global-mean Tas [global surface air temperature (GSAT)], and in CMIP5 models, 1850–2015 ΔGSAT averaged 24% larger than when model data were handled similarly to the HadCRUT4 GMST record (Richardson et al. 2016). This difference was mostly due to incomplete spatial data coverage, and a further part was due to the treatment of sea ice changes (Cowtan et al. 2015). The effect of using ocean Tas rather than Ts on warming through 2100 averaged 4% of global warming, but even this small bias has consequences for the actions necessary to achieve global climate change targets. For example, the Paris Agreement aims to limit global warming below 2°C, but did not specify whether this is in terms of ΔGMST or ΔGSAT. If ΔGSAT were selected rather than ΔGMST, then cumulative emissions would have to be 37 GtC lower to achieve a 2°C target (Richardson et al. 2018), which is equivalent to over 3 years of human emissions.

GMST datasets have since improved spatial coverage (Morice et al. 2021; Vose et al. 2021) and some changed sea ice treatment (Rohde and Hausfather 2020), but with no standard treatment for TasTs blending, ΔGMST is sometimes scaled by a model-derived factor to estimate ΔGSAT (Clarke and Richardson 2021). Ship and buoy data disagree even about the sign of ocean δTs trends (Junod and Christy 2020; Rubino et al. 2020), but dataset uncertainties are currently too large to allow confident conclusions (Morice et al. 2021).

Referring to δTs, the Intergovernmental Panel on Climate Change Sixth Assessment Report (IPCC AR6) stated that “there is no simple explanation based on physical grounds alone for how this difference responds to climate change” (Gulev et al. 2021). This paper’s primary motivation is to provide a simple physical explanation for differences in model ΔGSAT and ΔGMST, so the analysis targets nonpolar ocean within ±60°S/N which includes most global ocean. Complications from polar and land processes are therefore excluded, but future work there could allow understanding of how, for example, in situ land ΔTas should be compared with satellite-retrieved ΔTs.

A secondary motivation is that the model treatment of δTs and near-surface processes is also intricately linked to the hydrological cycle and its anticipated intensification under global warming (Andrews et al. 2009). Modeled global precipitation increases at just ∼2% °C−1 while specific humidity rises at ∼7% °C−1, and several studies have investigated this difference with reference to δTs. Richter and Xie (2008) stated that shrinking δTs reduces evaporation by ∼1 W m−2, and they argued that this “is consistent with the high heat capacity of the ocean.” Lorenz et al. (2010) also described δTs as limiting evaporation increases, but stated that causality could act the other way and that evaporation “will act to increase Ta relative to Ts.” More recently, Siler et al. (2019) used a Penman–Monteith framework to link changes in the surface energy budget to evaporation. They noted that evaporation transports heat away from the surface so efficiently that δTs must change to maintain energy conservation, as previously described for some extreme paleoclimate states by Pierrehumbert (2002). Here I show that contrary to Richter and Xie (2008)’s stated causality, ocean heat uptake does not cause long-term ΔδTs < 0, rather there is stronger support for the energetic description of Siler et al. (2019) in which evaporation drives ΔδTs < 0. In addition to the temperature-mediated (“feedback”) effect, there is also a direct effect of atmospheric adjustments to CO2 radiative forcing.

This study only considers CO2-related changes, since CO2 is the dominant cause of recent warming and there is a suite of model tools to evaluate CO2 forcing scenarios. The conclusions may not extend to other forcings such as aerosols, which have been important for recent ΔGMST progression. The results show an effective equilibrium attribution of 34% ± 13% to forcing, and 66% ± 13% to feedbacks (ensemble mean ± standard deviation). CO2 forcing directly reduces δTs through rapid adjustments driven primarily by atmospheric longwave heating (e.g., Kamae et al. 2015). Warming then strongly increases evaporation, which cools Ts and further decreases δTs.

I will proceed as follows: section 2 shows model ΔδTs and uses millennium-length simulation output to demonstrate that ocean heat uptake cannot explain the long-term ΔδTs. The long simulation shows a distinction between a short-term forcing-dominated ΔδTs followed by a longer-term feedback-related ΔδTs. This section also summarizes canonical rapid atmospheric changes to CO2 forcing and argues that they explain the short-term ΔδTs. The remainder of the paper is devoted to a feedback analysis, beginning with section 3, which derives how surface feedbacks drive ΔδTs. Feedback calculations begin in section 4 using radiative kernels from the HadGEM2-ES climate model. Kernels are ideal for this purpose since they uniquely isolate surface contributions from those of the atmosphere, but are only available for some energy-budget terms and for few models. The analysis then proceeds to the standard Gregory regression (Gregory et al. 2004) decomposition using abrupt4xCO2 output to evaluate all feedback components in 23 models. The regression methodology and validation for surface feedbacks is described in section 5 and the results are presented in section 6. Section 7 discusses the study and section 8 presents the conclusions.

2. Model changes in surface temperature discontinuity under CO2-forced warming

This section describes the typical phase 5 of the Coupled Model Intercomparison Project (CMIP5) model δTs behavior in CO2-forced simulations. It highlights how ocean differs from other surfaces and uses long-run simulation output to show that there are both forcing and feedback contributions. Figure 1 maps ΔδTs between years 1–10 and 61–80 in eight CMIP5 1% yr−1 CO2 ramping simulations (1pctCO2). These eight models provide all properties necessary for later analysis, and years 61–80 cover atmospheric CO2 doubling. There is widespread ΔδTs < 0°C over nonpolar ocean, intermodel disagreement over land, and ΔδTs > 0°C in polar regions. By year 140, mean nonpolar ocean Tas warms by 5%–10% more than Ts in all models (Fig. S2).

Fig. 1.
Fig. 1.

Simulated change in surface temperature discontinuity in 1pctCO2 simulations, year 61–80 mean minus year 1–10 mean.

Citation: Journal of Climate 36, 9; 10.1175/JCLI-D-22-0215.1

As proposed by Richter and Xie (2008), water may warm less than the overlying air due to the oceans’ large heat capacity, so ΔδTs < 0 may disappear once the ocean warms to equilibrium. This hypothesis is testable using recently available LongRunMIP output (Rugenstein et al. 2019) from an abrupt4xCO2 simulation in which atmospheric CO2 is quadrupled and then held fixed. If ocean heat uptake dominates, then ΔδTs should transiently decrease then increase back to equilibrium. However, Fig. 2a shows that for nonpolar ocean, ΔδTs < 0 even after 1300 years. Figures 2b and 2c changes differ for nonpolar land and polar regions, so this study’s conclusions only apply to nonpolar oceans. Returning to Fig. 2a, the year 1 abrupt4xCO2 δTs is roughly 0.1°C below preindustrial, and this is followed by a longer-term decrease of approximately 0.2°C. I argue that these two features can be understood in terms of a standard forcing–feedback decomposition.

Fig. 2.
Fig. 2.

Annual δTs simulated by HadGEM2-ES over (a) ocean within ±60°S/N, (b) land within ±60°S/N, and (c) polar regions from 60° to 90°S/N. Blue is the control simulation output with no forcing, and orange is from a LongRunMIP run in which atmospheric CO2 is instantaneously quadrupled at the beginning of the simulation and then held constant.

Citation: Journal of Climate 36, 9; 10.1175/JCLI-D-22-0215.1

Importantly, the effect of CO2 forcing on the atmosphere is well-established and can explain the rapid modeled δTs decrease. To the author’s knowledge, the link between ΔδTs and CO2 forcing adjustments has not previously been made explicit, so this understanding is now summarized. Additional CO2 causes instantaneous radiative forcing (iRF) that heats the lower atmosphere. Doubled-CO2 longwave heating rates approach 0.1°C day−1 in the low to midtroposphere, with smaller positive values extending to the surface (Collins et al. 2006). Rather than iRF, a more commonly used value is effective radiative forcing (ERF), which includes atmospheric adjustments to the forcing agent that are independent of surface temperature. They often occur within days to weeks and so can dominate short-term atmospheric changes (Cao et al. 2012; Dong et al. 2009). The canonical over-ocean adjustments include warming air temperature (Ta) with drying aloft and PBL moistening, which suppresses evaporation. These adjustments are described in Kamae et al. (2015). Since ERF refers to changes that are independent of Ts, CO2-driven ERF adjustments with ΔTas > 0 therefore mean ΔδTs < 0. Model ERF is commonly approximated with reference to globally fixed Tas (Gregory et al. 2004) or fixed Ts over oceans (Hansen et al. 2005) and Hansen-method CMIP5 simulations indeed show ΔδTs < 0 over oceans (Fig. S3). Not all of Fig. 2’s first year changes are due to forcing since warming begins immediately, but most of the rapid changes will be forcing related.

Henceforth the CO2 ERF adjustments are taken as explained, and the analysis focusses on (i) interpreting how individual feedbacks drive ΔδTs and (ii) separately quantifying the contributions of ERF and feedbacks to ΔδTs. Addressing (i) and (ii) requires establishing the forcing–feedback framework and linking individual feedback terms to changes in δTs.

3. Interpreting feedback-driven changes in the surface temperature discontinuity

The standard forcing–feedback decomposition of a time series ΔX(t) is
ΔX(t)=ΔFX(t)+λXΔT(t),
where ΔFX(t) refers to forcing and λX = dΔX/dΔT is a feedback parameter. I use Eq. (1) for any property, for example, if X = δTs then ΔFδTs represents the forcing-related adjustment in δTs (in °C). The Eq. (1) assumption of fixed λX is supported by section 6 results, at least for transient changes over approximately a century.

I define λX,Tas as the response of property X to full-atmosphere warming consistent with ΔTas = 1°C. This is analogous to standard practice where TOA feedbacks often refer to response to ΔTas, even though temperature, humidity, and cloud properties change throughout the atmosphere. Results will be shown both for λX,Tas defined for ΔTa(P) = ΔTas at all levels in the atmosphere (uniform warming profile) and for a model’s typical warming profile (including lapse rate changes). When X is a flux term, λX,TasΔTX,as is directed downward and λX,TsΔTX,Ts upward. There are also turbulent fluxes at the surface which are controlled, in part, by the surface temperature discontinuity δTs. I account for this through a term λNs,δTsΔδTs, which is defined as positive upward, and for the turbulent heat fluxes the understanding is that λX,Tas=0 and the λX,Ts captures uniform warming of both Ts and Tas.

Equilibrium occurs when net surface flux, Ns = 0 W m−2, so if the equilibrium flux change through region boundaries is small then
ΔFNs=λNs,TsΔTs+λNs,δTsΔδTsλNs,TasΔTas.
I will now show that this surface energy balance means that the sign of ΔδTs depends on the relative strength of the feedback terms λNs,Tas and λNs,Ts. By substituting ΔTs = ΔTas + ΔδTs into Eq. (2):
ΔδTs=1λNs,Ts+λNs,δTs(ΔFNs+λNs,TasΔTasλNs,TsΔTas).
Differentiation of Eq. (3) with respect to λNs,Ts and λNs,Tas tells us whether each feedback term acts to increase or decrease ΔδTs:
dΔδTsdλNs,Ts=1(λNs,Ts+λNs,δTs)2[ΔFNs+(λNs,Tas+λNs,δTs)ΔTas],
dΔδTsdλNs,Tas=ΔTas(λNs,Ts+λNs,δTs).
Equation (4) says that ΔδTs gets smaller as λNs,Ts gets larger, while Eq. (5) says that ΔδTs gets larger as λNs,Tas gets larger. This is because the numerators of Eqs. (4) and (5) are all positive. To identify the threshold that defines the sign of the feedback-driven ΔδTs, first divide both sides of Eq. (3) by ΔTas. At equilibrium ΔFNs/ΔTas=λNs,Tas so the sign of ΔδTs/ΔTas=λδTs is
λδTs{>0if2λNs,Tas>λNs,Ts=0if2λNs,Tas=λNs,Ts<0if2λNs,Tas<λNs,Ts.
All terms with λδTs cancel out during this derivation, so the sign of the feedback contribution of ΔδTs only depends on the feedback strengths defined with respect to λNs,Tas and λNs,Ts. Figure 2 shows that CMIP5 feedbacks drive ΔδTs < 0 so the bottom case is required. Ignoring the relatively small geothermal flux (Hofmann and Morales Maqueda 2009), Ns is
Ns=L+H+LWLW+SWSW,
where L is latent heat, H is sensible heat, SW means shortwave radiation, and LW means longwave radiation. Arrows indicate flux direction. This Section has established that coupled-model ΔδTs < 0 from feedbacks requires large λNs,Ts relative to λNs,Tas, next I investigate the feedback terms of Eq. (7) to interpret the processes driving ΔδTs. In observations or coupled model output it is extremely hard to isolate feedbacks and response, especially for longwave radiation (Vargas Zeppetello et al. 2019). Furthermore, model tools do not currently exist to isolate terms such as λL,Ts, which could be calculated by warming ΔTs, holding everything else constant, and then diagnosing latent heat flux changes offline. While such “kernel” calculations are not available for the turbulent terms, they exist for radiative surface fluxes. Section 4 applies available HadGEM2-ES temperature and moisture radiative kernels to demonstrate that non–cloud radiative feedbacks cannot explain the decrease in modeled δTs. Sections 5 and 6 will turn to Gregory regression of abrupt4xCO2 simulations, from which I identify evaporation as the dominant feedback for ΔδTs < 0.

4. Radiative kernel analysis

a. Theory, data, and processing

Adopting similar notation to Soden et al. (2008), an atmosphere with layers i = 1, …, N has temperatures Ti and moisture values qi. A linear approximation of flux change ΔR is
ΔR=iR¯dqiδq¯i+R¯dTiδTi¯=iKq,iδq¯i+KT,iδTi¯,
where Kq,i and KT,i represent the change in surface radiation following water vapor or temperature changes in the ith atmospheric layer, and depend on time and location. Kernels are calculated by perturbing each Ti or qi from the preindustrial state then performing offline radiative transfer calculations. The model’s fixed preindustrial cloud conditions are assumed, which partially mask the radiative changes so I term derived values “noncloud” responses. Cloud variation or nonlinearity will introduce errors, but they are generally small for modern warming. Surface kernels are provided for Ts (in W m−2 °C−1) and so λTs=KTs, while the surface feedback to atmospheric changes, λTas must be derived from the kernels, for example for temperature:
λT,Tas=i=138ΔTa,iΔTasKT,iΔPi,
where ΔPi is the pressure thickness of the ith layer. The moisture calculation is performed analogously, assuming fixed relative humidity.

I use the published HadGEM2-ES kernels since they fully decouple Ts and Ta (Smith et al. 2018; Smith 2018). Several other kernel datasets combine changes in Ts and in the lowest atmospheric layer Ta,i=1, so cannot separate λTas and λTs (Soden et al. 2008; Kramer et al. 2019; Pendergrass et al. 2018). I annually average on the model’s 1.25° latitude × 1.875° longitude grid and assume ΔTa,i = 1°C. Poleward of 60°N the stratified polar atmosphere traps warming near the surface and the changed lapse rate affects surface feedbacks (Graversen et al. 2014; Manabe and Wetherald 1975; Pithan and Mauritsen 2014). However, the nonpolar oceans show small lapse rate changes at the altitudes that affect surface radiation, so results here are unaffected by assuming uniform vertical warming (Fig. S4).

b. Kernel results

Figure 3 shows non–cloud radiative λSW+LW,TasλLW,Ts. Assuming ΔT(P) = 1°C, nonpolar oceanic λSW+LW,Tas¯=5.77Wm2°C1 and λLW,Ts¯=5.70Wm2°C1 so radiative λ¯Tsλ¯Tas is small and negative. Following Eq. (6), if non–cloud radiative feedbacks are λTsλTas, then they are nowhere near the λTs>2λTas requirement to explain ΔδTs < 0. Figure 3 implies a large role for water vapor in the spatial structure of the feedback balance, which Fig. 4 confirms. This is because the atmosphere is cooler and has lower emissivity than the surface, so λT,Tas<λT,Ts everywhere. However, water vapor increases the effective emissivity, which increases λTas and means that radiation even further favors ΔδTs > 0 in moist areas. From Fig. 4, there is no latitude where ocean clear-sky radiation λTs>2λTas and there is confirmation that lapse rate changes play a minor role within ±60°S/N. I now turn to fully coupled CMIP5 outputs to investigate other processes that could provide the substantial λTs increases necessary to obtain ΔδTs < 0 from feedbacks.

Fig. 3.
Fig. 3.

Global map of λas minus λs calculated assuming vertically uniform warming and constant relative humidity. Positive values represent areas where these radiation responses favor an increase in δTs.

Citation: Journal of Climate 36, 9; 10.1175/JCLI-D-22-0215.1

Fig. 4.
Fig. 4.

Over-ocean net surface radiative fluxes downward from changes in water vapor (blue), temperature (orange), and combined (black). The red line is the absolute value of the surface kernel; where the black line is above half the red line, the non–cloud radiation feedbacks favor ΔδTs > 0. Solid lines are derived from the abrupt4xCO2 mean ΔT(z)/ΔTas profile at each latitude. Dashed lines are calculated assuming all atmospheric layers warm by 1°C.

Citation: Journal of Climate 36, 9; 10.1175/JCLI-D-22-0215.1

5. CMIP5 methods

a. Overview of approach

Gregory regression (Gregory et al. 2004) was developed to estimate forcing and feedback strengths for global-mean TOA flux in response to global-mean ΔTas. It was subsequently used to study regional feedbacks (e.g., Andrews et al. 2015). Here I use it to calculate individual surface energy budget terms over nonpolar oceans. To justify interpretation based on the Gregory-derived parameters, I require that the parameters accurately predict output from fully coupled 1pctCO2 simulations.

b. Data sources

I use CMIP5 preindustrial control (piControl) and abrupt4xCO2 scenarios, taking the first run from each model (labeled r1i1p1) if they provide monthly Ts, Tas, and all surface and TOA fluxes (N = 23 models, see Table S1). Those models with matching 1pctCO2 output (N = 8) are used to test the regression performance. Model drift in abrupt4xCO2 is removed following DeAngelis et al. (2015) by subtracting the centered 21-yr mean from the corresponding model piControl simulation in each grid cell. If the abrupt4xCO2 fork year is not provided, then I match piControl years 1–21 to abrupt4xCO2 year 1.

c. Separation of forcing and feedbacks

1) Regional Gregory decomposition

The Gregory method was originally based on the linear Eq. (1) for net TOA fluxes in response to global ΔTas,glob in an abrupt4xCO2 simulation:
ΔNTOA(t)=ΔF4xCO2+λgregΔTas,glob(t).
Regressing ΔTas,glob(t) against ΔNTOA(t) gives a gradient λgreg and ΔTas = 0°C intercept ΔF4xCO2. The fit line projected to ΔNTOA = 0 W m−2 then gives “effective” equilibrium ΔT4xCO2. Metrics are usually reported for CO2 doubling, and since CO2 forcing is approximately logarithmic in concentration, ΔT4xCO2/2 is termed the effective equilibrium climate sensitivity to doubled CO2 [ECSeff, see discussion in Grose et al. (2018) or Sherwood et al. (2020)].
I perform Gregory regressions for each property X in each latitude–longitude grid cell i, j following previous work (Andrews et al. 2015; Stephens et al. 2016):
Xi,j(t)=ΔFgreg,Xi,j,4xCO2+λgreg,Xi,jΔTas,glob(t).
Regressions are performed over the simulation length, either years 1–140 or 1–150. By regressing against global Tas, the area-weighted mean of λX,greg or ΔFX,4xCO2 reproduces the values derived by regressing global-mean X against global-mean Tas. The net feedback parameters (those for L, H, SWnet or LWnet) can be interpreted as
λgreg,X=λX,TsΔTs+λX,δTsΔδTsλX,TasΔTasΔTas,glob,
where all terms except ΔTas,glob refer to gridcell values. Clearly the single value of λgreg,X is sensitive to λX,Ts, λX,Tas, and λX,δTs, but they cannot be separated as they can using kernels. These gridded parameters (e.g., λgreg,X) are converted to a nonpolar ocean average by taking the area-weighted mean scaled by gridcell ocean fraction derived from the binary 0.125° land–sea mask of the ECMWF interim reanalysis (Dee et al. 2011).

The surface–atmosphere feedback relationship described in Eq. (6) defines whether δTs increases or decreases in response to feedbacks. The term λgreg,Ns is the sum of components at the air–sea boundary. However, if ΔNs does not return to near-zero at equilibrium, then Eq. (6) would no longer apply and an additional flux divergence term would be needed. For nonclosed systems, changes in heat uptake could contribute to ΔδTs. This may occur locally due to, for example, changes in ocean circulation, but later results will show that nonpolar ocean ΔNs ≈ 0 W m−2 at equilibrium, such that we can neglect its contribution to ΔδTs.

2) Evaluating Gregory method

The spatial distribution of ΔNs and ΔTas activates regional feedbacks and changes global-mean responses (Dong et al. 2019; Rose et al. 2014; Armour et al. 2013; Gregory et al. 2015; Knutti and Rugenstein 2015). The recently observed spatial ΔTas pattern implies 30-yr mean TOA λ that can be 100% different from that associated with the simulated long-term warming pattern (Zhou et al. 2016). Furthermore, quadrupled-CO2 responses are not precisely twice those experienced under doubled-CO2 (Mitevski et al. 2022).

This raises concerns about the accuracy of Gregory parameters, so for validation I use them to predict time series of 1pctCO2 output for each property ΔX(t) via
ΔX(t)=ΔFX(t)ΔFgreg,X,4xCO2+λgreg,XΔTas,global(t).
Here ΔTas,global(t) is from the 1pctCO2 simulation and ΔFgreg,X,4xCO2 and λgreg,X are from the abrupt4xCO2 Gregory fits for that model. ΔFXxCO2 increases linearly from year 1 to 140 up to ΔFX,4xCO2 in all models except for GFDL-ESM2M, whose CO2 increase stops in year 70 after a doubling. For that model, ΔFX(t) stays flat after year 70. Performance is evaluated by comparing the 1pctCO2 ΔX(t) output with that predicted by Eq. (13).

3) Attributing discontinuity change to feedbacks and forcing

The fraction of ΔδTs due to feedbacks can be expressed as a function of total global-mean warming, ΔTas,glob via
αΔTas,glob=λδTsΔTas,globΔFδTs+λδTsΔTas,glob.
Substituting ΔTas,glob = ECSeff and ΔFδTs at doubled CO2 into Eq. (14) gives the effective-equilibrium attribution fraction to feedbacks, with the forcing fraction being one minus that value. I report the statistics of the N = 23 abrupt4xCO2 results, noting that intermodel spread is not a true measure of uncertainty.

6. Results

a. Validation of Gregory decomposition

Figure 5 shows that the Eq. (11) Gregory-based reconstruction provides accurate predictions of 1pctCO2 output. However, Gregory regression produces some nonphysical results since its ERF is inferred from a statistical fit extended to global ΔTas = 0°C, which implies land warming and ocean cooling. The ocean cooling, seen as the blue lines in Figs. 5a and 5b, is clearly unphysical and means that some local feedback effects will be included as forcing. From Fig. 5a, the cooling is equivalent to approximately −7% of the transient warming, so forcing terms in Figs. 5c–5h will include an artificial component equivalent to approximately −7% of each feedback term. Section 7c will discuss how ERF estimates depend on the calculation method, and concludes that forcing definition has a minor effect on this study’s conclusions.

Fig. 5.
Fig. 5.

CanESM2 1pctCO2 simulated changes for oceans within ±60°S/N in (a) Tas, (b) Ts, (c) δTs, (d) latent heat, (e) sensible heat, (f) net absorbed shortwave, (g) net absorbed longwave, and (h) net surface heat uptake. Black lines are the model output, and the red line is the prediction using global Tas with the Gregory-fit regression parameters derived from this model’s abrupt4xCO2 simulation. Blue and orange lines respectively represent the estimated time series of the forcing and feedback terms.

Citation: Journal of Climate 36, 9; 10.1175/JCLI-D-22-0215.1

In terms of reconstructing the coupled model output, the worst performance is for SWnet, which has large cloud-driven interannual variability relative to its long-term change. Across the eight 1pctCO2 runs, errors are typically <10% by years 61–80 (Fig. S5). The results support a Gregory-method decomposition over nonpolar oceans so the derived forcing and feedback parameters for all 23 models can be used to interpret the physical drivers of ΔδTs.

Also from Fig. 5, for properties where feedbacks are relatively more important than ERF, there is more curvature in the response. This is because global ΔTas,global is delayed by heat uptake Ns and slowly accelerates as atmospheric CO2 accumulates. Properties with large feedback components, such as evaporation, therefore, show more notable curvature. This is consistent with the results of Yeh et al. (2021), who noted asymmetric precipitation responses in models when CO2 is ramped up versus ramped down.

b. Ensemble Gregory forcing and feedback responses

1) Changes in ΔTs

The derived forcing, feedback and effective equilibrium responses of δTs and surface fluxes are displayed for nonpolar ocean in Fig. 6a. Feedbacks are divided by oceanic λTas,greg so are expressed per degree Celsius of nonpolar ocean Tas warming. All 23 models show ΔδTs < 0°C in both forcing and feedback responses with no clear correlation between them (Table S1).

Fig. 6.
Fig. 6.

Gregory-fit results for each CMIP5 model over nonpolar ocean. (a) Forcing, feedback, and effective equilibrium ΔδTs, where effectiveequilibrium=ΔF2xCO2+λ×ECS. (b) Derived forcing responses for surface fluxes, (c) feedback parameters for surface fluxes, and (d) effective equilibrium for each surface flux. Note that this figure shows the feedback strengths necessary to interpret the argument of Eq. (6), so scales vary between panels. See Fig. S6 in the supplemental material for results showing λ × ECS with consistent units.

Citation: Journal of Climate 36, 9; 10.1175/JCLI-D-22-0215.1

Section 7 argues that the small-magnitude λδTs,greg outlier BCC-CSM1-1M is most likely due to an erroneous diagnosis of Tas relative to Ts. Its mean δTs of 0.06°C is unrealistically low and far below the 1.10°C average of the other models (Table S1). Excluding its λδTs,greg of −0.001°C °C−1, the remaining models span −0.020° to −0.070°C °C−1. The MPI models all show stronger responses than the others but are not outliers in terms of flux feedbacks nor in mean δTs. A more detailed study would be required to understand why the MPI model ΔδTs feedback responses are relatively strong.

2) Changes in surface fluxes

Figures 6b–6d show Gregory-derived flux responses and include cloud radiative effects (CRE), the difference between all-sky radiation and what the radiation would be in the absence of clouds. In these panels, signs are selected so that values greater than zero are of the correct direction to support ΔδTs < 0. For forcing, Fig. 6b changes follow the previously described atmospheric adjustments to CO2, with net longwave surface heating and suppressed L and H establishing a large ΔNs.

For feedbacks in Fig. 6c results must be interpreted with care, as Eq. (12) states that the Gregory feedbacks reported here are a combination of response to changes in Ts, Tas, and δTs so cannot be directly applied to Eq. (6). There is a large range in SW CRE that fits with the changes in oceanic low clouds that cause large intermodel spread in ECSeff (Bony and Dufresne 2005). Atmospheric moistening shifts all-sky SWnet toward less surface absorption relative to SW CRE alone. The LWnet feedback is of the wrong sign to support ΔδTs < 0 and the net surface SW feedback has models with either sign. The LW and SW CRE components anticorrelate, resulting in a residual net CRE feedback of +0.6 W m−2 °C−1, of a sign that acts to decrease δTs. The Gregory-derived radiation feedback parameters are qualitatively consistent with the kernel results, suggesting that λLW,TsλLW+SW,Tas and therefore that radiation feedbacks cannot explain why feedback-related ΔδTs < 0.

The sensible heat flux H is typically parameterized in models as proportional to δTs, and so its Gregory feedback is likely to be dominated by λH,δTsΔδTs rather than representing λTs. For evaporation, all models simulate a strong L increase with an ensemble mean of 3.6 W m−2 °C−1. Latent heat flux parameterizations generally use the near-surface moisture gradient, and if RH and dynamics are fixed then the latent heat feedback λL,Ts is +7% °C−1 (Siler et al. 2019), or approximately +7 W m−2 °C−1 over nonpolar ocean in these models. This is larger than the widely reported global model range of 1%–3% °C−1 because ocean evaporation response is greater than that of land. The Gregory λL,greg<λL,Ts since λL,greg implicitly includes changes in circulation, relative humidity, and δTs which suppress evaporation increase.

Figure 6d’s effective-equilibrium values show the combined forcing and feedback effects at ΔTas = ECSeff, and the range of ECSeff causes much of the spread in results. Crucially, the implied equilibrium ΔδTs (Fig. 6a) is negative in all models, while ΔNs is very small (from −1.2 to +0.2 W m−2) relative to the changes in other terms such as evaporation (4.2–11.7 W m−2). This further supports that heat uptake changes do not explain ΔδTs. The equilibrium ΔNs represents transport between nonpolar oceans and other areas, in particular increased transport to the polar regions (Hwang et al. 2011; Holland and Bitz 2003; Newsom et al. 2021).

Taken together:

  1. Figure 6d’s minor ΔNs at equilibrium justifies the approach resulting in Eq. (6).

  2. Figure 6c’s radiation terms plus the kernel results rule out radiation feedbacks from explaining ΔδTs on their own.

  3. Figure 6c’s H feedback sign rules out turbulent heat, while the L feedback represents a large cooling effect on Ts consistent with evaporation driving decreased δTs.

Assuming that λL,greg is a minimum bound and the Clausius-Clapeyron limit an upper bound, then over nonpolar oceans climate models likely have 3.6λTs7.0Wm2°C1. From Eq. (6) and the range of radiation feedbacks estimates, a λL,Ts of order 5 W m−2 °C−1 or greater is required. By process of elimination, evaporation is the necessary process to obtain a feedback-related ΔδTs < 0, and in models it must be sufficient to do so. However, it is possible that the real-world λL,Ts could be smaller and ultimately insufficient to achieve the threshold necessary for ΔδTs < 0. For example, if real-world ΔTs directly causes a far greater near-surface moistening or slowdown of winds than is seen in models, then this is one way in which λL,s could be overestimated in models.

c. Attribution of δTs change between forcing and feedbacks for nonpolar ocean

Figure 7 applies Eq. (14) and expresses the fraction of ΔδTs due to feedbacks as a function of global ΔTas divided by ECSeff. ΔδTs is initially dominated by ERF, before warming triggers feedbacks that drive further ΔδTs. According to the Gregory regression parameters, when warming reaches ECSeff the feedbacks explain a mean of 66% of ΔδTs with an intermodel range of 48%–92%. Year 70 in 1pctCO2 simulations is commonly used as a measure of transient response, with warming approximately 50%–60% of ECSeff, and at this point the forcing–feedback split is roughly even. Nonpolar oceanic ΔδTs in the modern day therefore likely contains similar-magnitude contributions both from CO2 forcing adjustments and temperature-mediated feedbacks. Neither the intermodel ΔδTs nor the attribution fraction strongly correlate with any surface energy budget term, so understanding intermodel variability would require a more detailed analysis. Section 7c will discuss how this results in a small overestimate of the feedback contribution.

Fig. 7.
Fig. 7.

Fraction of change in nonpolar ocean δTs explained by temperature-mediated feedbacks rather than forcing adjustments, plotted by change in global ΔTas. Here x = 0 is ΔT = 0°C, so the feedback contribution is 0. The value x = 1 represents the new effective equilibrium state at ΔTas = ECSeff. Each line is one climate model.

Citation: Journal of Climate 36, 9; 10.1175/JCLI-D-22-0215.1

7. Discussion

a. Summary of results

Changes in the surface temperature discontinuity δTs can bias model–observation comparisons of global mean temperature change and are intricately tied to the surface energy budget. This paper provides a simple, physical mechanism to explain modeled ΔδTs over nonpolar oceans, which IPCC AR6 identified as lacking. The explanation comes in two parts:

  1. CO2 heats the lower atmosphere and subsequent rapid adjustments cause Tas to warm more than Ts, therefore ΔδTs < 0,

  2. Warming then increases surface evaporation so that Ts warms less than Tas, therefore ΔδTs < 0.

Both processes have been reported elsewhere, but here I confirm this model behavior and quantify their contributions to ΔδTs. Heat uptake ΔNs shrinks to near zero by ECSeff over oceans, so it cannot explain equilibrium ΔδTs. This is consistent with the interpretation of Siler et al. (2019) rather than Richter and Xie (2008), the latter of which proposed that Ns reduces δTs. The presented results are only for large-area means, however, and Ns may be important locally.

This paper’s analysis began when only CMIP5 had sufficient outputs available, but CMIP6 shows similar ERF adjustments (Smith et al. 2020), evaporation feedback (Pendergrass 2020), and decreased ΔδTs (e.g., Liang et al. 2020), so the process conclusions likely apply to CMIP6 as well. CMIP6 features more models with higher ECSeff, which may result in larger equilibrium ΔδTs, but with minor present-day differences.

It is only nonpolar ocean where ΔδTs < 0 in all models so observational datasets, which combine Ts over ocean and Tas elsewhere, will report less long-term warming than either global Ts or global Tas. Other regions may have limited moisture availability that limits surface evaporation (Gregory and Webb 2008) or changes in surface type, such as from sea ice retreat, that would further complicate changes (see Fig. S7 for all surface Gregory results). Note that the effect of ΔδTs changes reported here are proportionally smaller than those reported in Richardson et al. (2016) since sea ice changes are excluded here.

b. Radiative kernel interpretation and model treatment of non–cloud radiation changes

The radiative kernel results use just HadGEM2-ES, which is not an outlier in terms of ΔδTs or flux changes so its findings may extend more broadly. The kernel-based λTs is sensitive to ocean emissivity (ε, assumed to be unity) and Ts, neither of which have large known errors. HadGEM2-ES mean Ts is typically within ±2°C of observations (Wang et al. 2014; Richter et al. 2014), while real-world ocean ε is approximately 0.95 but poorly constrained in the far-infrared (Feldman et al. 2014).

For ΔδTs, ongoing model mean-state biases (Xu et al. 2022) can influence calculated λTas. Relevant factors include model vertical layering (Räisänen 1996), subgrid moisture variability (Kim et al. 2020) and treatment of absorption bands (DeAngelis et al. 2015). However, atmospheric kernel errors are likely too small to overturn the conclusions since observation-based kernels (Kramer et al. 2019), which use similar approximations, largely capture month-to-month variability in measured surface radiation (Dai et al. 2021).

The surface is both warmer and more emissive than the atmosphere so for uniform vertical warming the temperature component of λTs always exceeds that of λTas. In HadGEM2-ES, moistening over much (but not all) of the nonpolar ocean is sufficient to tip non–cloud radiative λTas into exceeding λTs. Areas where λTas>λTs are the surface equivalent of so-called “super greenhouse effect” regions that have been studied for TOA fluxes and occur for similar physical reasoning (Stephens et al. 2016).

The moisture kernel calculations assumed fixed relative humidity (RH), while models typically show increases over ocean (Byrne and O’Gorman 2016) since specific humidity changes similarly over land and ocean but land warms faster (Simmons et al. 2010). Higher RH would favor ΔδTs > 0, so relaxing the fixed-RH assumption would likely only further rule out non–cloud radiative effects from explaining the coupled-model ΔδTs. Finally, cloud masking will change with warming, but the clear-sky kernel-derived feedbacks differ by just 0.3 W m−2 °C−1, which is far too small to overturn the main conclusions. Taken together, the kernel results suggest a minor role for non–cloud radiation in explaining the feedback-driven ΔδTs.

c. Gregory decomposition limitations and interpretation

As discussed in section 6a, Gregory regression can produce nonphysical forced oceanic cooling since it is fit to global ΔTas = 0. The Hansen method avoids artificial ocean cooling but allows land temperature response (Fig. S3). Either standard method has errors in separating forcing from feedback, and for the four models that also provide fixed-SST outputs the Hansen ΔFδTs mean is 30% larger than the Gregory ΔFδTs mean (Table S2, Fig. S3). This likely explains the small underestimate of the ΔδTs magnitude when 1pctCO2 ΔδTs is reconstructed from Gregory parameters (Fig. S5), and if applied to all models then the equilibrium attribution fraction would shift from 66% feedbacks to 60% feedbacks.

Land Tas warming in the Hansen calculations could affect coastal areas, so one may anticipate that Hansen ΔFδTs is biased high, while Gregory ΔFδTs is biased low. These issues can be corrected (Smith et al. 2020) or avoided by also fixing land temperatures (Andrews et al. 2021) but very few CMIP5 models provide the relevant outputs. Fortunately, the results are only weakly sensitive to method for models with available outputs.

Gregory regression also assumes linear responses to global Tas, which is violated over multiple centuries (Rugenstein et al. 2020). It seems unlikely that this would counteract short-term forcing adjustments and there is no evidence of later suppression of evaporation (Schwarzwald et al. 2021). Therefore, the effective equilibrium mechanisms should qualitatively apply in the long term. Importantly, when 1pctCO2 outputs of nonpolar ocean properties are reconstructed using Gregory-derived parameters, errors are of order <10% in the transient representation of all terms (Fig. S5), so conclusions relevant to historical warming seem unaffected by nonlinearity. Ultimately, the feedback-related L changes are large and consistent, and I argue that their physical link to a cooling of Ts is simple enough to justify the argument that it drives decreased δTs.

d. Model parameterizations and ΔδTs

1) Model treatment of near-surface properties

Common modeling choices could consistently bias CMIP simulations. For example, IPCC AR6 notes that all CMIP5 and CMIP6 models use Monin–Obukhov similarity theory (Monin and Obukhov 1954; Obukhov 1971) in their PBL schemes to diagnose Tas and turbulent fluxes. There is evidence that BCC-CSM1-1-M has some error in either Tas or Ts derivation, with a preindustrial ocean δTs mean of just 0.06°C (Table S1). This is far smaller than the other 22 models or in situ measurements from, for example TAO (McPhaden et al. 1998) or PIRATA (Servain et al. 1998) buoys. I discuss below the credibility and testability of model representations of forcing- and feedback-driven ΔδTs. For feedbacks in particular, the energetics framework adopted here means that errors in the PBL scheme alone would be insufficient to overturn the conclusions unless they changed surface fluxes in ways that are potentially measurable.

2) Forcing-related changes

Strong evidence validates line-by-line radiation codes (e.g., Tjemkes et al. 2003), CO2’s surface iRF spectral signature has been observed (Feldman et al. 2015) and known iRF uncertainties are a small fraction of the mean (Mlynczak et al. 2016). It is unlikely that all CMIP models have consequential errors in CO2’s direct radiative effects, but the atmospheric adjustments that translate from iRF to ERF and result in Tas warming are not, to my knowledge, directly validated with observations. The real world experiences simultaneous changes in forcings, temperature, and internal variability, so isolating CO2-only ERF adjustments seems exceptionally challenging. Some confidence may be drawn from how CO2-driven rapid adjustments are similar across the model hierarchy, including in a multiscale modeling framework (Xu et al. 2020) and in large-eddy simulations (LES) of marine stratocumulus regions (Bretherton and Blossey 2014; Blossey et al. 2016). LES resolution is up to 1000 times finer than that of CMIP models, ruling out errors in some CMIP subgrid parameterizations. However, there could be common errors across the full model hierarchy.

3) Feedback-related changes

Feedback-driven ΔδTs < 0 can, I argue, be understood from the relative strengths of feedbacks defined with respect to Tas and Ts (for radiation) or Ts and δTs (for turbulent fluxes), with a requirement that λNs,Ts>2λNs,Tas. In CMIP5 models it appears that for radiation λLW,TsλLW,Tas+λSW,Tas and there are good reasons to expect that sensible heat λH,Ts0, since its changes are dominated by λH,δTs. By process of elimination, evaporation is therefore necessary to explain ΔδTs < 0.

The Gregory-derived λL,greg combines both λL,Ts and λL,δTs but given that model ΔδTs suppresses evaporation, λL,Ts>λL,greg and model λL,Ts must be large enough to ensure that λNs,Ts>2λNs,Tas but it is currently accepted that λL,Ts cannot be determined from first principles or from observations (Siler et al. 2019). All studied CMIP models agree that feedback-driven ΔδTs < 0, but it is possible that a common modeling error means that the evaporation response to ΔTs is misestimated. For example, if the modeled near-surface RH response to ΔTs is consistently biased, then model λL,Ts would then be biased in the opposite direction.

It may be possible to indirectly infer whether real-world evaporation changes are consistent with models. First, ΔL will be matched by changes in precipitation, which in turn is controlled by the atmospheric energy budget (Manabe and Wetherald 1975; Takahashi 2009). Model errors would likely have to extend above the PBL to restrict surface evaporation from playing a large role. Some inference could also be obtained from trends in PBL RH or height, since rising PBL RH limits evaporation increase (Lorenz et al. 2010) and PBL RH tends to anticorrelate with PBL height (e.g., Zhang et al. 2013). In situ ocean evaporation datasets show increasing trends, but have sparse spatial sampling and large trend uncertainties (Zhang et al. 2018). Other signatures of evaporation include amplified tropical upper troposphere warming. Satellite microwave sounding unit (MSU) and weather-balloon datasets disagree about the existence of this amplification (Santer et al. 2017; Spencer et al. 2017; Mitchell et al. 2020; Allen and Sherwood 2008). Global Navigation Satellite System-Radio Occultation (GNSS-RO) records (Gleisner et al. 2022) are more stable in time than MSU or radiosonde records, and could potentially support or refute the feedback effect identified here. Lakes have been called “sentinels” of climate change (Adrian et al. 2009) and have similar surface physics to oceans. Detailed lake modeling reports low-latitude lake changes that are similar to my nonpolar ocean results here, with ΔδTs < 0 and increased evaporation (Wang et al. 2018). However, lakes are strongly affected by nearby land and are sensitive to stratification changes that are dissimilar to those of oceans (Kraemer et al. 2015; Anderson et al. 2021; Stetler et al. 2021).

e. Future research priorities

If observations supported multidecadal ΔδTs > 0, that would suggest serious errors in modeled surface energy exchange. It could, for example, require smaller precipitation increase with warming or imply large errors in currently understood atmospheric forcing adjustments. Therefore, improved observational evidence is exceptionally important. This includes indirect information, for example the PREFIRE (L’Ecuyer et al. 2021) and FORUM (Palchetti et al. 2020) missions will improve knowledge of far-infrared ε and therefore reduce errors in calculated surface feedbacks.

Confirmation of similar CMIP6 behavior would be useful, although section 7a argues the conclusions are unlikely to change. Conclusions may differ over land and polar regions, especially where moisture is limited. Results may also be sensitive to the forcing agent, either due to different ERF adjustments or if they express a different spatial pattern of heating or cooling and so activate a feedback pattern effect. The results of the Precipitation Driver Model Intercomparison Project [PDRMIP, Samset et al. (2016)] indicate large disagreements in ERF-related changes depending on the forcing agent while in Andrews et al. (2021), solar ERF has approximately half of CO2’s effect on ΔδTs. Models disagree strongly on the effects of absorbing aerosols which warm the atmosphere (Johnson et al. 2019), driving larger ΔδTs than seen for CO2. Meanwhile, sulfate aerosols are a major source of forcing uncertainty and were linked to decreased pan evaporation over land during the late twentieth century (Roderick and Farquhar 2002).

Finally, the results presented here are relevant for long-term forced changes in CMIP models. Changes in the shorter term, or for periods when feedbacks differ from those simulated in CMIP models may be different. Recent decades may show different ΔδTs due to the “pattern effect” since recent temperature trend patterns, particularly in the Pacific, are not commonly simulated by CMIP models (Fueglistaler and Silvers 2021; Watanabe et al. 2021).

8. Conclusions

This paper explains why models report more warming of global air temperatures than the combined air–water global surface temperature datasets (Cowtan et al. 2015; Richardson et al. 2016). Decreased δTs can be understood from surface–atmosphere energy exchange rather than the oceans’ large transient heat uptake, so models project ΔδTs < 0 even at equilibrium. CO2 forcing adjustments preferentially warm the air, and warming-driven evaporation preferentially cools the surface. Combined, these provide a simple physical explanation for changes in the surface temperature discontinuity.

Future model research could explain changes over land or polar surfaces, or in response to non-CO2 forcing agents such as aerosol while current datasets are too uncertain to allow confident conclusions about trends in δTs. An alternative approach would be to indirectly constrain the relevant processes. For example, modeled extra warming of air relative to water is fundamentally linked to increased evaporation under global warming. Observations could be targeted to determine whether changes in precipitation and atmospheric heating structure are consistent with the simulated surface evaporative cooling, and this would be a key step in evaluating whether model simulation of near-surface changes are realistic.

Acknowledgments.

Government sponsorship acknowledged. This research was carried out at the Jet Propulsion Laboratory, California Institute of Technology under a contract with NASA. The author thanks Dr. Matthew D. Lebsock and Prof. Graeme L. Stephens for helpful discussions; Dr. Ryan Kramer and Dr. Chris Smith for assistance with radiative kernels; and Prof. Maria Rugenstein and Dr. Jonah Bloch-Johnson for help with the LongRunMIP output.

Data availability statement.

The CMIP5 data used here are available from the https://esgf-node.llnl.gov/search/cmip5/ and the HadGEM2 radiative kernels are at https://archive.researchdata.leeds.ac.uk/382/. LongRunMIP data for Fig. 2 are accessible by following the instructions at http://www.longrunmip.org/ (access is free but a password must be requested). The relevant kernel and LongRunMIP citations are in the text.

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