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

Mark T. Richardson

doi:10.1175/JCLI-D-22-0215.1

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Journal of Climate

Abstract
- Significance Statement
1. Introduction
2. Model changes in surface temperature discontinuity under CO2-forced warming
3. Interpreting feedback-driven changes in the surface temperature discontinuity
4. Radiative kernel analysis
- a. Theory, data, and processing
- b. Kernel results
5. CMIP5 methods
6. Results
7. Discussion
8. Conclusions
Acknowledgments.
Data availability statement.
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Fig. 1.

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

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Fig. 2.

Annual δT_s 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.

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Fig. 3.

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

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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 ΔδT_s > 0. Solid lines are derived from the abrupt4xCO2 mean ΔT(z)/ΔT_as profile at each latitude. Dashed lines are calculated assuming all atmospheric layers warm by 1°C.

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Fig. 5.

CanESM2 1pctCO2 simulated changes for oceans within ±60°S/N in (a) T_as, (b) T_s, (c) δT_s, (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 T_as 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.

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Fig. 6.

Gregory-fit results for each CMIP5 model over nonpolar ocean. (a) Forcing, feedback, and effective equilibrium ΔδT_s, where $effective equilibrium = Δ F_{{2xCO}_{2}} + λ \times ECS$ . (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.

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Fig. 7.

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

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Article Type:: Research Article

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

Mark T. Richardson

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

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https://orcid.org/0000-0001-7063-631X

Online Publication:: 23 Mar 2023

Print Publication:: 01 May 2023

DOI:: https://doi.org/10.1175/JCLI-D-22-0215.1

Page(s):: 2857–2871

Received:: 01 Apr 2022

Accepted:: 09 Nov 2022

Published Online:: 23 Mar 2023

Displayed acceptance dates for articles published prior to 2023 are approximate to within a week. If needed, exact acceptance dates can be obtained by emailing amsjol@ametsoc.org.

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Abstract

Modeled global warming is often quantified using global near-surface air temperature (T_as). Meanwhile, long-term temperature datasets combine observations of T_as over land with sea surface temperature (SST) over ocean. Modeled ocean T_as warms more than SST, which can bias model–observation comparisons. Skin temperature (T_s), which is typically warmer than T_as, follows SST changes so the ocean surface temperature discontinuity δT_s = T_s − T_as decreases with warming. Here I show that under CO₂ forcing, decreased δT_s is consistently simulated for nonpolar ocean within ±60°S/N, but not for other regions. I investigate the causes of oceanic δT_s 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 T_as increase, and therefore a δT_s 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 T_s warming relative to T_as and further shrinks δT_s. 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.

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

Abstract

Significance Statement

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

Keywords: Land surface; Sea/ocean surface; Anthropogenic effects/forcing; Feedback; Radiative forcing; Surface temperature

1. Introduction

The surface temperature discontinuity δT_s refers to the difference between the temperature of the skin layer T_s and of the overlying air T_as, typically at a height of 2 m. The standard convention is that δT_s = T_s − T_as and it is generally positive, driving turbulent heat and moisture fluxes from the surface to the atmosphere above. Changes in δT_s 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 δT_s (ΔδT_s, 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 T_as 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 T_s (Merchant et al. 2014; Hausfather et al. 2017). In models, changes in T_s 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) T_as diagnosis method is left to modeling groups, for an example see section 5 of Oleson et al. (2010), where it depends on properties including T_s and the temperature of the lowest atmospheric layer.

Historically, many comparisons used model global-mean T_as [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 T_as rather than T_s 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 T_as − T_s 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 δT_s 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 δT_s, 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 ΔT_as should be compared with satellite-retrieved ΔT_s.

A secondary motivation is that the model treatment of δT_s 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 δT_s. Richter and Xie (2008) stated that shrinking δT_s 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 δT_s as limiting evaporation increases, but stated that causality could act the other way and that evaporation “will act to increase T_a relative to T_s.” 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 δT_s 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 ΔδT_s < 0, rather there is stronger support for the energetic description of Siler et al. (2019) in which evaporation drives ΔδT_s < 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 δT_s through rapid adjustments driven primarily by atmospheric longwave heating (e.g., Kamae et al. 2015). Warming then strongly increases evaporation, which cools T_s and further decreases δT_s.

I will proceed as follows: section 2 shows model ΔδT_s and uses millennium-length simulation output to demonstrate that ocean heat uptake cannot explain the long-term ΔδT_s. The long simulation shows a distinction between a short-term forcing-dominated ΔδT_s followed by a longer-term feedback-related ΔδT_s. This section also summarizes canonical rapid atmospheric changes to CO₂ forcing and argues that they explain the short-term ΔδT_s. The remainder of the paper is devoted to a feedback analysis, beginning with section 3, which derives how surface feedbacks drive ΔδT_s. 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 δT_s 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 ΔδT_s 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 ΔδT_s < 0°C over nonpolar ocean, intermodel disagreement over land, and ΔδT_s > 0°C in polar regions. By year 140, mean nonpolar ocean T_as warms by 5%–10% more than T_s in all models (Fig. S2).

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 ΔδT_s < 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 ΔδT_s should transiently decrease then increase back to equilibrium. However, Fig. 2a shows that for nonpolar ocean, ΔδT_s < 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 δT_s 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.

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 δT_s decrease. To the author’s knowledge, the link between ΔδT_s 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 (T_a) 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 T_s, CO₂-driven ERF adjustments with ΔT_as > 0 therefore mean ΔδT_s < 0. Model ERF is commonly approximated with reference to globally fixed T_as (Gregory et al. 2004) or fixed T_s over oceans (Hansen et al. 2005) and Hansen-method CMIP5 simulations indeed show ΔδT_s < 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 ΔδT_s and (ii) separately quantifying the contributions of ERF and feedbacks to ΔδT_s. Addressing (i) and (ii) requires establishing the forcing–feedback framework and linking individual feedback terms to changes in δT_s.

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

The standard forcing–feedback decomposition of a time series ΔX(t) is

Δ X (t) = Δ F_{X} (t) + λ_{X} Δ T (t),

(1)

where ΔF_X(t) refers to forcing and λ_X = dΔX/dΔT is a feedback parameter. I use Eq. (1) for any property, for example, if X = δT_s then

Δ F_{δ T_{s}}

represents the forcing-related adjustment in δT_s (in °C). The Eq. (1) assumption of fixed λ_X is supported by section 6 results, at least for transient changes over approximately a century.

I define $λ_{X, T_{as}}$ as the response of property X to full-atmosphere warming consistent with ΔT_as = 1°C. This is analogous to standard practice where TOA feedbacks often refer to response to ΔT_as, even though temperature, humidity, and cloud properties change throughout the atmosphere. Results will be shown both for $λ_{X, T_{as}}$ defined for ΔT_a(P) = ΔT_as 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, $λ_{X, T_{as}} Δ T_{X, as}$ is directed downward and $λ_{X, T_{s}} Δ T_{X, T_{s}}$ upward. There are also turbulent fluxes at the surface which are controlled, in part, by the surface temperature discontinuity δT_s. I account for this through a term $λ_{N_{s}, δ T_{s}} Δ δ T_{s}$ , which is defined as positive upward, and for the turbulent heat fluxes the understanding is that $λ_{X, T_{as}} = 0$ and the $λ_{X, T_{s}}$ captures uniform warming of both T_s and T_as.

Equilibrium occurs when net surface flux, N_s = 0 W m⁻², so if the equilibrium flux change through region boundaries is small then

Δ F_{N_{s}} = λ_{N_{s}, T_{s}} Δ T_{s} + λ_{N_{s}, δ T_{s}} Δ δ T_{s} - λ_{N_{s}, T_{as}} Δ T_{as} .

(2)

I will now show that this surface energy balance means that the sign of ΔδT_s depends on the relative strength of the feedback terms

λ_{N_{s}, T_{as}}

and

λ_{N_{s}, T_{s}}

. By substituting ΔT_s = ΔT_as + ΔδT_s into Eq. (2):

Δ δ T_{s} = \frac{1}{λ_{N_{s}, T_{s}} + λ_{N_{s}, δ T_{s}}} (Δ F_{N_{s}} + λ_{N_{s}, T_{as}} Δ T_{as} - λ_{N_{s}, T_{s}} Δ T_{as}) .

(3)

Differentiation of Eq. (3) with respect to

λ_{N_{s}, T_{s}}

and

λ_{N_{s}, T_{as}}

tells us whether each feedback term acts to increase or decrease ΔδT_s:

\frac{d Δ δ T_{s}}{d λ_{N_{s}, T_{s}}} = - \frac{1}{{(λ_{N_{s}, T_{s}} + λ_{N_{s}, δ T_{s}})}^{2}} [Δ F_{N_{s}} + (λ_{N_{s}, T_{as}} + λ_{N_{s}, δ T_{s}}) Δ T_{as}],

(4)

\frac{d Δ δ T_{s}}{d λ_{N_{s}, T_{as}}} = \frac{Δ T_{as}}{(λ_{N_{s}, T_{s}} + λ_{N_{s}, δ T_{s}})} .

(5)

Equation (4) says that ΔδT_s gets smaller as

λ_{N_{s}, T_{s}}

gets larger, while Eq. (5) says that ΔδT_s gets larger as

λ_{N_{s}, T_{as}}

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 ΔδT_s, first divide both sides of Eq. (3) by ΔT_as. At equilibrium

Δ F_{N_{s}} / Δ T_{as} = λ_{N_{s}, T_{as}}

so the sign of

Δ δ T_{s} / Δ T_{as} = λ_{δ T_{s}}

λ_{δ T_{s}} {\begin{matrix} > 0 & if 2 λ_{N_{s}, T_{as}} > λ_{N_{s}, T_{s}} \\ = 0 & if 2 λ_{N_{s}, T_{as}} = λ_{N_{s}, T_{s}} \\ < 0 & if 2 λ_{N_{s}, T_{as}} < λ_{N_{s}, T_{s}} \end{matrix} .

(6)

All terms with

λ_{δ T_{s}}

cancel out during this derivation, so the sign of the feedback contribution of ΔδT_s only depends on the feedback strengths defined with respect to

λ_{N_{s}, T_{as}}

and

λ_{N_{s}, T_{s}}

. Figure 2 shows that CMIP5 feedbacks drive ΔδT_s < 0 so the bottom case is required. Ignoring the relatively small geothermal flux (Hofmann and Morales Maqueda 2009), N_s is

N_{s} = L + H + {LW}_{↑} - {LW}_{↓} + {SW}_{↑} - {SW}_{↓},

(7)

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 ΔδT_s < 0 from feedbacks requires large

λ_{N_{s}, T_{s}}

relative to

λ_{N_{s}, T_{as}}

, next I investigate the feedback terms of Eq. (7) to interpret the processes driving ΔδT_s. 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

λ_{L, T_{s}}

, which could be calculated by warming ΔT_s, 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 δT_s. Sections 5 and 6 will turn to Gregory regression of abrupt4xCO2 simulations, from which I identify evaporation as the dominant feedback for ΔδT_s < 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 T_i and moisture values q_i. A linear approximation of flux change ΔR is

Δ R = \sum_{i} \frac{\bar{\partial R}}{d q_{i}} δ {\bar{q}}_{i} + \frac{\bar{\partial R}}{d T_{i}} δ \bar{T_{i}} = \sum_{i} K_{q, i} δ {\bar{q}}_{i} + K_{T, i} δ \bar{T_{i}},

(8)

where K_q_,_i and K_T_,_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 T_i or q_i 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 T_s (in W m⁻² °C⁻¹) and so

λ_{T_{s}} = K_{T_{s}}

, while the surface feedback to atmospheric changes,

λ_{T_{as}}

must be derived from the kernels, for example for temperature:

λ_{T, T_{as}} = \sum_{i = 1}^{38} \frac{Δ T_{a, i}}{Δ T_{as}} K_{T, i} Δ P_{i},

(9)

where ΔP_i 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 T_s and T_a (Smith et al. 2018; Smith 2018). Several other kernel datasets combine changes in T_s and in the lowest atmospheric layer T_a_,_i₌₁, so cannot separate $λ_{T_{as}}$ and $λ_{T_{s}}$ (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 ΔT_a_,_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 $λ_{SW+LW, T_{as}} - λ_{LW, T_{s}}$ . Assuming ΔT(P) = 1°C, nonpolar oceanic $\bar{λ_{SW+LW, T_{as}}} = 5.77 W m^{- 2} ° C^{- 1}$ and $\bar{λ_{LW, T_{s}}} = 5.70 W m^{- 2} ° C^{- 1}$ so radiative ${\bar{λ}}_{T_{s}} - {\bar{λ}}_{T_{as}}$ is small and negative. Following Eq. (6), if non–cloud radiative feedbacks are $λ_{T_{s}} \approx λ_{T_{as}}$ , then they are nowhere near the $λ_{T_{s}} > 2 λ_{T_{as}}$ requirement to explain ΔδT_s < 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 $λ_{T, T_{as}} < λ_{T, T_{s}}$ everywhere. However, water vapor increases the effective emissivity, which increases $λ_{T_{as}}$ and means that radiation even further favors ΔδT_s > 0 in moist areas. From Fig. 4, there is no latitude where ocean clear-sky radiation $λ_{T_{s}} > 2 λ_{T_{as}}$ 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 $λ_{T_{s}}$ increases necessary to obtain ΔδT_s < 0 from feedbacks.

Fig. 3.

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

Fig. 4.

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 ΔT_as. 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 T_s, T_as, 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 ΔT_as,glob in an abrupt4xCO2 simulation:

Δ N_{TOA} (t) = Δ F_{4 {xCO}_{2}} + λ_{greg} Δ T_{as,glob} (t) .

(10)

Regressing ΔT_as,glob(t) against ΔN_TOA(t) gives a gradient λ_greg and ΔT_as = 0°C intercept

Δ F_{{4xCO}_{2}}

. The fit line projected to ΔN_TOA = 0 W m⁻² then gives “effective” equilibrium

Δ T_{{4xCO}_{2}}

. Metrics are usually reported for CO₂ doubling, and since CO₂ forcing is approximately logarithmic in concentration,

Δ T_{{4xCO}_{2}} / 2

is termed the effective equilibrium climate sensitivity to doubled CO₂ [ECS_eff, 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):

X_{i, j} (t) = Δ F_{greg, X_{i, j}, 4 xCO2} + λ_{greg, X_{i, j}} Δ T_{as,glob} (t) .

(11)

Regressions are performed over the simulation length, either years 1–140 or 1–150. By regressing against global T_as, the area-weighted mean of λ_X_,greg or

Δ F_{X {,4xCO}_{2}}

reproduces the values derived by regressing global-mean X against global-mean T_as. The net feedback parameters (those for L, H, SW_net or LW_net) can be interpreted as

λ_{greg, X} = \frac{λ_{X, T_{s}} Δ T_{s} + λ_{X, δ T_{s}} Δ δ T_{s} - λ_{X, T_{as}} Δ T_{as}}{Δ T_{as,glob}},

(12)

where all terms except ΔT_as,glob refer to gridcell values. Clearly the single value of λ_greg,_X is sensitive to

λ_{X, T_{s}}

λ_{X, T_{as}}

, and

λ_{X, δ T_{s}}

, but they cannot be separated as they can using kernels. These gridded parameters (e.g., λ_greg,_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 δT_s increases or decreases in response to feedbacks. The term $λ_{greg, N_{s}}$ is the sum of components at the air–sea boundary. However, if ΔN_s 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 ΔδT_s. This may occur locally due to, for example, changes in ocean circulation, but later results will show that nonpolar ocean ΔN_s ≈ 0 W m⁻² at equilibrium, such that we can neglect its contribution to ΔδT_s.

2) Evaluating Gregory method

The spatial distribution of ΔN_s and ΔT_as 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 ΔT_as 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

Δ X (t) = \frac{Δ F_{X} (t)}{Δ F_{greg, X, 4 {xCO}_{2}}} + λ_{greg, X} Δ T_{as,global} (t) .

(13)

Here ΔT_as,global(t) is from the 1pctCO2 simulation and

Δ F_{greg, X, 4 {xCO}_{2}}

and λ_greg,_X are from the abrupt4xCO2 Gregory fits for that model.

Δ F_{X {xCO}_{2}}

increases linearly from year 1 to 140 up to

Δ F_{X, 4 {xCO}_{2}}

in all models except for GFDL-ESM2M, whose CO₂ increase stops in year 70 after a doubling. For that model, ΔF_X(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 ΔδT_s due to feedbacks can be expressed as a function of total global-mean warming, ΔT_as,glob via

α_{Δ T_{as,glob}} = \frac{λ_{δ T_{s}} Δ T_{as,glob}}{Δ F_{δ T_{s}} + λ_{δ T_{s}} Δ T_{as,glob}} .

(14)

Substituting ΔT_as,glob = ECS_eff and

Δ F_{δ T_{s}}

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 ΔT_as = 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.

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 SW_net, 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 ΔδT_s.

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 ΔT_as,global is delayed by heat uptake N_s 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 δT_s and surface fluxes are displayed for nonpolar ocean in Fig. 6a. Feedbacks are divided by oceanic $λ_{T_{as},greg}$ so are expressed per degree Celsius of nonpolar ocean T_as warming. All 23 models show ΔδT_s < 0°C in both forcing and feedback responses with no clear correlation between them (Table S1).

Fig. 6.

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

Section 7 argues that the small-magnitude $λ_{δ T_{s}, greg}$ outlier BCC-CSM1-1M is most likely due to an erroneous diagnosis of T_as relative to T_s. Its mean δT_s of 0.06°C is unrealistically low and far below the 1.10°C average of the other models (Table S1). Excluding its $λ_{δ T_{s}, greg}$ 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 δT_s. A more detailed study would be required to understand why the MPI model ΔδT_s 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 ΔδT_s < 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 ΔN_s.

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 T_s, T_as, and δT_s 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 ECS_eff (Bony and Dufresne 2005). Atmospheric moistening shifts all-sky SW_net toward less surface absorption relative to SW CRE alone. The LW_net feedback is of the wrong sign to support ΔδT_s < 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 δT_s. The Gregory-derived radiation feedback parameters are qualitatively consistent with the kernel results, suggesting that $λ_{LW, T_{s}} \approx λ_{LW+SW, T_{as}}$ and therefore that radiation feedbacks cannot explain why feedback-related ΔδT_s < 0.

The sensible heat flux H is typically parameterized in models as proportional to δT_s, and so its Gregory feedback is likely to be dominated by $λ_{H, δ T_{s}} Δ δ T_{s}$ rather than representing $λ_{T_{s}}$ . 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 $λ_{L, T_{s}}$ 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 $λ_{L, greg} < λ_{L, T_{s}}$ since λ_L_,greg implicitly includes changes in circulation, relative humidity, and δT_s which suppress evaporation increase.

Figure 6d’s effective-equilibrium values show the combined forcing and feedback effects at ΔT_as = ECS_eff, and the range of ECS_eff causes much of the spread in results. Crucially, the implied equilibrium ΔδT_s (Fig. 6a) is negative in all models, while ΔN_s 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 ΔδT_s. The equilibrium ΔN_s 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:

Figure 6d’s minor ΔN_s at equilibrium justifies the approach resulting in Eq. (6).
Figure 6c’s radiation terms plus the kernel results rule out radiation feedbacks from explaining ΔδT_s on their own.
Figure 6c’s H feedback sign rules out turbulent heat, while the L feedback represents a large cooling effect on T_s consistent with evaporation driving decreased δT_s.

Assuming that λ_L_,greg is a minimum bound and the Clausius-Clapeyron limit an upper bound, then over nonpolar oceans climate models likely have $3.6 \leq λ_{T_{s}} \leq 7.0 W m^{- 2} ° C^{- 1}$ . From Eq. (6) and the range of radiation feedbacks estimates, a $λ_{L, T_{s}}$ 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 ΔδT_s < 0, and in models it must be sufficient to do so. However, it is possible that the real-world $λ_{L, T_{s}}$ could be smaller and ultimately insufficient to achieve the threshold necessary for ΔδT_s < 0. For example, if real-world ΔT_s directly causes a far greater near-surface moistening or slowdown of winds than is seen in models, then this is one way in which λ_L_,_s could be overestimated in models.

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

Figure 7 applies Eq. (14) and expresses the fraction of ΔδT_s due to feedbacks as a function of global ΔT_as divided by ECS_eff. ΔδT_s is initially dominated by ERF, before warming triggers feedbacks that drive further ΔδT_s. According to the Gregory regression parameters, when warming reaches ECS_eff the feedbacks explain a mean of 66% of ΔδT_s 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 ECS_eff, and at this point the forcing–feedback split is roughly even. Nonpolar oceanic ΔδT_s in the modern day therefore likely contains similar-magnitude contributions both from CO₂ forcing adjustments and temperature-mediated feedbacks. Neither the intermodel ΔδT_s 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.

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 δT_s 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 ΔδT_s over nonpolar oceans, which IPCC AR6 identified as lacking. The explanation comes in two parts:

CO₂ heats the lower atmosphere and subsequent rapid adjustments cause T_as to warm more than T_s, therefore ΔδT_s < 0,
Warming then increases surface evaporation so that T_s warms less than T_as, therefore ΔδT_s < 0.

Both processes have been reported elsewhere, but here I confirm this model behavior and quantify their contributions to ΔδT_s. Heat uptake ΔN_s shrinks to near zero by ECS_eff over oceans, so it cannot explain equilibrium ΔδT_s. This is consistent with the interpretation of Siler et al. (2019) rather than Richter and Xie (2008), the latter of which proposed that N_s reduces δT_s. The presented results are only for large-area means, however, and N_s 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 ΔδT_s (e.g., Liang et al. 2020), so the process conclusions likely apply to CMIP6 as well. CMIP6 features more models with higher ECS_eff, which may result in larger equilibrium ΔδT_s, but with minor present-day differences.

It is only nonpolar ocean where ΔδT_s < 0 in all models so observational datasets, which combine T_s over ocean and T_as elsewhere, will report less long-term warming than either global T_s or global T_as. 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 ΔδT_s 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 ΔδT_s or flux changes so its findings may extend more broadly. The kernel-based $λ_{T_{s}}$ is sensitive to ocean emissivity (ε, assumed to be unity) and T_s_, neither of which have large known errors. HadGEM2-ES mean T_s 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 ΔδT_s, ongoing model mean-state biases (Xu et al. 2022) can influence calculated $λ_{T_{as}}$ . 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 $λ_{T_{s}}$ always exceeds that of $λ_{T_{as}}$ . In HadGEM2-ES, moistening over much (but not all) of the nonpolar ocean is sufficient to tip non–cloud radiative $λ_{T_{as}}$ into exceeding $λ_{T_{s}}$ . Areas where $λ_{T_{as}} > λ_{T_{s}}$ 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 ΔδT_s > 0, so relaxing the fixed-RH assumption would likely only further rule out non–cloud radiative effects from explaining the coupled-model ΔδT_s. 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 ΔδT_s.

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 ΔT_as = 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 $Δ F_{δ T_{s}}$ mean is 30% larger than the Gregory $Δ F_{δ T_{s}}$ mean (Table S2, Fig. S3). This likely explains the small underestimate of the ΔδT_s magnitude when 1pctCO2 ΔδT_s 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 T_as warming in the Hansen calculations could affect coastal areas, so one may anticipate that Hansen $Δ F_{δ T_{s}}$ is biased high, while Gregory $Δ F_{δ T_{s}}$ 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 T_as, 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 T_s is simple enough to justify the argument that it drives decreased δT_s.

d. Model parameterizations and ΔδT_s

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 T_as and turbulent fluxes. There is evidence that BCC-CSM1-1-M has some error in either T_as or T_s derivation, with a preindustrial ocean δT_s 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 ΔδT_s. 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 T_as 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 ΔδT_s < 0 can, I argue, be understood from the relative strengths of feedbacks defined with respect to T_as and T_s (for radiation) or T_s and δT_s (for turbulent fluxes), with a requirement that $λ_{N_{s}, T_{s}} > 2 λ_{N_{s}, T_{as}}$ . In CMIP5 models it appears that for radiation $λ_{LW, T_{s}} \approx λ_{LW, T_{as}} + λ_{SW, T_{as}}$ and there are good reasons to expect that sensible heat $λ_{H, T_{s}} \approx 0$ , since its changes are dominated by $λ_{H, δ T_{s}}$ . By process of elimination, evaporation is therefore necessary to explain ΔδT_s < 0.

The Gregory-derived λ_L_,greg combines both $λ_{L, T_{s}}$ and $λ_{L, δ T_{s}}$ but given that model ΔδT_s suppresses evaporation, $λ_{L, T_{s}} > λ_{L, greg}$ and model $λ_{L, T_{s}}$ must be large enough to ensure that $λ_{N_{s}, T_{s}} > 2 λ_{N_{s}, T_{as}}$ but it is currently accepted that $λ_{L, T_{s}}$ cannot be determined from first principles or from observations (Siler et al. 2019). All studied CMIP models agree that feedback-driven ΔδT_s < 0, but it is possible that a common modeling error means that the evaporation response to ΔT_s is misestimated. For example, if the modeled near-surface RH response to ΔT_s is consistently biased, then model $λ_{L, T_{s}}$ 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 ΔδT_s < 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 ΔδT_s > 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 ΔδT_s. Models disagree strongly on the effects of absorbing aerosols which warm the atmosphere (Johnson et al. 2019), driving larger ΔδT_s 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 ΔδT_s 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 δT_s can be understood from surface–atmosphere energy exchange rather than the oceans’ large transient heat uptake, so models project ΔδT_s < 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 δT_s. 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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A Physical Explanation for Ocean Air–Water Warming Differences under CO2-Forced Warming

Abstract

Significance Statement

Abstract

Significance Statement

1. Introduction

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

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

4. Radiative kernel analysis

a. Theory, data, and processing

b. Kernel results

5. CMIP5 methods

a. Overview of approach

b. Data sources

c. Separation of forcing and feedbacks

1) Regional Gregory decomposition

2) Evaluating Gregory method

3) Attributing discontinuity change to feedbacks and forcing

6. Results

a. Validation of Gregory decomposition

b. Ensemble Gregory forcing and feedback responses

1) Changes in ΔTs

2) Changes in surface fluxes

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

7. Discussion

a. Summary of results

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

c. Gregory decomposition limitations and interpretation

d. Model parameterizations and ΔδTs

1) Model treatment of near-surface properties

2) Forcing-related changes

3) Feedback-related changes

e. Future research priorities

8. Conclusions

Acknowledgments.

Data availability statement.

REFERENCES

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

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

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

d. Model parameterizations and ΔδT_s