GEOPHYSICAL RESEARCH LETTERS, VOL. ???, XXXX, DOI:10.1029/,
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2
What can moist thermodynamics tell us about
circulation shifts in response to uniform warming?
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2
Tiffany A. Shaw , Aiko Voigt
Corresponding author: T. A. Shaw, Department of the Geophysical Sciences, 5734 S. Ellis
Ave., Chicago, IL, 60637 USA. ([email protected])
1
Department of the Geophysical Sciences,
The University of Chicago, Chicago, IL,
USA.
2
Lamont-Doherty Earth Observatory,
Columbia University, New York, NY, USA
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Aquaplanet simulations exhibit a robust expansion of the Hadley cell and
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poleward jet shift in response to uniform warming of sea-surface tempera-
5
ture. Here moist thermodynamic and dynamic frameworks are combined to
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make predictions of circulation responses to warming. We show Clausius-Clapeyron
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(CC) scaling of specific humidity with warming predicts an expansion of the
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Hadley circulation according to convective quasi-equilibrium dynamics. A
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poleward jet shift follows from the control-climate relationship between the
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Hadley cell edge and jet stream position. CC scaling of specific humidity with
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warming also predicts decreased diffusivity and a poleward shift of the lat-
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itude of maximum latent and dry-static energy transport according to mixing-
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length theory. Finally, atmospheric cloud-radiative changes shift the latitude
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of maximum energy transport poleward in most models. Our results show
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moist thermodynamics can predict meridional shifts of the circulation when
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combined with dynamical frameworks, however additional feedbacks are im-
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portant for the simulated response.
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1. Introduction
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Confidence in the projected thermodynamic and dynamic response of the climate sys-
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tem to anthropogenic climate change requires a physical understanding of the underlying
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mechanisms. It is well understood that the thermodynamic response to increased CO2
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involves warming, increased near-surface specific humidity over the ocean following the
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Clausius-Clapeyron (CC) relation, warming of the tropical-upper troposphere and a rais-
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ing of the tropopause [e.g. Held , 1993; Allen and Ingram, 2002; Held and Soden, 2006;
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Vallis et al., 2015]. Held and Soden [2006] used CC scaling to predict the “wet-get-wetter,
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dry-get-drier” response to warming. The dynamic response to increased CO2 , e.g. the
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response of the Hadley cell and jet stream, is less well understood [Shepherd , 2014; Vallis
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et al., 2015]. However, the majority of coupled-climate models, atmosphere only mod-
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els and aquaplanet models participating in the Coupled Model Intercomparison Project
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Phase 5 (CMIP5) project a robust (in terms of model agreement) poleward expansion
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of the circulation, including a poleward shift of the edge of the Hadley cell and zonal-
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mean jet stream position, in response to anthropogenic climate change [Held , 1993; Vallis
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et al., 2015; Medeiros et al., 2015]. While models may not agree on the magnitude of
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the response, the meridional direction is robust and motivates the search for a physical
34
explanation.
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Given our understanding of the moist thermodynamic response to global warming, we
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ask the question: What can moist thermodynamics tell us about the circulation response
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to uniform warming? Previous authors have linked moist thermodynamics, in particular
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warming of the tropical upper troposphere and increased tropopause height, to Hadley
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circulation expansion a posteriori [Held , 2000; Lu et al., 2007; Vallis et al., 2015]. Building
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on those results here we put forward physical arguments linking moist thermodynamic
41
changes to dynamic responses using different theoretical frameworks. We focus on two dif-
42
ferent moist thermodynamic responses to warming. The first is the increase of near-surface
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specific humidity with warming following CC scaling. We investigate the implication of
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this increase for near-surface moist entropy and moist-static energy changes, which are
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linked to dynamical responses following convective quasi-equilibrium dynamics [Emanuel
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et al., 1994; Emanuel , 1995] and mixing-length theory [Held , 2000; Kushner and Held ,
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1998]. In both cases we show increased specific humidity following CC scaling can be used
48
to predict meridional shifts of the circulation in response to uniform warming.
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The second response to warming we consider is changes in atmospheric cloud-radiative
50
effects (ACREs). ACRE changes can result from both thermodynamic as well as dynamic
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changes [Stevens and Bony, 2013; Voigt and Shaw , 2015]. An important cloud response
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to warming is the rise of tropical high clouds that is expected from the fixed-anvil temper-
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ature hypothesis [Hartmann and Larson, 2002; Kuang and Hartmann, 2007; Zelinka and
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Hartmann, 2010]. Here we consider ACRE changes as a thermodynamic response in the
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sense that they change the energy balance of the atmosphere and demand a change in the
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meridional energy transport [Hwang et al., 2011]. The ACRE-induced energy transport
57
can impact the latitude of maximum energy transport. The latitude of maximum energy
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transport occurs in the extratropics where storm tracks dominate the energy transport.
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We investigate the connection between moist thermodynamic and dynamic responses
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to uniform warming using prescribed sea surface temperature (SST) aquaplanet models.
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Aquaplanet models are an important part of the model hierarchy and provide an idealized
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setting (comprehensive moist physics with simplified lower boundary condition) for un-
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derstanding the circulation response to global warming [Blackburn et al., 2013; Medeiros
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et al., 2015]. CMIP5 aquaplanet model simulations exhibit a robust poleward expansion
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of the tropics and poleward shift of the eddy-driven jet stream in response to uniform
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warming [Medeiros et al., 2015] consistent with the response in coupled-climate models
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with realistic boundary conditions [Vallis et al., 2015].
2. Data
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We make use of the aquaControl and aqua4K CMIP5 prescribed SST aquaplanet model
69
experiments [Taylor et al., 2012]. Most models prescribed the aquaControl SST follow-
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ing the QOBS distribution of Neale and Hoskins [2001], however the FGOALS-g2 and
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MIROC5 models used the CTRL distribution [Medeiros et al., 2015]. Aqua4K mimics
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global warming by uniformly increasing the aquaControl SST by 4K. We use monthly
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and zonally-averaged zonal wind (ua), temperature (ta), specific humidity (hus), radia-
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tion (rlut, rlutcs, rlus, rlds, rldscs, rsut, rsutcs, rsus, rsds, rsdscs) and surface flux (hfls,
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hfss) data from ten CMIP5 models (CCSM4, CNRM-CM5, FGOALS-g2, FGOALS-s2,
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HadGEM2-A, IPSL-CM5A-LR, MIROC5, MPI-ESM-LR, MPI-ESM-MR, MRI-CGCM3).
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The data are interpolated onto a common latitude grid with 0.1◦ resolution. Since the
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aquaplanet climate is equatorially symmetric, data from the Northern and Southern hemi-
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spheres are averaged together. We quantify inter-model spread as ± 1 standard deviation.
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Maximum values are obtained by a quadratic fit using the maximum grid point and two
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adjacent points.
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3. Results
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We begin by documenting shifts of the Hadley cell edge and eddy-driven jet stream
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position in response to uniform SST warming by 4K. We define the edge of the Hadley
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cell as the latitude where the zonal-mean zonal wind transitions from tropical easterlies
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to extratropical westerlies at 925 hPa, i.e., the latitude of zero zonal wind. The eddy-
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driven jet stream position is defined as the latitude of maximum zonal-mean zonal wind
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at 925 hPa. The Hadley cell edge and jet stream position in aquaControl are significantly
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correlated (r = 0.96, p = 0.00) and a linear regression accounts for 92% of the model
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spread (Fig. 1a, solid black line). A similar relationship occurs for aqua4K (r = 0.95,
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p = 0.00, r2 = 0.90, Fig. 1a, dashed black line).
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All ten CMIP5 aquaplanet models exhibit a poleward shift of the Hadley cell edge (Fig.
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1b, y-axis) and jet stream position (Fig. 1c, y-axis) in response to uniform warming. Our
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results are consistent with alternative metrics of the Hadley cell edge, e.g. the latitude
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where the mean-meridional streamfunction vertically integrated between 700 and 300 hPa
95
equals zero [see Fig. 5 of Medeiros et al., 2015] and jet stream position, e.g. the latitude
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where zonal-mean zonal wind averaged between 850 and 700 hPa is maximum [see Fig. 6
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of Medeiros et al., 2015].
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In the following subsections we provide examples of how moist thermodynamic changes
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can be used to infer circulation shifts in response to uniform warming. We focus on two
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thermodynamic changes in response to uniform warming: 1) increased specific humidity
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following CC scaling and 2) ACRE changes.
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3.1. Circulation changes predicted from CC scaling
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Following Held and Soden [2006] we assume changes in near-surface specific humidity q
exhibit CC scaling in response to warming, i.e.,
δq ≈ αδT q
(1)
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where α = L/RT 2 ≈ 0.07K−1 , L is the latent heat of vaporization, R is the dry gas
105
constant, T is temperature, and δT = 4K. The change in specific humidity affects two
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important thermodynamic variables: near-surface or sub-cloud (925 hPa) moist entropy,
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sb = cp ln θe ≈ cp ln(θ + Lq/cp ), and moist-static energy, ms = cp T + Lq + Φ, where cp is
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the specific heat at constant pressure, θe and θ are the near-surface equivalent potential
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temperature and potential temperature, respectively, and Φ is geopotential.
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Following CC scaling, the near-surface moist entropy and moist-static energy responses
to uniform warming are
δsb ≈ cp
δT (cp + αLq)
δθe
≈
θe
θe
(2)
δms ≈ cp δT + Lδq ≈ δT (cp + αLq).
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(3)
These responses are largest in the tropics implying an increased meridional gradient, i.e.,
1 ∂δsb
1 ∂
q
L 1 ∂q
L q ∂T
≈ αδT L
≈ αδT
≈ α2 δT
a ∂φ
a ∂φ θe
θe a ∂φ
θe a ∂φ
1 ∂δms
1 ∂q
q ∂T
≈ αδT L
≈ α2 δT L
.
a ∂φ
a ∂φ
a ∂φ
(4)
(5)
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where a is the radius of the Earth and we have assumed constant relative humidity with
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latitude in the last step, which is a reasonable approximation for aquaControl (Supple-
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mentary Fig. 1a). We neglect −Lq∂θe /∂φ/θe2 in (4) because specific humidity dominates
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the equivalent potential temperature gradient in low latitudes (Supplementary Fig. 1b).
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These thermodynamic responses to uniform warming can be connected to dynamical re-
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sponses via two frameworks: 1) quasi-equilibrium dynamics and 2) mixing-length theory.
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In both cases we make predictions of circulation shifts in response to uniform warming
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and compare them to the simulated response (aqua4K-aquaControl).
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Quasi-equilibrium connects thermally-direct circulations to the region of supercritical
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near-surface moist entropy and constrains the vertical structure of the atmosphere to be
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moist adiabatic [Emanuel et al., 1994]. The moist adiabatic assumption is reasonable for
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Earth’s tropics and subtropics [Korty and Schneider , 2007] and quasi-equilibrium is a
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reasonable approximation over the tropical oceans [Brown and Bretherton, 2007] and in
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Monsoon regions [Boos and Emanuel , 2009; Nie et al., 2010].
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According to quasi-equilibrium dynamics, the balanced component of the surface zonal
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wind us is related to the degree of supercriticality of the near-surface moist entropy sb ,
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i.e.,
us =
(Ts − Tt ) ∂
(sb − scrit )
fa
∂φ
(6)
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where scrit is the critical value of moist entropy, Ts and Tt are the temperatures at the
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surface and tropopause, respectively, and f is the Coriolis parameter [see equation(18)
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in Emanuel , 1995]. The tropopause is defined following the World Meteorological Orga-
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nization’s definition. The critical value of moist entropy is connected to the onset of a
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thermally direct circulation. Here we estimate the critical value following equation (11)
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in Emanuel [1995], i.e.,
Ω2 a2
(cos2 φm − cos2 φ)2
= cp ln(θe,crit ) = cp ln θem exp −
2cp (Ts − Tt )
cos2 φ
(
scrit
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(7)
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where θem is the maximum equivalent potential temperature located at latitude φm and
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Ω is the rotation rate. According to quasi-equilibrium dynamics the multi-model mean
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edge of the Hadley cell is located where sb − scrit is minimum, i.e., at 22.5◦ , as compared
139
to its actual location of 24.6◦ in aquaControl.
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The surface zonal wind response to uniform warming can be decomposed as
δus =
δ(Ts − Tt ) ∂
(Ts − Tt ) ∂
(Ts − Tt ) ∂
(sb − scrit ) +
δsb −
δscrit
fa
∂φ
fa
∂φ
fa
∂φ
(8)
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[see (6)]. We focus on the predicted zonal-wind response due to changes in moist entropy
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following CC scaling [see (4)], which dominate in the tropics and subtropics (Supplemen-
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tary Fig. 1c), i.e.,
δus ≈
(Ts − Tt )
L ∂q
(Ts − Tt ) 2 Lq ∂T
(Ts − Tt ) ∂
δsb ≈
αδT
≈
α δT
< 0.
fa
∂φ
fa
θe ∂φ
fa
θe ∂φ
(9)
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This predicted decrease in zonal wind enhances tropical easterlies and shifts the Hadley
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cell edge poleward.
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The predicted shift of the Hadley cell edge in response to uniform warming following
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CC scaling, quasi-equilibrium dynamics and using only information from aquaControl, is
148
poleward when the predicted zonal-wind response is added to the aquaControl zonal wind
149
(3.2◦ ±0.6◦ , Fig. 1b). The predicted poleward shift overestimates the simulated (aqua4K-
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aquaControl) zonal wind response and Hadley cell edge shift (1.6◦ ±0.3◦ , Fig. 1b). The
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predicted response is not correlated with the simulated response across the models.
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Given the predicted Hadley cell edge for the warmed climate, we predict the jet stream
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position for the warmed climate using the linear relationship between Hadley cell edge and
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jet position in aquaControl (Fig. 1a, top left). Consistent with the linear relationship,
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a poleward shift of the edge of the Hadley cell following CC scaling leads to a poleward
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shift of jet stream position (3.8◦ ±0.7◦ , Fig. 1c). Once again the predicted poleward shift
157
generally overestimates the aqua4K-aquaControl response (2.8◦ ±0.7◦ , Fig. 1c) and the
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predicted response is not correlated with the simulated response across the models.
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Changes in specific humidity following CC scaling also affect the near-surface moist-
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static energy gradient, which is connected to the kinematic diffusivity D and vertically-
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integrated meridional transport of moist-static energy hvmi via mixing-length theory,
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i.e., hvmi ≈ −(D/a)∂ms /∂φ where h·i represents a vertical integral between the surface
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and 10 hPa weighted by the acceleration due to gravity. The diffusivity in aquaControl,
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i.e., D ≡ −(1/a)hvmi/(∂ms /∂φ), involves midlatitude (38.7◦ ) and high-latitude (65.5◦ )
165
maxima (Fig. 2a, vertical black lines). The diffusivity maxima are related to latent and
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dry-static energy transport, respectively (Supplementary Fig. 2a).
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Following mixing-length theory, changes in moist-static energy transport can be decomposed as
δhvmi ≈ −
δD ∂ms D ∂δms
−
.
a ∂φ
a ∂φ
(10)
169
In contrast to previous studies that examined heat transport changes assuming fixed
170
diffusivity, i.e., δD ≈ 0, and hence circulation [e.g. Frierson et al., 2007; Kang et al.,
171
2009], here we are interested in diffusivity changes as a proxy for the circulation response
172
to uniform warming. Assuming δhvmi ≈ 0, i.e., compensation occurs between dry-static
173
and latent energy transport [see Supplementary Fig. 2b, Frierson et al., 2007; Manabe et
174
al., 1965, 1975; Held and Soden, 2006; Hwang et al., 2011], and following CC scaling [see
175
(5)] we obtain
δD ≈ −
∂δms /∂φ
∂q/∂φ
∂T /∂φ
D ≈ −αδT L
D ≈ −α2 δT Lq
D < 0.
∂ms /∂φ
∂ms /∂φ
∂ms /∂φ
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Thus, CC scaling predicts diffusivity will decrease in response to uniform warming.
The predicted latent and dry-static energy transport responses to uniform warming
following CC scaling and mixing-length theory are:
L
∂q
L
∂T
δhLvqi ≈ − (δD + αδT D)
≈ − (δD + αδT D)αq
,
a
∂φ
a
∂φ
δD ∂T
δD ∂s
≈ −cp
,
δhvsi ≈ −
a ∂φ
a ∂φ
(12)
(13)
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which satisfy δhvmi ≈ 0 assuming (11). We note that a diffusive latent energy transport
180
prediction is not accurate for the deep tropics, however we are interested in changes
181
in the latitude of maximum transport, which occur in midlatitudes where the diffusive
182
approximation is valid. We label the terms in (12)-(13) proportional to δD as dynamic
183
transport responses and those proportional to δT as thermodynamic transport responses.
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Note there is no predicted thermodynamic dry-static energy transport response to uniform
185
warming (there is no temperature gradient change). We cannot make predictions assuming
186
compensation and fixed diffusivity in response to uniform warming because δhvmi = δD =
187
0 → ∂δms /∂φ = 0 [see (10)].
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The predicted diffusivity decrease in response to uniform warming following CC scal-
189
ing is largest in high latitudes (Fig. 2a, red line). However, the largest fractional de-
190
crease occurs in the subtropics and high latitudes (Fig. 2b, red line). The predicted
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subtropical decrease leads to a poleward shift of the latitude of maximum midlatitude
192
diffusivity (0.4◦ ±0.2◦ , Fig. 2c). However, the predicted shift underestimates the aqua4K-
193
aquaControl response (3.5◦ ±0.8◦ , Fig. 2d) and the two responses are not significantly cor-
194
related. The underestimate occurs because the aqua4K-aquaControl diffusivity increases
195
in midlatitudes (Fig. 2a,b, black lines) enhancing the poleward shift. The predicted diffu-
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sivity decrease in high latitudes leads to an equatorward shift of maximum high-latitude
197
diffusivity (-0.4◦ ±0.3◦ , Fig. 2c). This prediction is not accurate: the simulated high-
198
latitude diffusivity shifts poleward in most models (1.8◦ ±1.7◦ , Fig. 2d). The discrepancy
199
occurs because the aqua4K-aquaControl diffusivity does not change in high-latitudes (Fig.
200
2a,b, black line) instead the largest decrease occurs further south, which leads to the pole-
201
ward shift. We discuss the discrepancy between the predicted and simulated high-latitude
202
diffusivity response below.
203
The predicted dynamic latent-energy transport decreases in response to uniform warm-
204
ing (Fig. 3a, solid red line) and shifts the latitude of maximum latent energy transport
205
poleward in most models (0.2◦ ±0.2◦ , Fig. 3c), which agrees with the aqua4K-aquaControl
206
response (0.8◦ ±0.5◦ , Fig. 3c). However, this is partly offset by increased thermodynamic
207
transport (Fig. 3a, dashed red line). The predicted dynamic dry-static energy transport
208
decreases in response to uniform warming (Fig. 3b, solid red line) and shifts the latitude
209
of maximum dry-static energy transport poleward (0.6◦ ±0.2◦ , Fig. 3d). However, the
210
aqua4K-aquaControl dynamic dry-static energy transport response increases in midlati-
211
tudes (Fig. 3b, black solid line) and shifts the latitude of maximum transport equatorward
212
(-2.2◦ ±0.7◦ , Fig. 3d). The aqua4K-aquaControl thermodynamic dry-static energy trans-
213
port response (Fig. 3b, dashed black line), which is not considered in the prediction [see
214
(13)], leads to a poleward shift of the latitude of maximum dry-static energy transport.
215
The discrepancy between predicted and simulated diffusivity (Fig. 2a,b red versus black
216
lines) and energy transport (Fig. 3a,b, red versus black lines) responses suggests a missing
217
component of the mixing-length theory prediction. The difference between the simulated
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and predicted diffusivity response (Supplementary Fig. 3a, black line) is due to changes
219
in moist-static energy transport (assumed to be zero in the prediction) and deviations of
220
the moist-static energy gradient response from CC scaling in response to uniform warm-
221
ing. The simulated increase of moist-static energy transport in response to warming leads
222
to increased diffusivity, particularly in high latitudes (Supplementary Fig. 3a, red line).
223
Deviations of the moist-static energy gradient response from CC scaling leads to increased
224
mid-latitude diffusivity (Supplementary Fig. 3a, blue line), which dominates the discrep-
225
ancy between the simulated and predicted dynamic latent and dry static energy transport
226
responses (Supplementary Fig. 3b, solid lines). The discrepancy between the simulated
227
and predicted thermodynamic latent and dry static energy transport responses is domi-
228
nated by deviations of the moist-static energy gradient response from CC scaling. The
229
change in dry static energy gradient (dominated by temperature) and the change in la-
230
tent energy gradient both produce meridional dipoles of energy transport (Supplementary
231
Fig. 3b, dashed lines). Meridional dipoles of latent energy transport occur in response to
232
internal eddy-zonal flow feedbacks [Boer et al., 2001; Lorenz and Hartmann, 2001, 2003;
233
Thompson and Woodworth, 2014], thus these feedbacks might be a missing component of
234
the predictions.
3.2. Circulation changes inferred from ACRE response
235
The second response to warming we consider is ACRE changes. ACRE is defined as
236
the difference of CRE at the top of the atmosphere and surface, including both longwave
237
sf c
toa
and shortwave components, i.e., ACRE = (F toa − Fclr
) − (F sf c − Fclr
) where F is the
238
total radiative flux, Fclr is the clear-sky radiative flux, sf c refers to the surface, and toa
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refers to the top of the atmosphere. The radiative fluxes are defined as positive in the
240
downward direction. Here we assess how ACRE changes in response to uniform warming
241
affect moist-static energy transport, in particular its impact on the latitude of maximum
242
transport. In contrast to the previous subsection where we made predictions following
243
CC scaling solely based on information from aquaControl, the predictions made here use
244
information from both aquaControl and aqua4K, i.e., the ACRE response to uniform
245
warming is taken as given.
246
The ACRE response to uniform warming generally increases in the tropics and robustly
247
decreases in high latitudes (Fig. 4a). (We removed the global average but that does not
248
affect our conclusions.) Longwave radiation dominates the ACRE response (Supplemen-
249
tary Fig. 4a). We note that ACRE changes are an indirect measure of the cloud-radiative
250
response. We confirmed the ACRE changes for the MPI-ESM-LR and IPSL-CM5A-LR
251
models agree with the cloud-radiative response diagnosed from forward partial radiative
252
perturbation calculations following Weatherald and Manabe [1988] (see Supplementary
253
Fig. 4b).
254
255
The ACRE changes can be converted into a meridional moist-static energy transport
response following Hwang and Frierson [2011], i.e.,
δFACRE =
"Z
φ
−π/2
Z 2π
2
a cos φ(δACRE)dλdφ +
0
Z π/2 Z 2π
φ
#
2
a cos φ(δACRE)dλdφ /2. (14)
0
256
The ACRE changes increase poleward energy transport in both hemispheres (Fig. 4b).
257
When the ACRE-induced energy transport response is added to moist-static energy trans-
258
port in aquaControl, there is a poleward shift of the latitude of maximum energy transport
259
in all but one model (0.63◦ ± 0.40◦ , Fig. 4c).
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The ACRE-induced poleward shift of the latitude of maximum energy transport is
261
consistent with the poleward shift for aqua4K-aquaControl (0.53◦ ±0.31◦ , Fig. 4c). How-
262
ever, the predicted transport shift is smaller than the predicted jet shift (Fig. 1c) most
263
likely because ACRE changes are small in midlatitudes. Previous work has shown height-
264
dependent midlatitude cloud-radiative changes in response to uniform warming, which do
265
not project onto vertically-integrated ACRE, shift the jet poleward.
4. Conclusion and Discussion
266
A complete understanding of the response to anthropogenic climate change must involve
267
an understanding of the linkages between thermodynamic and dynamic responses. Here,
268
using physical arguments and aquaplanet simulations, we linked moist thermodynamic
269
and dynamic responses to uniform warming. We focused on CMIP5 aquaplanet simu-
270
lations because they exhibit robust poleward circulation shifts in responses to uniform
271
warming [Medeiros et al., 2015] and therefore provide an idealized setting for understand-
272
ing the circulation response in coupled-climate model simulations with realistic boundary
273
conditions. Our results build upon previous work that connected thermodynamic and
274
dynamic responses to global warming a posteriori [e.g. Lu et al., 2007; Vallis et al., 2015]
275
and used dry dynamical core simulations to investigate circulation responses [e.g. Butler
276
et al., 2010; Mbengue and Schneider , 2013; Lu et al., 2014].
277
We focused on two moist thermodynamic responses to uniform warming and what they
278
tell us about meridional shifts of the circulation. The first is increased specific humidity
279
with warming following CC scaling. According to quasi-equilibrium dynamics, the in-
280
creased meridional gradient of sub-cloud moist entropy in response to uniform warming
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following CC scaling amplifies tropical easterlies and shifts the edge of the Hadley cell,
282
defined here as the latitude of zero near-surface zonal-mean zonal wind, poleward. The
283
control-climate relationship between the Hadley cell edge and jet position predicts the jet
284
will shift poleward following CC scaling. While quasi-equilibrium dynamics is an approx-
285
imate framework, we have shown it predicts a robust direction for the circulation shift
286
in response to uniform warming (e.g., it predicts a poleward not an equatorward shift)
287
and provides an explanation for the circulation shift (related to increased moist-entropy
288
gradients following CC scaling).
289
According to mixing-length theory, the increased meridional gradient of moist-static
290
energy in response to uniform warming following CC scaling decreases diffusivity assum-
291
ing moist-static energy transport changes are small. The diffusivity decrease is largest is
292
the subtropics and high latitudes and shifts the latitude of maximum midlatitude diffu-
293
sivity (related to moisture transport) poleward and latitude of maximum high latitude
294
diffusivity (related to dry-static energy transport) equatorward. The diffusivity changes
295
can be connected to dynamic energy transport responses that lead to poleward shifts of
296
the latitude of maximum latent and dry-static energy transport in response to uniform
297
warming.
298
Discrepancies exist between the simulated and mixing-length theory predicted re-
299
sponses, in particular, simulated diffusivity actually increases in midlatitudes and does
300
not change significantly in high latitudes in response to uniform warming. The increased
301
simulated diffusivity is due to increased moist-static energy transport (e.g., due to ACRE
302
changes), which is not accounted for in the prediction, and to deviations of the moist-static
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303
energy gradient response from CC scaling in response to uniform warming. The differ-
304
ences between the simulated and predicted thermodynamic transport responses involve
305
meridional dipoles that reflect changes in temperature and moisture gradients. Meridional
306
dipoles of energy transport have been shown to occur in response to eddy-zonal flow feed-
307
backs [Boer et al., 2001; Lorenz and Hartmann, 2001, 2003; Thompson and Woodworth,
308
2014]. These feedbacks, which are not included in the prediction, might be important for
309
determining the full magnitude of the circulation response to warming.
310
The second moist thermodynamic response to uniform warming examined here is
311
changes in ACRE and its impact on moist-static energy transport. ACRE mostly in-
312
creases in the tropics and robustly decreases in high latitudes in response to uniform
313
warming. The inferred meridional moist-static energy transport response is poleward in
314
most models and maximizes poleward of the latitude of maximum energy transport in the
315
control climate. Consequently, the latitude of maximum energy transport shifts poleward
316
in all but one CMIP5 aquaplanet model. Our results support previous work that has
317
shown the cloud radiative response to warming induces a poleward jet shift [Voigt and
318
Shaw , 2015; Ceppi and Hartmann, 2016] and contributes to model spread in moist-static
319
energy transport responses [Hwang et al., 2011].
320
The moist thermodynamic-dynamic links examined here suggest circulation shifts in
321
response to warming may be fundamentally related to moisture gradients in the current
322
climate and ultimately to temperature gradients assuming fixed relative humidity [e.g.
323
eqns. (9), (11), (12), (13)]. They occur even when the warming perturbation is spatially
324
uniform. The aquaplanet responses to uniform warming are correlated with meridional
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325
temperature gradients in the control climate (Supplementary Fig. 5), highlighting a po-
326
tential emergent constraint on the circulation response to uniform warming. Additional
327
research is needed to assess the connection across an ensemble of coupled-climate models
328
with realistic boundary conditions to determine if a robust constraint emerges.
329
The circulation shifts predicted from the moist thermodynamic changes and dynamical
330
frameworks considered here are approximate. While they correctly predict the direction
331
of multi-model-mean meridional shift of the circulation, they could not account for the
332
magnitude of the simulated responses. Furthermore, the predicted shifts were not sig-
333
nificantly correlated with the simulated shifts in most cases suggesting thermodynamic
334
changes alone are not sufficient to predict model spread. An assessment across a larger
335
range of models is needed. The results suggest that thermodynamic [Voigt and Shaw ,
336
2015; Ceppi and Hartmann, 2016] and dynamic feedbacks [Lu et al., 2014] are likely im-
337
portant for determining the simulated circulation responses to warming. Nevertheless
338
our results show moist thermodynamics can be combined with physical arguments and
339
dynamical frameworks to make predictions of circulation shifts in response to uniform
340
warming.
341
Acknowledgments. AV and TAS are supported by the David and Lucile Packard
342
Foundation. TAS is also supported by NSF award AGS-1255208 and the Alfred P. Sloan
343
Foundation. We thank the reviewers whose comments helped to improve the manuscript.
344
The model data in this study are available from TAS upon request. We thank N. Hender-
345
son and H. Liu for help downloading the CMIP5 data. We acknowledge the World Cli-
346
mate Research Programme’s Working Group on Coupled Modelling, which is responsible
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347
for CMIP, and we thank the climate modeling groups for producing and making available
348
their model output. For CMIP the U.S. Department of Energy’s Program for Climate
349
Model Diagnosis and Intercomparison provides coordinating support and led development
350
of software infrastructure in partnership with the Global Organization for Earth System
351
Science Portals.
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(a)
latitude jet (deg.)
48
(r,p) = (0.96,0.00)
y = 1.16x + 9.00, r2 = 0.92
44
Multi−model mean
CCSM4
CNRM−CM5
FGOALS−g2
FGOALS−s2
HadGEM2−A
IPSL−CM5A−LR
MIROC5
MPI−ESM−LR
MPI−ESM−MR
MRI−CGCM3
40
36
32
20
22
24
26
28
latitude u=0 (deg.)
30
32
(b)
Simulated ∆latitude u=0 (deg.)
2.5
(r,p) = (0.27,0.42)
Multi−model mean
CCSM4
CNRM−CM5
FGOALS−g2
FGOALS−s2
HadGEM2−A
IPSL−CM5A−LR
MIROC5
MPI−ESM−LR
MPI−ESM−MR
MRI−CGCM3
2
1.5
1
1.5
2
2.5
3
3.5
Predicted ∆latitude u=0 (deg.)
4
4.5
(c)
Simulated ∆latitude jet (deg.)
4
(r,p) = (0.44,0.18)
Multi−model mean
CCSM4
CNRM−CM5
FGOALS−g2
FGOALS−s2
HadGEM2−A
IPSL−CM5A−LR
MIROC5
MPI−ESM−LR
MPI−ESM−MR
MRI−CGCM3
3
2
1
1
Figure 1.
2
3
4
Predicted ∆latitude jet (deg.)
5
6
(a) Latitude of eddy-driven jet stream versus latitude of the Hadley cell edge in
aquaControl (circles) and aqua4K (squares). The aquaControl correlation (r = 0.96, p = 0.00),
and linear regression (r2 = 0.92, black line, regression coefficients top left) are statistically
significant. Similar results are obtained for aqua4K (r = 0.95, p = 0.00, r2 = 0.89, dashed line).
(b) Simulated shift (aqua4K-aquaControl) of the Hadley cell edge versus the predicted shift in
response to uniform warming. The correlation and p-value are in the top-left corner. (c) Same
as (b) but for the jet shift predicted using the linear relationship in Fig. 1a.
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(a)
(b)
10
0
0
δD/D (%)
δD (x109 kgs−1)
2
−2
−10
−4
−20
−6
10
20
30
40
latitude
50
60
(c)
20
30
40
latitude
50
60
70
(d)
5
(r,p) = (−0.05,0.88)
4
Multi−model mean
CCSM4
CNRM−CM5
FGOALS−g2
FGOALS−s2
HadGEM2−A
IPSL−CM5A−LR
MIROC5
MPI−ESM−LR
MPI−ESM−MR
MRI−CGCM3
3
2
0
0.5
Predicted ∆latitude max. D (deg.)
1
Simulated ∆latitude max. D (deg.)
Simulated ∆latitude max. D (deg.)
10
70
6
(r,p) = (0.33,0.31)
4
Multi−model mean
CCSM4
CNRM−CM5
FGOALS−g2
FGOALS−s2
HadGEM2−A
IPSL−CM5A−LR
MIROC5
MPI−ESM−LR
MPI−ESM−MR
MRI−CGCM3
2
0
−2
−1.5
−1
−0.5
0
Predicted ∆latitude max. D (deg.)
0.5
Figure 2. (a) Predicted (red) and simulated (aqua4K-aquaControl, black) diffusivity response
to uniform warming. (b) Same as in (a) but for percent change. The vertical black lines indicate
locations of diffusivity maxima in aquaControl. (c) Simulated shift (aqua4K-aquaControl) of the
latitude of maximum midlatitude diffusivity versus the predicted shift in response to uniform
warming. The correlation and p-value are in the top-left corner. (d) Same as (c) but for the
latitude of maximum high-latitude diffusivity.
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(b)
(a)
0.2
0.1
0.15
0.05
PW
PW
0.1
0.05
0
0
−0.05
−0.05
−0.1
10
20
30
40
latitude
50
60
70
20
30
40
latitude
50
60
70
80
2
(r,p) = (−0.52,0.09)
Multi−model mean
CCSM4
CNRM−CM5
FGOALS−g2
FGOALS−s2
HadGEM2−A
IPSL−CM5A−LR
MIROC5
MPI−ESM−LR
MPI−ESM−MR
MRI−CGCM3
1
0
−1
−0.5
Figure 3.
0
Predicted ∆latitude max. vq (deg.)
0.5
Simulated ∆latitude max. vs (deg.)
(d)
(c)
Simulated ∆latitude max. vq (deg.)
−0.1
10
80
(r,p) = (−0.54,0.08)
−1
Multi−model mean
CCSM4
CNRM−CM5
FGOALS−g2
FGOALS−s2
HadGEM2−A
IPSL−CM5A−LR
MIROC5
MPI−ESM−LR
MPI−ESM−MR
MRI−CGCM3
−2
−3
−4
0
0.5
1
Predicted ∆latitude max. vs (deg.)
1.5
Predicted (red) and simulated (aqua4K-aquaControl, black) dynamic (solid) and
thermodynamic (dashed) (a) latent and (b) dry-static energy transport responses to uniform
warming following mixing-length theory. Note there is no predicted change of thermodynamic
dry static energy transport in response to uniform warming (no dashed red line in Fig. 3b). The
vertical black lines indicate the position of maximum transport in aquaControl. (c) Simulated
shift (aqua4K-aquaControl) of the latitude of maximum latent energy transport [see (12)] versus
the predicted shift in response to uniform warming. The correlation and p-value are in the
top-left corner. (d) Same as (c) but for the shift of the latitude of maximum dry-static energy
transport [see (13)].
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(a)
30
20
Multi−model mean
CCSM4
CNRM−CM5
FGOALS−g2
FGOALS−s2
HadGEM2−A
IPSL−CM5A−LR
MIROC5
MPI−ESM−LR
MPI−ESM−MR
MRI−CGCM3
Wm−2
10
0
−10
−20
−80
−60
−40
−20
0
latitude
20
40
60
80
(b)
0.15
0.1
Multi−model mean
CCSM4
CNRM−CM5
FGOALS−g2
FGOALS−s2
HadGEM2−A
IPSL−CM5A−LR
MIROC5
MPI−ESM−LR
MPI−ESM−MR
MRI−CGCM3
PW
0.05
0
−0.05
−0.1
−0.15
−80
−60
−40
−20
0
latitude
20
40
60
80
Simulated ∆latitude max. vm (deg.)
(c)
1.5
(r,p) = (0.39,0.23)
1
Multi−model mean
CCSM4
CNRM−CM5
FGOALS−g2
FGOALS−s2
HadGEM2−A
IPSL−CM5A−LR
MIROC5
MPI−ESM−LR
MPI−ESM−MR
MRI−CGCM3
0.5
0
−0.5
−0.5
Figure 4.
0
0.5
1
1.5
Predicted ∆latitude max. vm (deg.)
2
(a) ACRE response to uniform warming (aqua4K-aquaControl). (b) Moist-static
energy transport response due to ACRE changes [see (14)]. The vertical black line indicates
the position of maximum moist-static energy transport in aquaControl. (c) Simulated shift
(aqua4K-aquaControl) of the latitude of maximum energy transport from the ACRE-induced
energy transport response versus the predicted shift. The correlation and p-value are in the
top-left corner.
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