Geophysical Research Letters
Supporting Information forConnecting Tropical Climate Change with Southern Ocean Heat Uptake

Yen-Ting Hwang1,2, Shang-Ping Xie2, Clara Deser3, and Sarah M. Kang4
Department of Atmospheric Sciences, National Taiwan University, Taipei, Taiwan
Scripps Institution of Oceanography, University of California San Diego, La Jolla
Climate and Global Dynamics, National Center for Atmospheric Research, Boulder, COSchool of Urban and Environmental Engineering, Ulsan National Institute of Science and Technology,Ulsan, Korea

Contents of this file
Text S1Figures S1 to S2Introduction
This supporting information includes supplementary Text S1 and Figures S1 to S2.
Text S1 describes the derivation of SST diagnostic equation (Eq.2 in the maintext), using mixed layer energy budget analysis and the bulk formula forevaporation. Figure S1 shows the changes in surface flux in the idealized slab
ocean experiments and the CMIP5 fully coupled models. Figure S2 demonstrates
the time series of zonal mean SST after quadrupling CO2.

Text S1.
SST diagnostic equation derivation
In order to understand the cause of the east-west asymmetry, we perform an energy
budget analysis of the mixed layer ocean. As described in the main text, the mixed layer
energy budget can be written asρC p H∂T= Q'sw +Q'lw +Q'lh +Q'sh +O'∂t(Eq.S1)(Xie et al. 2010; Deser et al. 2010). The term on the left hand side is the storage term (or€the tendency term), which is very close to zero in the quasi-equilibrium tropics. ρ isdensity, Cp is the specific heat of seawater, H is mixed layer depth, and∂Tis∂ttemperature tendency. The right hand side includes all of the factors that would affect the€mixed layer energy budget: net longwave radiation (Qlw), net shortwave
radiation (Qsw),
latent heat flux (Qlh), sensible heat flux (Qsh), and the contribution from ocean dynamics(O), including advection, diffusion, and vertical mixing. Downward fluxes are defined aspositive, which heat the mixed layer ocean. In the slab ocean setting, the changes ofoceanic heat advection, the last term O, is zero. The prime symbol (‘) refers to changes
between the two quasi-equilibrium states: the average over years 10-19 after quadruplingCO2 minus the 50-year climatology.

The changes of net longwave radiation ( Q'lw ) and sensible heat flux ( Q'sh ) are small. We
can further decompose the two main terms:

Q'sw = Q'sw,clr +Q'sw,cld€€,(Eq.S2) €where Q'sw,clr is the changes of shortwave radiation at the surface in clear sky andQ'sw,cld is changes of shortwave cloud radiative forcing at the surface.
€ In the tropics, latent heat flux is mostly due to evaporation. Following the standard bulk€

formula for evaporation,

Q'E = Lv CE ρaW (qs − qa ) = Lv CE ρaW [qs (T) − RH • qs (T + ΔT)],(Eq.S3)

we decompose the changes of latent heat flux Q'lh as (see Jia and Wu 2012):€Q'lh ≅ −Q'E = −

∂QE
∂Q
∂Q
∂Q
T' − E W ' − E RH' − E ΔT'
∂T
∂W
∂RH
∂ΔT,

(Eq.S4)€

where QE is evaporation, Lvis the latent heat of evaporation, CE is the transfer€coefficient, ρ a is the surface air density, T is sea surface temperature, W is the surface€ wind speed, RH€
is the surface humidity, and ΔT = T€− T ,a

Ta is the surface air€temperature.
The four terms on the right hand side are changes in latent heat flux relatedwith Newtonian cooling, changes in€wind, changes€in humidity, and changes in stability,respectively. The more detailed expressions are as follow:

Q'E ,SST =Q'E,W =€∂QE
Q
W ' = E W ',∂W
W

Q'E ,RH =∂QE−Q
RH' = −α ΔT E
RH',
∂RH
e− RH

Q'E,ΔT =∂QE−α Q RH
ΔT' = −α ΔT E
ΔT',
∂ΔTe− RH€€
where€∂QE
T' = αQE T',∂T

α = Lv /(RvT 2 )(Eq.S5)is assumed to be a constant 0.06 K-1, with

Rv being the gas

constant for moist air. Note that the changes and the climatological values of each month€
are considered separately.

We can substitute Eq.S5 to Eq.S1:

Q'sw,cld +Q'sw,clr +Q'lw −α QE T' −Q'E,W −Q'E,RH −Q'E,ΔT +Q'sh = 0,

(Eq.S6)and obtain a diagnostic equation for changes in SST:

€T' =Q'sw,cld +Q'sw,clr +Q'lw −Q'E ,W −Q'E,RH −Q'E ,ΔT +Q'sh
α QE(Eq.S7)

This diagnostic equation interprets the SST pattern as a forced response problem. In our€quasi-steady slab ocean analysis, the numerators can be understood as atmosphericforcings, including changes in shortwave cloud radiative forcing, changes in shortwave inclear sky, changes in longwave radiation, changes in evaporation due to variations inwind, relative humidity, or near surface stability, and changes in sensible heat flux. The
denominator is the Newtonion cooling coefficient,

α QE, which captures the ocean’sability to limit SST warming by evaporation. The climatological evaporation is the same€
between the deepSO and the control experiments and contributes very little to theeast-west SST gradient. Thus, we demonstrate the results in the following form:

Q'sw,cld Q'sw,clr Q'lw −Q'E,w −Q'E,RH −Q'E,ΔT Q'sh++++++α QE
α QE α QE α QE
α QE
α QE
α QE
= T'sw,cld +T'sw,clr +T'lw +T'lh,w +T'lh,RH +T'lh,ΔT +T'sh .

T' =€(Eq.S8)

a151010W/m

2500−5-10−10−15-20−20b−25SP60S30S

EQ

30N60N

NP60S30S

EQ

30N60NNP

151010W/m

2500−5-10−10−15-20−20−25SPSP60S

30S

EQ

30N

60N

NPFigure S1. Surface flux changes. Zonal mean upward surface flux changes (year 10~19after quadrupling CO2 minus the 20-year average pre-industrial climatological condition
before increasing CO2) in control (red) and deepSO (blue) experiments (a) andabrupt4xCO2 experiments in CMIP5 (b). Each line is one model and multi-model means
are in bold. Note this plot is qualitatively similar to Figure A1(a) in Rose et al. 2014.

a60N

10940N

8720N

660N

EQ

5(K)

20S

4 10
3940N

240S

120N

bEQ60S

2468101214161860N

6958 420S

7 320N

6 240S60S

0 71040N

8EQ

54220S

468101214

16

18

3

10240S

160S

246810121416

180year (after 4xCO2)
Figure S2. Zonal mean SST response (K) as a function of latitude and time after
instantaneously quadrupling CO2. Anomalous zonal mean SST relative to the 20-year
average before quadrupling CO2 in control (a) and deepSO (b) experiments. Black lines
mark the latitudes of maximum annual mean precipitation.