Chapter 4. Dependency of tropical mean climate pattern on the water vapor shortwave
7. Summary
97
98
Southern Ocean cooling is first propagated into the equator by atmospheric eddies and climatological southeasterlies over the eastern Pacific, which is then amplified by the wind-evaporation-SST feedback, equatorial upwelling, and subtropical low cloud feedback. The degree of ITCZ shift β which indicates the teleconnection strength β largely depends on the subtropical low cloud feedback, supported by regional cloud locking experiments. Interestingly, the subtropical cloud feedback is underestimated in most state-of-the-art climate models, implying that the remote impact of the Southern Ocean on the anti-symmetric precipitation spread is stronger than previously thought. Indeed, the northward ITCZ shift corresponding to observational subtropical cloud feedback can reduce the anti-symmetric precipitation bias by as much as 49% of the multi-model mean bias. The seasonal and regional characteristics of tropical precipitation biases are investigated in Chapter 6. The symmetric precipitation bias and inter-model spread is dominated by the western and Central Pacific, which is persistent throughout the year. On the other hand, the anti-symmetric precipitation bias and inter- model spread is dominated by the eastern Pacific and Atlantic with the maximum strength over boreal Spring. The increase in water vapor SW absorptivity desiccates equatorial precipitation over the western and central Pacific regardless of season, while the Southern Ocean cooling effectively shifts the eastern Pacific and Atlantic ITCZ northward with pronounced responses in boreal spring.
In this thesis, we discover that the water vapor SW absorptivity affects the tropical SST pattern through the interactions with low clouds. Since the radiative transfer calculation for the SWA is now accurate at the expense of computational cost, the tropical mean state biases due to water vapor SW absorptivity have enough room to improve. The accurate parameterizations of water vapor SW absorptivity could also improve the low cloud representations because low clouds are often tuned after the other parameterizations are fixed. In addition, we reveal the teleconnection from the Southern Ocean to the tropical Pacific, of which the strength is regulated by the subtropical cloud feedback. This finding not only matters for the tropical mean state biases but also for the climate projections. The climate forcings over the Southern Ocean β such as Antarctic freshwater influx (Bronselaer et al., 2018), Antarctic ice melt (England et al., 2020), and Sothern Ocean heat uptake (Armour et al., 2016) β have exhibited similar teleconnection impact, of which magnitude would also depend on the subtropical cloud feedback. The teleconnection from the Southern Ocean delayed heat release (e.g., Kug et al., 2022) under the CO2 quadrupling scenario is now investigated.
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Appendix A: Extension of APRP method
Figure A1. Schematic of one-layer radiation model used in this study. π, π, πΎ, and πΌ indicate the insolation, atmospheric absorptivity, atmospheric reflectivity, and surface albedo. TOA (SFC) is abbreviation for top-of- atmosphere (surface).
For the APRP method, the one-layer radiation model is adopted to represent the interaction of SW fluxes between the atmosphere and surface (Figure A1). Of the incident solar radiation S, a fraction π is absorbed by the atmosphere, a fraction πΎ is reflected by the atmosphere, and the remainder is transmitted to the surface. Of the solar radiation transmitted through the atmosphere, a fraction πΌ is reflected at the surface, of which a fraction πΎ is reflected from the atmosphere back toward the surface again on the return pass. This is repeated for infinite passes. Note that the atmospheric absorption and reflection occur simultaneously at the first downward pass motivated by Donohoe and Battisti (2011).
In this one-layer radiation model, the total reflected SW radiation at TOA (SWβTOA) and total incident SW radiation toward SFC (SWβSFC) can be expressed as the sum of an infinite geometric series, with πΌπΎ as the common ratio. Then, the planetary albedo (A) and surface incident ratio (Qs) are expressed as a function of radiative properties:
A(πΌ, πΎ, π) =SWβTOA
π = πΎ + (1 β π β πΎ)(1 β πΎ)πΌ(1 + πΌπΎ + πΌ2πΎ2+ β― )
= πΎ +(1 β π β πΎ)(1 β πΎ) 1 β πΌπΎ πΌ
(A1) Qs(πΌ, πΎ, π) =SWβSFC
π = (1 β π β πΎ) (1 + πΌπΎ + πΌ2πΎ2+ β― ) = (1 β π β πΎ)
1 β πΌπΎ
(A2)
100
To account for the effect of clouds, all-sky radiative fluxes at each grid point (R) are divided into the clear-sky (Rclr) and overcast-sky (Roc) fluxes, weighted by the total-column cloud area fraction (clt) following Taylor et al. (2007):
R = (1 β clt) β Rclr+ clt β Roc
(A3) Note that Roc can be calculated from the standard model outputs R, Rclr and clt. The one-layer radiation model is applied to each of Rclr and Roc. Accordingly, radiative properties for the single- column model are calculated for clear- and overcast- sky fluxes:
A =SWβTOA
π , Qs=SWβSFC
π , πΌ =SWβSFC SWβSFC
(A4) The atmospheric absorptivity is defined as the difference between the fraction of net SW fluxes absorbed at TOA and SFC:
π = (1 β A) β Qs(1 β πΌ)
(A5) The atmospheric reflectivity is then derived from Eq. (A2):
Ξ³ =1 β π β Qs 1 β πΌQs
(A6) In Eq. (A3-A6), the radiative properties for clear-sky (πΌπππ, ππππ, πΎπππ) and overcast-sky (πΌππ, πππ, πΎππ) are fitted to the climate model output. Radiative properties for the overcast-sky are calculated
assuming that the non-cloud atmospheric constituents in the overcast-sky absorb and reflect the same amount of SW fluxes as in the clear-sky. That is, the transmittance in overcast-sky is the product of transmittance in clear-sky and cloud, applied to π and πΎ in the same way:
1 β πππ = (1 β ππππ) β (1 β ππππ) 1 β πΎππ = (1 β πΎπππ) β (1 β πΎπππ)
(A7) This results in seven radiative properties (clt, πΌclr, πΌoc, πclr, πcld, πΎclr, πΎcld) representing the SW radiative transfer in the climate model. Next, we extend the methodology for TOA SW decomposition in the original APRP method (Taylor et al. 2007) to the surface component in a parallel way. First, A (Eq. (A1)) and Qs (Eq. (A2)) of the climate model become a function of the seven radiative properties:
101
Aclr(πΌπππ, πΎπππ, ππππ) = πΎπππ+(1 β ππππβ πΎπππ)(1 β πΎπππ) 1 β πΌππππΎπππ πΌπππ
(A8) Aoc(πΌππ, πΎπππ, ππππ, πΎπππ, ππππ) = πΎππ+(1 β πππβ πΎππ)(1 β πΎππ)
1 β πΌπππΎππ πΌππ, where πππ = 1 β (1 β ππππ) β (1 β ππππ), πΎππ = 1 β (1 β πΎπππ) β (1 β πΎπππ)
(A9) π΄(clt, πΌπππ, πΌππ, ππππ, ππππ, πΎπππ, πΎπππ) = (1 β clt) β Aclr+ clt β Aoc
(A10) Qs,clr(πΌπππ, πΎπππ, ππππ) =(1 β ππππβ πΎπππ)
1 β πΌππππΎπππ
(A11) Qs,oc(πΌππ, πΎπππ, ππππ, πΎπππ, ππππ) =(1 β πππβ πΎππ)
1 β πΌπππΎππ ,
where πππ = 1 β (1 β ππππ) β (1 β ππππ), πΎππ = 1 β (1 β πΎπππ) β (1 β πΎπππ)
(A12) Qs(clt, πΌπππ, πΌππ, ππππ, ππππ, πΎπππ, πΎπππ) = (1 β clt) β Qs,clr+ clt β Qs,oc
(A13) The changes in planetary albedo (Ξ΄A) and surface incident ratio (Ξ΄Qs) due to each radiative property can be estimated by Eq. (A10) and (A13). The forward and backward substitution are averaged to estimate a contribution from each radiative property, following Colman (2003):
Ξ΄Aπ‘ =1
2[A(π‘2, π1) β A(π‘1, π1)] + 1
2[A(π‘2, π2) β A(π‘1, π2)],
(A14) Ξ΄Qs,π‘=1
2[Qs(π‘2, π1) β Qs(π‘1, π1)] + 1
2[Qs(π‘2, π2) β Qs(π‘1, π2)],
(A15) where π‘ denotes target radiative property, π denotes all other 6 radiative properties, and πΏ denotes the difference between state 1 and state 2.
Meanwhile, the net SW flux at the TOA and SFC are:
102
SWnetTOA= π β SWβTOA= (1 β A)π
(A16) SWnetSFC = SWβSFCβ SWβSFC= Qs(1 β πΌ)π
(A17) And the changes in SW flux at the TOA and SFC are:
Ξ΄SWnetTOA= Ξ΄[(1 β A)π] = (1 β A)Ξ΄π β πΞ΄A
(A18) Ξ΄SWnetSFC = Ξ΄[Qs(1 β πΌ)π] = Qs(1 β πΌ)Ξ΄π β QsπΞ΄πΌ + (1 β πΌ)πΞ΄Qs,
(A19) where the terms without Ξ΄ are the average between the two states, and the co-variance terms are ignored.
Substituting Eq. (A14) into (A18) and Eq. (A15) into (A19), SW flux responses at the TOA and SFC can be attributed to the change in each radiative property:
Ξ΄SWnetTOA = (1 β A)Ξ΄π β π[Ξ΄AπΌπππ + Ξ΄AπΌππ] βββ
βπ[Ξ΄Aclt+ Ξ΄Aππππ+ Ξ΄AπΎπππ] β π[Ξ΄AπΎπππ+ Ξ΄Aππππ]
= Ξ΄SWπTOA+ Ξ΄SWπΌTOA+ Ξ΄SWcldTOA+ Ξ΄SWncldTOA
(A20) Ξ΄SWnetSFC = Qs(1 β πΌ)Ξ΄π + {βQsπΞ΄πΌ + π(1 β πΌ)[Ξ΄Qs,πΌπππ+ Ξ΄Qs,πΌππ]} βββ
+π(1 β πΌ)[Ξ΄Qs,clt+ Ξ΄Qs,ππππ+ Ξ΄Qs,πΎπππ] + π(1 β πΌ)[Ξ΄Qs,ππππ+ Ξ΄Qs,πΎπππ]
= Ξ΄SWπSFC+ Ξ΄SWπΌSFC+ Ξ΄SWcldSFC+ Ξ΄SWncldSFC
(A21) where subscripts π, πΌ, cld, and ncld denote the contributions from the change in insolation, surface albedo, cloud properties and non-cloud atmospheric constituents.
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Appendix B: Decomposition of the change in latent heat flux
The standard bulk formula for the latent hear flux (LHF) is:
LHF = πΏvπΆEπaWND(qsβ qref) = πΏvπΆEπaWND(qs(Ts) β RH β qs(Ts+ ΞT)),
(B1) where πΏv = 2.5 Γ 106 J β Kgβ1 is the latent heat of vaporization, πΆE is the transfer coefficient, πa is the surface air density, WND is the surface wind speed, RH is the relative humidity at model reference level, ΞT = Trefβ Ts, Tref is reference level temperature, Ts is surface temperature, and qs is the saturation specific humidity at the ocean surface. From the Clausius-Clapeyron (CC) equation, qs could be further expressed as
qs(T) = q0eπ½T,
(B2) where q0 is a constant and Ξ²= πΏv/(π vT2). Note that π v= 461.5 J β Kgβ1β Kβ1. Substitution of Eq.
(B2) into Eq. (B1) yields:
LHF = πΏvπΆEπaWND(1 β RHeπ½ΞT)qs(Ts)
(B3) The change in LHF could be represented as below, assuming Ξ΄LHF as function of four independent variables β Ts, WND, RH and ΞT:
Ξ΄LHF = βLHF
βTs Ξ΄Ts+βLHF
βW Ξ΄W +βLHF
βRH Ξ΄RH + βLHF
β(ΞT)Ξ΄(ΞT),
(B4) where the partial derivative of LHF are resulted in the expressions composed of constants and base state variables:
βLHF
βTs = LHFΜ Μ Μ Μ Μ
qs(TΜ )s
β
βTs(qs(Ts)) = Μ Μ Μ Μ Μ LHF
qs(TΜ )s (π½qs(TΜ )) = π½LHFs Μ Μ Μ Μ Μ ,
(B5)
βLHF
βWND= LHFΜ Μ Μ Μ Μ
WNDΜ Μ Μ Μ Μ Μ Μ
β
βWND(WND) = LHFΜ Μ Μ Μ Μ
WNDΜ Μ Μ Μ Μ Μ Μ ,
(B6)
βLHF
βRH = LHFΜ Μ Μ Μ Μ
1 β RHΜ Μ Μ Μ eπ½ΞTΜ Μ Μ Μ
β
βRH(1 β RHeπ½ΞT) = LHFΜ Μ Μ Μ Μ
1 β RHΜ Μ Μ Μ eπ½ΞTΜ Μ Μ Μ (βeπ½ΞT) = βLHFΜ Μ Μ Μ Μ
eβπ½ΞTΜ Μ Μ Μ β RHΜ Μ Μ Μ ,
104
(B7)
βLHF
β(ΞT)= Μ Μ Μ Μ Μ LHF 1 β RHΜ Μ Μ Μ eπ½ΞTΜ Μ Μ Μ
β
β(ΞT)(1 β RHeπ½ΞT) = LHFΜ Μ Μ Μ Μ
1 β RHΜ Μ Μ Μ eπ½ΞTΜ Μ Μ Μ (βπ½RHΜ Μ Μ Μ β eπ½ΞT) =βπ½LHFΜ Μ Μ Μ Μ β RHΜ Μ Μ Μ
eβπ½ΞTΜ Μ Μ Μ β RHΜ Μ Μ Μ , (B8) where overbar denotes the reference climatology. Eventually, substitution of Eq. (B5), (B6), (B7), (B8) into Eq. (B4) leads to the attribution of Ξ΄LHF to the change in Ts, WND, RH and ΞT (F. Jia & Wu, 2013):
Ξ΄LHF = (π½LHFΜ Μ Μ Μ Μ )Ξ΄Ts+ (LHF WΜ
Μ Μ Μ Μ Μ
) Ξ΄W + ( βLHFΜ Μ Μ Μ Μ
eβπ½ΞTΜ Μ Μ Μ β RHΜ Μ Μ Μ ) Ξ΄RH + (βπ½LHFΜ Μ Μ Μ Μ β RHΜ Μ Μ Μ
eβπ½ΞTΜ Μ Μ Μ β RHΜ Μ Μ Μ ) Ξ΄(ΞT)
= Ξ΄LHFTs+ Ξ΄LHFWND+ Ξ΄LHFRH+ Ξ΄LHFΞT
(B9) Note that the sensitivity of the LHF change to each climate variables is proportional to its climatological magnitude.
105
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