Vertical energy fluxes – radiative and turbulent heat fluxes at top of the atmosphere and surface– are the physical driver of temperature changes. The careful decompositions of the energy fluxes inform the physical mechanisms responsible for the difference between two mean states. For example, if the cloud radiative anomalies dominate the differences in vertical energy fluxes, we can focus on the cloud processes to seek the mechanisms. In this thesis, we adopt several methods between climate models and experiments, thereby investigating the mechanisms of the tropical mean state biases. This auxiliary chapter focus on describing such methods. One may directly jump into Chapter 3 for skipping technical details.
2.1. Radiative kernel technique
Radiative fluxes in the climate model are adjusted by the climate variables such as temperature, water vapor, surface albedo, and clouds. Soden & Held (2006) proposed a radiative kernel technique, approximately quantifying the contribution of each climate variable to the radiative flux change. The technique decomposes each contribution into two components; the first component is pre-calculated flux adjustment for a standard change in each climate variable (radiative kernel) and the second component is the actual model response of each climate variable. Assuming each component adjusts linearly with the change in climate variable, the net change in longwave and shortwave fluxes both at TOA and surface could be decomposed as
δLW = (∂LW
∂Ts)
k
δTs+ (∂LW
∂Ta)
k
δTa+ (∂LW
∂q )
k
δq + δLWcld,
(2.1) δSW = (∂SW
∂q )
k
δq + (∂SW
∂α )
k
δα + δSWcld,
(2.2) where LW (SW) is longwave (shortwave) radiative flux at either TOA or surface, Ts and Ta are the temperature at the surface and atmosphere, q is the atmospheric specific humidity, δLWcld (δSWcld) is the LW (SW) adjustments due to the cloud change (cloud radiative anomalies), and α is surface albedo estimated by the ratio between upward and downward surface shortwave radiative fluxes. Subscript k indicates the term derived from the radiative kernel, pre-calculated with CESM-CAM5 both for TOA and surface (Pendergrass et al., 2018). The radiative kernels are multiplied to the responses of climate variables at every grid point for each month of seasonal mean data, vertically integrated to quantify the change in radiative fluxes at each horizontal grid points. The contribution of the cloud is highly non-linear thus calculated indirectly by subtracting the kernel-derived cloud masking effect from the
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cloud radiative effect, where the latter is the subtraction of the clear-sky from the total-sky flux (Soden et al., 2008). The kernel technique has been widely employed to quantify the contributions from the different feedback processes with reasonable error (Block & Mauritsen, 2013; Chung &
Soden, 2015; Fläschner et al., 2016; Shell et al., 2008). However, The SW fluxes could not be successfully decomposed by the radiative kernel, when the radiative transfer algorithm is changed or the solar insolation is perturbed as will be in this study. We extend the Approximate Partial Radiative Perturbation (APRP) method (Taylor et al., 2007) to decompose the SW fluxes in such cases.
15 2.2. Approximate Partial Radiative Perturbation method
In the APRP method, a one-layer radiation model with seven radiative properties approximates the interactions of SW fluxes within a single climate state. These seven properties are atmospheric absorption and reflection, and surface albedo, each of which are separately estimated for clear and overcast skies, and a cloud area fraction. By fitting the seven radiative properties to the total cloud area fraction and SW fluxes from standard model output, the interactions that result in SW fluxes within each climate state can be captured with reasonable accuracy. Comparison can be made between two climate states by making perturbations to radiative properties to attribute the net TOA SW responses to the various combinations of radiative property changes (see the Appendix A for details).
APRP allows us to reasonably separate the TOA SW responses to the radiative effects of changes in surface albedo, cloud, and non-cloud atmospheric constituents, which are poorly captured with the radiative kernel technique due to nonlinear interactions that are nonetheless straightforward in the APRP framework (Dong et al., 2020a; Frey et al., 2017; Hwang et al., 2013; Yoshimori et al., 2011).
Furthermore, it relies on variables that are commonly archived for climate model simulations.
Here, we extend the conventional APRP method focusing on atmospheric SW fluxes to the surface SW fluxes. We do this while maintaining the assumption of simultaneous atmospheric absorption and reflection at the first pass among infinite passes through a one-layer radiation model, motivated by Donohoe & Battisti (2011). We apply this assumption to the estimation of cloud radiative effects following Taylor et al. (2007),
δSW = δSWSaprp+ δSWαaprp+ δSWcldaprp+ δSWncldaprp, (2.3) where δ indicates the difference between two climate states, SW indicates the shortwave flux at either TOA or surface, the superscripts aprp denote the calculation method, and the subscripts S, α, cld, and ncld, respectively, denote the contribution from the insolation, surface albedo, cloud, and non-cloud atmospheric constituents. The δSWcldaprp can be further decomposed into the contribution from low cloud changes by assuming that the cloud radiative anomalies are dominated by low clouds when the absolute ratio of the longwave to shortwave cloud radiative anomalies is smaller than tan22.5° (Webb et al., 2006). The derivation for the extended APRP method is given in Appendix A. Note that we use the APRP and radiative kernel method not only for the responses in one climate model, but also apply it to the inter-model spread, by setting multi-model mean as the reference climate state and individual models as target climate states.
16 2.3. Decomposition of change in latent heat flux
To understand the processes responsible for change in evaporation, the response in latent heat flux (LHF) over ocean is decomposed into the contributions from surface temperature (δLHFTs), surface wind speed (δLHFWND), relative humidity at model reference level (δLHFRH) and near-surface atmospheric stability (δLHFΔT) following Jia & Wu (2013):
δLHF = δLHFTs+ δLHFWND+ δLHFRH+ δLHFΔT
= (βLHF̅̅̅̅̅)δTs+ (LHF WND̅̅̅̅̅̅̅
̅̅̅̅̅̅̅
) δWND + ( −LHF̅̅̅̅̅
e−β̅̅̅̅ΔT̅̅̅̅− RH̅̅̅̅) δRH + (−βLHF̅̅̅̅̅ ∙ RH̅̅̅̅
e−β̅̅̅̅ΔT̅̅̅̅− RH̅̅̅̅) δ(ΔT), (2.4) where Ts denotes surface temperature, WND the surface wind speed, RH the relative humidity at model reference level, neat-surface atmospheric stability ΔT = Tref− Ts with Tref the reference level temperature, overbar indicates reference climatology, and 𝛽 = 𝐿v
𝑅vT̅̅̅̅ s2 with latent heat of vaporization 𝐿v= 2.5 × 106 J Kg−1 and 𝑅v= 461.5 J Kg−1K−1 . The detailed derivations are provided in Appendix B.
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