The sensitivity of climate and climate change to the efficiency of atmospheric heat transport

Abstract

Atmospheric heat transport (AHT) moderates spatial gradients in surface temperature, and its efficiency (hereinafter referred to as diffusivity) shapes the distribution of moist static energy and the hydrological cycle. Using a linear downgradient rule for AHT, we diagnose zonal-mean diffusivity using observational and model data. We find it varies two- to threefold with season and latitude, but is nearly invariant across different climate states. We then employ a moist energy balance model (MEBM) to explore the impacts of changing the magnitude and spatial pattern of diffusivity on the climatology and climate response to forcing. Spatial anomalies in diffusivity in the extra-tropics have a larger impact on temperature and hydrology than diffusivity anomalies in the tropics. We demonstrate that compensating dynamical adjustments in the MEBM act to mute the impact of changing diffusivity patterns on the resulting climate. We isolate the impacts of spatial patterns of forcing, ocean heat uptake, radiative feedbacks, and diffusivity on the spatial pattern of climate change; and find that the pattern of climate change is least sensitive to the detailed pattern of diffusivity. Overall, these results suggest that although diffusivity is far from spatially invariant, understanding the climatology and spatial patterns of climate change does not depend on a detailed characterization of the spatial pattern of diffusivity.

Appendix A

See Appendix Table 1.

Table 1 CMIP5 models used in this study

We follow Siler et al. (2018) in implementing a hydrologic cycle within the MEBM. We specify a Gaussian weighting function, $w\left(x\right)$, to separate the total heat transport into eddy (${F}_{\mathrm{eddy}}\left(x\right)$) and Hadley Cell (${F}_{\mathrm{HC}}\left(x\right)$) components:

$${F}_{\mathrm{eddy}}\left(x\right)=\left[1-w\left(x\right)\right]F\left(x\right)$$

(A1)

$${F}_{\mathrm{HC}}\left(x\right)=w\left(x\right)F\left(x\right)$$

(A2)

We set $w\left(x\right)=\mathrm{exp}[-{\left(x/{\sigma }_{x}\right)}^{2} ]$, where ${\sigma }_{x}=\mathrm{sin}\left(15^\circ \right)\approx 0.26$, so that ${F}_{\mathrm{eddy}}\left(x\right)$ accounts for nearly all energy transport in mid-to-high latitudes, while ${F}_{\mathrm{HC}}\left(x\right)$ accounts for most energy transport in low latitudes within 15°. ${F}_{\mathrm{HC}}\left(x\right)$ is quantified by

$${F}_{\mathrm{HC}}\left(x\right)=\psi \left(x\right)g\left(x\right)$$

(A3)

where $\psi \left(x\right)$ is the Hadley Cell mass transport (with southward transport in the lower branch equal to northward transport in the upper branch,) and $g\left(x\right)$ is the gross moist stability of the atmosphere, defined as the difference between MSE in the upper and lower branches at each latitude. Following Held (2001), we assume that MSE is uniform ( $\equiv {h}_{u}$), throughout the upper branch of the Hadley cell such that variations in $g(x)$ are primarily caused by meridional variations in near-surface MSE: $g\left(x\right)={h}_{u}-h\left(x\right)$, where we set ${h}_{u}=1.07 h(x=0)$, or 7% above the near-surface MSE at the equator, which is a reasonable approximation to the observed profile (Siler et al. 2018). We can get $g\left(x\right)$ from the MEBM output fields, and hence solve for $\psi \left(x\right)$ from (A2) and (A3). Finally, assuming the upper branch of the Hadley Cell is dry, moist heat transport (${F}_{\mathrm{HC},q}$) is confined in the lower branch, implying that

$${F_{{{\rm HC}},q}}\left( x \right) = - \psi \left( x \right)Lq\left( x \right)$$

(A4)

Finally, we derive $E-P$ by taking the divergence of ${{F}_{eddy, q}+F}_{\mathrm{HC},q}$.