Land-sea warming contrast: the role of the horizontal energy transport

Abstract

In this study we investigate the role of the mechanisms at play in the magnitude of the land-sea warming contrast and its intermodel spread in the fifth coupled models intercomparison project (CMIP5) simulations. In this aim, an energy-balance model (EBM), with one box representing the land area and two other boxes the near-surface and the deep ocean, is developed. In particular, a simple parameterization of the horizontal energy transport (HET) change between these two regions is proposed. The EBM is shown to capture the variation of the land and the ocean temperature responses and of the land-sea warming ratio in different idealized climate change experiments. By using this framework, we first show that the land-sea warming contrast is explained by the asymmetry in the strength of the HET between the land and ocean and not by land-sea differences in radiative feedbacks. Then we use a method of analysis of variance to infer the contributors to the intermodel spread in the land-sea warming ratio of climate models participating to CMIP5. The main contributor is found to be the HET with a contribution of about 70 %. Finally, our results suggest that the asymmetric character of the HET dependency to the land and the ocean temperature responses may be primarily explained by the land-sea differences in surface specific humidity change for a given temperature change.

Appendix

1.1 Non-linear LO-EBM

As in Held et al. (2010) and Geoffroy et al. (2013b), two additional climate response parameters, $\lambda _{o}^{d}$ and $\lambda _{l}^{d}$ (which can be related to that associated with the ${\mathrm {CO}}_{2}$ forcing with an efficacy factor), and two HET parameters, $\alpha _o^{d}$ and $\alpha _l^{d}$, are introduced to take into account the non-linear evolutions:

$$\begin{aligned} 0 \,= \, & {} {\mathcal {F}}_l -\lambda _l \left( \varDelta T_{l}-\varDelta T_{l}^{d}\right) + \frac{\alpha _{o}}{f_l} \left( \varDelta T_{o}-\varDelta T_{o}^{d}\right) -\frac{\alpha _{l}}{f_l} \left( \varDelta T_{l}-\varDelta T_{l}^{d}\right) \end{aligned}$$

(24)

$$\begin{aligned} 0= & {} -\lambda _{l}^{d} \varDelta T_{l}^{d}+ \frac{\alpha _{o}^{d}}{f_l} \varDelta T_{o}^{d} -\frac{\alpha _{l}^{d}}{f_l} \varDelta T_{l}^{d},\end{aligned}$$

(25)

$$\begin{aligned} C_o \frac{d \varDelta T_{o}}{dt} \,= \, & {} {\mathcal {F}}_o - \lambda _o \left( \varDelta T_{o}-\varDelta T_{o}^{d}\right) - \frac{\alpha _{o}}{1-f_l} \left( \varDelta T_{o}-\varDelta T_{o}^{d}\right) +\frac{\alpha _{l}}{1-f_l} \left( \varDelta T_{l}-\varDelta T_{l}^{d}\right) \end{aligned}$$

(26)

$$\begin{aligned} 0= & {} - \lambda _o^{d} \varDelta T_{o}^{d}- \frac{\alpha _{o}^{d}}{1-f_l} \varDelta T_{o}^{d} +\frac{\alpha _{l}^{d}}{1-f_l} \varDelta T_{l}^{d}- \gamma \left( \varDelta T_{o} - \varDelta T_{do}\right) . \end{aligned}$$

(27)

where $\varDelta T_{o}^{d}$ and $\varDelta T_{l}^{d}$ are the mean surface air temperature responses associated with the deep-ocean heat-uptake, over the ocean and over the land, respectively.

By adding Eqs. 24 and 25 and using Eqs. 27 and 28, the system of equations for $\varDelta T_o$ reads:

$$\begin{aligned} C_o \frac{d \varDelta T_{o}}{dt}=\, & {} {\mathcal {F}}_o^{*} - \lambda _o^{*} \varDelta T_o - \gamma _o^{*} (\varDelta T_o - \varDelta T_{do}),\end{aligned}$$

(28)

$$\begin{aligned} C_{do}^{*} \frac{d \varDelta T_{do}}{dt}=\, & {} \gamma _o^{*} (\varDelta T_o - \varDelta T_{do}) \end{aligned}$$

(29)

with:

$$\begin{aligned} {\mathcal {F}}_o^{*}=\, & {} {\mathcal {F}}_o+\frac{\alpha _l}{1-f_l} \varDelta T_l^{adj}\end{aligned}$$

(30)

$$\begin{aligned} \lambda _o^{*}=\, & {} \lambda _o +\frac{\alpha _o}{1-f_l} - \frac{\alpha _l}{1-f_l}\frac{\alpha _o/f_l}{\lambda _l+\alpha _l/f_l}\end{aligned}$$

(31)

$$\begin{aligned} \lambda _o^{d*}=\, & {} \lambda _o^{d} +\frac{\alpha _o^{d}}{1-f_l} - \frac{\alpha _l^{d}}{1-f_l}\frac{\alpha _o^{d}/f_l}{\lambda _l^{d}+\alpha _l/f_l}\end{aligned}$$

(32)

$$\begin{aligned} \gamma _o^{*}=\, & {} \gamma _o \frac{\lambda _o^{*}}{\lambda _o^{d*}}\end{aligned}$$

(33)

$$\begin{aligned} C_{do}^{*}=\, & {} C_{do} \frac{\lambda _o^{*}}{\lambda _o^{d*}} \end{aligned}$$

(34)

The analytical solution of this system for an abrupt and a linear forcing is given in Geoffroy et al. (2013a, b).

From Eqs. 24 and 25, the land surface air temperature response $\varDelta T_l$ reads:

$$\begin{aligned} \varDelta T_{l} = \varDelta T_{l}^{adj} + \frac{\alpha _o / f_l}{\lambda _l + \alpha _l/f_l}(\varDelta T_{o}-\varDelta T_{o}^{d}) + \frac{\alpha _o^{d} / f_l}{\lambda _l^{d} + \alpha _l^{d}/f_l}\varDelta T_{o}^{d}, \end{aligned}$$

(35)

The formula of $\varDelta T_{l}^{adj}$ is unchanged (but the values of the parameters are different) and the formula of $\phi$ has an additional term.

The calibration of the parameters is performed iteratively by using the linear LO-EBM as initial values. Then, the following iterations are performed in three steps:

• 1. The radiative parameters ${\mathcal {F}}_l, \lambda _l, \lambda _l^{d},{\mathcal {F}}_o, \lambda _o, \lambda _o^{d}$ are computed from a multilinear regression of $\varDelta N_i$ against $\varDelta T_i$ (value of the climate model) and $\varDelta T_{i}^{d}$ (analytical solution) for the land and the ocean region ($i=l$ and $i=o$, respectively).

• 2. The thermal inertia parameters $C_o$, $C_{do}$ and $\gamma _o$ are calculated from two fits of $\varDelta T_o$ against time as in Geoffroy et al. (2013a) and Geoffroy et al. (2013b).

• 3. The HET parameters are computed by multilinear regression of $\varDelta T_l$ against $(\varDelta T_{o}-\varDelta T_{o}^{d})$ and $\varDelta T_o^{d}$. Equation 35 can be written as the following:

  $$\begin{aligned} \varDelta T_l= \varDelta T_l^{adj} + k_{eq} (\varDelta T_{o}-\varDelta T_{o}^{d}) + k_d (\varDelta T_{o}^{d}). \end{aligned}$$

  (36)

  Hence, the intercept of the multilinear regression gives $\alpha _l$ (Eq. 12) then $k_{eq}$ gives $\alpha _o$ (Eq. 35) and $\alpha _l^{d}$ and $\alpha _o^{d}$ are computed from $k_d$ by assuming $\alpha _l/\alpha _o=\alpha _l^{d}/\alpha _o^{d}$.