Sensitivity of subtropical stationary circulations to global warming in climate models: a baroclinic Rossby gyre theory

Abstract

Time-mean, zonally asymmetric circulations maintain an intense hydrologic contrast between monsoon regions and subtropical drylands in Earth’s present climate. Climate model simulations suggest that this hydrologic contrast will increase in twenty-first-century global warming scenarios, but the response of the zonally asymmetric circulations to global mean temperature is poorly understood. Here we adapt a simple theory for the strength of time-mean, subtropical, zonally asymmetric circulations (hereafter called stationary circulations) and demonstrate its relevance to summer stationary circulation changes in the Northern Hemisphere in an ensemble of comprehensive climate model simulations of global warming. The theory, which is based on the dynamics of a subtropical Rossby gyre that is in Sverdrup balance and has the vertical structure of a first-baroclinic mode, shows that the weakening of stationary ascent with global warming in the multi-model mean can be represented as a compensation between two processes: a lifting of the tropical tropopause and a decrease of the tropospheric zonal temperature gradient, which respectively require strengthening and weakening of vertical mass flux in the Rossby gyre. A large fraction of the intermodel variance in global warming-induced changes in stationary ascent is associated with intermodel variance in zonal tropospheric temperature gradient changes, which we in turn attribute to intermodel variance in zonal sea surface temperature gradient changes. These results show that much of the sensitivity of subtropical hydrologic contrasts to global mean temperature can be understood in terms of a linear vorticity balance and properties of moist adiabats.

Appendix: Temperature mode definition

In this section, we provide an expression of the temperature mode in (7), which is used to define the vertical wind mode in (10). Its profile is central to our understanding of stationary ascent variability with climate change.

In Levine and Boos (2016) the temperature mode was defined as the sensitivity of tropospheric temperature to a temperature anomaly at the lifting condensation level (LCL). Here, we define the temperature mode as the magnitude of temperature anomalies associated with a unit temperature anomaly at any level above the LCL, i,e.

$$A_1(p)= \frac{1 + \gamma (p_r) + \beta (p_r)}{1 + \gamma (p) + \beta (p)} \quad {\mathrm{for}} \quad p_t \le p \le p_b,$$

(14)

$$A_1(p)= \left( \frac{p}{p_b} \right) ^{\kappa } \frac{1 + \gamma (p_r) + \beta (p_r)}{1 + \gamma (p_b) + \beta (p_b)} \quad {\mathrm{for}} \quad p_b \le p \le p_s,$$

(15)

with,

$$\gamma = \partial _T q_0^{sat},$$

(16)

$$\beta = \partial _T z_0.$$

(17)

Here $(.)_b$ denotes the LCL pressure, $(.)_r$ denotes the reference level, and $\partial _T$ is a partial derivative with respect to temperature. This general definition of the temperature mode is identical to that derived in Levine and Boos (2016) when the reference level is the LCL. In this study, we define the LCL as the 925 hPa isobar, and the reference level is the 400 hPa isobar. The temperature mode (15) is substituted in the definition of horizontal and vertical wind modes, i.e.

$$\begin{aligned} \varOmega _1 = \frac{1}{p_s} \int _{p_s}^{p} V_1 \, {\mathrm{d}}p, \end{aligned}$$

(18)

where $V_1$ is the horizontal wind mode,

$$\begin{aligned} V_1 = A_1^{+} - \frac{1}{p_t - p_s} \int _{p_s}^{p_t} A_1^{+} \, {\mathrm{d}}p, \end{aligned}$$

(19)

and $A_1^{+}$ is a wind basis derived from the momentum budget,

$$\begin{aligned} A_1^{+} = \int _{p_s}^{p} \frac{A_1}{p} \, {\mathrm{d}}p. \end{aligned}$$

(20)

A detailed derivation of the first-baroclinic wind modes can be found in Levine and Boos (2016), and this derivation is based on the earlier work on first-baroclinic mode dynamics (Yu et al. 1998; Neelin and Zeng 2000). The vertical wind mode in the ensemble-mean of the CMIP5 simulations and in the ERA-40 reanalysis are shown in Fig. 6a.