## 3 Results
### Influence of Climate Change on the Growth Rate of Unstable Waves
#### 3.2.3 Estimating Climate Change Impact on Eddy Meridional Moisture Transport  
The Effect of Static Stability on Eddy Meridional Moisture Transport  
In order to estimate the effect of static stability on eddy meridional moisture transport, we need to define a climate change scenario that includes estimates of both surface and upper tropospheric temperature changes. Surface temperature change is a well-studied phenomenon and thus we will use the estimate provided in the WMO report [2], according to which the average surface temperature has increased by roughly 1 \({}^{\circ}\)C over the last century. Temperature change in upper troposphere is significantly more uncertain given the fact that various measurement techniques (e.g., radiosondes, satellites) produce inconsistent results. For the purposes of this study, we will make use of an estimate provided in [60], which found that the increase in upper tropospheric temperature outpaces the increase in surface temperature by about 2 \({}^{\circ}\)C in mid-latitudes. In this scenario, the temperature lapse rate \(\Gamma=-dT/dz\) has decreased from the initial (base) value of 6.5 \({}^{\circ}\)C/km to 6.3 \({}^{\circ}\)C/km. This change leads to the following dynamical effects: the temperature in the middle troposphere increases by about 1.8 \({}^{\circ}\)C, the dry static stability parameter also increases slightly (by about 0.7%). However, the effective static stability parameter \(\Gamma_{eff}\) actually demonstrates the opposite behavior: \(\Gamma_{eff}\) decreases by more than 5.4%. Thus, dry and moist models provide completely distinct results both quantitatively and qualitatively. The growth rate \(kc_{i}\) of the most unstable mode obtained using the dry \(f\)-plane model decreases slightly, by about \(0.2\times 10^{-2}\) day\({}^{-1}\), which is 0.36% of the base value shown in Table 1. On the other hand, the moist \(f\)-plane model shows an increase in the growth rate \(kc_{i}\) of \(\sim 2.2\times 10^{-2}\) day\({}^{-1}\), which is \(\sim\)2.8% of the base value (see Table 1). In dry \(\beta\)-plane model, the growth rate of the most unstable wave decreases by about \(0.3\times 10^{-2}\) day\({}^{-1}\), which is 0.7% of the base value shown in Table 1, while in the moist version of this model the growth rate increases by more than \(2.4\times 10^{-2}\) day\({}^{-1}\), which is \(\sim\)3.6% of the base value. Changes in the growth rates of unstable waves cause changes in AMEMF. This effect can be estimated from the Equation (9). For the dry \(f\)-plane and \(\beta\)-plane models, the decrease in AMEMF is insignificant, only about 0.5% for both models, while in the moist \(f\)-plane and \(\beta\)-plane models there is an increase in AMEMF by about 4.5% and more than 5%, respectively. Hence the results obtained with \(f\)-plane and \(\beta\)-plane models are quite similar. The Effect of Meridional Temperature Gradient on Eddy Meridional Moisture Transport  
Let us now consider the effect of changes due to the global warming in the second control parameter, MTG, on the growth rate of unstable baroclinic waves and, consequently, on the AMEMF. The thermal wind equation relates MTG to the vertical wind shear, which in \(f\)-plane and \(\beta\)-plane models is characterized by parameters \(\Lambda\) and \(u_{T}\), respectively. In general, the larger the equator-to-pole temperature difference, the stronger the resulting wind shear will be. If we know the MTG variation caused by climate change, then we can find the corresponding changes in the parameters \(\Lambda\) and \(u_{T}\) by solving the thermal wind equation. In the next step, after the variations \(\delta\Lambda\) and \(\delta u_{T}\) have been calculated, we can analytically estimate their influence and, therefore, the effect of MTG variations on the change in the growth rates of unstable modes by using Equations (14) and (17) and taking into account the known values of sensitivity functions \(S_{\Lambda}\) and \(S_{u_{T}}\) (see Table 2).