## 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
However, we first need to determine the variation in MTG caused by the climate change. It has previously been shown that in polar areas changes in surface air temperature \(T_{sfc}\) caused by a change in the planetary energy balance are greater than changes in \(T_{sfc}\) in the mid-latitude and equatorial areas. Known as polar amplification, this climatic phenomenon is more profound in the northern hemisphere than in the southern hemisphere [88; 89]. The earth's energy imbalance can be caused by various natural and human factors and, in particular, by changes in the concentrations of anthropogenic greenhouse gases in the atmosphere [90; 91]. As a specific example, we consider the northern hemisphere. Because of Arctic amplification, the surface air temperature at high latitudes of the northern hemisphere increased at about twice the rate of global mean surface temperature since the middle of the 20 th century [92]. Arctic amplification is tracednear the surface and in the lower troposphere, weakening MTG and, thus, reducing the vertical wind shear and contributing to the weakening of the westerly mid-latitude jet stream. In the upper and middle troposphere, however, climate change enhances MTG, thereby increasing the vertical wind shear and contributing to strengthening the zonal flow [93; 94; 95; 96]. Exploration of historic trends in the upper-tropospheric vertical wind shear in the North Atlantic region based on three independently created reanalysis datasets has shown that in the area of interest the vertical wind shear has increased by about 15% over the last few decades [94]. As noted in [94], a stronger MTG and a correspondingly stronger vertical wind shear in the upper troposphere are masked by a weaker MTG and a correspondingly weaker vertical wind shear in the lower troposphere. Climate modeling results show that changes in the upper-tropospheric MTG play a primary role in the formation of large-scale atmospheric dynamics at mid-latitudes, affecting the intensity of vertical wind shear and zonal flow, while changes in the lower tropospheric MTG play a secondary role [97; 98]. The annual-mean equator-to-pole temperature difference over the troposphere is about 40 \({}^{\circ}\)C, so the average tropospheric MTG is about 4 \({}^{\circ}\)C per 1000 km [99]. However, MTG varies with latitude. The strongest MTG is concentrated in the middle latitudes, contributing to the formation of the so-called upper tropospheric frontal zone and the associated zonal flow, the speed of which increases with height [20; 99]. In this study, we have assumed that the vertical wind shear parameter \(\Lambda\) used in \(f\)-plane model is 30 ms\({}^{-1}\) bar\({}^{-1}\)[21; 42]. Accordingly, the parameter \(u_{T}\) that characterises the vertical wind shear in \(\beta\)-plane model is 7.5 ms\({}^{-1}\). This vertical wind shear is associated with an upper-tropospheric frontal zone which in our case extends over the entire thickness of the troposphere and has an MTG of \(\sim\) 7.54 \({}^{\circ}\)C per 1000 km. Note that in well-developed upper-tropospheric frontal zones, the temperature contrast can reach 11-12 \({}^{\circ}\)C per 1000 km in mid-latitudes. Based on preceding discussion, when determining the MTG value, we assume that climate change weakens the annual MTG in the lower troposphere through more significant heating of higher latitudes, whereas in the upper troposphere MTG increases because of a strong upper-tropospheric warming of lower latitudes. For a climate change scenario discussed in this paper, the response of the mass-weighted vertically averaged annual mean MTG to increase in the surface temperature by 1 \({}^{\circ}\)C is about \(-\)0.2 \({}^{\circ}\)C per 1000 km, which is \(\sim\)2.7% of the base value. Accordingly, this change in MTG generates the following variations in the parameters \(\Lambda\) and \(u_{T}\) that characterize the vertical wind shear: \(\delta\Lambda=+\) 0.8 ms\({}^{-1}\) bar\({}^{-1}\) and \(\delta u_{T}=+\) 0.2 ms\({}^{-1}\).