## 3 Results
### Qualitative Analysis
Estimating the total sensitivity coefficient \((1/L_{R})(dL_{R}/dT)\) using Equation (20) is not a trivial task since this requires a priori knowledge of interdependence between the temperature increase and the lapse rate change. It should be added that to take into consideration the effects of atmospheric moisture on sensitivity coefficients (21) and (23), instead of dry adiabatic lapse rate \(\Gamma_{d}\) we would have to use the \"effective\" lapse rate defined by \(\Gamma_{e}=\Gamma_{d}-(\Gamma_{d}-\Gamma_{m})\delta_{cloud}\), where \(\Gamma_{m}\) is the moist adiabatic lapse rate and \(\delta_{cloud}\) is a cloud fraction. However, the sensitivity coefficient (21) can be estimated by using observations and/or results of climate modeling. For example, for mid-latitudes, the estimates of the total and partial sensitivity coefficients (21)-(23) were obtained in [84] from NCEP/NCAR reanalysis data and from climate modeling. The estimate of \((1/L_{R})(dL_{R}/dT)\) is about \(-0.0016\) (\(\pm 0.0096\)) K\({}^{-1}\) from the reanalysis data, and \(-0.0013\) K\({}^{-1}\) and \(-0.021\) K\({}^{-1}\) from the results of simulations for dry and moist atmosphere respectively. The estimate of partial sensitivity coefficient \((1/L_{R})(\partial L_{R}/\partial T)\) is about 0.009 (\(\pm 0.007\)) K\({}^{-1}\) from the reanalysis data and 0.002 K\({}^{-1}\) from the modeling results. In turn, the estimate of partial sensitivity coefficient \((1/L_{R})(\partial L_{R}/\partial T)\) is \(-0.309\) (\(\pm 0.062\)) km K\({}^{-1}\) from the reanalysis data, and \(-0.132\) kmK\({}^{-1}\) and \(-0.270\) kmK\({}^{-1}\) from the outcomes of simulations for dry and moist atmosphere respectively. Thus, the atmospheric vertical stratification (the lapse rate \(\Gamma\)), which changes with global warming, and atmospheric moisture can affect the horizontal length of baroclinic extratropical transient eddies, leading in aggregate to a decrease in \(L_{R}\). However, this decrease is insignificant. For example, results of numerical modeling show that the climate change leads only to the 2% decrease in characteristic length of large-scale eddies [84; 85]. We should note that it is not possible to compare sensitivity functions \((1/L_{R})(\partial L_{R}/\partial T)\) and \((1/L_{R})(\partial L_{R}/\partial T)\) as they are sensitivities with respect to different quantities and thus have different dimensions and equivalence classes. For reference purpose, we also consider the influence of global warming on cyclones' frequency of occurrence using the sensitivity coefficient \((1/n)(dn/dT)\), where \(n\) is the annual mean number of extratropical cyclones in the northern (or southern) hemisphere [86]:  
\[\frac{1}{n}\frac{dn}{dT}\cong-\frac{3}{2T}+\frac{1}{\Delta T_{p}^{e}}\frac{d \Delta T_{p}^{e}}{dT}-\frac{1}{2(\Gamma_{e}-\Gamma)}\frac{d(\Gamma_{e}- \Gamma)}{dT} \tag{26}\]  
where \(\Delta T_{p}^{e}\) is the surface temperature differences between the pole and the equator. First, we consider the partial sensitivity coefficients which reflect the sensitivity of \(n\) with respect to \(T\), \(\Delta T_{p}^{e}\) and \(\Gamma\):  
\[\frac{1}{n}\frac{\partial n}{\partial T}\cong-\frac{3}{2T} \tag{27}\]  
\[\frac{1}{n}\frac{\partial n}{\partial\Delta T_{p}^{e}}\cong\frac{1}{\Delta T _{p}^{e}} \tag{28}\]  
\[\frac{1}{n}\frac{\partial n}{\partial\Gamma}\cong\frac{1}{2(\Gamma_{e}- \Gamma)} \tag{29}\]  
Substituting the characteristic values for variables (\(T=288\) K, \(\Delta T_{p}^{e}=45\)\({}^{\circ}\)C; and \(\Gamma=6.5\) K / km) into Equations (27)-(29) results in \((1/n)(\partial n/\partial T)\approx-0.0052\) K\({}^{-1}\), \((1/n)\big{(}\partial n/\partial\Delta T_{p}^{e}\big{)}\approx-0.022\) K\({}^{-1}\); while for \((1/n)(\partial n/\partial\Gamma)\approx-0.152\) kmK\({}^{-1}\).