The Earth’s atmosphere has a layered structure including the typical layers of the troposphere, stratosphere, mesosphere, thermosphere, and external layer exosphere, which are distinct in temperature. The troposphere, which is the layer of the atmosphere from the surface to the height of 8–9 and up to 15–17 km in the polar and equatorial latitudes, respectively, also has boundary and surface layers [1–4]. The troposphere exhibits a linear temperature drop with height: ~6 K/km, on average [5–7]. On the basis of temperature variations in the annual cycle at different levels of the atmosphere and in different latitudinal zones of the Northern and Southern hemispheres and using the method of amplitude phase characteristics, it was quantitatively substantiated [8, 9] that the thickness of the atmospheric layer, which is heated during the annual cycle from the Earth’s surface, corresponds to the thickness of the troposphere: the height of the tropopause. The latter corresponds to the height of the temperature skin layer in the atmosphere for the annual insolation cycle, whereas the surface layer corresponds to the corresponding skin layer for the annual cycle.

Depending on the latitude and the height, the key features of the annual temperature cycle of the atmosphere revealed in [8, 9] can be described qualitatively by the scanner-model [10] with vertical thermal conductivity in the atmosphere and a horizontally moving (scanning) heat source (see also [3]). The ozone-related heating in the higher atmospheric layers (stratosphere) was also taken into account. The analysis of the simulation results with a detailed model of the general circulation of the atmosphere [11] reproduces the general features of variations in the temperature regime of the atmosphere in the annual cycle revealed in [8, 9] from the observation data. The results of the analysis of the model simulations generally support the idea that the thickness of the troposphere corresponds to the typical height of the temperature skin layer for the present-day length of the annual cycle.

The aim of this work is analysis of the changes in the temperature field of the atmosphere including the variations in the height of the tropopause for a variable length of the annual cycle according to the simulations with the climate model of general circulation.

This analysis is based on a version of the coupled general circulation model (CGCM) of the atmosphere and ocean elaborated at the Obukhov Institute of Atmospheric Physics, Russian Academy of Sciences (IAP RAS). Its first results of the climate dynamics are presented in [12], in particular, the analysis of results of control modeling for a 150-year period. The CGCM in [12] uses blocks of the general atmospheric circulation ECHAM5 [13] and the general oceanic circulation MOM5 [14]. The atmospheric (T31L39) and oceanic (with a resolution of 1.125° × 1.125°) blocks are combined using the OASIS coupling system [15].

This analysis uses the simulations with the IAP RAS CGCM for 30-year periods at the end of the 100-year numerical simulations of the present-day climate and corresponding simulations for half of the length of the annual cycle. The modeling results with this version of the IAP RAS CGCM adequately reproduce the main features of the present-day distributions for the key climate characteristics (including surface air temperature, sea level pressure, etc.), as well as the key features of the El Niño quasi-cyclic processes, which are related to the strongest interannual variability of the global surface air temperature. This model can also reproduce the features of repeatability of phase transitions for the El Niño processes [12]. The modeling results are compared with the reanalysis data.

Figure 1 shows the seasonal latitude-height distribution of temperature in the troposphere and the lower stratosphere in December–February (left) and June–August (right) according to the ERA-Interim reanalysis data for 1979–2018 (upper row) and according to model simulations at the current length of the annual cycle (middle row) and half of this length (lower row). According to Fig. 1, the IAP RAS CGCM adequately describes the seasonal latitude-height features of the temperature field of the troposphere and stratosphere in comparison with reanalysis data including areas of the tropopause and polar latitudes. The height of the corresponding temperature isochrones decreases in all latitudes both in summer and in winter for half of the current length of the annual cycle, which is especially evident for the tropical tropopause.

Figure 2 shows the vertical temperature profiles in the atmosphere of different latitudes in summer according to the simulations with the IAP RAS CGCM at the current length of the annual cycle T1ω and at the half of the current length T2ω. Similar profiles are obtained for other latitudes of the Northern and Southern hemispheres for summer and winter. According to Fig. 2, the height of the tropopause, which has a break in the temperature profile, changes in the model simulations at the current length of the annual cycle from ~15 km near the equator and to ~8 km in the subpolar latitudes. The vertical temperature gradient (lapse rate) in the troposphere also decreases from the equator to the pole. According to the present-day data, the average vertical temperature gradient in the troposphere varies from 6.5 K/km in the tropical latitudes to 4.5 K/km in the polar latitudes [7]. At half of the current length of the annual cycle, the height of the tropopause, as is seen from Fig. 1, decreases to ~11 km near the equator and up to 6–7 km in the subpolar latitudes.

Fig. 1.
figure 1

Seasonal latitude-height distributions of temperature in the troposphere and lower stratosphere in December–February (left) and June–August (right) according to the ERA-Interim reanalysis data for 1979–2018 (upper row) and according to model simulations at the current length of the annual cycle (middle row) and half of the current length (lower row).

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Fig. 2.
figure 2

Vertical temperature profiles in the atmosphere of different latitudes in summer according to simulations at the current length of the annual cycle (365 days) and at the half of the current length (182.5 days).

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Figure 3 shows the winter and summer values of the squares of the height of the tropopause at different latitudes of the Northern and Southern hemispheres according to the simulations with the IAP RAS CGCM at half (than the real length of the annual cycle) T2ω depending on the corresponding squares of the tropopause height \(H_{{1\omega }}^{2}\) at the current period of the annual cycle T1ω. This figure also presents the results of simulations for the equator and subtropical (30°), middle (45° and 50°), and subpolar (60°) latitudes of both hemispheres and both poles (90°). The inclination angle of the line corresponding to the linear regression \(H_{{2\omega }}^{2}\)to \(H_{{1\omega }}^{2}\) is 0.5. This corresponds to a root correlation of the tropopause height and the duration of the annual cycle H ~ T1/2 (or H ~ ω–1/2) similarly to the correlation for the corresponding temperature skin layer.

Fig. 3.
figure 3

Winter and summer values of the squares of the height of the tropopause at different latitudes of the Northern and Southern hemispheres according to simulations at the lower (half) length of the annual cycle depending on corresponding squares of values of the tropopause height at the current length of the annual cycle and the result of the corresponding linear regression (straight line). Dotted lines mark the boundaries of the confidence (at 0.95 level) interval.

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Thus, our results of simulations with the IAP RAS CGCM confirm the previous conclusion [8, 9], which is based on analysis of the climate data using a special method of amplitude phase characteristics, that the thickness of the troposphere (the height of the tropopause) corresponds to the height of the temperature skin layer for the atmosphere, which is heated from the surface due to periodic radiation forcing: the annual insolation cycle and absorption of shortwave solar radiation. This indicates the important corresponding mechanism of the formation of the tropopause taking into account stratospheric heating related with the absorption of solar radiation by the ozone layer.