Quantifying Polar Mesospheric Clouds Thermal Impact on Mesopause

Abstract

The article is focused on the quantitative assessment of the thermal impact of polar mesospheric clouds (PMCs) on the mesopause caused by the emission of absorbed solar and terrestrial infrared (IR) radiation by cloud particles. For this purpose, a parameterization of mesopause heating by PMC crystals has been developed, the main feature of which is to incorporate the thermal properties of ice and the interaction of cloud particles with the environment. Parametrization is based on PMCs zero-dimensional (0-D) model and uses temperature, pressure, and water vapor data in the 80–90 km altitude range retrieved from Solar Occultation for Ice Experiment (SOFIE) measurements. The calculations are made for 14 PMC seasons in both hemispheres with the summer solstice as the central date. The obtained results show that PMCs can make a significant contribution to the heat balance of the upper atmosphere, comparable to the heating caused, for example, by the dissipation of atmospheric gravity waves (GWs). The interhemispheric differences in heating are manifested mainly in the altitude structure: in the Southern Hemisphere (SH), the area of maximum heating values is 1–2 km higher than in the Northern Hemisphere (NH), while quantitatively they are of the same order. The most intensive heating is observed at the lower boundary of the minimum temperature layer (below 150 K) and gradually weakens with altitude. The NH heating median value is 5.86 K/day, while in the SH it is 5.24 K/day. The lowest values of heating are located above the maximum of cloud ice concentration in both hemispheres. The calculated heating rates are also examined in the context of the various factors of temperature variation in the observed atmospheric layers. It is shown in particular that the thermal impact of PMC is commensurate with the influence of dissipating gravity waves at heights of the mesosphere and lower thermosphere (MLT), which parameterizations are included in all modern numerical models of atmospheric circulation. Hence, the developed parameterization can be used in global atmospheric circulation models for further study of the peculiarities of the thermodynamic regime of the MLT.

1. Introduction

The MLT (60–110 km) dynamics are affected by a complex combination of meridional advection and wave processes of different scales (e.g., [1]). The modulation of planetary waves (PWs) by thermal tides occurs in the MLT, providing an opportunity for penetration of the first ones into the thermosphere [2]. Here, the orographic gravity waves [3] and most of the spectrum of internal gravity waves (IGWs) are finally dissipated [4]. Among other things, the MLT has a unique feature during the summer season: in the polar mesopause, the air temperature drops to the lowest values (below 150 K). One of the important sources of objective information on the dynamic processes in the upper atmosphere are the PMCs formed in the 80–85 km layer during summer at the mentioned temperatures and relatively low concentrations of water vapor (3–6 ppmv). PMCs exist from May to August in the NH and from November to February in the SH. Observation of cloud fields allows studying atmospheric perturbations of different spatial and temporal scales: both GWs [5], PWs (e.g., [6]), and atmospheric tides.

Residual meridional circulation features [7], leading to MLTs adiabatic cooling [8] and meteoric smoke (Fe, Mg, etc.), serving as condensation nuclei, presented in the upper atmosphere lead to heterogeneous formation of 20–80 nm ice particles. The PMC fields usually cover almost the entire polar cap and are observed from the Earth, as a rule, at high latitudes (65–70°). Information on the microphysical characteristics of clouds has been repeatedly confirmed by satellite measurements (e.g., [9,10]). The so-called noctilucent clouds (NLCs) and PMC differ somewhat in their optical characteristics and the way they are observed. Registered from the ground, NLCs exist from July to August in the NH in the latitudinal band of 60–80° N and are visible against the background of the twilight sky, illuminated by the light of the setting/rising sun. PMCs are traditionally observed in the entire polar region during the summer season from space by various spacecraft in a wide range of the solar radiation spectrum.

When discussing the PMC/NLC, their connection with the 11-year solar cycle, in particular with the solar flux at a wavelength of 10.7 cm (F10.7), is usually considered. Romejko et al. [11] analyzed various NLC characteristics obtained from ground-based observations over a 40-year period (1962–2001). Based on the results of statistical analysis, the authors stated that the period of variation of the NLC brightness is 1–1.5 years shorter than the 11-year variation of the F10.7 flux. At the same time, they emphasize fluctuations with a period of 2–5 years, which may be due to interactions between atmospheric layers and interhemispheric inhomogeneities. In addition, PMC observations from space also allow us to analyze the long-term variability of their characteristics. UV radiation with wavelengths of 250–300 nm, fully absorbed by O₃ molecules in the stratosphere, is backscattered in the presence of PMC from the cloud layer and can be detected by a spacecraft sensor and converted into a hydrodynamic characteristic. Using such a technique, DeLand and Thomas [12] derived and analyzed ice water content (IWC) time series from 1979 to 2013 from limb measurements by the Solar Backscattered Ultraviolet (SBUV) sensors. Until the end of the last century (1979–1997), the IWC value in bright clouds slowly increased but has remained almost constant since 1998 [12]. The response of solar activity over its 24th cycle in the PMC signal of the NH is much weaker than in previous cycles. However, in the SH, clouds are more strongly affected by variations in the solar radiation fluxes. Similar results were also obtained using SBUV data and numerical modeling [13]: the observed changes in PMC parameters are accompanied by a cooling of the mesopause (−0.5 ± 0.2 K/decade at 77° N) and an increase in water vapor concentration (0.07 ± 0.03 ppmv/decade).

The variations in GW energy density, IWC, particle radius, and cloud albedo were also investigated [14]. It was shown that GWs activity affects the formation of PMCs. In the NH, the increase in GW is associated with an increase in IWC and occurs about 0–23 days before the summer solstice. In the SH, the peak of GW activity occurs about 55 days after the solstice, and the increase in IWC begins about 20 days before the solstice. These results demonstrate a close connection between the dynamics of GWs and PMC formation in both hemispheres.

Further study of the PMCs impact on the environment is important for understanding the circulation features and chemistry of the upper atmosphere. Despite already known patterns, new details about the properties of the summer mesopause of both hemispheres are constantly being discovered by various authors. For example, Siskind et al. [15] described the relationship of mesopause dehydration, driven by water vapor sublimation, with the depletion of atomic hydrogen (H) at 95 km at mid and high latitudes. The authors suggest that PMC may play a key role in the transport of H to the upper atmosphere. Also, they found that the same sublimation of water vapor leads to an increase in mesospheric O₃ above the cloud layer, as far as O₃ anti-correlates with H₂O [16]. The ongoing global warming caused by anthropogenic emissions of greenhouse gases (H₂O, CH₄, and CO₂) into the troposphere also affects the upper atmosphere. According to numerical projections, the temperature in the MLT will gradually decrease until the end of the 21st century [17]. An increase in stratospheric and mesospheric water vapor concentrations accompanied by a positive trend [18] will lead to changes in PMC characteristics such as their extent [19]. In addition, PMC occurrence is predicted to increase at midlatitudes (55–60°). Lower temperatures cause downwelling of cloud crystals, which affects the decreasing of the PMC layer [20]. PMCs are capable of making a significant contribution to the thermodynamic regime of the MLT area, for example, both through the release of latent heat during water vapor sublimation and through the absorption of IR radiation.

The purpose of this article is to quantify the thermal impact of PMCs on the environment caused by the re-emission by cloud particles of the absorbed fluxes of incoming and outgoing IR radiation. To achieve the mentioned goal, a parameterization of the mesopause heating by PMC crystals due to the aforementioned absorption, described in Section 2.1, was developed. The calculations, as described in Section 2.2, are performed using background temperature, pressure, and water vapor data from SOFIE measurements for 7 cloud seasons in the NH and 7 in the SH. Section 3 and Section 4 are dedicated to a discussion of the results and relations with other possible sources of MLT heating. Final remarks and conclusions are presented in Section 5.

2. Methodology

2.1. Parameterization of PMC Thermal Impact

To calculate the thermal impact of PMC, we use a numerical scheme (parameterization) based on the PMC 0-D model developed by Hervig et al. [21], whose input information is the vertical profiles of temperature (T), water vapor (Q_V), and pressure (p). PMCs are modeled using T and Q_V, in the first instance assuming that ice exists in local thermodynamic equilibrium (LTE). To determine the atmospheric regions where PMC can exist, the condition is used that for H₂O sublimation into ice, the partial pressure of water vapor must exceed the saturation pressure over ice at a given temperature [16]. The critical temperature, also called the “frost point” (T_s), depends on p and Q_V at a given altitude [22]:

T_s = 6077.4/(25.548 − lnQ_V − lnp).

(1)

If there are regions at mesopause heights where the atmospheric temperature is below the frost point temperature (T < T_s), it is assumed that PMCs are formed under such conditions. The volume mixing ratio of the supersaturated water vapor (Q_s) is related to the volume mixing ratio of the sublimated vapor (Q_ice) by the following equation:

Q_ice = Q_s − Q_V,

(2)

where Q_s depends on saturation pressure—p_s. In supercooled water, p_s can be approximated by an exponential law as a function of T [23]:

p_s = exp(9.550426 − 5723.265/T + 3.53968 lnT − 0.00728332 T)

(3)

where p_s is in Pa. Then Q_s = p_s/p.

After sublimation of water vapor, PMC crystals begin to exchange heat with the environment. Based on the ice’s thermal properties, the equation of the radiation budget of a cloud particle can be written in the following form (e.g., [24,25]):

P_terr + P_sol − P_rad − P_col = 0,

(4)

where the last two terms are responsible for the heat sinks due to emission of the particle’s radiation (P_rad) and collisions with other molecules (P_col). At the same time, PMC crystals also absorb radiation at some parts of the spectrum: short-wave infrared (SWIR) solar radiation (P_sol; ~3 μm) and outgoing long-wave (thermal) infrared radiation (P_terr; 10–14 μm). The P_terr term depends mainly on the type of emitting surface and, consequently, its temperature.

Table 1. Intensity of P_terr fluxes from different emitting surfaces.

Surface Type	Temperature (K)	Pterr (W/cm3)
Cloud top	220	17
Ocean surface	263	41
Soil	283	56

[26] lists the different types of surfaces, their average temperatures, and emission rates.

Despite the fact that variations in the albedo of the radiating surface can vary significantly in time and space, the thermal radiation flux can be simplified and assumed to be P_terr = 24 W/cm³ [26]. The SWIR flux, in turn, experiences insignificant diurnal variations at high latitudes of the summer MLT region (due to the polar day and, consequently, close to uniform distribution of incoming radiation). This allows us to consider it constant: P_sol = 16 W/cm³. Thus, the heating of the environment by cloud particles due to absorption of IR radiation and its re-emission will depend only on the concentration of ice crystals:

ε_PMC = dT/dt = 0.68 P_tot Q_ice,

(5)

where ε_PMC is in K/s, α = 0.68 cm³/(J/K), and Q_ice is in ppmv. In Equation (5), P_tot = P_terr + P_sol. The formula is proposed by Siskind et al. [26] and is an adaptation of the results obtained by Espy and Jutt [25]. This form of the equation of thermal impact on the environment takes place in the approach that all sublimated H₂O absorbs incoming radiation in the corresponding parts of the spectrum, and the flux of latent heat during sublimation is not considered.

2.2. Solar Occultation Data

Spatiotemporal distributions of T, Q_V, and p in the mesopause, used in parameterization (see Section 2.1), are taken from the measurements of the Solar Occultation for Ice Experiment (SOFIE; [27]) onboard the sun-synchronous satellite of the Aeronomy of Ice in the Mesosphere (AIM; [28]), which started to operate in 2007, on April 25. The sensor measures solar radiation flux, attenuated by passing through the atmospheric limb, both at the rising and setting of the star above the horizon relative to the satellite position. Based on the collected information, vertical profiles of T, p, and five gas components (H₂O, O₃, CH₄, NO, and CO₂) are retrieved, such as aerosol extinction coefficients at several wavelengths. SOFIE has 8 channels, each tuned to a pair of spectral bands, and covers a wide wavelength range from 0.3 to 5 µm. The sensor performs 15 sunrise and 15 sunset scans per day in the latitude band 65–85° in both hemispheres (except for 2016–2018, when AIM orbit changes were performed and measurements did not extend beyond midlatitudes; see Figure 1). Each vertical profile covers an altitude range of 20–95 km and has a 0.2 km vertical resolution.

The main measured parameter serving as a basis for reconstructing the geophysical characteristics of the atmosphere is the atmospheric transmittance, which is the ratio between the intensity of radiation that has passed through the atmosphere (V) and external (outside the atmosphere) radiation (V₀): V/V₀. The main advantage of the sensor is the ability to retrieve PMC characteristics (ice crystal radius, ice mass density, mesopause height, etc.) from the measured spectra. The sensor was operational throughout the entire AIM lifetime from 2007 to 2023, except when the satellite′s solar array failure occurred. After 2021, measurements on Sunrise were terminated. In 2023, AIM′s battery completely failed, and contact with the satellite was lost. In August 2024, after drifting in near-Earth space and constantly losing altitude, the satellite entered the dense layers of the Earth′s atmosphere. The SOFIE Level 2 version v1.3 data used in this study is freely available at http://sofie.gats-inc.com. SOFIE measurements for 7 summer seasons in the NH (2007–2013) and 7 seasons in the SH (2007/2008–2013/2014) were analyzed. The use of other satellite sensors imposes significant limitations within the context of our research for several reasons: (1) the need for high vertical resolution to study the altitudinal structure of the observed process; (2) the availability of continuous measurements throughout the PMC season. For example, the Microwave Limb Sounder (MLS) on board the Aura satellite has only 3 vertical levels in the 80–90 km layer: 0.01, 0.005, and 0.002 hPa [29], making it unsuitable for studying the vertical distribution of parameterized heating. The Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) [30] on the Envisat (Environmental Satellite) and the Submillimeter Radiometer (SMR) onboard the Odin satellite [31] have limited spatiotemporal data sampling in the polar region where PMCs are formed. The Atmospheric Chemistry Experiment Fourier Transform Spectrometer (ACE-FTS) on Canadian SciSat-1 (Scientific Satellite) scans the atmosphere at latitudes > 60° in both hemispheres for short periods of time every few months [32], as does the Sounding of the Atmosphere Using Broadband Emission Radiometry (SABER) [33]. Therefore, it is appropriate to use such a sensor that provides high vertical resolution of the retrieved atmospheric parameters as well as a continuous series of measurements at high latitudes during the PMC season.

3. Results

3.1. Parameterization Sensitivity to Temperature and Water Vapor

To understand the effect of external factors on heating variability, the sensitivity of the parameterization to variations in background conditions (T and p) was calculated. The 0-D model allows us to automate the search for areas where PMC formation is possible using the frost point and different Q_V concentrations. T_s values were calculated for five different Q_V concentrations (1, 3, 5, 7, and 9 ppmv) and a range of p values equivalent to altitudes of 75–95 km. Depending on p and Q_V, the frost point can vary over a wide range, but as can be seen in Figure 2a, for values of Q_V > 7 ppmv, T_s changes are relatively small. Moreover, starting from the level of 0.01 hPa (equivalent to an altitude of about 80 km), the bottom of the cloud formation layer, all T_s values are overestimated relative to the actually observed temperatures in the mesopause (e.g., [34]), which is a favorable condition for sublimation of water vapor into ice.

One can conclude that the smaller the Q_V and the lower the p, the lower the real temperature must be for PMCs to form. Moreover, such calculations allow us to estimate the necessary values of water vapor and temperature concentration necessary for induction of heating of the environment by 1 degree. Figure 2b shows the necessary water vapor concentrations at different values of T and 3 levels of p (0.01, 0.005, and 0.002 hPa) required for 1 K/day heating. Figure 2b shows that at temperatures below 138 K, ε_PMC is virtually insensitive to water vapor variations. Similarly, heating is also virtually insensitive to variations in Q_V at p = 0.01 hPa. The situation changes if the real temperature is above 139 K. Then, the lower the atmospheric pressure, the more Q_V is needed to achieve a given value of ε_PMC.

3.2. Heating Quantifying

The PMC season lasts from May to August in the NH and from November to February in the SH. Complete dissipation of the PMC occurs due to the change of the thermodynamic regime of the polar MLT. The central date of each cloud season is the summer solstice. Vertical profiles of T, Q_V, and p were selected for the T_s calculation. Further, all values of temperature when T > T_s were excluded from the subsequent calculations, as far as the conditions necessary for cloud formation were not achieved. After calculating $Q_{ice}$ and other related variables, heating rates (ε_PMC, K/s) were calculated for each remaining vertical profile. Then these heating rates were averaged for each day and converted to daily rates (K/day). Figure 3 and Figure 4 show the altitudinal and temporal structures of daily mean ε_PMC values for the 14 seasons considered. It can be seen that the maximum ε_PMC values are concentrated in the bottom part of the low-temperature region; the 150 K isotherm is drawn in these figures to indicate its boundaries.

The minimum temperatures, which are also commonly referred to as the mesopause temperature, T_mes (e.g., [20]), are usually located in the central part of the above-mentioned region, and the maximum ε_PMC is located at altitudes of 81–82 km in the NH and 82–83 km in the SH, i.e., below the T_mes. Three conclusions follow from these results. First, since the only varying term in Equation (5) is Q_ice, the variations of ε_PMC will depend on the distribution of sublimated H₂O in time and space. Sublimating above T_mes, ice crystals under the gravity force begin to descend as their concentration and radius increase. This process continues till the lower boundary of the low temperature level, then cloud particles begin to melt due to the increase in T and lose their thermophysical properties. Consequently, the maximum concentrations of Q_ice and hence ε_PMC are located there (i.e., at the lower boundary of the low temperature level). Second, the interhemispheric differences in ε_PMC maximum heights are due to inhomogeneities in the structure of the mesopause of both hemispheres: as a rule, PMCs are 1–2 km higher in the SH compared to the NH (e.g., [35]). Third, interannual variability, diurnal variations, and any fluctuations in ε_PMC values are due to local thermodynamic and chemical processes affecting the mesopause and, consequently, the PMC ice crystal fields. For example, the presence of GWs leads to both the appearance and complete destruction of cloud fields due to temperature perturbations reaching several degrees, which can play a significant role in the processes of sublimation or evaporation of ice crystals [36]. On the other hand, solar activity, manifested in changes in the mesopause temperature, may be responsible for the multiyear variability of PMC parameters, which also affects, for example, the start of the PMC season [11,12,19].

Figure 5 shows histograms of the distribution of ε_PMC values for all seasons in both hemispheres. For quantitative assessment, the ε_PMC was divided into layers: layers above and below the T_mes level. The histograms in Figure 5a,b correspond to the area of maximum Q_ice values (where the maximum heating is concentrated). The median values for NH and SH are 5.86 and 5.24 K/day, respectively, i.e., the differences are about 11%. It should be noted that the distribution in both hemispheres is symmetric with respect to each other. Maximum ε_PMC values > 10 K/day occur in the same zone. Above the T_mes level (Figure 5c,d), small ε_PMC values are concentrated, and the interhemispheric differences are ~7%. The shape of the distribution in the NH is also different, which is probably due to the large number of measurement gaps. Overall, the heating patterns both above and below T_mes in both hemispheres are similar. That is, PMCs affect the mesopause heat balance equally in both the NH and SH. At the same time, according to the calculations, an increase in Q_V is expected to enhance the formation of PMCs and, consequently, to strengthen the parameterized heating.

4. Discussion

Calculated in the present study, heating rates due to absorption of IR radiation by PMC ice particles are additions to other heating/cooling rates caused by different atmospheric gases and dynamical processes. It is therefore particularly important to examine the results obtained in the context of the various factors of temperature variation at these altitudes.

At altitudes of 80–85 km, the heating rate of the atmosphere due to absorption of solar energy is ε_s~4–10 K/day (e.g., [37]). Near the mesopause, this solar heating is mainly compensated by atmospheric IR cooling, having the rate ε_IR comparable in magnitude to ε_s but having the negative sign [37]. Important dynamical processes in the region of PMC formation are IGWs, which create wave structures of the cloud fields.

Traveling IGW structures in the PMC were widely observed (e.g., [38,39]). A statistical analysis of IGW structures in PMC observed in Norway during the years of 2007–2010 was made by [40]. Using a Fourier transform technique, they found the IGW horizontal wavelength, λ_h, phase speed, c_h, period, τ, and the amplitude of PMC relative intensity variations, which are proportional to the relative density variations, |ρ′/ρ|. For latitudes 64–72° N, ref. [40] found broad distributions of the above parameters within the following ranges: λ_h~3–40 km, c_h~10–60 m/s, τ~6–50 min, and |ρ′/ρ|~2–10%. These ranges correspond to other observations of IGW structures in PMC (see [38,39]).

IGWs propagating from below produce upward momentum and heat fluxes. Dissipation of waves leads to a decrease in those fluxes with altitudes. IGW mode becomes convectively unstable at the breaking level, at which the amplitude of horizontal velocity variations becomes U = |u₀ − c_h|, where u₀ is the projection of the mean wind on the direction of wave propagation. Above the breaking level, IGWs produce turbulence and become saturated. The conception of IGW saturation supposes that the transport of wave energy to turbulence totally balances the IGW amplitude growth due to decreasing the atmospheric density with height [41]. The heating rate (wave heat flux divergence) produced by saturated IGWs can be estimated using the following expression [37,41]:

ε_GW = σU³/(2NH),

(6)

where σ is the IGW observable frequency, U is the amplitude of wave variations of horizontal velocity, and N is the Brunt-Vaisala frequency. The IGW dispersion equation and polarization relations for low-frequency short IGW [42] give U ≈ g |ρ′/ρ₀|/N, where g is the acceleration due to gravity. After this substitution, Equation (6) takes the following form:

ε_GW = σg³/(2N⁴H) |ρ′/ρ₀|³.

(7)

Near the mesopause at the mean temperature T₀ = 145–150 K typical for PMC events [43] N² ≈ g²/(T₀c_p), where c_p is the atmospheric air heat capacity at constant pressure. Assuming that smaller IGW periods correspond to smaller amplitudes in the above-mentioned ranges of periods, τ, and amplitudes |ρ′/ρ| of IGWs observed in PMC by [40], we can estimate ε_GW~3–40 K/day. These values can be comparable with the additional heating by PMC ε_PMC shown in Figure 3 and Figure 4. Studies of turbulence near the mesopause with sounding rockets showed that atmospheric heating caused by dissipation of turbulence produced by breaking IGWs can reach 10–20 K/day [43]. This generally corresponds to obtained ε_GW values; however, Equation (7) may give overestimated values for low-frequency IGWs with large amplitudes. This may show that not all IGWs observed in PMC might be saturated.

Ref. [40] found that most relatively short IGWs observed in PMC are subject to strong dissipation and cannot be explained with models of wave propagation from the lower atmosphere. Ref. [44] simulated IGWs at altitudes from the lower to the upper atmosphere. They found that primary IGWs propagating from the troposphere can dissipate and deposit energy and momentum in the stratosphere and lower mesosphere. Inhomogeneities of these depositions can generate secondary wave modes. This process can reiterate, producing higher-order IGWs in the thermosphere having larger scales than those of the primary IGWs. Generation of secondary IGWs near critical levels was also demonstrated with high-resolution numerical IGW simulations [45].

Except for heating due to dissipation of wave and turbulent energy, the background and wave-induced turbulence can produce a heat outflow and cooling of the atmosphere. The rate of turbulent heating/cooling of the atmosphere is described as follows [37,46]:

ε_t0 = 1/ρ₀ ∂/∂z [ρ₀ c_p K_teff (∂T₀/∂z + g/c_p)],

(8)

where K_teff is the mean over wave period effective coefficient of turbulent heat conduction. Cooling (ε_t0 < 0) occurs when ∂T₀/∂z > −g/c_p. Ref. [37] made a simulation of solar and IR heat influxes as well as GW heating and turbulent cooling at altitudes of 60–130 km. They found that approximately heating ε_s is balanced by cooling ε_IR, and heating ε_GW is balanced by cooling ε_t0 at a wide range of IGW intensities. Therefore, the heat balance near the mesopause involves many different heating/cooling impacts, and inclusion of the additional comparable heating rate due to PMC ice particles may produce substantial effects, which require further studies.

Despite the fact that calculations of the PMC thermal impact on the environment were made only for a small number of years out of the entire period of satellite observations of the PMC, the obtained ε_PMC values also allow us to make the following assumption. Heating due to absorption of infrared (SWIR and thermal) radiation fluxes by PMC particles increases the vertical temperature gradient, which, in turn, increases the value of the vertical wind component and, as a consequence, may cause additional adiabatic cooling of the overlying atmosphere. Such an effect was demonstrated, for example, by [26]: an increase in the temperature of the polar mesopause at altitudes of 80–90 km is accompanied by cooling of the overlying layers. Thus, the predicted decrease in the mesopause temperature caused by climate change, as well as the increase in water vapor concentration and, as a consequence, the increase in the PMC area and their spreading toward the middle latitudes, lead to the strengthening of the ε_PMC. This triggers a series of positive feedback through the amplification of the vertical wind, which causes additional adiabatic cooling of the mesopause above the PMC layer. To further analyze this process, we plan to implement this parameterization of heating from the PMC into a general atmospheric circulation model.

When discussing the various factors influencing the thermodynamic regime of the mesopause, it is also necessary to mention the PWs. For instance, the 2- and 5-day PWs, which play an important role in the dynamics of the summer polar MLT. Dalin et al. studied the NH polar mesopause in the summer of 2007 and 2008 and found that the temperature variations caused by these PWs reached values of 2.5–3 K, and their maximum occurred at the 80–110 km layer [47]. By analyzing 16 years of Aura Microwave Limb Sounder (MLS) measurements in the NH (2007–2022), it was found that if a westward 5-day PW with a wave number of 1 intensifies at the start of the PMC season (~15–28 May), the first cloud fields will form in its cold trough [6]. Stationary planetary waves are also capable of causing significant variations in hydrodynamic parameters in the MLT [48]. Their impact is concentrated mainly in the polar latitudes during the winter season. However, the contribution of these waves to the PMC/NLC variability is not comparable to the contribution made by IGWs, having horizontal scales of 10–100 km. These waves can lead to temperature perturbations from several to tens of degrees (see also [40]). Atmospheric thermal tides (especially migrating ones) also play a significant role in the MLT [1]. The amplitudes of temperature variations due to tides increase in low latitudes and are of the order of several degrees in the lower thermosphere. Their influence increases in the higher layers of the atmosphere. The heating of the mesosphere-lower thermosphere is also significantly affected by variations in incoming solar radiation within the 11-year solar cycle [49,50]. However, these studies will remain outside the scope of our article.

5. Conclusions

This article describes the calculation of the thermal impact of polar mesospheric clouds on the environment caused by the emission of absorbed incoming and outgoing IR radiation fluxes by cloud particles. To calculate this effect, a parameterization of mesopause heating due to the absorption of IR radiation flows by PMC crystals was developed, the main feature of which is the consideration of the thermophysical properties of ice and the interaction of cloud particles with the environment. Fluxes of solar radiation in a narrow band near 3 μm and terrestrial radiation in the wavelength range of 10–14 μm, absorbed by cloud particles, are re-emitted back into the atmosphere, causing its heating, contributing to the change of the thermodynamic conditions of the mesopause. The parameterization is based on T, Q_V, and p data retrieved from the solar radiation spectra measured by the SOFIE sensor. We present the results of heating calculations for 14 PMC seasons: 2007–2013 in NH and from 2007/2008 to 2013/2014 in SH.

Based on the results obtained, the following conclusions are derived:

• Since the parameterization depends solely on Q_ice, the most intense ε_PMC heating values are concentrated at the altitudes of maximum ice crystal concentrations: 81–82 km in NH and 82–83 km in SH.
• Any variations of atmospheric parameters, caused, for example, by IGWs, and perturbing the Q_ice distribution in time and space, lead to perturbations in the heating intensity. An increase in water vapor concentration is expected to enhance the formation of PMC and, as a consequence, enhance radiative heating.
• The median ε_PMC values centered below the T_mes heights are 5.86 and 5.24 K/day in NH and SH, respectively, and their distribution is symmetric in both hemispheres.
• The lowest values of heating are located above the maximum of cloud ice concentration in both hemispheres. The maximum values of the calculated heat influx are concentrated at the lower boundary of the cloud layer, which is due to the behavior of sublimated crystals: appearing above 85 km, small cloud particles settle, shifting to the zone of low temperatures, where the radius of the crystals increases.

Thus, it is shown that PMCs can make a significant contribution to the heat budget of the upper atmosphere, comparable to the heating caused, e.g., by the dissipation of IGWs, the parameterization of which is included in all global atmospheric circulation models (e.g., [51,52,53]). The results obtained are comparable with the calculations by [26].

The integration of the developed parameterization into climate and atmospheric general circulation models will improve the accuracy of describing and predicting changes in the condition of the upper atmosphere. In particular, in the future, in order to study in detail the feedback that can cause cooling of the MLT region above the PMC/NLC layer, it is planned to implement the developed parameterization into the global atmospheric circulation models, including the Model of the Middle and Upper Atmosphere (MUAM).