A state-of-the-art numerical weather model (MPAS) was run for five years to simulate the weather on Kerbin. An hourly climatology of Kerbin was developed from this Kerbin-Like simulation by averaging the results of this year-long simulation by the hour. A second Earth-Like simulation was performed which kept Kerbin's terrain and land use characteristics but utilized Earth's eccentricity (~0.017), obliquity (~23.5°), and rotation period (~ 24 h).

 

Zonally Averaged Climatology

The following charts depict zonal average quantities as a function of latitude and height/pressure. Variables such as temperature, humidity, and wind are averaged in time at each model grid point. Zonal averages are then calculated by taking the mean value of a variable (e.g. average temperature) along a line of latitude. Note that the results shown below are insensitive to the order in which averaging is performed (e.g. time - latitude or latitude - time). In all of the charts below, grid lines are depicted in grey, and contours are shown in black. The vertical axes are labeled in both pressure (left axis) and height (right axis).

The Climate of the Troposphere

temperatureXwind.png

The figure above displays the zonal mean temperature (shaded) and wind speed (contoured) as a function of latitude and pressure/height. On the left, the results from a simulation with an Earth-Like 24-h day. On the right, the results from the primary Kerbin-Like simulation with a 6-h day. In both plots, the freezing (0°C) line is displayed as a dashed white line. On a faster rotating planet, the acceleration due to the rotation of the planet (i.e., Coriolis acceleration) is larger. One consequence of this is that the amount of heat transported from the tropics to the poles is reduced, resulting in a larger equator to pole temperature gradient (Kaspi and Showman, 2015; Komacek and Abbot, 2019). On the Earth-Like planet, the difference in temperature between the equator and poles is around 55°C. When the planetary rotation rate speeds up by a factor of 4 the equator to pole temperature difference increases to 85°C. Despite having a larger equator-to-pole temperature gradient the average near-surface temperature at the equator is colder in the Kerbin-Like simulation than in the Earth-Like simulation. This result is partly explained by the shortened day length in the Kerbin-Like simulation, which limits the amount of time the sun (Kerbol) has to heat the surface. With only 3-h of sunlight per day, high temperatures are limited by the time it takes for the land/ocean surface to warm. This is why on Earth the warmest part of the day is typically around 3-4 hours after solar noon. 

 

The planetary rotation rate doesn’t just influence the latitudinal temperature distribution it also influences the wind. On faster rotating planets there is a tendency for more jet streams to develop (Kaspi and Showman, 2015). In the Earth-Like simulation, a single jet is visible in each hemisphere. This jet is strongest at ~200 hPa at around 40°N and 40°S. In the Kerbin-Like simulation, there is a slight bifurcation of the jet, especially in the Northern Hemisphere (N.H.). This bifurcation is visualized in the zonal average wind contours (black) which take on a W-like shape above 500 hPa. The jet strength is stronger over the N.H., in the Kerbin-Like simulation, because the temperature gradient is greater between the equator and the North Pole than between the equator and the South Pole. The difference in equator-to-pole temperature gradient can be explained in part by the fact that the N.H. has more landmass than the S.H. of Kerbin. Approximately 62% of Kerbin’s N.H. is landmass while only 46% of its S.H. is covered by land. Since land heats up and cools down faster than the ocean, temperatures can reach greater extremes in the N.H. This is especially true around Kerbin’s the North Pole which is bordered by two continents. In contrast, Kerbin’s South Pole is largely surrounded by an ocean which has a moderating effect on temperature.

rhxwind.png

The zonal mean relative humidity (shaded) and wind speed (contoured) as a function of latitude and pressure (i.e. height) is displayed above. On the left, the results from a simulation with an Earth-Like 24-h day. On the right, the results from the primary Kerbin-Like simulation with a 6-h day. In both simulations, the relative humidity is greatest in the lower troposphere, near the poles, and is lowest in the stratosphere. The relative humidity is typically low in the stratosphere since in this layer of the atmosphere, temperature increases with height. This temperature inversion prevents tropospheric air from rising into the stratosphere largely capping moisture to the troposphere. As air rises it expands and cools. When a parcel of air rises into the stratosphere it quickly becomes cooler than the air around it and tends to sink back down toward its original position. There are rare exceptions to this, for example in deep convective thunderstorms strong updrafts can have enough momentum to push into the stratosphere, temporarily overcoming negative buoyancy (see overshooting tops).

A notable difference between the two simulations is observed around the tropics where the Hadley Cell dominates the atmospheric circulation. The Hadley cell is an atmospheric circulation wherein moist air converges and rises at the equator producing precipitation. The moist air rises and remains buoyant until it reaches the top of the troposphere. Since the air cannot rise it is forced poleward. As the air moves toward the poles it cools and is deflected eastward by the planet’s rotation (i.e. Coriolis acceleration). By the time the air reaches the subtropics it is cool and dry, this causes the air to sink which results in further warming and drying.

In the Earth-Like simulation, the descending branch of the Hadley cell is visible as two patches of lower humidity in the subtropics. This dry branch of the Hadley cell is not as well defined in the Kerbin Like simulation. 

wwxwind.png

The ascending and descending branches of the Hadley Cell are more easily visualized in the figure above which depicts the zonal mean: vertical velocity (shaded), wind speed (contoured), and meridional-vertical (v-w) circulation as a function of latitude and pressure (i.e. height). Vertical motions in the Kerbin-Like simulation are notably stronger, on average than in the Earth-Like simulation. This is partly due to the fact that in the Earth-Like simulation there are seasons. The ascending branch of the Hadley Cell shifts toward the summer hemisphere with the seasons. Thus, when averaged over the course of a year, seasonal effects result in reduced mean vertical velocity as the upward branch of the Hadley Cell isn’t always over the Equator. In contrast, in the Kerbin-Like simulation, there are no seasons. In this simulation, the vertical velocity does not vary seasonally and is thus robust in the mean. In both simulations the descending branch of the Hadley cell is visible between 15°-30° N/S, stretching vertically from near the surface to the upper troposphere. In the Kerbin-Like simulation, the descending branch of the Hadley cell extends equatorward in the mid-troposphere, between 700 hPa and 400 hPa. This reduces ascent along the periphery of the ascending branch as dry descending air mixes with moist rising air. For this reason, the branches of the Hadley cell in the Kerbin-Like simulation are less distinct in the relative humidity figure shown above.

In the Kerbin-Like simulation, sinking motion is strongest in the N.H. where the equator-to-pole temperature gradient is larger and the jet strength is greater. The strength of the jet scales with the strength of the Hadley cell (Kaspi and Showman, 2015). On average, downward (upward) motion is observed on the equatorward (poleward) side of the jet.

cloudxwind.png

Vertical motions like those shown in the previous figure are associated with the presence or absence of clouds. The figure above displays the zonal mean cloud fraction (shaded) and vertical velocity (contoured) as a function of latitude and pressure (i.e. height). Solid contours indicate positive vertical velocity (upward motion) while dashed contours show negative vertical velocity (downward motion). The cloud fraction is defined as the fraction of a model grid box covered with clouds. In both simulations, low cloud fraction (< 700 hPa) is reduced in the tropics and enhanced near the poles. Overall, the cloud fraction is greater throughout the mid-latitudes and polar regions in the Kerbin-Like simulation. In this simulation, high (> 400 hPa) cloud fraction is also greater in the tropics. This suggests that tropical cirrus may be more extensive in the Kerbin-Like simulation. More cirrus clouds over the tropics, in combination with a shorter day length, could explain the equatorial temperature difference between the two simulations.

Clear skies are associated with downward air motion while clouds are associated with upward motion. When air ascends it cools. Eventually, the air cools to the dew point and the moisture in the air condenses into liquid water droplets forming clouds. When air descends it warms. If the amount of moisture in the air doesn’t change and the temperature increases; the relative humidity of the air decreases and cloud formation is suppressed. In the figure above, cloud cover aloft is typically greater where vertical motions are strongest. In the Kerbin-Like simulation, high-cloud cover over the tropics is coincident with strong upward air motion. In both simulations, the cloud-free areas near the surface are located below areas where large-scale descending motion is observed (e.g. -30°S to 30°N). Near the surface, above the equator, there is a small peak in low cloud fraction between 900-800 hPa. This could likely be attributed to low-level scattered cumulus clouds over the tropics.

The Climate of the Stratosphere and Mesosphere

temperatureXwind_upper.png

This figure displays the zonal mean temperature (shaded) and wind speed (contoured) as a function of latitude and pressure/height through the full depth of the atmosphere. On the left, the results from a simulation with an Earth-Like 24-h day. On the right, the results from the primary Kerbin-Like simulation with a 6-h day. In both plots, pressure is displayed on the vertical axis on a logarithmic scale. Solid black contours depict westerly winds while black dashed contours depict easterly winds. The two dashed white contours depict the border between the troposphere and stratosphere (i.e tropopause) and the border between the stratosphere and mesosphere (stratopause). The lower dashed contour depicts the tropopause which is higher over the equator than over the poles. The upper dashed contour shows the stratopause which lies between 50-60 km. In both simulations, the temperature declines with height in the troposphere and mesosphere. In the stratosphere, temperature increases with height due to the presence of ozone, which absorbs energy from incoming ultraviolet radiation from the sun (Kerbol). While the height of the stratopause is fairly consistent, the tropopause height varies significantly. Over the equator, the tropopause height is around 18-km while over the poles the tropopause height is as low as 8-10 km. The height of the tropopause is related to the average temperature of the layer beneath it (i.e. the troposphere). Over the poles, the average temperature of the troposphere is extremely low. Since cold air is denser than warm air, a column of cold air will be shorter (i.e. more compact) than a column of warm air. At the equator, the lower density of warm air results in an expansion of the layer producing a higher tropopause height. In addition, frequent thunderstorm activity in the tropics produces turbulence and mixing that helps extend the tropopause height.

Counterintuitively, the coldest temperatures are observed around the equatorial tropopause. In the troposphere, temperature decreases with height at an average rate of -6.5°C/km. Since the troposphere is deepest in the tropics the air temperature at the tropical tropopause can reach as low as -90°C. Regions of extreme cold can also be observed in the lower stratosphere over the polar regions, most notably in the Kerbin-Like simulation. In both simulations, the south polar region exhibits the lowest stratospheric temperatures. This result is partly explained by the fact that both MPAS simulations utilized Earth’s monthly average ozone concentration. On Earth, ozone concentrations over the southern polar region are lower. This reduction in ozone concentration is famously known as the ozone hole. Less ozone in this region results in less heating, hence the colder temperatures in the southern polar stratosphere. 

The greatest difference between the two simulations is observed in the zonal average wind speed. In the Kerbin-Like simulation, high-latitude jet streams of fast-moving air extend through the stratosphere and into the mesosphere. These strong westerly jet streams circle the polar regions forming a vortex. In both simulations, the southern polar vortex is strongest. Kerbin’s southern hemisphere has fewer major mountain ranges and is covered by more water than land. Large mountain ranges and temperature contrasts between continents and oceans can help create large-scale waves in the atmosphere, which propagate into the stratosphere (Jucker et al., 2013). These atmospheric waves can break in the stratosphere, like waves on a beach, reducing the strength of the polar vortex by increasing the temperature and amount of ozone in the lower stratosphere. Since Kerbin’s S.H. has fewer mountain ranges and has more water than land mass these planetary-scale waves are less common in the S.H. As a result, Kerbin’s southern polar vortex tends to be more robust. 

In the Earth-Like simulation, zonal mean wind speeds throughout the stratosphere and mesosphere appear quite low. Recall that in the Earth-Like simulation there are seasons as the axial tilt (obliquity) was set equal to Earth's. On Earth, the stratospheric polar vortex is observed during the winter (Palmeiro, 2018). In the summer, the direction of the flow in the stratosphere switches signs, becoming easterly (Lim et al., 2018). Thus, when averaged over the course of a full year, seasonal variations in the direction and strength of the stratospheric flow result in a reduced zonal mean wind speed. In the Kerbin-Like simulation, there are no seasons, the sun never rises at the poles, and the polar vortex persists throughout the year.

In contrast to the poles, the tropical stratosphere is characterized by easterly winds. On Earth, the direction of the flow in the tropical lower stratosphere reverses direction every 28-29 months in what is called the quasi-biennial oscillation (QBO). While it is likely that Kerbin also experiences this phenomenon it is unclear from this figure, which displays the zonal mean wind averaged over a 5-year period. Since the amplitude of the easterly phase of the QBO is twice as large as that of the westerly phase an average over a 5-year period should produce easterly flow in the mean.

wwxwind_upper.png

Above, the zonal mean: vertical velocity (shaded), wind speed (contoured), and meridional-vertical (v-w) circulation are displayed as a function of latitude and pressure (i.e. height) through the full depth of the atmosphere. As in the previous figure, vertical motions in the Kerbin-Like simulation are notably stronger, on average than in the Earth-Like simulation. This is due to the fact that in the Earth-Like simulation there are seasonal shifts in the sign of vertical velocity which tend to cancel out in the annual average. In the Kerbin-Like simulation, a deep meridional (north-south) circulation, known as the Brewer-Dobson circulation (BDC) is observed in the stratosphere. In the BDC, the air rises through the tropical stratosphere, ascending slowly, before gradually moving poleward and downward. On Earth, the air in the mesosphere typically propagates from the summer to the winter hemisphere. This unique pole-to-pole circulation is not observed in the Kerbin-Like simulation since there are no seasons. In this simulation, the zonal mean flow in the lower mesosphere is westerly. Drag from atmospheric (gravity) waves adds a meridional (north-south) component to the flow in the mesosphere (Norton and Thunburn, 1999). The result is a deep meridional circulation that transports air poleward and then downward into the polar stratosphere. Descending air in the polar regions of the lower mesosphere helps explain why the polar stratopause is slightly warmer than the equatorial stratopause in the previous figure.

It's important to note that unlike the real atmosphere the MPAS model simulation has a hard upper boundary (i.e. model top) at 70 km. The presence of this hard boundary contributes to the meridional circulation observed in the lower mesosphere. When air rises through the tropical stratosphere and hits the model top it's forced to spread out and move poleward. This artificial constraint could help explain the intensity of the meridional circulation which may be dubious. Nevertheless, the observed zonal mean wind speed and vertical velocity in the Kerbin-Like simulation are consistent with model simulations of Earth's stratosphere/mesosphere during equinox (Garcia and Soloman, 1987) and in the annual mean (Hoppe et al., 2016).

References:

Garcia, R. R., and Solomon, S. (1985), The effect of breaking gravity waves on the dynamics and chemical composition of the mesosphere and lower thermosphere, J. Geophys. Res., 90( D2), 3850– 3868, https://doi.org/10.1029/JD090iD02p03850.

Hoppe, C. M., Ploeger, F., Konopka, P., and Müller, R.: Kinematic and diabatic vertical velocity climatologies from a chemistry climate model, Atmos. Chem. Phys., 16, 6223–6239, https://doi.org/10.5194/acp-16-6223-2016.

Jucker, M., S. Fueglistaler, and G. K. Vallis, 2013: Maintenance of the Stratospheric Structure in an Idealized General Circulation Model. J. Atmos. Sci., 70, 3341–3358, https://doi.org/10.1175/JAS-D-12-0305.1.

Kaspi, Y., Showman A. P., 2015: Atmospheric Dynamics of Terrestrial Exoplanets Over a Wide Range of Orbital and Atmospheric Parameters. The Astrophysical Journal, 804, http://dx.doi.org/10.1088/0004-637X/804/1/60

Komacek, D., Abbot S. D., 2019: The Atmospheric Circulation and Climate of Terrestrial Planets Orbiting Sun-like and M Dwarf Stars over a Broad Range of Planetary Parameters. The Astrophysical Journal, 871, https://doi.org/10.3847/1538-4357/aafb33

Lim, E.‐P., Hendon, H. H., & Thompson, D. W. J. (2018). Seasonal Evolution of Stratosphere‐Troposphere Coupling in the Southern Hemisphere and Implications for the Predictability of Surface Climate. Journal of Geophysical Research: Atmospheres, 123, 12,002-12,016. https://doi.org/10.1029/2018JD029321

Norton, W. A., and Thuburn, J. (1999), Sensitivity of mesospheric mean flow, planetary waves, and tides to strength of gravity wave drag, J. Geophys. Res., 104( D24), 30897– 30911, https://doi.org/10.1029/1999JD900961.

Palmeiro, F. M., 2018: Sudden Stratospheric Warmings and the Brewer-Dobson Circulation: diagnostics and interactions. [Thesis] 

https://eprints.ucm.es/49857/1/T40523.pdf