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3. Properties

3.a Statistics of relative humidity and supersaturation

Relative humidity is a field quantity that usually displays a very intricate structure in space and time. Since it depends on both absolute humidity and temperature, fluctuations of both these fields translate into relative humidity fluctuations. Even instantaneous fluctuations on a scale of 300 X 300 km² (which is a typical grid size for general circulation models) can be quite large; the statistical distribution of these fluctuations are heavy-tailed (Gierens et al., 1997). Under these circumstances it is at first surprising that by and large the relative humidity in the lowermost stratosphere and in ice-supersaturated regions in the upper troposphere seems to obey a very simple statistical law (Gierens et al.,1999): Three years of data obtained by MOZAIC revealed
(1) for the lowermost stratosphere that the probability to find a certain relative humidity value decreases exponentially with this value, and
(2) for tropospheric ice-supersaturated regions that the probability to find a certain degree of supersaturation decreases exponentially with the supersaturation.

Expressed by formulae, this reads:

  P_RHi(u) = a exp(-au)  in the lowermost stratosphere

  P_Si(s)   = b exp(-bs)   in tropospheric ISSRs

where a, b are constants, RHi is relative humidity wrt ice, Si is supersaturation with respect to ice, and u, s are variables on the RH and Si axes, respectively. P means probability density.

Cloud cleared Microwave Limb Sounder (MLS) data of upper tropospheric humidity on the 215 hPa pressure level have been evaluated in the same way to determine the global statistics of relative humidity with respect to ice. In agreement with the MOZAIC study we find that in the lowermost stratosphere the probability to get a certain value of relative humidity decreases exponentially with the relative humidity. In the Antarctic data class (data south of 55°S, mainly winter data) we also find an exponential distribution for RHi but with less steep slope. There is no change in the slope of the exponential distribution function at ice saturation. In the upper troposphere there are corresponding exponential distributions for RHi in ISSRs and in subsaturated regions (for 20%<RHi<100%), however with different slopes, viz. a steeper one in ice-supersaturated regions. In the cases of the tropospheric and antarctic data there is no indication of homogeneous ice nucleation at high humidities of RHi >150%, and the exponential distributions extend without change of slope up to 180-200%. Such extreme humidity events occur mostly in the tropics and at the edge of Antarctica. Their origin is currently unknown (maybe incidental lack of aerosol).

3.b Distributions of temperature and absolute humidity, sources of ISSRs

ISSRs are generally colder (1-10 K) and moister (factor 1.5 to 3) than their subsaturated environment. The differences vary with the considered geographical region, the altitude, and between troposphere and stratosphere.

The following figures show mean values and standard deviations of temperatures and specific humidities inside ISSRs (bullets) and outside - i.e. in subsaturated air (open circles).



This indicates two different sources or formation mechanisms of ISSRs, namely:
(1) adiabatic cooling of an airmass leads to supersaturation (this seems not to be important in the tropics, since the temperatures are very close together);
(2) moisture advection leads to supersaturation.

3.c Horizontal and vertical sizes of ISSRs

ISSR's horizontal sizes and vertical extensions are Weibull distributed. The horizontal sizes are pathlengths from the MOZAIC data. Since shapes of ISSRs are not known, and since MOZAIC aircraft cross ISSRs in a random manner, the pathlength distribution might not be very relevant for the true size distribution of ISSRs. When we assume that all ISSRs have circular shape, we can try to determine a true size distribution from the measured pathlength distribution. However, there is a serious sampling bias: Since the aircraft trajectories are random in the field of ISSRs, it is much more probable that a large ISSR is crossed by a certain trajectory than that a small one is crossed. This selection bias leads to a surprising result: whereas the mean pathlength is 150 km, the average true horizontal size could be as small as 6 km. That is, there might be very many small ISSRs around that however are never crossed by an aircraft since they are too small; only the larger ones are crossed and therefore counted in the statistics.

The largest ISSRs we have found in the MOZAIC data have pathlengths exceeding 1000 km. One example is shown in the next figure.

Meteosat, 18 Dec. 1995, 15 UTC

The yellow line marks the flight path of a MOZAIC flight from Frankfurt, Germany to a location near Rio de Janeiro, Brasil. Look at the part close to the northwest African coast. The flight path is there parallel to a warm front that is approaching Africa. This is where we have found the huge ISSR (more than 3000 km flight in supersaturated air). In front of the front air is slowly uplifting and adiabatically cooling. A certain distance to the east from the front and from the flight trajectory one can see the clouds that form in the cooling air. This flight was therefore in a supersaturated airmass, that was however at the flight position not yet sufficiently moist for cirrus formation. The cooling necessary for cirrus formation was only reached further to the east.

Vertical extensions could be obtained from radiosonde data from the Meteorological Observatory in Lindenberg, Germany. Unfortunately, this data set does not allow to distinguish between data in clear air (proper ISSRs) and in cloudy air (improper ISSRs). In spite of this, the statistics show up two regimes, one of which can be attributed to cirrus clouds and the other probably to ISSRs. This can be seen when the data are plotted on a so-called Weibull plot.

weibull-plot A Weibull plot is constructed in such a way, that random numbers drawn from a Weibull distribution lie on a straight line. The slope of the line is the power in the expression of the Weibull distribution. In our case the data are located on two straight lines which cross at a height of 1000 m. The data points referring to larger vertical extensions are probably taken inside cirrus clouds, which are typically thicker in the vertical than 1000 m. The slope of the line in this part is 1.0, which means that the Weibull distribution here is simply an exponential distribution. The other part of the plot, i.e. H < 1000 m, probably contains data from true ISSRs and perhaps sub-visible cirrus. The mean height in this regime is about 500 m. This is also a characteristic vertical extension of sub-visible cirrus clouds.

3.d The situation of ice-supersaturation layers relative to the tropopause

The possibility to detect ice-supersaturation with a thoroughfully gauged radiosonde allows to study the location of ice-supersaturation layers relative to the local thermal tropopause. Here we say "ice-supersaturation layers" instead of the usual "ice-supersaturated regions", because the latter notion refers to cloud free regions, whereas we have no possibility to decide whether the radiosonde was in a true ISSR or in a cirrus cloud.

Ice-supersaturation layers appear mostly in a broad region below the tropopause, sometimes their tops reach into the stratosphere. This is shown in the following three plots. The red line marks the local thermal tropopause, the ice-supersaturation layers are marked by the vertical blue bars.




In the following plot, all pressure levels refer to the tropopause pressure. This shows how the ice-supersaturation layers are concentrated in a broad region below the tropopause.


The depth of the upper tropospheric region that contains ice-supersaturation layers varies seasonally. It is relatively shallow in summer, and relatively deep in winter. The layer depths varies between 150 and 250 hPa. Ice-supersaturation layers extend often into the lowermost stratosphere, but not more than about 25 hPa in the Lindenberg data that we have analysed.


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