The Grey Table

References:
However, the formation of cirrus
requires higher relative humidity than for contrail persistence: Ice particles form from the abundant
small droplets by homogeneous freezing only at high relative humidity with respect to ice-saturation,
at RHi of the order 145 to 165 % or higher
http://aero-net.info/fileadmin/aeronet_files/links/documents/DLR/Schumann_Contrails.pdf
<Lets take RHi 145% at -40 Celsius
Which is RH: 97.7747808496%   >
or homogeneous nucleation,
 which is probably the dominant mechanism for forming ice crystals at low temperatures

 (T<38C) relative humidities in the range 140–170% RHi, depending on temperature
http://www.sfb641.uni-frankfurt.de/Publikationen/pdf/B9/fusina_etal07.pdf
Actually the lower the temperature, the less humidity is needed. So my guess is that RHi 170% is reffering to -40 Celsius but I let it be for the moment.
Important I found the remark: " or homogeneous nucleation,
 which is probably the dominant mechanism for forming ice crystals at low temperatures "
The solid curve where all solutions freeze is the freezing temperature threshold. For
example, at temperatures lower than 233 K (-40◦C) this process requires airmasses in a
state of substantial supersaturation which is generally larger than 40% (Spichtinger et al.,
2003)).
presented by
MARTIN BRABEC
Dipl. Geogr., University of Zurich
born 16 March 1978
citizen of Switzerland
accepted on the recommendation of
Prof. Dr. T. Peter, examiner
Dr. F. G. Wienhold, co-examiner
Dr. H. Všomel, co-examiner
/pol/chem/tracking/eth-5071-02.pdf
<" substantial supersaturation which is generally larger than 40%"
Which is: RH 94.4032366824%   at -40 Celsius
 >
The solid curve where all solutions freeze is the freezing temperature threshold. For
example, at temperatures lower than 233 K (-40◦C) this process requires airmasses in a
state of substantial supersaturation which is generally larger than 40% (Spichtinger et al.,
2003)).
presented by
MARTIN BRABEC
Dipl. Geogr., University of Zurich
born 16 March 1978
citizen of Switzerland
accepted on the recommendation of
Prof. Dr. T. Peter, examiner
Dr. F. G. Wienhold, co-examiner
Dr. H. Všomel, co-examiner
/pol/chem/tracking/eth-5071-02.pdf
<" substantial supersaturation which is generally larger than 40%"
Which is: RH 94.4032366824%   at -40 Celsius
>
The relative humidity with respect to ice increases up to a
critical threshold RHcrit of supersaturation as high as 150%,
before nucleation begins under conditions of low temperature
and large difference between the vapour pressures of liquid
water and ice saturation.
P. Mahapatra, M. Milz and S. Buehler
Satellite Atmospheric Science Group, Department of Space Science, Luleć University of Technology, Kiruna, Sweden
/tracking/mahapatra09_report_nearlyfinal.pdf
<"of supersaturation as high as 150%,"
Lets assume he meant at minus 38 Celsius ( makes the counting easier )
Rhi  148,3% at -40 Celsius is
RH 100% at -40 Celsius
>
-40C = 100% RH with respect to water. 148.3% with respect to ice
file:/tracking/RH_WMO.pdf

150% supersaturation with regards to ice translates in 101% saturation with regards to water.
Under natural conditions. You add human made nuclei delieverd via aircraft and the game changes. See pdf document RH_WMO ....

RH-WMO = RH with regards to water
RH-Standard = RH with regards to ice
Above 100% is "supersaturated"

Cirrus clouds in the cold upper troposphere (T . −40C) are generally thought to
form mainly by homogeneous freezing of aqueous solution droplets (e.g. Sassen and
25 Dodd, 1988; Heymsfield and Sabin, 1989; Heymsfield and Miloshevich, 1993). When
there is enough background aerosol present, homogeneous nucleation is a thermo-
dynamically controlled process, that is, it takes place when a critical supersaturation
(dependent on temperature) is reached in an airmass. It has been shown in the laboratory
by Koop et al. (2000) that the critical supersaturation is independent of the
chemical nature of the aerosol. Gierens et al. (2000), comparing and correlating data
5 of ice–supersaturation from MOZAIC, Measurement of Ozone from Airbus–in–Service
Aircraft (Marenco et al., 1998), of subvisible cirrus from SAGE II, Stratospheric Aerosol
and Gas Experiment II (Wang et al., 1996), and of thermodynamic conditions for cirrus
formation from re–analysis data of the European Centre for Medium Range Weather
Forecast (Sausen et al., 1998), could show that cirrus formation seems to be ther
modynamically controlled in the tropics and in the southern midlatitudes upper troposphere,
but not in the same way in the northern midlatitudes, where the thermodynamic
control is much weaker. This result can suggest that the composition of the freezing
aerosol has a more important effect in the polluted northern hemisphere compared
to the cleaner regions of the world. Since homogeneous nucleation seems not to
 depend on the aerosol composition one may conclude that then heterogeneous processes
must play a bigger role for cirrus formation in the northern midlatitudes. Such
heterogeneous effects could be brought about inter alia by aircraft soot emissions. Indeed,
Str šom and Ohlsson (1998) found that cirrus ice crystals in a region of heavy air
traffic (southern Germany) often contain some kind of “absorbing material” (probably
 soot), and moreover such inclusions were most frequent in those altitudes where the
air routes are concentrated (8–12 km).
acpd-2-2343-2002
http://hal.archives-ouvertes.fr/docs/00/29/52/51/PDF/acp-3-437-2003.pdf
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