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I am busy with the development of an "environment" model that can be used for flight simulation of all kinds of flight vehicles — ranging from quad-copters, unmanned aerial vehicles, manned aircraft, up to rocket launchers for satellites. The model consists of sub-models for terrestrial gravity; the earth's size, shape, and motions; the geomagnetic field; the atmosphere; and so on.

Currently I am using the COSPAR International Reference Atmosphere (CIRA-86) to calculate air pressure and temperature for heights up to 120 km. But, to be able to calculate air density, I also need to model the effects of humidity. I know that water vapour is only present in varying quantities in the troposhere, and that high humidity is therefore more likely at lower altitudes.

Does anybody have models of the probability of experiencing some value of relative humidity as a function of height above sea level?

Edit. As an example of what I really need, the MIL-F-8785C model for wind speed and turbulence, for example, gives the mean wind speed at a height of 6.1 m above the ground, given the logarithm of the probability of exceeding the wind speed. So, a model of the humidity as a probability of exceeding the the mean humidity as a function of height is what I really need. Do you know of any models that provide this?

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    $\begingroup$ why not just use the reanalysis data that is available on daily basis ? $\endgroup$ – gansub Nov 4 '16 at 11:17
  • $\begingroup$ @gansub, I have to do Monte-Carlo simulations that will give probabilities over a long time. To perform statistical analyses on the daily data is probably outside the scope of the work I want to do. $\endgroup$ – Christo Nov 4 '16 at 13:15
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Humidity strongly varies as a function of time and space, which is why standard atmospheres like CIRA may choose to omit it at all. It simply doesn't make sense to include an “average” humidity profile, because such an average is not meaningful.

However, there are other sources for relative humidity profiles. You can obtain them from reanalysis data. If you want probabilities, you could calculate them from reanalysis. I have not used probabilities, but I have used profiles from Anderson et al. (1986) in the past:

Anderson, G. P., S. A. Clough, F. X. Kneizys, J. H. Chetwynd, and E. P. Shettle (1986), AFGL atmospheric constituent profiles (0–120 km), AFGL, TR-86-0110.

Anderson transcribes them in his paper, which is in PDF and not ideal to read. The same data are distributed along with the Atmospheric Radiative Transfer Simulator (see also Wikipedia article). This radiative transfer model comes with a set of XML files, that includes profiles from both CIRA and from Anderson et al. Those are not probabilities but “typical” H₂O profiles for five scenarios: tropical, mid-latitude summer, mid-latitude winter, sub-arctic summer, and sub-arctic winter. For example, a mid-latitude summer H₂O profile can be found at this link. The data are in XML so should be easy to read, but they also provide reading routines for Matlab and Python. The unit is volume mixing ratio, which may actually be more suitable than relative humidity if you are interested in calculating air density.

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  • $\begingroup$ Thank you for the answer, @gerrit. That helps a lot. As an example of what I really need, the MIL-F-8785C model for wind speed and turbulence gives the mean wind speed at a height of 6.1 m above the ground, given the logarithm of the probability of exceeding the wind speed. So, a model of the humidity as a probability of exceeding the the mean humidity as a function of height is what I really need. Do you know of any models that provide this? $\endgroup$ – Christo Nov 4 '16 at 13:04
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    $\begingroup$ @Christo No, but it should be not too difficult to calculate the frequentist probability from reanalysis data. $\endgroup$ – gerrit Nov 4 '16 at 13:10

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