From: sweeney@dionheinz.uchicago.edu (Jeff Sweeney)
Subject: Re: getting temperature from weather maps
Organization: University of Chicago
Distribution: usa
Date: Thu, 7 Jan 1993 16:15:30 GMT

In article <1993Jan6.205337.15845@wuecl.wustl.edu> dls@wuee1.wustl.edu (Donald L. Snyder) writes:
>
>Weather satellites yield visible and infrared images of large parts of
>the earth.  My question is: how can the temperature at a given location
>be determined from such a map?  I'll venture a guess at the risk of
>exposing my ignorance about this.  Assume black body radiation with
>temperature as an unknown parameter.  Assume something about the
>spectral response of the sensor on the satellite.  Multiply the sensor
>response by the black-body spectrum and integrate.  Select a location
>with a known temperature to determine the scale factor between the
>integrated spectrum and the brightness (grey level) in the weather map at
>that location.  Then, to get the temperature at an unknown location,
>adjust the temperature until the integrated spectrum matches the
>the observed brightness at that location in the weather map (with the
>scale factor taken into account).
>
>OK, blast away at this approach.  What is the way to do it?  What is
>the spectral response of the sensors that are used?  Is there a
>reference you can suggest where I can investigate this?
>
>           Don Snyder     dls@saturn.wustl.edu

Temperatures can be measured by non-contact methods (pyrometry,
spectral radiometry) using various approximations. If the emissivity
of the hot object is one at all wavelengths, then it is a blackbody
and Planck's blackbody equation applies. The problem is greatly
simplified by assuming a constant emissivity at all wavelengths (the
grey-body approximation) and fitting Planck's blackbody equation for
both temperature and emissivity. Of cource, Planck's function is
non-linear in these parameters so non-linear regression would be
required. The problem can be made linear in its parameters using the
Wien approximation. Just remove the '-1' from Planck's function, take
the log of both sides and rearrange. This approximation is extremely
good for most applications.

Others have suggested that temperatures can be determined rigorously
by choosing a form for emissivity as a function of wavelength, making
this substitution in Planck's equation and solving for all the
parameters by non-linear regression. In principal, with perfect data
at enough wavelengths this can be done. However, at least for our
application with imperfect data, the strong correlation between
emissivity and temperature make the technique impractical.

Regarding measurement of the temperature of the surface of the Earth:
It seems to me that the intervening atmosphere would pose the greatest
difficulty. The atmosphere is full of water vapor and CO2. This mix of
gases is not equally transparent to all wavelengths of light. It is
not a simple neutral-density filter. This problem could be overcome by
proper calibration except for the fact that H2O and C02 vary greatly
over time and space. Now, if you want to measure the 'effective
temperature' of the Earth by measuring radiation from the
atmosphere...

-- 

Jeff Sweeney		sweeney@dionheinz.uchicago.edu
Newsgroups: sci.optics