Case 3: Check of the Radiative Transfer Implementation, up looking geometry.

***************************************************************************
The aim of this case is to check the implementation correctness of the
radiative transfer algorithm, for a up looking instrument. 

Pre-calculated absorption coefficients will be used as input. 
For specified calculation procedure and instrumental characteristics, the
participants shall provide both, pencil beam monochromatic spectra and
spectra as recorded by the instrument. No refraction is considered.
 
The instrument is assumed to have a perfect antenna, and to be a perfect
single sideband. In other words, only the effect of the spectrometer
will be considered. 

Spectrometer 
------------ 
The output of the spectrometer is a weighted
mean of the signal (monochromatic pencil beam) around some discrete
frequencies (sensor frequencies), channels, that together generate a
spectrum. Each channel is described by a response function. The
response function is assumed to have a Gaussian shape (FWHM = 10MHz).
All the channels are treated to have the same response.  

Input - Output Files
 --------------------

 Format:
 ======== 
  The files are ASCII files, in ARTS format.
  They can easily be recognized by the extension 'aa'. 
  The file can start with an arbitrary number of comment lines.  These
  lines starts with the hash symbol (#) The first row after the
  comment lines give the number of matrices in the array. After this
  follows, for each matrix, a row giving the matrix size followed by
  the data in row order.

Input:
======

 - Freq_mono_Up.aa -->> the frequency vector for which the absorption 
   coefficients were calculated.
 - p_z_abs_Up.aa -->> the pressure (altitude) levels corresponding to 
   pre-calculated absorption coefficients. The file is in ARTS format,
   a 2 columns matrix: column 1 gives the levels in pressure units
   [Pa], while column 2 gives the corresponding levels in geometric altitude 
   units [m]

 - Up.abs.aa -->> pre-calculated absorption coefficients, in ARTS
   format. Each row data gives the absorption coefficients (given
   p_z_abs_Up.aa) for all frequencies values given in Freq_mono_Up.aa
   and one atmospheric level (given in p_z_abs_Up.aa). 
 - Up_specifications.txt -->> the file gives the numerical values for
   platform altitude and ground specifications (temperature, altitude,
   emissivity). 
 - za_pencil_Up.aa -->> zenith angles for the pencil
   beam calculation.  
 - Freq_sensor_Up.aa -->> the frequencies
   observed by the sensor (the middle points of the backend
   channels).
 - channel_response_Up.aa -->> the file defining the
   backend channel response. The response of all channels are assumed
   to be identical. The channel file has ARTS format, a 2 column
   matrix where column 1 gives relative frequencies (with respect the
   middle points of the backend channel), and column 2 gives response
   values.

Output:
=======      
 - the pencil beam monochromatic spectra (brightness temperature) for the 
   viewing direction specified in za_pencil_Up.aa.
 - the spectra seen by instrument (including the effect of the spectrometer).
  The output data should have ARTS format: each row gives the spectra
  corresponding to one viewing direction.