=====Remote sensing of cloud optical thickness and effective radius=====
Nadir radiances (TOA, viewing direction 'umu 1', straight downwards) at the two wavelengths 750 nm and 2160 nm

In the following we simulated the backscattered radiation for a given optical thickness of a cloud and a given effective radius. From it we try to find a connection between radiation and optical properties of the cloud.

Looking at backscattered radiance at 750 nm we can conclude that there is no dependence on the effective radius.
Therefore it should be possible to get a quite good estimate of the optical thickness.
{{:teaching:radiative_transfer:plot750.png|}}

Looking at 2160 nm there is a strong dependency on the effective radius. So given the optical thickness you can estimate the effective radius. 
{{:teaching:radiative_transfer:plot2160.png|}}


The classical method for cloud remote sensing of optical thickness and effective radius is descibed {{:teaching:radiative_transfer:nakajima90.pdf|Nakajima and King (1990)}}. 

{{:teaching:radiative_transfer:nakajima_king.png|}}




Calculate nadir radiances (viewing direction 'umu 1', straight downwards) at the two wavelengths 750 nm and 2160 nm respectively for effective radii between 1 µm and 25 µm and for cloud optical thicknesses between 1 and 30 and plot the results. When you have radiance measurements at both wavelengths, would it be possible to retrieve cloud optical thickness and effective radius?   

Use a shell script to do the calculations. It could for example look like this: 
<file bash runit.sh>
lambda=2160

rm result$lambda\nm.dat 

for tau in `seq 1 30`; do
    for reff in `seq 1 25`; do
	
       	sed 's/LAM/'$lambda'/' disort.tmplt | sed 's/TAU/'$tau'/' > disort.inp
	sed 's/REFF/'$reff'/' wc.tmplt > wc.dat

	uvspec15 < disort.inp | gawk '{print '$tau', '$reff', $1}' \
	    >> result$lambda\nm.dat 

    done
done
</file>

The file disort.tmplt is a template for a uvspec input file where the wavelength and the cloud optical thickness are replaced by the shell script. The template looks as follows: 
<file bash uvspec.tmplt>
                         # specify libRadtran data path
data_files_path          /local/emde/libRadtran/data

sza 30                   # solar zenith angle
 
                         # extraterrestrial solar radiation 
source solar               kurudz_1.0nm.dat
              
                         # Location of atmospheric profile file. 
atmosphere_file          us-standard

albedo 0.0               # Surface albedo

rte_solver disort2       # Radiative transfer equation solver 
                         # disort2 with intensity correction, disort1 without

nstr 16                  # number of streams used in DISORT
   
wavelength  LAM          # Wavelength range [nm]

mol_abs_param  LOWTRAN   # gas absorption parameterization

wc_file 1D               wc.dat
wc_properties mie interpolate
wc_modify set tau  TAU

zout TOA                 # position
umu 1                    # viewing direction
phi 0

output_user uu           # Output radiance value

quiet
</file>

A second template file is needed to specify the effective radius of the cloud (wc.tmplt). 

The best is to plot the result as a contour plot, here is a python example:

<file python plot_radiance.py>
result750=loadtxt('result750nm.dat')

figure(1)
contourf(result750[:,2].reshape(30,25))
colorbar()
xlabel('effective radius [um]')
ylabel('cloud optical thickness')
title('radiance [mW / (m^2 nm sr)] @ 750 nm')
</file>