====== TOA radiance at 10 μm as function of cloud height ======

Calculate the radiance at the top of the atmosphere at a wavelength of 10 μm assuming that the atmosphere includes a cloud layer. How does the radiance depend on cloud altitude?

//Hints:// 

  * Use the libRadtran input file and the plotting script from [[teaching:radiative_transfer:disort_nstr1|exercise 6]] to start.
  * Look at [[teaching:radiative_transfer:disort_nstr2|exercise 8]] to see how a cloud layer is defined in libRadtran.

<file bash 13.inp>
data_files_path /local/libRadtran-1.5-beta/data
atmosphere_file us-standard
mol_abs_param lowtran
source solar kurudz_1.0nm.dat
albedo 0.0
sza 30.0
rte_solver disort2
wavelength 10000
wc_file 1D /usr/users/westermayer/Desktop/RadiativeTransfer/cloud1.dat 
zout toa
umu 0.9
phi 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360
</file>

<file bash cloud1.dat>
# height LWC	Reff
# km	g/m^3	µm
3.0	0	0
2.0	0.1	10.0
1.0	0.1	10.0
</file>

<file bash cloud6.dat>
# height LWC	Reff
# km	g/m^3	µm
8.0	0	0
7.0	0.1	10.0
6.0	0.1	10.0
5.0	0	0
4.0	0	0
3.0	0	0
2.0	0	0
1.0	0	0
</file>


{{:teaching:radiative_transfer:clouddata13.dat|}}





{{:teaching:radiative_transfer:plot13.png|}}



<file bash loop.sh>
#!/bin/bash

# this shell script calculates radiances for clouds at differnt heights. zmin is the bottom 
# of the cloud, zmax the top.

rm radiance.dat

for zmin in `seq 1 8`; do

    # zmax should be 1 km higher than zmin -> cloud layer thickness is 1 km
    let zmax=zmin+1
    echo "zmin: "$zmin" zmax: "$zmax

    # Make template for wc_file where the altitudes are replaced using sed
    sed 's/ZMIN/'$zmin'/' wc.tmplt | sed 's/ZMAX/'$zmax'/' > wc.dat

    # execute uvspec
    uvspec < uvspec.inp > dummy

    # write result (zmin, zmax, radiance) into file
    gawk '{print '$zmin', '$zmax', $2}' dummy >> radiance.dat

done    
</file>

<file bash uvspec.inp>
                         # specify libRadtran data path
data_files_path  /local/emde/libRadtran/data

                         # Location of atmospheric profile file. 
atmosphere_file          us-standard

correlated_k             lowtran

albedo 0                 # Surface albedo

rte_solver disort2       # Radiative transfer equation solver

wavelength 10000         # Wavelength range [nm] 

wc_file wc.dat

source thermal            # Emission from Earth surface is source of radiation

zout toa                  # surface or toa

umu 1
phi 0 

output per_nm            # output unit

output_user lambda uu
</file>

<file bash wc.tmplt>
ZMAX 0 0 
ZMIN 0.1 10
</file>

<file python plot_rad.py>
from pylab import *

# Planck function to calculate radiance for given wavelength and temperature. 
# Note the difference (factor pi) to task 1 where irradiances were calculated.
def planck(lam, T):
 
    c= 2.99792458e8 # speed of light
    k= 1.380662e-23 # Boltzmann constant
    h= 6.626180e-34 # Planck constant
 
    return 2*h*c*c/(lam**5 * (exp(h*c/(lam*k*T))-1.))


# simulated radiance
bt=loadtxt('radiance.dat')
# atmospheric profile
atm=loadtxt('/local/emde/libRadtran/data/atmmod/afglus.dat')

plot(bt[:,2], bt[:,1], 'o', label='simulated radiance')
plot(planck(10e-6,atm[:,2])*1e-9, atm[:,0], label='B( T(z) )')
ylim(0,10)
xlim(0,0.015)
ylabel('cloud top height [km]')
xlabel('radiance [W/(m^2 nm sr)]')
legend()

savefig('cloudheight.png')
</file>


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