1)  Right after a rain shower, there is almost no aerosol in the air.  A sunphotometer is an instrument that looks at visible light coming in a straight line directly from the sun.  At one point it measures an irradiance of I1 W/m2, but when a cloud passes overhead this drops to I2 W/m2. Assuming sun zenith angle θ degrees:
a) What is the optical depth of the cloud? (10 pts)

If the cloud would be twice as thick, what intensity would the sunphotometer measures when the cloud passed overhead? (5 pts)
Calculate the transmittance for case (b) if Rayleigh and aerosol scattering are also taken into account with optical thicknesses τR and τa respectively (5 points). 

2) Given remote sensing reflectance spectrum in Table 2 use MATLAB to: a) plot this spectrum as a function of wavelength, b) calculate chlorophyll -a concentration using VIIRS algorithm. (15 points)

3)A pixel completely filled with vegetation has a reflectance in the red of Rred, 0.02and in the NIR of 0.25RNIR.  A pixel filled with soil has a reflectance of 0.1R2red in the red and R2NIR 0.4in NIR.   What would be the reflectances for a pixel γ0.6 filled with vegetation?  Calculate the NDVI and VI indices for this mixed pixel (15 pts)
4)Compute the ground track speed of a satellite with H740 km altitude, the time that satellite rotates one complete orbit around the earth and the number of orbits per day (15pts). 
5)Download NetCDF (.nc) file from the blackboard. Identify mostly vegetated areas and areas with clouds above vegetation and water areas. Show corresponding images. (15 points)

6) 

Create a code in MATLAB to calculate the lidar power return ratio p = P/P0 (power detected over power of the laser) for 0 to 10 km range using the following inputs:

Particle cross section in the atmosphere σ = 10^(-13), number of particles at the surface level N0 = 10^(12).
Lidar ratio between extinction coefficient α, [m-1] and the value of the scattering phase function at 180° β, [m-1/sr] is S = 10 sr. 
Consider the lidar constant C=1.

Make a plot for p-R dependence.
Hint: you need to take into account the dependence of number of particles on the height (see lectures 4 and 5). (20 points)
 
Problem 1
Problem 3
Pr. 4
I1
I2
θ
τR
τa
Rred
RNIR
R2red
R2NIR
γ
H
130
89
47
0.05
0.15
0.02
0.25
0.1
0.4
0.6
740
Table 2
λ, nm
410
443
486
551
671
Rrs, sr-1
0.00137
0.00163
0.00269
0.00580
0.00236