# HW5_2016a

```EE/Ae 157a
Homework #5
Due Date: December 3, 2015
The microwave temperature of a soil surface covered by a vegetation canopy can be written as
T  1  i  Tg e  Tc 1  e   iTc 1  e  e
where Tg and Tc are the temperatures of the soil and the canopy, respectively. The subscript i
refers to the polarization (either horizontal or vertical). The optical depth  of the canopy is a
function of the vegetation water content according to
  bWc
The constant b is a vegetation opacity coefficient that is determined experimentally and has a
value of approximately 0.1 at L band.
For dawn (6am local time) orbit overpasses, the soil and vegetation temperatures are
approximately equal to the surface air temperature, and the brightness temperature can be
written:
T  Ta 1  i e 2 
where Ta is the surface air temperature. Assume that the soil has a dielectric constant of 15.
Calculate the expected change in microwave temperature for a 5% change in soil dielectric
constant, and plot this as a function of the vegetation water content.
```