Chapter 13 — Question 5

For a sea level summer image (Landsat 5), the following atmospheric parameters
are determined with MODTRAN4:

•

The atmospheric transmissivity

τ

is 0.7.

•

The upwelling radiance L ↑ is 2.4 W m

−

2

sr

−

1

µ

m

−

1

.

•

The downwelling radiance L ↓ is 3.7 W m

−

2

sr

−

1

µ

m

−

1

.

The broad-band surface emissivity

ε

is 0.98 and the radiance L

sat

observed at the

satellite is 8.82 W m

−

2

sr

−

1

µ

m

−

1

.

- Calculate the black-body radiance L

BB

.

- Determine the surface radiant and kinetic temperatures.

Answer

If you transform equation 13.8, you can isolate L

BB

on one side. Then fill in the

given values.

Result:
L

BB

= 9.283 W m

−

2

sr

−

1

µ

m

−

1

T

rad

= 299.2 K (using equation 13.7)

T

kin

= 276.0 K (using equation 13.6)

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