Land Surface Temperature (LST) Retrieval from GOES Satellite Observations - Satellite-based Applications on Climate Change - page 300

For a specific land surface type with surface emissivity close to unity, based on
Eq. 19.28 , the radiance error introduced by the atmosphere, ΔR , can be represented as

Z

1

d

ΔR ¼B λ; T s ð ÞRðλ; μÞ¼B λ; T s ð ÞB λ; T s ð Þ τ 0 ðλ; μÞ B λ; T p τðλ; μ; pÞ

τ 0

Z

1

Z

1

d

¼ B λ; T s ð Þ d τðλ; μ; pÞ B λ; T p τðλ; μ; pÞ

τ 0

τ 0

Z

1

d

¼ B λ; T s ð ÞB λ; T p τðλ; μ; pÞ ð : Þ

19 31

τ 0

In the atmospheric window regions, the absorption is weak, so that

τ ¼ e k λ u 1 k λ u (19.32)

where k λ and u is absorption gas

optical path (mainly water vapor in window channel). Under this assumption,
Eq. 19.31 can be rewritten as

is the absorption coefficients at wavelength λ

Z 1 Z 1

u s ¼ ρ d s ¼ ρ sec θ d z (19.33)

0

0

u s is the total optical depth from the surface to the top of atmosphere. From the
Planck function, we get

T s T s T λ

Þ @ B
@T

ΔR ¼ B λ; T s ð ÞRðλ; μÞ¼B λ; T s ð ÞB λ; T λ ð ð Þ (19.34)

From ( 19.33 ) and ( 19.34 ), it follows that

Z

u s

d l

T s T λ ¼ k λ T s T p (19.35)

0

m (night), two such equations
with different absorption coefficient k λ can be solved simultaneously to yield

Using the two window channels 11.0 and 3.9 μ

T 11 T 3 : 9

k 11
k 3 : 9 k 11

T s T 11 ¼ ð Þ (19.36)