Global Land Cover Classification Based on Microwave Polarization and Gradient Ratio (MPGR) - Geoinformatics for Intelligent Transportation - page 20

s function (Eq. 1 ) describes the relationship between spectral radiance
emitted by a black body and real temperature, where T is the temperature in Kelvin,
B f (T) is the spectral radiance of the blackbody at T Kelvin, h is the Planck constant,
f is the frequency of the wave band, c is the light speed, and k is Boltzman constant.
On the basis of the Taylor series expansion equation, Planck

Planck '

' s function can be

written as Eq. 2 .

2

B f T ðÞ ¼ 2kT =k ð 3 Þ

1 s f T a þ

T a T f ¼ s f e f T soil þ 1 s f e f ð 1 s i Þ ð 4 Þ

In most passive microwave applications, the value of the term hf/kT can be
assumed to be zero. Hence Planck

ed as Eq. ( 3 ). For land
cover surface temperature ground emissivity and atmospheric effects are considered
in the general radiance transfer equations for passive microwave remote sensing
[ 14 , 15 ] so Eq. 3 can be rewrite as Eq. ( 4 ), where Tf is the BT in frequency f, Tsoil
is the average soil temperature, Ta is the average atmosphere temperature, Bf
(Tsoil) is the ground radiance, Bf (Ta

' s function can be simpli

) and Bf (Ta ) are the down-welling and

↓ ↑

up-welling path radiance, respectively, τ f( ʸ ) is the atmosphere transmittance in

frequency f at viewing direction f is the ground

emissivity. From Eq. ( 4 ), a linear relationship is evident between remotely sensed
BT and land surface temperature.
Furthermore, we assume that a vegetation layer can be considered a plane,
parallel, absorbing, and scattering medium at a constant temperature Tc upon the
soil surface. The brightness temperature Tp( τ , µ ) of the radiation emitted by veg-
etation canopy at an angle

ʸ (zenith angle from nadir), and ʵ

ʸ from the zenith can be written as follows [ 13 ]:

T c þ e p T soil e

s= l s= l

T p s; ðÞ ¼ ð 1 w Þ 1 e ð 5 Þ

where p stands for horizontal (H) or vertical (V) polarization, is the

equivalent optical depth, w is the single scattering albedo. The two parameters
(background and atmospheric effect) can characterize the absorbing and scattering
properties of vegetation, respectively.

= cos ʸ . τ

µ

ʵ p is the soil emissivity for the p polarization.
MPGR Eq. ( 6a ) and ( 6b ) is an effective indicator for characterizing the land
surface vegetation cover density. The polarization ratio used in the study can be
described as Eq. ( 6a )
PR f ¼½

= ½ þ ð 6a Þ

BT( f V) BT( f H) BT( f V) BT( f H)

And the gradient ratio as Eq. ( 6b )

¼

BT f 1p BT f 2p

=

BT f 1p þ BT f 2p

ð 6b Þ

GR f 1p f 2p