Ecoinformatics and Soil-Plant Formations - New Ecoinformatics Tools in Environmental Science: Applications and Decision-making - page 711

is covered by plants, it is useful to consider simple parametrical descriptions of this
dependence. A simpli ed microwave model can be written as the following

integral:

2 3 2 3

Z

H

Z

H

Z

y

4 5 þ 4 5 dy þ fð H Þ

T B ð H Þ ¼e s T s exp cð x Þ dx T ð y Þcð y Þ exp cð x Þ dx

0 0 0

ð 8 : 19 Þ

where ʳ is the absorption coef cient, e s is the soil emissivity coef cient, T s is the

soil temperature, T is the temperature of atmosphere, and ʶ is the model precision.

There exist different simpli cations of equation ( 8.19 ). For example, various

approximations for T(y) and ʳ (y) are often used:

T 2 ; 0 y h

;

or T ð y Þ ¼T 0 þ T 1 y þþ T n y n

T ð y Þ ¼

T 1 ; y H

:

h \

and :

For the satellite monitoring case it can be shown that

cð y Þ ¼ c 0 þ c 1 y or c ðÞ ¼const

T B ¼ e s T s p sat þ X

n 1

D l ð 0 Þ ð 8 : 20 Þ

l¼1

where p sat is the atmospheric transmittance between soil surface and satellite,

dT ð h Þ
dh ; ...; D l ¼

dD l 1 ð h Þ
dh

1
cð h Þ

1
cð h Þ

D 1 ¼ T ð h Þ; D 2 ¼ ; ... :

le T(h) into
consideration, formula ( 8.20 ) will calculate the brightness temperature T B with an
error equal to D n (0).
The more simpli

Taking different analytical representations for the vertical pro

ed microwave model ( 8.19 ) for the canopy-surface brightness
temperature is given as:

T B ðk; hÞ ¼e 2 T 2 þ R 21 ðhÞ T B ; sky ðh 1 ; h 2 Þ ð 8 : 21 Þ

where is the angle of incidence and T B,sky is the sky brightness temperature

incident on the canopy level from a direction (

ʸ

ʸ 1 , ʸ 2 ), with zenith and azimuth

angles ʸ 2 , respectively.

Model ( 8.21 ) simpli

ʸ 1 and

uence of canopy temperature and
wind speed, for example, on the variations of the brightness temperature. This
analysis is possible with knowledge of the canopy roughness as a function of wind
speed.

es the analysis of the in fl