Algorithm Theoretical Based Document (ATBD) - CESBIO

SO-TN-ESL-SM-GS-0001
Issue 1.a
Date: 31/08/2006
SMOS level 2 processor
Soil moisture ATBD
ε
'
w
= ε
ε
− ε
w0
w∞
w∞ +
Eq 37
2
1 + (2πrτ
w f )
:
'' 2π
rτ
w f ( ε w0
− ε w∞
) σ i
ε w =
+
2
1+
(2π
rτ
f ) 2πε
f
w
0
Eq 38
Note that in the following equations (Eq 39a Eq 41e) the temperature, T, is in °C.
σ i is the ionic conductivity for saline water (in S/m) function of temperature and salinity:
i
−φ
( ) ( )
( S,
∆
S,
T = σ 25, S ⋅e
)
σ Eq 39a
Where ( 25 S )
i
i ,
i
σ is the ionic conductivity of sea water at 25°C and is given by:
2
3
( 25,
S ) = S ⋅ ( ow + ow ⋅ S + ow ⋅ S + ow ⋅ S )
σ Eq 39b
23
And the function φ depends on S and ∆ = 25 −T
24
25
2
2
( ∆, S ) = ∆ ⋅ ( ow + ow ⋅ ∆ + ow ⋅ ∆ − S ⋅ ( ow + ow ⋅ ∆ + ow ⋅ ∆
)
27
28
29
26
φ Eq 39c
For pure water S=0, thus the ionic conductivity is also null, σ ( 0 , T ) = 0
The magnitude of the high frequency dielectric constant
30
31
i
32
ε
w∞
was determined by Lane and Saxton [69] to be 4.9.
There are separate algorithms for calculating the static dielectric constant, ε w0
and the relaxation time, 2 πrτ w , of
fresh and saline water..
• The static dielectric constant of fresh water, ε w0 , is a function of temperature as described by Klein and Swift [70]:
2
3
( T ) = ow + ow · T + ow · T ow T
ε Eq 40a
w 0 1 2 3 + 4 ·
The relaxation time of pure water, rτ w , is given by Stogryn [71]:
2
3
( T ) = ow + ow · T + ow · T ow
2π rτ
w + T
Eq 40b
14 15 16 17·
• For saline water with a salinity SAL or SSS = S, the static dielectric constant of water, ε sw0 , is given [70] as
ε sw0 (S,T) = ε sw0 (T,0) a ST (S,T)
with
2
3
( T, ) = ow + ow ⋅T
+ ow ⋅T
+ ow ⋅T
sw0 0
5
6
7
8
Eq 41a
ε Eq 41b
a ST
2
3
( S, T ) ow + ow ⋅ S ⋅T
+ ow ⋅ S + ow ⋅ S + ow ⋅ S
= Eq 41c
9
10
The relaxation time of saline water, rτ sw , is given by Stogryn [71]:
11
( S,
T ) 2π
r ( T ) b ( S T )
12
13
2π rτ
= τ
Eq 41d
b ST
sw w ST ,
2
3
( S, T ) ow + ow ⋅ S ⋅T
+ ow ⋅ S + ow ⋅ S + ow ⋅ S
= Eq 41e
18
19
Coefficients OW1 to OW32 are supplied in TGRD UPF.
20
21
Idealised forward/inverse modelling indicates that a 1% (absolute) underestimate in the weighted field of view occupied
by water can give rise to a 0.01 m 3 m -3 error in soil moisture retrieval, in cases of high soil moisture (0.4 m 3 m -3 ) and
dense vegetation cover (optical depth 0.6).
22
.
43