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
Therefore rain occurrences are a matter for flagging rather than correcting. As stated above, the heavy clouds should be
associated with rain events.
3.1.5.1.1.2 Mathematical description of algorithm
3.1.5.1.1.2.1 Radiative transfer for gaseous components
From the physics, it is concluded that atmospheric contributions must be computed for oxygen and water vapour.
Numerical simulations show that, for L band, the up welling and down welling radiative contributions are extremely
close one to each other and can be assumed equal to a single value TB atm in equation Eq 46. Therefore what is needed
is:
τ = τ + τ ; TB = TB + TB
Eq 48
atm
O2
H2O
atm
O2
H2O
Contributions to absorption come from the whole thickness of the atmosphere. However, for oxygen it is not necessary
to consider altitudes higher than a level ZM ≈ 30 km, where absorption becomes completely negligible. For water
vapour, the altitude range to be considered is limited to ZM ≈ 10 km.
Over the required altitude range, the exact computation requests knowledge of altitude profiles for T and P; then, the
atmosphere is divided in slices δz. For each slice and for each component, the elementary optical thickness δτ G (where
G is replaced by either O2 or H2O) is computed from the lineic absorption coefficient (expressed in dB km -1 ) κ G :
δτ
κG
δz /10
G
= 1−1/10
Eq 49a
Where the effect of incidence angle θ on optical thickness is introduced:
δ z(
θ ) = δz
NADIR
/ cos( θ )
Eq 49b
The total optical thickness τ G is obtained by summing the δτ G over the relevant altitude range:
∑
τ Eq 49c
G
= δτ
G
(z)
Z=
0→ZM
The radiative contribution TB G is (taking the up welling case) computed as:
TB
∑
∑
G
= T(z)
G
(z) exp[ − δτ
G
(z')]
Z= 0→ZM
Z' = Z→ZM
δτ Eq 49d
This formulation yields the up welling contribution. The down welling contribution is found very close, with
differences well below 0.01K.
Since the attenuation through an elementary layer is very small, and the physical temperature variation at this scale is
linear, the estimate for the physical temperature T(z) in (Eq 49d) can be taken as the average between T values for the
bottom and the top of the elementary layer.
3.1.5.1.1.2.2 Empirical laws for computing atmospheric terms
Three ways are contemplated for computing τ O2 and TB O2 :
1. Carry out the integrations as indicated in equations (Eq 49). The estimated necessary altitude ranges ZM are 20
km for O2, 10 km for H2O; the necessary resolution along the vertical is better than 100m.
2. Tabulate the τ G and T G as functions of some parameters (e.g. surface atmospheric temperature T0, the surface
pressure P0, some parameter describing the structure of the temperature profile, surface humidity,…) and then
interpolate from these tables.
3. Build empirical laws to compute the τ G and T G .
For the land surface, the required accuracy is estimated to be about 0.2K (circa 0.1% for soil moisture). Then method 1
is not necessary and the algorithm proposed below uses method 3.
The most efficient (and physically meaningful) way to do this consists in writing the emission of each component as the
product of optical thickness by an equivalent layer (physical) temperature, which is conveniently defined by its
difference DT with the surface air temperature T0:
TB G = (T0 – DT G ) τ G
Eq 50
.
51