Algorithm Theoretical Based Document (ATBD) - CESBIO

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SO-TN-ESL-SM-GS-0001 Issue 1.a Date: 31/08/2006 SMOS level 2 processor Soil moisture <strong>ATBD</strong> 2θ TB p SMOS sensor TB Sk TB atm External Contributions TB atm Atmosphere atm , TB atm τ Layer Above Surface Layer T c τ ,ω , c T c Tc T g Surface Layer Soil e , T gp g Figure 3 : Contributions to TOA brightness temperature Consider now a mixed L1c scene with n = 1 to NF mean (over incidence angle) fractions FM n . Of course NF is actually a small number. For each L1c view, incidence angle dependant values FV n for fractions are to be computed. For ease of writing we rewrite Eq 9 as follows: TB p = TB atm + exp (-τ atm ) [TB atm +TB sk exp(-τ atm )] R1 Eq 9a + exp (-τ atm ) R2 Where only the expressions R1 (dimensionless) and R2 (in Kelvin) depend on the fraction n. Then the aggregated fwd model, for each view, is derived from Eq 9 where: R1 becomes: SUM n=1:NF { FV n R1 n }; R2 becomes: SUM n=1:NF { FV n R2 n } The contributions R1 n and R2 n are computed with the help of forward models described in following subsections of section 3.1. Fractions FM n and FV n are presented in section 3.2.2.5 and in the decision tree section 3.2.3. 3.1.1.4 Towards elementary radiative models In the following, elementary radiative models are described whenever available. If no model exists (i.e. urban) it is proposed to put a place holder with a proxy model (in this case some sort of a bare soil). Then: • We are mainly interested in scenes devoid of strong topographic features, possibly covered by low vegetation, for which volume surface moisture can be defined. This will be called the nominal SMOS target (in short NO for nominal, or LV for low vegetation). Forward models are available. • It may happen that, although soil moisture is in principle relevant, forward models are poorly known or not validated. This is e.g. the case for strong topography, snow cover. . 29
SO-TN-ESL-SM-GS-0001 Issue 1.a Date: 31/08/2006 SMOS level 2 processor Soil moisture <strong>ATBD</strong> • In some cases, soil moisture is no longer relevant. Examples are open water, ice. We will now address the details of nominal models as well as other cases. The nominal case develops the way to model surface roughness as well as the vegetation layer. Note that • surface roughness is also present for other cases excepting all water surfaces; • vegetation layer is also present for other cases, excepting free water surfaces but including wetlands 3.1.2 Nominal case (vegetated soil) The modelling approach used here relies on an extensive review of current knowledge and previous studies. It accounts for, as much as possible, emission from various land covers, from bare soil to full vegetation-covered surfaces, snowcovered surfaces, open water, and atmospheric effects The nominal case is the case where we believe soil moisture retrievals will be feasible. It consists of “normal” soil with low vegetation, eventually a manageable amount of free water. The "manageability" is expressed by thresholds for which values are suggested in the decision tree section but will often require confirmation. 3.1.2.1 Bare Soil Bare soils are quasi-opaque at 1.4 GHz, so the radiative budget is mainly ruled by their emissivity e and reflectivity r, for each polarisation p, with: e + r 1 Eq 10 gp gp = The emission of microwave energy is governed by the product of the soil effective temperature, T s , and soil emissivity, e gp . At L band, the emissivity e gp is in turn is a function of the soil’s characteristics, i.e. moisture, texture, roughness and eventually salinity 3.1.2.2 Smooth Bare Soil Dielectric Properties The theory behind the microwave remote sensing of soil moisture is based on the large variation of emissivity with soil water content. This is due to the fact that the real part of the dielectric constant value of “ordinary” soil varies between that of dry soil (< 4) and that of liquid water (~ 80) depending on its actual water content. Consequently, as soil moisture increases, the emissivity (all other things remaining constant) decreases, and this change is detectable by microwave sensors. This qualitative description is formalized as follows. The reflectivity r bp of a perfectly smooth surface is given by the Fresnel law that defines the partition of electromagnetic energy at a flat dielectric boundary [34]. The Fresnel reflection coefficients r bH and r bV at H and V polarizations, respectively (a rigorous notation would be r bgH , with the "b" subscript standing for smooth and bare (bald) soil) are given by: r bH ( θ ) µ cos 2 ( θ ) − µ sε b − sin ( θ ) 2 ( θ ) + µ ε − sin ( θ ) 2 r ( θ ) ε cos = 2 ( θ ) − µ sε b − sin ( θ ) 2 ( θ ) + µ ε − sin ( θ ) s b = Eq 11 bV µ s cos s b ε b cos s b where µ s is the soil magnetic permeability, assumed to be unity; ε b, is the complex, smooth, bare soil dielectric constant (medium dependant), and θ is the incidence angle. Then, for smooth bare soil, the up-welling soil brightness temperature may be written as a function of the soil effective temperature T g and soil reflectivity r bp computed from the Fresnel equation: TB p = (1 – r bp ) T g Eq 12 2 According to the Dobson model [35, 36], the dielectric constant of wet soil can be calculated as ε ′ = b ε ′′ = b α β ′ α ( 1+ ( ρb / ρ s ) ( ε pa −1) + ( SM )( ε ′ fw ) − SM ) β ′′′ α (1/ α ) ( SM )( ε ′′ ) fw (1/ α ) Eq 13 where • ε 0s = soil dielectric constant for bare soil . 30
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