Modeling and Inversion in Thermal Infrared Remote Sensing over ...

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268 F. Jacob et al.functionally equivalent to aerodynamic temperature (Eq. 10.3). Second, they provideinformation for monitoring vegetation photosynthesis and soil respiration.ird-00392669, version 1 - 9 Jun 200910.6.4 Directional Emissivity and Soil/Vegetation TemperaturesSingle directional radiometric temperature can be split into soil and vegetation componentsby closing energy balance for each. However, this relies on strong assumptionsabout vegetation water status [231–233]. The promising approach is then usingmultiangular TIR observations [20, 68, 71, 118, 119, 189]. No literature was foundabout retrieving soil and vegetation temperatures by inverting simulation modelsover multiangular data. Nevertheless, such models have been used for parameterizingthe soil and vegetation radiative transfer equation which is directly invertible(Eq. 10.10). These parameterizations were designed considering the [8–14] µmspectral range.10.6.4.1 Parameterizing the Soil/Vegetation Radiative Transfer EquationInverting Eq. 10.10 requires estimating the involved parameters (ensemble emissivityε(λ j ,θ), vegetation transmittance τ can (θ), and vegetation fraction of emittedradiance ω(θ,ε veg (λ j ))), with optional simplifications for easier use. Variouscomplexity degrees have been proposed, listed in Table 10.3 (P1–P8). This yieldsintroducing two new parameters. Hemispherical gap fraction σ f is directional gapfraction integrated over illumination angles, to account for atmospheric thermal irradiancedown to the soil via the vegetation. The cavity effect coefficient α is theratio of canopy to vegetation hemispherical-directional reflectance, to account forradiation trapping within the canopy.The finest parameterization (P1), proposed by [118], accounts for multiple scatteringand cavity effect. The latter, which does not depend on LAI, was previouslycalculated as a function of LIDF and view zenith angle, by using the probabilisticsimulation model from [139]. Similarly, [127] introduced effective directional gapF ef ffsoil(θ) and cover Fef veg (θ) fractions (P2). F ef fsoil(θ) included single scattering of soilemission by vegetation. Fveg ef f (θ) included single scattering of vegetation emissionby soil and vegetation. Half complex parameterizations (P3–P5) account for multiplescattering, with optional linearizations [68, 71]. The simplest parameterizations(P6–P8) do not account for cavity effect nor multiple scattering. They differ by theirlinearization degrees, and their assumptions about soil and vegetation emissivities[71, 119, 189].Some of these parameterizations were assessed in direct mode for simulatingdirectional ensemble emissivity and radiometric temperature [68]. The conclusionswere apart from simplest versions, most provided close results for directionalcanopy emissivity, with discrepancies lower than 0.01. For radiometric temperature,all provided similar results, with differences lower than 1 K. Next, differencesUncorrected Proof
10 Modeling and Inversion in Thermal Infrared Remote Sensing 269ird-00392669, version 1 - 9 Jun 2009Table 10.3 Listing of existing parameterizations (P1–P8) for the soil and vegetation radiativetransfer equation (Eq. 10.10), with a decreasing complexity. The spectral dependence was removedsince these parameterizations were designed considering the [8–14] µm spectral range. Labels f irefer to specific functions proposed by the corresponding references. The dependence on LAI andLIDF is implicitly included into directional gap and cover fractions F soil (θ) and F veg (θ), the cavityeffect coefficient α(θ), and hemispherical gap fraction σ f [68].Standard formulationε(θ) B(T rad (θ)) = τ can (θ) ε soil B(T soil )+ω(θ,ε veg ) B(T veg )Label From Formulations RemarksP1 [118] ε(θ)= f 3(Fsoil (θ),ε soil ,ε veg ,σ f ,α(θ) ) Accounts forτ can (θ)=F soil (θ)(ω(θ,ε veg )= f 4 Fsoil (θ),F veg (θ),ε soil ,ε veg ,σ f ,α(θ) )P2 [127] ε(θ)=F ef fsoil (θ) ε soil + Fveg ef f (θ) ε vegτ can (θ)=F ef fsoil (θ)multiple scatteringand cavity effectAccounts formultiple scatteringω(θ,ε veg )=Fveg ef f (θ) ε vegand cavity effectF ef fsoil (θ)= f ( )1 Fveg (θ),σ f EffectiveFveg ef f ( )(θ)= f 2 Fsoil (θ),σ f parameterizationP3 [68] ε(θ)= f 5 (F soil (θ),F veg (θ),ε soil ,ε veg ,σ f ) Accounts forτ can ( )(θ)= f 6 Fsoil (θ),ε soil ,ε veg ,σ f multiple scattering( )ω(θ,ε veg )= f 7 Fsoil (θ),F veg (θ),ε soil ,ε veg ,σ fP4 [71] Linearizing P3 considering B(T ) ≈ σ T 4 Accounts forP5 Linearizing P3 considering B(T ) ≈ σ T multiple scatteringP6 [119] ε(θ)=F soil (θ) ε soil + F veg (θ) ε vegτ can (θ)=F soil (θ)ω(θ,ε veg )=F veg (θ) ε vegP7 [71] Linearizing P6 considering B(T ) ≈ σ TP8 Simplifying P7 considering ε veg = ε soil = 1decreased with atmospheric irradiance which compensates emission (Eq. 10.7).However, this is minor under clear sky conditions, with irradiance lower than 30W. m −2 between 8 and 14 µm [234]. Finally, [127] observed analytical formulationP2 significantly diverged from a ray tracing reference when soil and vegetationemissivities were very different.10.6.4.2 Inverting the Soil/Vegetation Radiative Transfer EquationThe various parameterizations reported above have been assessed in inverse modeconsidering dual angle observations, nadir and 45 or 55 ◦ off nadir. Given soil andvegetation emissivities, dual angle measurements allow retrieving component temperatures.Off nadir angles above 45 ◦ are required to capture large angular dynamicsUncorrected Proof
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