Difference between revisions of "Radiometric operations"

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(Land Surface Temperature (LST))
 
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=== 3.1.2 Radiometric corrections ===
+
__TOC__
 +
{{scientific}}
 +
== fAPAR estimation and atmospheric correction (Gobron et al., 2006) ==
 +
This procedure, published by [[References|Gobron et al. (2006)]], uses the TOA-reflectances in the BLUE, RED and NIR bands (R<sub>aB</sub>, R<sub>aR</sub>, R<sub>aN</sub>) and combines the atmospheric correction and fAPAR-extraction as follows (the functions Fn and band-specific parameter sets P<sub>ni</sub> are explained later):
  
==== 3.1.2.1 fAPAR estimation and atmospheric correction (Gobron et al., 2006) ====
+
* '''''BRDF-correction with the RPV-model''''': First the directional R<sub>ai</sub> in the three bands i are converted into more standardized hemispherical reflectances &rho;<sub>ai</sub> via the equation &rho;<sub>ai</sub> =F<sub>1</sub>(R<sub>ai</sub>, &theta;<sub>s</sub>, &Phi;<sub>s</sub>, &theta;<sub>v</sub>, &Phi;<sub>v</sub>, P1<sub>i</sub>)which also uses the known angles and the band-specific parameter sets P<sub>1i</sub>.
 +
* '''''Atmospheric correction''''': Next, "rectified" surface reflectances are computed for RED (&rho;<sub>sR</sub>) and NIR (&rho;<sub>sN</sub>) with the following equations: &rho;<sub>sR</sub> = F<sub>2R</sub>(&rho;<sub>aB</sub>, &rho;<sub>aR</sub>, P<sub>2R</sub>) and &rho;<sub>sN</sub> = F<sub>2N</sub>(&rho;<sub>aB</sub>, &rho;<sub>aN</sub>, P<sub>2N</sub>), where P<sub>2R/N</sub> are band-specific parameter sets. The underlying idea is that the radiative state of the atmosphere can be assessed from the reflectance differences between the BLUE and the other bands (the BLUE is indeed very susceptible for atmospheric scattering).
 +
* Finally '''''fAPAR''''' is estimated from the rectified reflectances and parameter set P<sub>3</sub>, via fAPAR= F<sub>3</sub>(&rho;<sub>sR</sub>, &rho;<sub>sN</sub>, P<sub>3</sub>).
  
This procedure, published by Gobron et al. (2006), uses the TOA-reflectances in the BLUE, RED and NIR bands (R<sub>aB</sub>, R<sub>aR</sub>, R<sub>aN</sub>) and combines the atmospheric correction and fAPAR-extraction as follows (the functions Fn and band-specific parameter sets P<sub>ni</sub> are explained later):
+
To define the specific functions F<sub>n</sub> and parameter sets P<sub>ni</sub>, [[References|Gobron et al. (2006)]] coupled three simulation models: 6S links the satellite-registered radiance L<sub>a</sub> with the surface reflectance &rho;<sub>s</sub>, the latter is simulated via Gobron's Semi-Discrete canopy reflectance model (SDRM), while the leaf optical properties (one of the SDRM-inputs) are predicted by PROSPECT. All three models require additional information, such as the leaf chlorophyl content (PROSPECT), the LAI (SDRM) and the atmospheric aerosol content (6S). A multitude of "scenario's", i.e. combinations of all these external parameters, is defined in advance. All together they should represent the variability observed in the real world (all vegetation types x atmospheres x viewing conditions ...). The coupled model is then run to compute for each scenario a number of outputs, which also include fAPAR (via the adapted SDRM) and the mentioned intermediate reflectances (BRDF-corrected &rho;<sub>aB</sub>/&rho;<sub>aR</sub>/&rho;<sub>aN</sub> and rectified &rho;<sub>sR</sub>/&rho;<sub>sN</sub>). The functions F<sub>n</sub> and parameter sets P<sub>ni</sub> are then defined by statistical analysis of the scenario database. De facto, the functions F<sub>n</sub> are ratio's of polynomials and the parameter sets P<sub>ni</sub> contain their coefficients.
  
    * '''''BRDF-correction with the RPV-model''''': First the directional R<sub>ai</sub> in the three bands i are converted into more standardized hemispherical
+
Compared to SMAC, the combined approach of [[References|Gobron et al. (2006)]] does not need ancillary information on the distribution of ozone, water vapour and aerosols. But the method is only applicable for sensors such as VGT and MODIS which (in addition to the omni-present RED and NIR) also have a BLUE band. This band lacks for AVHRR, for which another method to derive fAPAR is used (see [[Vegetation indicator procedures#fAPAR (Weiss et al., 2010)|fAPAR (Weiss et al., 2010)]]).
      reflectances &rho;<sub>ai</sub> via the equation &rho;<sub>ai</sub> =F<sub>1</sub>(R<sub>ai</sub>, &theta;<sub>s</sub>, &Phi;<sub>s</sub>, &theta;<sub>v</sub>, &Phi;<sub>v</sub>, P1<sub>i</sub>)
 
      which also uses the known angles and the band-specific parameter sets P<sub>1i</sub>.
 
    * '''''Atmospheric correction''''': Next, "rectified" surface reflectances are computed for RED (&rho;<sub>sR</sub>) and NIR (&rho;<sub>sN</sub>) with the following equations:
 
      &rho;<sub>sR</sub> = F<sub>2R</sub>(&rho;<sub>aB</sub>, &rho;<sub>aR</sub>, P<sub>2R</sub>) and &rho;<sub>sN</sub> = F<sub>2N</sub>(&rho;<sub>aB</sub>, &rho;<sub>aN</sub>, P<sub>2N</sub>),
 
      where P<sub>2R/N</sub> are band-specific parameter sets. The underlying idea is that the radiative state of the atmosphere can be assessed from the reflectance
 
      differences between the BLUE and the other bands (the BLUE is indeed very susceptible for atmospheric scattering).
 
    * Finally '''''fAPAR''''' is estimated from the rectified reflectances and parameter set P<sub>3</sub>, via fAPAR= F<sub>3</sub>(&rho;<sub>sR</sub>, &rho;<sub>sN</sub>, P<sub>3</sub>).  
 
  
To define the specific functions F<sub>n</sub> and parameter sets P<sub>ni</sub>, Gobron et al. (2006) coupled three simulation models: 6S links the satellite-registered radiance L<sub>a</sub> with the surface reflectance &rho;<sub>s</sub>, the latter is simulated via Gobron's Semi-Discrete canopy reflectance model (SDRM), while the leaf optical properties (one of the SDRM-inputs) are predicted by PROSPECT. All three models require additional information, such as the leaf chlorophyl content (PROSPECT), the LAI (SDRM) and the atmospheric aerosol content (6S). A multitude of "scenario's", i.e. combinations of all these external parameters, is defined in advance. All together they should represent the variability observed in the real world (all vegetation types x atmospheres x viewing conditions ...). The coupled model is then run to compute for each scenario a number of outputs, which also include fAPAR (via the adapted SDRM) and the mentioned intermediate reflectances (BRDF-corrected &rho;<sub>aB</sub>/&rho;<sub>aR</sub>/&rho;<sub>aN</sub> and rectified &rho;<sub>sR</sub>/&rho;<sub>sN</sub>). The functions F<sub>n</sub> and parameter sets P<sub>ni</sub> are then defined by statistical analysis of the scenario database. De facto, the functions F<sub>n</sub> are ratio's of polynomials and the parameter sets P<sub>ni</sub> contain their coefficients.
+
Go back to [[SPOT-VEGETATION]] or [[TERRA-MODIS]] pre-processing.
  
Compared to SMAC, the combined approach of Gobron et al. (2006) does not need ancillary information on the distribution of ozone, water vapour and aerosols. But the method is only applicable for sensors such as VGT and MODIS which (in addition to the omni-present RED and NIR) also have a BLUE band. This band lacks for AVHRR, for which another method to derive fAPAR is used (see fAPAR (Baret et al., 2007)).
+
==Land Surface Temperature (LST) ==
  
Go back to SPOT-VEGETATION or TERRA-MODIS pre-processing.
+
For the determination of the land surface temperature the split window method of Coll & Caselles (1997) is implemented. The brightness temperatures from channel 4 (TIR4) and channel 5 (TIR5) of AVHRR are combined with the surface emissivity (correcting for grey bodies) and the atmospheric water content is taken into account. The surface emissivity is derived from the vegetation cover fraction, in this case derived from the NDVI with the following method.
 +
 
 +
Method to calculate the vegetation cover fraction:
  
==== 3.1.2.2 Land Surface temperature (LST) ====
+
The vegetation cover fraction (P<sub>v</sub>) is calculated using the median of the pixels with the 5% highest NDVI values is NDVI, and the median of the pixels with the 5% lowest NDVI value is NDVI<sub>g</sub>.
 +
 
 +
<div class="formula_triple"><math>P_{v}=\frac{NDVI-NDVI_{g}}{NDVI_{v}-NDVI_{g}}</math></div>
 +
 
 +
with
 +
 
 +
{| border=0
 +
|-
 +
  | Pv
 +
  |  : Vegetation fraction [-]
 +
|-
 +
  | NDVI
 +
  |  : Normalized Difference Vegetation Index of the pixel [-]
 +
|-
 +
  | NDVIg
 +
  |  : maximum Normalized Difference Vegetation Index of a bare soil pixel [-]
 +
|-
 +
  | NDVIv
 +
  |  : minimum Normalized Difference Vegetation Index of a fully vegetated pixel [-]
 +
|}
 +
 
 +
 
 +
<!--- [[File:VegetationCoverFraction.png]] --->
 +
 
 +
The emissivity (ε, -) is calculated according to [[References|Valor and Caselles (1996)]] and [[References|Rubio et al. (1997)]].
  
For the determination of the land surface temperature the split window method of Coll & Caselles (1997) is implemented. The brightness temperatures from channel 4 (TIR4) and channel 5 (TIR5) of AVHRR are combined with the surface emissivity (correcting for grey bodies) and the atmospheric water content is taken into account. The surface emissivity is derived from the vegetation cover fraction, in this case derived from the NDVI with the following method.
 
  
Method to calculate the vegetation cover fraction:
+
<div class="formula_double"><math>\varepsilon =\varepsilon _{v} \cdot P_{v} +\varepsilon _{g} \cdot \left(1-P_{v} \right)+4\cdot \left\langle d\varepsilon \right\rangle \cdot P_{v} \cdot \left(1-P_{v} \right)</math></div>
  
[[File:VegetationCoverFraction.png]]
+
with:
  
The emissivity (ε, -) is calculated according to Valor and Caselles (1996) and Rubio et al. (1997).
+
{| border=0
 +
|-
 +
  | <div class="formula_single"><math>\varepsilon</math></div>
 +
  |  : pixel emmissivity [-]
 +
|-
 +
  | <div class="formula_single"><math>\varepsilon</math><sub>v</sub></div>
 +
  |  : the emmissivity of a fully vegetated pixel [-]
 +
|-
 +
  | <div class="formula_single"><math>\varepsilon</math><sub>g</sub></div>
 +
  |  : the emmissivity of a bare soil pixel [-]
 +
|-
 +
  | <div class="formula_single">d<math>\varepsilon</math></div>
 +
  |  : the estimated mean error on the values of <math>\varepsilon</math><sub>v</sub> and <math>\varepsilon</math><sub>g</sub> [-]
 +
|}
  
[[File:Emissivitiy.png]]
+
<!--- [[File:Emissivitiy.png|250]] --->
  
 
The difference of emissivity (∆ε) as a function of the vegetation cover fraction (P<sub>v</sub>) is calculated as:
 
The difference of emissivity (∆ε) as a function of the vegetation cover fraction (P<sub>v</sub>) is calculated as:
  
[[File:EmissivityDifference.png]]
+
<div class="formula_double"><math>\Delta \varepsilon =\left(\Delta \varepsilon _{\left(P_{v} =1\right)} -\Delta \varepsilon _{\left(P_{v} =0\right)} \right)\cdot P_{v} +\Delta \varepsilon _{\left(P_{v} =0\right)} \ </math></div>
 +
 
 +
with:
 +
 
 +
{| border=0
 +
|-
 +
  | <div class="formula_single"><math>\Delta \varepsilon</math></div>
 +
  |  : pixel emmissivity difference between channel 4 and 5 [-]
 +
|-
 +
  | <div class="formula_single"><math>\Delta \varepsilon</math><sub>(PV=1)</sub></div>
 +
  |  : the difference in emmissivity of a fully vegetated pixel [-]
 +
|-
 +
  | <div class="formula_single"><math>\Delta \varepsilon</math><sub>(PV=0)</sub></div>
 +
  |  : the difference in emmissivity of a bare soil pixel respectively [-]
 +
|}
 +
 
 +
<!--- [[File:EmissivityDifference.png]] --->
  
 
Corrections of the atmospheric influence on the brightness temperature:
 
Corrections of the atmospheric influence on the brightness temperature:
  
[[File:EmissivityCorrections.png]]
+
<div class="formula_single"><math>\alpha =W^{3} -8\cdot W^{2} +17\cdot W+40\ </math></div>
 +
 
 +
 
 +
<div class="formula_quint"><math>\beta =150\cdot \left(1-\frac{W}{4.5} \right)\ </math></div>
 +
 
 +
 
 +
<div class="formula_single"><math>offset=\alpha \cdot \left(1-\varepsilon \right)-\beta \cdot \Delta \varepsilon \ </math></div>
 +
 
 +
with:
 +
 
 +
{| border=0
 +
|-
 +
  | <math>\alpha</math>, <math>\beta</math> and offset
 +
  |  : corrections for emissivity and water content in the atmosphere [-]
 +
|-
 +
  | W
 +
  |  : the water content in the atmosphere [g.cm<sup>-2</sup>]
 +
|}
 +
 
 +
<!--- [[File:EmissivityCorrections.png]] --->
 +
 
 +
Finally the land surface temperature (LST) is determined according to the split-window principle [[References|(Coll and Caselles, 1997)]].
 +
 
 +
''LST'' = ''BT''4 + [1.34 + 0.39 <sup>.</sup> (''BT''4 - ''BT''5)] <sup>.</sup> (''BT''4 - ''BT''5) + 0.56 + ''offset''
 +
 
 +
{|-
 +
  | with:
 +
  |
 +
|-
 +
  |
 +
  | BT4, BT5: the brigtness temperatures of channel 4 and 5 [K]
 +
|}
 +
 
 +
<!--- [[File:LandSurfaceTemperature.png]] --->
 +
 
 +
<u>Parameters and their default values</u>
  
Finally the land surface temperature (LST) is determined according to the split-window principle (Coll and Caselles, 1997)
+
{| border=1
 +
|-
 +
! parameter
 +
! value
 +
|-
 +
  | <div class="formula_single"><math>\varepsilon</math><sub>v</sub></div>
 +
  | 0.985
 +
|-
 +
  | <div class="formula_single"><math>\varepsilon</math><sub>g</sub></div>
 +
  | 0.960
 +
|-
 +
  | <div class="formula_single">d<math>\varepsilon</math></div>
 +
  | 0.02
 +
|-
 +
  | <div class="formula_single"><math>\Delta \varepsilon</math><sub>(PV=1)</sub></div>
 +
  | -0.0023
 +
|-
 +
  | <div class="formula_single"><math>\Delta \varepsilon</math><sub>(PV=0)</sub></div>
 +
  | -0.009
 +
|}
 +
<!--- [[File:ParametersAndDefaultValues.png]] --->
  
[[File:LandSurfaceTemperature.png]]
 
  
Parameters and their default values:
+
Additional details can be found in [[References|Coll and Caselles,1997; Rubio et al., 1997 and Valor and Caselles, 1996]].
  
[[File:ParametersAndDefaultValues.png]]
+
Go back to [[NOAA-AVHRR]] or [[METOP-AVHRR]] pre-processing.
  
Additional details can be found in Coll and Caselles,1997; Rubio et al., 1997 and Valor and Caselles, 1996.
+
[[Category:Remote Sensing]]

Latest revision as of 14:51, 10 December 2013



fAPAR estimation and atmospheric correction (Gobron et al., 2006)

This procedure, published by Gobron et al. (2006), uses the TOA-reflectances in the BLUE, RED and NIR bands (RaB, RaR, RaN) and combines the atmospheric correction and fAPAR-extraction as follows (the functions Fn and band-specific parameter sets Pni are explained later):

  • BRDF-correction with the RPV-model: First the directional Rai in the three bands i are converted into more standardized hemispherical reflectances ρai via the equation ρai =F1(Rai, θs, Φs, θv, Φv, P1i)which also uses the known angles and the band-specific parameter sets P1i.
  • Atmospheric correction: Next, "rectified" surface reflectances are computed for RED (ρsR) and NIR (ρsN) with the following equations: ρsR = F2RaB, ρaR, P2R) and ρsN = F2NaB, ρaN, P2N), where P2R/N are band-specific parameter sets. The underlying idea is that the radiative state of the atmosphere can be assessed from the reflectance differences between the BLUE and the other bands (the BLUE is indeed very susceptible for atmospheric scattering).
  • Finally fAPAR is estimated from the rectified reflectances and parameter set P3, via fAPAR= F3sR, ρsN, P3).

To define the specific functions Fn and parameter sets Pni, Gobron et al. (2006) coupled three simulation models: 6S links the satellite-registered radiance La with the surface reflectance ρs, the latter is simulated via Gobron's Semi-Discrete canopy reflectance model (SDRM), while the leaf optical properties (one of the SDRM-inputs) are predicted by PROSPECT. All three models require additional information, such as the leaf chlorophyl content (PROSPECT), the LAI (SDRM) and the atmospheric aerosol content (6S). A multitude of "scenario's", i.e. combinations of all these external parameters, is defined in advance. All together they should represent the variability observed in the real world (all vegetation types x atmospheres x viewing conditions ...). The coupled model is then run to compute for each scenario a number of outputs, which also include fAPAR (via the adapted SDRM) and the mentioned intermediate reflectances (BRDF-corrected ρaBaRaN and rectified ρsRsN). The functions Fn and parameter sets Pni are then defined by statistical analysis of the scenario database. De facto, the functions Fn are ratio's of polynomials and the parameter sets Pni contain their coefficients.

Compared to SMAC, the combined approach of Gobron et al. (2006) does not need ancillary information on the distribution of ozone, water vapour and aerosols. But the method is only applicable for sensors such as VGT and MODIS which (in addition to the omni-present RED and NIR) also have a BLUE band. This band lacks for AVHRR, for which another method to derive fAPAR is used (see fAPAR (Weiss et al., 2010)).

Go back to SPOT-VEGETATION or TERRA-MODIS pre-processing.

Land Surface Temperature (LST)

For the determination of the land surface temperature the split window method of Coll & Caselles (1997) is implemented. The brightness temperatures from channel 4 (TIR4) and channel 5 (TIR5) of AVHRR are combined with the surface emissivity (correcting for grey bodies) and the atmospheric water content is taken into account. The surface emissivity is derived from the vegetation cover fraction, in this case derived from the NDVI with the following method.

Method to calculate the vegetation cover fraction:

The vegetation cover fraction (Pv) is calculated using the median of the pixels with the 5% highest NDVI values is NDVI, and the median of the pixels with the 5% lowest NDVI value is NDVIg.

P_{v}=\frac{NDVI-NDVI_{g}}{NDVI_{v}-NDVI_{g}}

with

Pv  : Vegetation fraction [-]
NDVI  : Normalized Difference Vegetation Index of the pixel [-]
NDVIg  : maximum Normalized Difference Vegetation Index of a bare soil pixel [-]
NDVIv  : minimum Normalized Difference Vegetation Index of a fully vegetated pixel [-]


The emissivity (ε, -) is calculated according to Valor and Caselles (1996) and Rubio et al. (1997).


\varepsilon =\varepsilon _{v} \cdot P_{v} +\varepsilon _{g} \cdot \left(1-P_{v} \right)+4\cdot \left\langle d\varepsilon \right\rangle \cdot P_{v} \cdot \left(1-P_{v} \right)

with:

\varepsilon
 : pixel emmissivity [-]
\varepsilonv
 : the emmissivity of a fully vegetated pixel [-]
\varepsilong
 : the emmissivity of a bare soil pixel [-]
d\varepsilon
 : the estimated mean error on the values of \varepsilonv and \varepsilong [-]


The difference of emissivity (∆ε) as a function of the vegetation cover fraction (Pv) is calculated as:

\Delta \varepsilon =\left(\Delta \varepsilon _{\left(P_{v} =1\right)} -\Delta \varepsilon _{\left(P_{v} =0\right)} \right)\cdot P_{v} +\Delta \varepsilon _{\left(P_{v} =0\right)} \

with:

\Delta \varepsilon
 : pixel emmissivity difference between channel 4 and 5 [-]
\Delta \varepsilon(PV=1)
 : the difference in emmissivity of a fully vegetated pixel [-]
\Delta \varepsilon(PV=0)
 : the difference in emmissivity of a bare soil pixel respectively [-]


Corrections of the atmospheric influence on the brightness temperature:

\alpha =W^{3} -8\cdot W^{2} +17\cdot W+40\


\beta =150\cdot \left(1-\frac{W}{4.5} \right)\


offset=\alpha \cdot \left(1-\varepsilon \right)-\beta \cdot \Delta \varepsilon \

with:

\alpha, \beta and offset  : corrections for emissivity and water content in the atmosphere [-]
W  : the water content in the atmosphere [g.cm-2]


Finally the land surface temperature (LST) is determined according to the split-window principle (Coll and Caselles, 1997).

LST = BT4 + [1.34 + 0.39 . (BT4 - BT5)] . (BT4 - BT5) + 0.56 + offset

with:
BT4, BT5: the brigtness temperatures of channel 4 and 5 [K]


Parameters and their default values

parameter value
\varepsilonv
0.985
\varepsilong
0.960
d\varepsilon
0.02
\Delta \varepsilon(PV=1)
-0.0023
\Delta \varepsilon(PV=0)
-0.009


Additional details can be found in Coll and Caselles,1997; Rubio et al., 1997 and Valor and Caselles, 1996.

Go back to NOAA-AVHRR or METOP-AVHRR pre-processing.