## Design Of The Seawifs Vegetation Index

Our optimized SeaWiFS vegetation index requires, as input, the three Bidirectional Reflectance Factor (BRF) values measured by this sensor in the blue, red and near-infrared spectral regions, in addition to the solar and viewing zenith angles and the relative azimuth angle between the sun and the satellite. The computation of the index requires three polynomial expressions as well as the anisotropy reflectance function delivered by the Rahman, Pinty and Verstraete (RPV) BRF parametric model (Rahman et al., 1993). The values of the RPV model parameters are optimally derived once and for all, using a training BRF data set generated for a large range of simulated geophysical scenarios.

Various geophysical quantities are estimated in the process of implementing the optimized SeaWiFS Vegetation Index (SeaWiFS-VI). First, the TOA channel values are "normalized" by the anisotropic function:

where X, stands for the wavelength (blue, red or near-infrared) of spectral band i, and f>"a(Q0,flv,A,) denotes the BRF values measured by the sensor in the spectral band as a function of the actual geometry of illumination and observation (Qv). These angular coordinates are fully defined by the zenith and relative azimuth angles for the incoming and exiting radiation, respectively, with respect to a nlane-narallel system. The spectral anisotropic reflectance function, F (Q0,Q.v,k\t&mxhPxtc), represents the shape of the radiance field, where the triplet (^¡,iiHG>.i,Aic) are the RPV's parameters optimized a priori for each spectral band X,.

The rectification process of the red and near-infrared bands is performed as follows:

and where

The polynomial coefficients /„„, have been optimized in such a way that the values generated by each spectral polynomial g„[p~(lbiu), p (^j)] correspond to the bi-directional reflectance factors that would be measured at the top of the canopy, normalized by the spectrally appropriate anisotropic reflectance function. In other words, the rectification process yields estimated values of spectral reflectances emerging at the top of the canopy, optimally decontaminated from atmospheric and angular radiative effects in the sense described in the various publications mentioned earlier.

The SeaWiFS-VI itself is then computed on the basis of these rectified channel values, and its formula is

h\pRnir hjPkred h

where the coefficients /0m of polynomial go are optimized a priori to force SeaWiFS-VI to take on values as close as possible to the FAPAR associated with the plant canopy scenarios used in the training data set. The numerical values of the various coefficients resulting from these successive optimizations are summarized in Tables 1 to 4.

Channel A, (nm) |
Parameter values | ||

Pkic |
kju |
^ At | |

443 |
0.23265 |
0.56184 |
-0.04125 |

670 |
-0.44444 |
0.70535 |
0.03576 |

865 |
0.63149 |
0.86644 |
-0.00102 |

Figure 1 illustrates the results obtained after performing the two step procedure described above. The right panel shows the isolines of the SeaWiFS-VI in the spectral space of the rectified channels centered at 670 and 865 nm. The left panel of the same Figure shows that the SeaWiFS-VI is a reliable estimator of the FAPAR with a root mean square deviation equal to 0.05. It can be seen that the SeaWiFS-VI varies between 0 and 1 over partially to fully vegetated surfaces. Most of the remaining variability between FAPAR and SeaWiFS-VI is induced by the large number and diversity of geophysical scenarios considered. In fact this variability results from conflicting requirements on the simultaneous insensitivity of the SeaWiFS-VI to soil,

Figure 1 illustrates the results obtained after performing the two step procedure described above. The right panel shows the isolines of the SeaWiFS-VI in the spectral space of the rectified channels centered at 670 and 865 nm. The left panel of the same Figure shows that the SeaWiFS-VI is a reliable estimator of the FAPAR with a root mean square deviation equal to 0.05. It can be seen that the SeaWiFS-VI varies between 0 and 1 over partially to fully vegetated surfaces. Most of the remaining variability between FAPAR and SeaWiFS-VI is induced by the large number and diversity of geophysical scenarios considered. In fact this variability results from conflicting requirements on the simultaneous insensitivity of the SeaWiFS-VI to soil, atmospheric and geometrical effects in the SeaWiFS spectral bands. In the present case, it was found that the signal to noise ratio of the SeaWiFS-VI is equal to 21.26. By comparison, the widely used Normalized Difference Vegetation Index (NDVI), computed on the basis of data from the original channels centered at 670 and 865 nm, exhibits a non-linear relationship with respect to FAPAR and a signal to noise ratio of only 7.04 (Figure 2).

Figure 1. The right panel shows the isolines of SeaWiFS-VI in the rectified (670 nm, 865 nm) spectral space together with the spectral rectified bidirectional reflectance factors computed with simulated radiances emerging at the top of the atmosphere. The left panel shows the relationship between the SeaWiFS-VI and the FAPAR values

Figure 1. The right panel shows the isolines of SeaWiFS-VI in the rectified (670 nm, 865 nm) spectral space together with the spectral rectified bidirectional reflectance factors computed with simulated radiances emerging at the top of the atmosphere. The left panel shows the relationship between the SeaWiFS-VI and the FAPAR values

RMS i |
O.U |
¡1* | |

S/M = |
7.04 |
v ft | |

ilk |
h »5 | ||

jf< |
: r r | ||

- |
i |
/Sr vi |
y?. |

W j |
/ i |
.,.. 1 |

Figure 2. The right panel shows the isolines of NDVI in the (670 nm, 865 nm) spectral space, together with the spectral bi-directional reflectance factors at the top of the atmosphere. The left panel shows the relationship between the NDVI and the FAPAR values

Table 3. Optimal values of the coefficients for the polynomial l1Y^0.66956 0.090485 Izr-1.343 8 ^io~0-99648

Table 4. Optimal values of the coefficients for the polynomial _

/orO.25130709 /02=0.305 89629 /03^0.0048298 /p4~0.3213674 /os=0.31415914_/06=-0.01Q74418

These results demonstrate the significant advances allowed by this approach in the analysis of SeaWiFS-VI. Furthermore, the optimization of the index formula so that it takes values statistically equivalent to the FAPAR permits us

1. to evaluate and monitor the state of land surfaces consistently over the globe in a quantitative physically sound manner,

2. to deliver, to the remote sensing user community, geophysical products relatively independent of atmospheric conditions and of the geometry of illumination and observation, and

3. to process vast amounts of remote sensing data at relatively minor computational costs, without any need for further pre- or post-processing.

For instance, many indices must be computed on the basis of data already partially corrected for atmospheric effects (e.g., Rayleigh scattering, such as in Kaufman and Tanré, 1992 and Huete et al., 1997), or yield values that are not of direct interest to the users.

The applicability of such an optimized index over heterogeneous surfaces, where three-dimensional effects might play a dominant role in controlling the radiation transfer regime, and for various aerosol types, is discussed further in Gobron et al. (2000a). It will be sufficient to state that the application of the same technique to different multispectral single view instruments will allow the development and implementation of high performance compositing methods based directly on FAPAR products, since they are all comparable and independent from the original source of the space data.

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