# Vegetation indicator procedures

## Contents

## NDVI

The Normalized Difference Vegetation Index (NDVI) is a band combination of RED and NIR reflectances and describes photosynthetic activity. It is calculated according to the following formula:

NDVI = ( NIR - RED ) / ( NIR + RED )

## fAPAR (Weiss et al., 2010)

For AVHRR (from NOAA and METOP), the fAPAR is computed from atmospherically corrected (using SMAC) surface reflectances R_{s} in the post-processing. The method was developed by INRA (Fred Baret, Marie Weiss), and is based on the CYCLOPES method, but modified to work with atmospherically corrected S10-daily composites of the different AVHRR sensor. The CYCLOPES method was described in detail by Baret et al. (2007) and the modified version by Weiss et al. (2010). The essence of the method consists of neural networks that relate surface reflectance data from AVHRR to biophysical parameters, such as fAPAR, LAI and fCover. These neural networks were trained on a large database of model-based examples of these relationships.

First step in the CYCLOPES approach is the establishment of a simulation tool by coupling the models PROSPECT (leaf optical properties) (Jacquemoud & Baret, 1990), SAILmix (canopy reflectance) (Verhoef & Bach, 2007)and 6S (atmosphere) (Vermote, et al., 2002) . SAILmix is Verhoef's classical model but extended with the additional parameter fCover in order to account for the mixed nature of the pixels. fCover quantifies the proportions of vegetation (to be treated with SAIL) and bare soil. When fed with the necessary spectral response curves, the modelling tool simulates the top-of-atmosphere reflectances R_{a} in all the shortwave bands of the concerned sensor (at least RED and NIR), and this for any land surface type, atmosphere and viewing geometry. When the simulation is repeated for the PAR-band (400-700nm), fAPAR comes out as a by-product of SAILmix. Here too, a wide range of scenario's is defined, each representing a possible real world state, and quantified via the external model inputs (leaf chlorophyl content, LAI, bare soil reflectance, fCover, sun/view angles, atmospheric state, etc.). For each scenario, the simulated R_{a} are computed and stored together with the mentioned inputs and fAPAR. Finally, the database with the results of all scenario's is analysed to define the relationship fAPAR=f(R_{a,RED}, R_{a,NIR}, ..., other known factors). This model inversion is realised by means of neural networks.

The CYCLOPES procedure was adapted and simplified by removing the atmospheric model 6S from the simulation tool, and repeating the analysis and inversion in terms of the surface reflectances. In this way, the method can be applied directly on the AVHRR-S10 data that contain SMAC-corrected values R_{s} instead of R_{a}-reflectances.

Compared to Gobron's method (see fAPAR (Gobron et al., 2006)), the CYCLOPES approach has the following advantages:

- The canopy reflectance model SAILmix explicitly accounts for mixed pixels
- The model inversion via neural networks is more powerful and straighforward than the approach of Gobron (ratio's of polynomials).
- The scenario database of CYCLOPES is wider and more realistic and it accounts for more external influence factors.
- Gobron's method strictly works with BLUE, RED and NIR. CYCLOPES is more flexible and can be calibrated for any combination of bands – thus also for AVHRR which lacks the BLUE.

More information on the formats and the headers of the fAPAR images can be found in the section Images.

## fAPAR (Gobron et al., 2006)

This method is explained in fAPAR (Gobron et al., 2006).

## Dry Matter Productivity (DMP)

Dry Matter Productivity or DMP (in kgDM/ha/day) is computed according to the general Monteith formulation, though with a specific variant designed for application on remotely sensed imagery (Veroustraete et al., 2002):

**Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): \noindent \textbf{DMP = R.$\varepsilon$${}_{P}$.\textit{f}APAR.$\varepsilon$${}_{RUE}$.$\varepsilon$${}_{T}$.$\varepsilon$${}_{CO2}$.$\varepsilon$${}_{AR}$[.$\varepsilon$${}_{RES}$]}**[1]

Some remarks:

- Incoming solar (shortwave) radiation R
_{T}is mostly reported in terms of kJT/m²/day with variations between 0 and 32 000. This corresponds with 320 GJT/ha/day (1 hectare is 10 000m², and 1 GJ is 1 000 000 kJ). - The fraction
_{P}of PAR (Photosynthetically Active Radiation, 400-700 nm) within the total shortwave (200-4000 nm) varies slightly around the mean of_{P}=0.48. -
_{RUE}is considered here as a constant equal to 2.54 kg of DM produced per GigaJoule of PAR-radiation absorbed by the green, photosynthetically active plant elements (modified after Wofsy*et al*., 1993). This value of_{RUE}holds for optimal conditions. - The behaviour of
_{T},_{CO2}and_{AR}is simulated via rather complex biochemical equations by Veroustraete*et al*. (2002), though in terms of the equivalent Net Primary Productivity (NPP, in gC/m²/day). However, the only influence factors dealt with are temperature (T) and CO2-concentration. Omitting all mathematical complexities, at the end the result of these combined efficiencies (_{P}._{RUE}._{T}._{CO2}._{AR}) turns out as depicted in the figure below. This behaviour, typical for C3-species, is similar to the one included in crop growth simulation models such as SUCROS/WOFOST. Apparently, vegetation growth peaks around 22°C and is slightly enhanced by higher CO_{2}-levels. - The factor
_{RES}(residual) is only added in equation 1 to emphasize the fact that some potentially important factors, such as the effect of droughts, nutrient deficiencies, pests and plant diseases, are clearly omitted here. As a consequence, our product might better be called “potential” DMP. On the other hand, it might be argued that the adverse effects of diseases and shortages of water or nutrients are manifested (sooner or later) via the RS-derived fAPAR.

The meteo-data, needed for the DMP-computation, are downloaded from the CGMS database in the form of ASCII-databases. These contain the daily values for the standard meteo-variables, and holding for the centres of the "meteo-grid", which has a spatial resolution of 25km.
The practical DMP-computation is achieved in the following way. Given the simple elaboration of the epsilons (and dropping the factor ε_{RES}), the general equation can be rewritten as:

**Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): \noindent \textbf{DMP = R.$\varepsilon$${}_{P}$.\textit{f}APAR.$\varepsilon$${}_{RUE}$.$\varepsilon$${}_{T}$.$\varepsilon$${}_{CO2}$.$\varepsilon$${}_{AR}$ = \textit{f}APAR.R.$\varepsilon$(T,CO${}_{2}$) = \textit{f}APAR.DMP${}_{max}$ }**[2]

with ε(T,CO2)=ε_{P}.ε_{RUE}.ε_{T}.ε_{CO2}.ε_{AR}. This formulation better highlights the fact that (within the limits of the described model) DMP is only determined by four basic factors: fAPAR, radiation, temperature and CO_{2}. However, in practice the CO_{2}-level is always considered as a global constant. At the same time, equation 2 provides a practical method which allows to bypass the differences in temporal and spatial resolution between the inputs. In practice, the meteorological inputs (R, T) are mostly provided on a daily basis and at a very low resolution (VLR), in this case 25km x 25km. On the contrary, fAPAR is derived from 10-daily composites of low resolution (LR) sensors such as NOAA-AVHRR and SPOT-VEGETATION (VGT), both having pixels with a size of around 1 km². Also the final DMP-product will have this 1km resolution and dekadal frequency.

In practice the following procedure is used (Eerens et al., 2004):

- Based on the meteorological inputs (R, T), the fixed value of the CO2-level and the above-mentioned variant of the Monteith model, images are generated with DMP
_{max}=R.ε(T,CO2)=R.ε_{P}.ε_{RUE}.ε_{T}.ε_{CO2}.ε_{AR}. DMP_{max}represents the maximum reachable DMP, for the (virtual) cases where fAPAR would be equal to one. Just like the inputs, the DMP_{max}images are VLR and daily (DMPmax,1). - At the end of every dekad, first a new image (DMP
_{max,10})is computed with the mean of the daily DMP_{max,1}scenes. The resulting image DMP_{max},10-image is then resampled (bilinear interpolation) to the same resolution as the fAPAR image, derived from SPOT-VGT (1km), AVHRR (1km) or MODIS (250m). And next, both are simply multiplied to retrieve the final image with the DMP estimates.

This practical approach can be formulated as follows (the subscripts 1 and 10 indicate daily and dekadal products, N_{d} is the number of days in each dekad):

**Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): \noindent \textbf{DMP${}_{10}$ = \textit{f}APAR${}_{10}$ . DMP${}_{max,10}$}**

with

**Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): \noindent DMP_{max,10} = \begin{Bmatrix}\sum DMP_{max,1}\end{Bmatrix} /Nd**[3]