After that, we defined a new vegetation index based on the method, namely VIPD.

Here, S_v and S_s indicate the "brightness" of standard vegetation and soil covers, respectively. "Brightness" means the sum of reflectances, which are used for the method.

It was demonstrated that VIPD was linear to the vegetation cover ratio [3] and the photosynthetic quantum efficiency [4]. The relationships are indicated in Fig. 1.

Figure 1: Relationships of VIPD to the vegetation cover ratio and the photosynthetic quantum efficiency.
The relationship between VIPD and vegetation cover ratio was obtained from the spectral reflectance measurements for the mixed area with leaf and soil. As for the quantum efficiency, we introduced the relationships from two measurements. One is the relationship between the quantum efficiency and chlorophyll content of leaves [5]. The other is the relationship between VIPD from spectral reflectance measurement of leaves and chlorophyll content of leaves by ourselves. From these results, we can obtain the relationship between VIPD and quantum efficiency via chlorophyll content of leaves.

3. Estimated model of net primary production
NPP depends on global primary production (GPP) and respectively loss (R_d) as described by Eq. (3).
NPP=GPP-R_d             (3)
At first, we consider GPP, which depends on the photosynthetic activity. GPP is obtained from the integration of photosynthetic quantum efficiency multiplied by incident solar energy because the photosynthetic quantum efficiency is the assimilation of CO₂ per unit time, area, and incident solar energy.

We can obtain the quantum efficiency from the photosynthetic curves. The definition of the efficiency is illustrated inside Fig. 2.

Figure 2. Illustration of the photosynthetic quantum efficiency inside the photosynthetic curve
Of course, we should be take account into the vegetation cover ratio (Rv) for an observed area. As a result, we obtain the following equation.
GPP=ò(R_v X QE X R_s)dt           (4)
Here, R_s is incident solar radiation. The incident solar energy should correspond to the photosynthetic active radiation (PAR).

As mentioned above, VIPD is linear to the photosynthetic quantum efficiency and the vegetation cover ratio. According to the relationships, we can rewrite the above equation as follows:
R_v X QE=0.070 X VIPD[mgCO₂/m²/cal]             (5)
At second, we consider respiratory loss. We used to the following empirical-derived equation for the estimation of the respiratory loss (R_d) because it depends on the air temperature (T[°C])[6].

Finally, in order to estimate NPP, we need three parameters, that is VIPD from the satellite data, solar radiation, and air temperature. VIPD reflects vegetation condition. We can take account into the environmental factors of the photosynthesis by including PAR and air temperature into the model.