# Estimating Carrot Gross Primary Production Using UAV-Based Multispectral Imagery
## 3 Results  
Figure 2 shows the GPP-VI samples, the regression line, and the RMSE and R\({}^{2}\) statistics. As can be seen from this figure, some VIs follow a linear trend more closely (SAVI, MSAVI, MSAVI2, TSAVI, GEMI, DVI, WDVI, and EVI2), others show moderate correlation (NDVI, IPVI, TNDVI, RVI, and WDRVI), while the remaining indexes show no correlation with the daily GPP. Figure 3 shows more compactly the RMSE and R\({}^{2}\) statistic of all the VIs. This figure allows us to extract the top seven VIs that correlate well with the GPP; they are SAVI, MSAVI, MSAVI2, DVI, WDVI, EVI2, and NIRv. It is a surprise that the simple DVI provides good regression results. Furthermore, it is noteworthy that all VIs based on the red-edge (NDRE, PSSR, RENDVI, Clred-edge) and green (GNDVI, Cigreen, GRVI) do not correlate with the GPP. This could mean that the red and NIR bands suffice to obtain a good estimation of the GPP in carrot crops. We selected the best models found to predict the daily GPP from VIs, which can be used in further studies of the GPP in carrot crops, under different environmental conditions and locations. The best VI was NIRv, with the lowest RMSE and highest R\({}^{2}\) score (0.8465), followed by MSAVI (0.8323), MSAVI2 (0.8317), SAVI (0.8257), EVI2 (0.8256), WDVI (0.8207), and DVI (0.8154). The results of the cross-validation are indicated in Table 1. The model indicates the mean intercept and the mean slope, and the BSE of these parameters is reported in parenthesis. The cross-validated RMSE and R\({}^{2}\) of the model are also indicated in the table. The \(p\)-value column contains the \(p\)-value for the intersect on the left and the \(p\)-value for the slope on the right column. With these seven indexes, we want to estimate the daily GPP and compare it with the EC-estimated daily GPP. Since we only have 11 dates and the image acquisition was from September 7 to December 27, i.e., 112 days, we need to interpolate either the VIs and use the models to estimate the daily GPP or to interpolate the GPP estimated on the 11 dates to the remaining dates. Here, we choose to interpolate the GPP directly, since simple linear interpolation of the Vis' time series leads to a linear time series of the GPP, which is incorrect. Figure 4 shows the estimated GPP as a function of the day of the year, using the NIRv index, which is the best (Table 1). This figure suggests that we can linearly interpolate the missing dates. Notice that this is not a model with parameters fitting the 11 points; rather, it is a simple interpolation between each pair of consecutive points. No cross-validation can be performed, since a LOOC will try to fit one single point from the remaining points and we do not want to estimate the points that we already have with a cross-validated model; instead, we want to estimate the daily GPP from the points we have. We could build a polynomial model to fit the points, but since there is a strong variability (Figure 4) the polynomial will be of a high order (high complexity), and we cannot report a polynomial model with its parameters cross-validated using just 11 points. It would be wrong to report a model that predicts GPP on any day of the crop growth cycle, since it would mean we no longer need VIs, just the day of the year. What we are proposing here is not a model to estimate the daily GPP, but rather an easy (model-free) way to interpolate the missing dates, with no training required. This simple strategy can be used on other datasets, which will most likely have different dates and probably a different behavior than the one observed here and, hence, we cannot evaluate this strategy as a model with parameters.