**3. Results**

#### *3.1. Crop Specific Models*

#### 3.1.1. Plant Height

Based on the analysis of the Pareto efficiency scores, the LiDAR plant height for each grid cell of 1 m2 is based on the top 10 points for potato, on the top 90 points for sugar beet, and for winter wheat on the top 30 points. The average height of these points serves as the LiDAR-based plant height estimation.

The correlation between field-measured height and LiDAR-based plant height is highest for sugar beet and winter wheat (Figure 3). Plant height was most accurately derived for winter wheat with an RMSE of 3.4 cm. Determining plant height for potato proved to be the most difficult, showing relatively large residuals.

**Figure 3.** Scatter plots showing measured plant height vs derived plant height, where potato is based on the 10 highest points within a pixel, sugar beet on top 90 highest points, and winter wheat on the top 30 highest points. The blue line in the Figure is the 1:1 line.

Figure 3 shows that there is a general over prediction of plant height for potato while winter wheat shows an underestimation. As winter wheat has a relatively open and erectophile structure, the number of returns in the top of the canopy could be lower, resulting in an underestimation of

height. Although sugar beet falls on the 1:1 line, the prediction of plant height has a higher spread than winter wheat, which is shown by the larger MAE and RMSE. The over prediction of potato is most likely the result of the complex canopy, which is explained in more detail in the discussion.

## 3.1.2. Biomass

Choosing k = 1 for potato and winter wheat and k = 3 for sugar beet results in the best fit for the biomass models. Values lower than k = 1 proved to be very unstable in the performance for the 3DPI algorithm, showing large fluctuation in R<sup>2</sup> values. Values higher than k = 3 became saturated and showed only minor increases in R2. For potato and winter wheat the model errors, NMAE and NRMSE are the smallest for k = 1 (Figure 4), while for sugar beets the errors are smallest for k = 3.

**Figure 4.** Error analysis for biomass derivation based on the 3-Dimensional Profile Index (3DPI) indicator, deviating K between 1, 2, or 3. Showing biomass estimations for potato, sugar beet, and winter wheat, including the dimensionless normalized in-sample.

Potato shows a relatively large difference between the NMAE and NRMSE compared to those of sugar beet and winter wheat. This indicates that the low R2 is most likely the result of large residuals (Figure 4). Furthermore, the spread in points for potato is less equally distributed between large and small residuals compared to the spread of points for sugar beet and winter wheat (Figure 5). This explains the larger NRMSE and NMAE of potato.

The prediction model for potato does not provide reliable estimates of biomass, especially for values higher than 3500 g/m2 (Figure 5) in which biomass is underestimated. Furthermore, the scatterplot does not show a strong relation. For sugar beet, there is a good correspondence between the fresh biomass in the field and the LiDAR predicted biomass (Figure 5). Also, the crop development during the growing season is captured well: during flight 1, the sugar beets were still small, and the field was only partially covered, while during flights 2 and 4 the sugar beets had grown, which is also derived from the UAV-LiDAR observations.

The biomass of winter wheat was determined most accurately. For flights 1 and 2, the points are practically on the 1:1 line (Figure 5). During the 4th flight, the wheat had ripened, which lowered the amount of fresh biomass.

**Figure 5.** Scatter plots showing the relation between measured biomass and predicted for potato (k = 1), sugar beet (k = 3) and winter wheat (k = 1). The blue line in the Figure is the 1:1 line.

#### *3.2. General Prediction Models*

#### 3.2.1. Crop Height

When combining the crops into a general prediction model for plant height, the RMSE is 10.1 cm (Figure 6). This error is much larger compared to the crop-specific models. For example, this accuracy was 3.4 cm for winter wheat in the single crop model (Figure 3).

**Figure 6.** Scatterplot showing measured plant height versus LiDAR-derived plant height and the residual plot for the general plant height. Showing the model residuals versus fitted plant height. The colours in the left Figure show each separate crop. The blue line indicates the 1:1 line.

The Pareto method is used to determine the optimized number of points to be used to calculate the height per pixel, which showed that using 100 points per pixel yielded the best fit for the general model, resulting in an R2 of 0.61 for the general model. This is lower than the R2 for sugar beet and winter wheat (0.70 and 0.78, respectively), but higher than that of potato (0.49). The residual plot shows a random distribution of points with one outlier (Figure 6). This point comes from the potato dataset, but no valid reason was found to exclude the point.

#### 3.2.2. Biomass

The general model for biomass performed worse for biomass prediction of winter wheat; the normalized error increased to 17.07% for the general model compared to 13.9% for the crop-specific model (Figure 7) based on tuning-parameter k = 3. The general models were fitted using different k-factors, where the R<sup>2</sup> was 0.47 for k = 1, 0.49 for k = 2 and 0.50 for k = 3. The generic model saturates for higher biomass predictions, especially for winter wheat (Figure 7). This indicates that a new model should be built for the higher biomass estimates. However, the general model can be used to predict biomass for potatoes (NRMSE = 22.1%) and sugar beet (NRMSE = 17.47%), in which NRMSE values are larger than those of the general model (NRMSE = 17.07%).

**Figure 7.** Scatter plot showing the relation between measured biomass and fitted biomass, for k = 3. The colours indicate the original crop data used for the model. The blue line in the Figure is the 1:1 line. On the right, the corresponding residual plot is shown. Showing the fitted plant height plotted against the model residuals.

The cross validated NRMSE shows that biomass can be predicted on a new dataset with an NRMSE\_cv of 17.61%. The NRMSE\_cv is 0.54 larger than the NRMSE for k = 3. This indicates that the model could be used for fields, where no biomass samples were taken for calibration.

## *3.3. Influence of Flight Characteristics on Plant Height*

Changes in flight characteristics (altitude and speed) result in differences in point cloud density (Figure 8), where a cross section (10 × 0.2 m) of the sugar beet point clouds of four flights with different flight characteristics are shown. The flights were done on two days, with one day in between, but we assumed that the crops did not change between those two days.

**Figure 8.** Profile plot for sugar beet showing a profile of 0.20 x 10 m. From top to bottom, it shows the flights DAY2-LA-MS, DAY2-LA-LS, DAY3-HA-HS, and DAY3-LA-LS. The green colours indicate plant material, where darker colours indicate a higher elevation of the point. The red points indicate the points classified as ground points.

Measured plant height is consistent for the different flight characteristics, except for the high and fast flight (DAY3-HA-HS: 90 m, 8 m/s). As can be seen in Figure 8, this results in a much lower point density and an underestimation of the crop height, shown by the lighter green colours in Figure 9. However, the spatial patterns of crop height between the four sets of flight characteristics are comparable. The locations with low and high crop height show a comparable location and distribution. For DAY3-LA-LS height map, the north-western corner of the field was not covered well by the pre-programmed flight path, which resulted in a lower point density and, thus, an underestimation of crop height. This indicates that the flight characteristics do not influence the spatial patterns of estimated crop height, but it is important to keep them consistent for measuring temporal changes in crop height.

**Figure 9.** Maps indicating the estimated plant height in meters for sugar beet for DAY2-LA-MS, DAY2-LA-LS, DAY3-HA-HS, and DAY3-LA-LS. Darker greens indicate a higher plant height.
