3.1. Crop Development
In the data collected on 9 June 2016, the different initial fertilization levels were clearly visible as horizontal zones in NDVI map of the potato field (
Figure 3a). Plot C and Plot D, the plots in the zone that did not receive any initial fertilization, stood out with clearly lower NDVI values. During the period between the two measurement days, there were two moments at which the potato plants on Plots B, D, F, and H received additional sensor-based nitrogen fertilization. This resulted in higher NDVI values in the plots in this section compared to the plots in the section that did not receive any additional fertilization. The effect of the different additional fertilization levels on the NDVI is most clearly visible, as the difference between Plots C and D on 19 July (
Figure 3b), where Plot D has clearly higher NDVI values.
Figure 3c shows the development of the LAI based on Cropscan measurements throughout the growing season. During Flight 1 on 9 June 2016, the potato crop was still at an early stage of growth with a haulm (leaves and stems) length of 0.4–0.6 m. The potato plants were standing upright above the ridges, showing a clear row structure. The LAI of all plots increased until the last week of June (
Figure 3c). During the first two weeks of July, the LAI decreased, which can be explained by growth-reducing effects caused by a dry period with high temperatures in the area where the study site was located. The insufficient water availability due to the lack of rain, combined with the high temperatures can affect the stomatal capacity of leaves, which in turn can cause a reduction biomass, and thus LAI [
52]. Flight 2 on 19 July 2016 occurred after the potato plants were flowered, and the haulm length increased to 0.6–0.9 m. Due to the drought and high temperatures, stems had fallen over and started filling up the space between the potato rows. This resulted in an increase in canopy cover at the date of the second flight, while the LAI remained more or less equal, or for some plots became even lower (
Table 4). After the second flight, the improved water availability due to rainfall and combined with the fertilizer addition of July 15 (
Table 1) resulted in an increase in LAI with the largest long-term effect for the Plots B, D, F and H (
Figure 3c).
3.3. Anisotropy Maps
For every georeferenced ground pixel in the study area at each measured wavelength, multi-angular observations as displayed in
Figure 5 were available. By fitting the RPV model through these multi-angular observations at every pixel, we created anisotropy maps that show the spatial distribution of the model parameters.
Figure 6 shows the parameter maps of the
,
, and
parameters at 658 nm and at 848 nm on 9 June 2016. The
parameter, which is closely related to the nadir reflectance, follows a typical vegetation trend, with low values at 658 nm (
Figure 6a) and higher values at 848 nm (
Figure 6d). Plots C and D, which did not receive any initial fertilization and therefore had a lower canopy cover, showed clearly lower
values at 848 nm. In general, pixels in both bands had
< 1, indicating a bowl-shaped anisotropy pattern (
Figure 6c,e). Both wavelengths showed clear backward scattering anisotropy (
< 0) over the full study area. This backward scattering was particularly strong at 658 nm (
Figure 6c) and less pronounced at 848 nm (
Figure 6f).
On 19 July 2016, the potato canopy was fully developed, resulting in general in higher
values at 848 nm (
Figure 7d). The pixels of Plot C, which was the plot in the zone that did not receive any initial fertilization nor additional sensor-based fertilization, had clearly lower
values at 848 nm than the other plots. The
parameter remained more or less the same as on the first measuring day. The
parameter, on the contrary, showed a strong increase at both wavelengths (i.e., the values became less negative), indicating a reduction of backward scattering intensity (compare
Figure 6c,f and
Figure 7c,f).
3.4. Plot Statistics
Figure 8 shows the interpolated polar plots of the ANIFs at 658 nm and 848 nm for all pixels within Plot C and Plot E, two plots that varied strongly in LAI and canopy cover. Pixels within a 3 m distance of tractor tracks, which were running through the center of the plots (
Figure 1), were excluded from this analysis. At both wavelengths, there was a clear backward scattering anisotropy in the plots, which was most pronounced at 658 nm. During the flight on 9 June 2016, we observed a weaker backward scattering anisotropy in Plot C at 658 nm compared to Plot E, as can be observed by the higher density of isolines. This was likely due to the fact that the potato plant rows in Plot C were not continuous due to gaps in the potato rows, either because of missing plants in the rows or because of the small size of the plants (
Figure 4b). This in turn resulted in fewer strong shadows and thereby a weaker backward scattering intensity. The rows of potato plants in Plot E, on the other hand, had fewer gaps and therefore displayed stronger shadows, and thus displayed a stronger backward scattering intensity. During the flight on 19 July 2016, the canopy of Plot E had fully developed into a closed surface with a row structure that was at that point hardly visible. This resulted in less pronounced shadows cast by the potato rows and thus in a weaker backward scattering on this date. On both dates, the backward scattering intensity for both plots at 848 nm remained more or less similar.
The average RPV parameters, based on the individually obtained RPV parameter values for every pixel within the experimental plots, are shown in
Figure 9. Again, pixels within a 3 m radius of the tractor tracks were excluded. The
parameter followed the pattern of a typical vegetation spectrum. In general, a higher
value was observed in the green and NIR wavelength region for plots that had a higher canopy cover on 19 July 2016. This is most clear for the plots where there was a strong increase in canopy cover between the two dates (
Table 4). The
parameter was in general <1 at all wavelengths, indicating a bowl-shaped anisotropy pattern for the whole sampled wavelength region. The
parameter, like the
parameter, followed in shape a vegetation spectrum. The strongest backward scattering effects (the lowest
values) were observed in the visible wavelength region, with a minimum at 674 nm, where shadow effects are strongest and multiple scattering effects are absent due to the absorption of radiance by chlorophyll in this region. In the NIR region, where shadow effects are diminished due to high reflectance and transmittance by vegetation, the
values were in general less negative than in the visible region. The
values obtained for the flight on Day 2 were consistently higher (less negative) than the
values obtained for the flight on Day 1, indicating a reduced backward scatting intensity with increased canopy cover.
3.5. RPV Parameters vs. Canopy Cover and LAI
Figure 10 shows the relation between the average RPV parameters of all pixels within each experimental plot and canopy cover at 658 nm and 848 nm, respectively. On both dates, an increased canopy cover resulted in a decrease in the
parameter at 658 nm and in an increase at 848 nm. This trend can be explained by the lower reflectance of vegetation at 658 nm compared to the soil background reflectance at this wavelength. A higher canopy cover therefore resulted in higher reflectance, and thus a higher
value. The opposite holds at 848 nm, where the soil reflectance was lower than the vegetation reflectance. On 9 June 2016 at 658 nm and on 19 July 2016 at 848 nm, the relations between
and canopy cover were strong, indicated by the R
2 of 0.764 and 0.753, respectively.
The relation between the parameter and canopy cover was less obvious. On Day 1 at 658 nm, we observed a slight decrease in the parameter with increased canopy cover (R2 = 0.478). On both dates at 848 nm, the relation between the parameter and canopy cover was very weak, indicated by the R2 of 0.262 and 0.211 on Day 1 and Day 2, respectively.
On Day 1, we observed a strong decrease in the parameter (which indicates increased backward scattering intensity) with an increase in the canopy cover at 658 nm. On Day 2, on the contrary, we observed an increase in the parameter with increasing canopy cover. The decrease in the parameter on Day 1 happened most likely due to the aforementioned gaps in the potato rows that were present in the plots with low canopy cover on this day: the gaps in the rows result in weaker shadows and thus weaker backward scattering. On Day 2, when there were hardly any gaps left in the rows, we observed a decrease in backward scattering intensity with increasing canopy cover. This is likely due to the disappearance of the row-structure since the potato rows started growing into each other, narrowing and disappearing the space between the rows, which cause strong shadow effects.
Finally, we studied the correlation of the RPV parameters with the canopy cover and LAI, respectively, for the different experimental plots at all measured spectral bands (
Figure 11). We calculated the Kendall’s tau ranking correlation coefficient, since not all canopy cover, LAI, and RPV parameter values were normally distributed, and the number of plots and thus number of observations (n = 8) was rather low. The Kendall’s tau correlation coefficient takes values between −1 and +1, where a positive value indicates that the ranks of both variables are increasing and a negative value indicates that the ranks of both variables are decreasing. The closer Kendall’s tau gets to +1 or −1, the stronger the correlation between the variables. Since the flight on Day 1 was performed at an early phase of the potato crop before it reached maximum LAI and the flight on Day 2 at a late phase after reaching maximum LAI, both flights are first analyzed separately and then combined.
The correlation of the
parameter with canopy cover (
Figure 11a, upper graph) on Day 1 was negative in the visible part of the spectrum, whereas it was positive in the NIR. On Day 2, this correlation was only negative in the red. A significant correlation at 5% confidence level (
p = 0.05) was only observed in the NIR for both dates. The pattern for the correlation between
and LAI was quite similar to the one found for canopy cover on both dates (compare
Figure 11b with
Figure 11a, upper graphs).
The correlation of the
parameter with canopy cover (
Figure 11a, middle graph) was strongest (negative) on Day 1 in the visible part of the spectrum. Only the correlation at 658 nm was significant. The correlations between the
parameter and LAI (
Figure 11b, middle graph) were quite similar to the one for canopy cover. No correlations were significant at the 5% level.
The correlation between the
parameter and canopy cover was negative in the visible part of the spectrum and positive in the NIR on Day 1, but they were not significant (
Figure 11a, lower graph). On Day 2, the correlations were close to zero, except for positive, non-significant correlations in the visible part. The correlations between the
parameter and LAI were similar to those of canopy cover. For LAI, the correlations were significant in the visible region on Day 1 (
Figure 11b, lower graph).
When we combine the data collected on both days, the correlation between the
parameter and canopy cover increased slightly over the whole spectrum (
Figure 11a, upper graph). On the contrary, the correlation between the
parameter and LAI decreased when both days were combined, which indicates that the
parameter was more sensitive to canopy cover than to LAI, and differences between the structure of the potato crop on both dates were not well represented by this parameter. This was likely due to the fact that the LAI did not change much between the two dates, while there was a strong increase in canopy cover (
Table 4). Over the whole spectrum, there was a positive correlation between the
parameter and canopy cover when the data of both dates were combined (
Figure 11a, lower graph), suggesting that in general there was a decrease in backward scattering intensity (increase in the
parameter) when the canopy cover increased.