Data acquisition was conducted during three years (growing seasons 2016/17, 2017/18 and 2018/19) at the Hohenschulen Experimental Farm (10.0 E, 54.3 N, 30 m a.s.l.) of the Kiel University, located in Northern Germany. The long-term average temperature is 8.9°C, the precipitation average 788 mm (Deutscher Wetterdienst, 2013). The site is characterized by a small-scale heterogeneous soil, the main soil type being a pseudogleyic sandy loam.

Destructive sampling for sensor calibration was conducted as additional measurement in different ongoing trials. In the growing season 2016/17, data were collected within Trial A and Trial B, in 2017/18 in Trial B and Trial C and in 2018/19 only in Trial C. Trial A is a four-field rotation since 2003, with winter wheat following winter oilseed rape. Four different nitrogen levels are tested in interaction with four different cultivars in four replications ( Table 1 ). Trial B and C are experimental sites, placed each year on a different field. In Trial B four different sowing densities of four cultivars are examined whereas in Trial C six cultivars and two nitrogen levels are tested ( Table 1 ). Except the treatments mentioned, the wheat crops were managed according to regional farmer’s practice.

The following sections (GAI Reference Measurement up to Advanced Predictive Models) describe the process from data collection through data processing to model calibration and evaluation. To clarify the procedure, it is illustrated schematically in Figure 1 .

At the very beginning, plots assessed as compromised in any manner (e.g. strong weed abundance, damages by game, lodging) were excluded of further consideration. This affected especially Trial B, as in 2017 the data of the whole sowing density 50 K m^-2-treatment were sorted out due to strong weed abundance and the data of sowing density 400 K m^-2 of the cultivar Solehio after early July due to lodging. In 2018 in Trial B, problems in crop establishment of the cultivar Dekan and additional waterlogging stress led to too little sampling material in the lowest sowing density variant at the end of May and in the two lowest sowing density variants in June.

Considering GAI, values above 7 m² m^-2 were excluded from the dataset because under local growing conditions these high values do never occur as a treatment mean and they were considered as more harmful then useful for calibration purposes (concerns six samples of the calibration dataset and one of the evaluation dataset). Furthermore July 18, 2017; June 27, 2017 and June 11, 2018 were omitted from GAI-dataset as the process of senescence had already started (see GAI Reference Measurement).

Finally, the data from Trial A and Trial B (2016/17 and 2017/18) were combined to form one single calibration dataset, covering a broad spectrum of GAI-values, crop managements, and environmental factors (e.g. irradiance at flight day, ground coverage, nitrogen levels and sowing densities), whereas the data from Trial C constitute the evaluation dataset (45% of the total data volume). Calibration and evaluation dataset never share a common date and flight, respectively. The result is a high level of independence between both data sets (final sample size for GAI-calibration: 474, GAI-evaluation: 383).

All statistical analysis was conducted in R Core Team, 2017.

None of the single bands performs convincingly (MAE_evaluation = 1.41–2.64 m² m^-2, Table S2 ). Combining the bands increases the performance considerably, especially if interactions between the bands are allowed (16 different terms, MAE_evaluation = 0.99 m² m^-2, Table S2 ). The single ratio-models perform noticeably better than the single band-models (MAE_evaluation = 0.55–0.81 m² m^-2, Table 4 ). The combination of different ratios provides considerably better results than the single ratios, with a lower MAE_calibration if interactions are allowed, but with a better performance at evaluation if not ( Table 4 ). It is noteworthy that the increase of the predictive error from calibration to evaluation is considerably lower for most of the Simple Ratio approaches (on average 61%, Table 4 ), than for the single band-models (on average 80%, Table S2 ) and that the increase of the single-band model with interaction is the highest (230%).

In summary, the combination of NIR/Green, NIR/Red, and NIR/RE without interaction convinces the most (MAE_evaluation = 0.45 m² m^-2 and RMSE_evaluation = 0.71 m² m^-2, Table 4 ), followed by the simple ratio of NIR/RE (MAE_evaluation = 0.55 m² m^-2 and RMSE_evaluation = 0.74 m² m^-2, Table 4 ).

These two were hence selected for further evaluation, together with the NDVI_exp as the most common VI. The VI combining all spectral bands provided by the Sequoia camera as NIR-based quotients was named VIQUO. The equations for the calibrated models are given in Table 4 .

On average, the advanced predictive models perform better than the VI-models, in terms of raw reflections, reflectance ratios, in the calibration and the evaluation ( Tables 4 , 5 , S2 and S3 ). While the raw data models provide similar MAEs in terms of calibration, their MAEs in the evaluation are at least 111% higher ( Tables 5 and S3 ).

Focusing on the ratio-based models, it is noticeably that the best predictive models in calibration are the worst in the evaluation (e.g. Boosted Trees with an increase of predictive error of 79%, Table 5 ). The best models in the evaluation are the SVMs with linear respectively radial Kernel and the Multivariate Adaptive Regression Spline (MAE_evaluation = 0.44 m² m^-2). Due to its relative simplicity, the SVM with linear Kernel (SVM, MAE_evaluation = 0.44 m² m^-2 and RMSE_evaluation = 0.71 m m^-2) is chosen to represent advanced predictive modeling methods for further investigation and comparison with the VI-models.

Comparing the performance of the selected VI-models with the SVM via their MAEs ( Tables 4 and 5 ), it can be stated that the SVM performs considerably better than the NDVI_exp and the NIR/RE, both in terms of calibration and evaluation, whether the VIQUO has a lower MAE_calibration as the SVM and its MAE_evaluation is only slightly higher. The increase of predictive error from calibration to evaluation is relatively high with the NDVI_exp-model (64%, Table 4 ), but nearly the same with the SVM-, the NIR/RE- and the VIQUO-model (22–29%, Tables 4 and 5 ). However, while the predictive error of SVM and VIQUO is increasing at high GAI-values, the predictions of NIR/RE meets the high GAIs well, but its predictions at low GAI-values scatter strongly, producing for the most part negative predictions ( Figure 2 ). Looking at Figure 2 , it is notably that several points in the high GAI-range in the evaluation are not met by any of the tested models. These data were obtained during the last sampling date in 2018, after a long period of drought. It is hence probable that they are already affected by senescence, which is not adequate depicted in destructive measurements.

Figure 3 allows a closer view to the topic of varying model-sensitivity through the season: With regard to the MAE, none of the examined VIs has considerable problems in predicting low GAIs (> 0 – < 0.25 & Dead Plants), with NIR/RE having the highest predictive error (MAE = 0.29 m² m^-2). Due to the exponential term, the NDVI_exp-model predicts very well in these classes, but it has considerable problems depicting high GAI-values, with the highest MAEs in every other GAI-class ( Figure 3 ) and a massive scattering when predicting GAIs > 2 ( Figure 2 ). SVM and VIQUO perform well at the low values and are very sensitive to medium-range GAIs, with only small differences between the two models. However, a saturation effect is visible at GAIs > 5. In contrast, while the NIR/RE-model is the worst in predicting low GAIs (0–0.25 & Dead Plants) and only slightly better at medium GAIs (< 2, 2–3 and 3–4), it shows the best results when depicting GAIs above four (MAE = 0.81 m² m^-2, rMAE = 16%) and is the only tested approach with no saturation effects at the highest measured GAI values.

For the assessment of cultivar-specific effects, the linear NIR/RE-model was chosen (due to the low number of predictors and the concern to not inflate the number of interactions between cultivars and predictors). No significant difference (p = 0.05) between the model with- and without the interaction between reflectance and cultivar information was determined by means of ANOVA and the MAEs of the two models in calibration and evaluation differ only slightly (without interaction: MAE_calibration = 0.40 m² m^-2, MAE_evaluation = 0.55 m² m^-2, with interaction: MAE_calibration = 0.39 m² m^-2, MAE_evaluation = 0.54 m² m^-2).

A whole season- and cultivar-transferable approach for GAI-prediction is preferable to specific models for several growth stages, concerning simplicity in data processing and communicability, both affecting transferability into practice. In our data, no significant cultivar-specific effect can be identified. When it comes to GAI-prediction, established calibration methods exist until the GAI-maximum is reached. But problems arise when the sensitivity of GAI-models is tested after the start of the senescence, as the accurate identification of the actual GAI is complicated or not possible at all due to the inhomogeneous senescence of the plant organs and the gradual degradation of leaf chlorophyll. Problems in estimating winter wheat GAI during senescence based on multispectral data have also been reported by other studies (Boegh et al., 2002; Haboudane et al., 2004; Lelong et al., 2008; Richter et al., 2012). They assumed that the decreasing performance of their calibrated models originates not from the informative value of the multispectral data but in the validity of the ground truth GAI-measurements. The method introduced in this study, enables the validation of our GAI-models during senescence and hence the confirmation of these considerations. It could thus be shown that the GAI-estimations of the tested models were valid and that the models, being calibrated without any senescence data (except dead plants), can provide reasonable GAI-predictions for this part of the season as well.

The quality of the whole-season GAI-predictions was tested further via the calculation of green area duration and the correlation with the final biomass. Hereby, 80% of the variation in the final biomass is explained by the NDVI_exp-model, which fits to the results of Wiegand et al. (1992) and Tucker et al. (1981) with handheld devices. The new GAI-models VIQUO and SVM explain even more of the observed variance (up to 85%).

The best model to derive GAI-information should provide reliable and precise GAI-information as simple as possible. In terms of both, model complexity and communicability, the models can be set in the same order: The application of raw bands is the simplest approach, followed by the traditional two-band ratios. The newly introduced VIQUO-model, based on all four bands the Sequoia camera provides, follows shortly afterwards and the advanced predictive models are for sure the most complex and the most difficult to communicate. Therefore, the central question to be answered is, if the increasing complexity is worth it.

Raw reflection driven models are clearly not sufficient to predict GAI adequately, regardless if they are integrated in an advanced predictive model or not. The increase in MAE from calibration to evaluation indicates instability in the relationship of single bands to GAI between different sampling dates. Problems in predicting crop characteristics with raw reflections under varying irradiance conditions were found by Tucker et al. (1981) and Verger et al. (2014) as well, both demonstrating at the same time that this problem can be solved by using ratios instead.

When applying a two- or more-band approach, the questions of band selection and their combination arise. Many studies have worked on the issue which bands are essential to predict crop characteristics, either based on a priori knowledge about plant reflection characteristics (Baret and Guyot, 1991; Haboudane et al., 2004) or by recording large number of wavelengths with hyperspectral sensors and testing all possible combinations (e.g. Thenkabail et al., 2000; Hansen and Schjoerring, 2003). Based on the finding that already simple ratios (as NIR/RE) provide relatively low MAEs and on the attempt to keep the GAI-models as simple as possible, we restricted our analysis on two-band simple ratios, the combination of all possible simple ratios in the VIQUO and the classical NDVI (with exponential fit), and did not test different band combination approaches. In accordance to the findings of other studies (Serrano et al, 2000; Haboudane et al., 2004; Pinty et al., 2009; Viña et al., 2011) it was shown that the NDVI_exp is insensitive in dense canopies (here: GAI > 2 m² m^-2). The NIR/RE, as best Simple Ratio, is superior in predicting high GAIs. This result is in accordance with many studies (e.g. Delegido et al.,2013; Zhou et al., 2017) that the RE-band provides information even at high canopy densities. However, the model performs inaccurately at low GAIs and the NIR/RE-calculated GAI-curves are not stable through the season. The latter could be a result of both, of lower sensitivity of NIR/RE in the phase of senescence or of technical problems of the RE-band (the RE-band is the narrowest of the used bands, which could result in instabilities in the measurements, for example at low irradiation).

The VIQUO- and the SVM-model can compensate the temporarily low sensitivity of the RE-band and provide stable GAI-predictions over the whole season. A stabilization of crop-characteristic estimations with regard to differing irradiance conditions by adding additional bands to the traditional two-band approach has been reported by Mistele and Schmidhalter (2010) as well. Other studies describe a decreasing saturation effect and an increase of sensitivity obtained through additional bands (Haboudane et al., 2004; Delegido et al., 2013). Haboudane et al. (2004) increased the sensitivity of their model to GAI-values > 4 m² m^-2 by adding a green-band to their NIR-Red-model and achieved a whole season RMSE of 0.79 – 1.28 m² m^-2. In our case, the VIQUO, including additionally the RE-band, is sensitive to GAI-values ≤ 5 m² m^-2 and produces even more accurate predictions (RMSE_evaluation = 0.72 m² m^-2). Due to a very high fraction of intercepted radiation at GAI-values ≥ 5, we hold that sensitivity at rather low values is more important for the model-selection. For different requirements, the NIR/RE-model with its high sensitivity at high GAI-values might be the adequate approach.

The advanced predictive models are able to produce lower RMSEs than the VI-models, with the SVM even surpassing the VIQUO (RMSE_evaluation = 0.71 m² m^-2). This improvement in GAI-prediction is in accordance to the findings of Hansen and Schjoerring (2003), but notably lower than that of Verrelst et al. (2015), where the advanced predictive model reduced the RMSE by nearly 30%. This could be due to their data set, as a simultaneous consideration of different crop types might require more complex model methods, or due to their evaluation approach, as they used a cross-validation instead of an independent dataset, increasing the probability of overparameterization. While there are no indications that the here presented SVM-model is overparametrized (same decrease in predictive power from calibration to evaluation than the testes Simple Ratio-models), it has the same saturation effect for GAI-values >5 as the VIQUO. Considering the sensitivity in the different GAI-classes, the SVM is predicting mostly, but not in every case, GAI more precise than the VIQUO. The GAI-curves estimated with these two different models are nearly the same and the correlation of green area duration to final biomass of the SVM-model is consequently not notably better. On this base we consider the higher complexity of the advanced predictive model as not justified.

Lastly, besides the validity through the whole season for different cultivars, the applicability of the GAI-calibration across seasons should be considered. In general, the transferability of purely statistic-based approaches, as the calibration here presented, might be regarded as problematic. Additionally, the use of destructive GAI-data restricts the size of the data set to the affordable workload and the local conditions of the respective study site (e.g. number of seasons, plots, cultivars, nitrogen levels). A concept to overcome these problems is the use of radiative transfer models, such as PROSAIL, to generate reflectance- and LAI-data sets for the sensor of interest (Richter et al., 2010; Verger et al., 2014). However, this approach relies on the estimation of several crop parameters (e.g. average leaf angle, dry matter content, leaf mesophyll parameter). These parameters may vary in plot trials, for example due to different cultivars and fertilization levels (as exemplarily shown above for two cultivars), and probably also on farm sites with heterogeneous crop growth. Furthermore problematic may be to depict the sensitivity of the raw bands to illumination conditions during image acquisition when generating artificially reflectance data (Verger et al., 2014) and the saturation effect when considering high GAIs (Richter et al., 2010; Verger et al., 2014). These effects could be examined closer in further investigations, using our data set as basis for evaluation. However, taking into account these restrictions of physically based calibration approaches, statistically-based approaches can probably be considered at least of equal standing and have shown to be stable over multiple seasons and many different measurement dates in the presented data set.