# Assessing Spatial Variability of Barley Whole Crop Biomass Yield and Leaf Area Index in Silvoarable Agroforestry Systems Using UAV-Borne Remote Sensing

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## Abstract

**:**

_{p}14.9%, LAI: R² 0.92, nRMSE

_{p}7.1%). Important variables for prediction included normalized reflectance, vegetation indices, texture and plant height. Maps were produced from model predictions for spatial analysis, showing significant effects of distance to trees on DM and LAI. Spatial patterns differed greatly between the sampled sites and suggested management and soil effects overriding tree effects across large portions of 96 m wide crop alleys, thus questioning alleged impacts of AFS tree rows on yield distribution in intensively managed barley populations. Models based on UAV-borne imagery proved to be a valuable novel tool for prediction of DM and LAI at high accuracies, revealing spatial variability in AFS with high spatial resolution and coverage.

## 1. Introduction

- Estimation of yield-related crop parameters in AFS at high spatial resolution and coverage utilizing UAV-borne RS.
- Identification of RS variables best suited for accurate modelling of barley DM and LAI.
- Evaluate the effect of distance to trees on barley DM and LAI.
- Evaluate the spatial variation of DM and LAI across the crop alley.

## 2. Materials and Methods

#### 2.1. Study Sites

#### 2.2. UAV-Borne Data Acquisition

#### 2.3. Manual Field Sampling

#### 2.4. RGB and Multispectral Data Processing

_{i}is a spectral vector for i = 1, …, n [54], in order to take different lighting conditions during data acquisition into account. The mean of normalized reflectance values per 1 m² subplot was calculated as:

#### 2.5. Random Forest Regression Model Building

_{p}and nRMSE

_{p}, with:

_{max}and y

_{min}are the maximum and minimum observed values, was calculated with the 100 corresponding validation datasets in form of the median value of 100 iterations. The importance of predictive variables in the training process was determined using the function ‘varImp’ from package ‘caret’. The model performance was optimized by tuning of its ‘hyper-parameter’ to an optimal value. The number of variables within a tree considered for each split in the training subset defined through the ‘hyper-parameter’ ‘mtry’ is thought to be “the primary tuning parameter, and has its greatest impact on the complexity of the final model” [68]. During model calibration (100 iterations), the ‘hyper-parameter’ defining the number of drawn candidate variables per split (‘mtry’) was optimized through repeated cross-validation (ten folds, five repeats) to a median value (most frequently occurring) of 5 and 4 randomly selected variables considered as split candidates per tree for DM and LAI respectively. To achieve a good balance between computational time and error, the number of trees was set at a value of 500 trees while node size, defining tree complexity, was kept constant at a value of 5 [68]. Final models for DM and LAI map prediction based on 100% of the data were calibrated subsequently with the optimal ‘hyper-parameters’ through repeated cross-validation (10 folds, five repeats).

#### 2.6. Map and Point Data Generation

#### 2.7. Spatial Analysis Using Linear Mixed Models

## 3. Results

#### 3.1. Field Data: Yield-Related Crop Parameters

#### 3.2. Random Forest Regression Model Performance

_{p}0.62, median RMSE

_{p}1.63 t/ha, median nRMSE

_{p}14.9%) and good precision and accuracy for LAI (median R²

_{p}0.92, median RMSE

_{p}0.3, median nRMSE

_{p}7.1%). Single models yielded much higher prediction precisions (see Table 3) but were not considered relevant, as stratified random sample selection for calibration and validation in 100 iterations indicated overoptimistic model assessment from single selections.

#### 3.3. Spatial Variability in Crop Traits

## 4. Discussion

#### 4.1. Model Performance

_{val}0.74, RMSE

_{val}1.2 t/ha). Näsi et al. [79] predicted barley DM at an early growth stage from hyperspectral and RGB images with high Pearson’s correlation coefficient (r = 0.95) but much higher relative root-mean-square error (RMSE 33.3%). In another study on barley, the higher correlation of DM (R² 0.83) with visible spectrum vegetation indices (VIs) and canopy surface height (CSH) may be explained by the multitemporal nature of the data acquisition throughout the growing season [37]. The same study reported that predictions deteriorated at late development stages of the barley crop, which likewise applies in the present study due to the proximity to harvest date. The use of a hyperspectral sensor likely also improved prediction accuracy as its narrow spectral bands allowed a better depiction of important spectral regions for VI calculation [80].

#### 4.2. Spatial Analysis

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Figure A1.**Comparisons of barley leaf area index (LAI) least squares means between distance classes. Distance classes for leeward and windward plots are based on real distance to western and eastern tree rows. Distances having no letter in common are significantly different (α = 0.05). Error bars show 95% confidence limits.

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**Figure 1.**Experimental Sites. (

**a**) Location of sampled AFS sites within Germany. (

**b**) Photo of AFS site Forst. Footprint of Plot and Subplots are indicated by white lines. (

**c**) Map of AFS site Forst.

**Figure 3.**Generation of point data from predicted raster data. (

**a**) Predicted DM at AFS site Forst. Spatial resolution is 1 m. (

**b**) Generated point values and subsets from the raster. (

**c**) Distribution of 1 m wide distance classes (real distance to tree row).

**Figure 4.**Observed versus predicted values for (

**a**) DM and (

**b**) LAI at each sampling site. Values from all sites were included in the model, represented by different colors. Blue line is the regression line, black line is 1:1 line.

**Figure 5.**Variable importance of all variables selected by variable selection using random forests (VSURF) for (

**a**) DM and (

**b**) LAI prediction. Prediction is based on (

**a**) normalized reflectance (e.g. “mean560nrm”), vegetation indices (e.g. “EVI”), texture variables (e.g. “B2_tex_median_cor”) and canopy surface height metrics (e.g. “csh_p95”).

**Figure 6.**Predicted maps for barley DM and LAI at milk ripeness (BBCH 75) at three study sites. Color scales differ between sites for improved visibility of spatial variability. Maps for AFS sites Dornburg and Wendhausen were rotated (see north arrow in true color map). Gaps in maps for Dornburg stem from damage done to barley plants during fieldwork (mixed 1 m pixels were deleted generally to prevent misinterpretation of erroneous spatial patterns).

**Figure 7.**Comparisons of barley total dry matter (DM) least squares means between distance classes. Distance classes for leeward and windward plots are based on real distance to western and eastern tree rows. Distances having no letter in common are significantly different (α = 0.05). Error bars show 95% confidence limits.

Tree Parameter | Forst | Dornburg | Wendhausen | |||
---|---|---|---|---|---|---|

Year of planting | 2010 | 2007 | 2008 | |||

Trees per ha | 8715 | 2222 | 10,000 | |||

Tree row width (m) | 10 | 12 | 11 | |||

Last harvest | 2017/2018 | 2014/2015 | 2017 (poplar), 2013/2014 (aspen) | |||

West | East | West | East | West | East | |

Species/variety | poplar “Max” | poplar “Max”, “Hybrid 275”, “Koreana” | poplar “Max”, “Hybrid 275”, “Koreana” (outer rows); aspen (inner row) | |||

Median height (m) | 3.01 | 4.85 | 7.86 | 7.66 | 5.15 | 7.37 |

**Table 2.**Descriptive statistics for DM and LAI values measured at subplots (SD = standard deviation, CV = coefficient of variation).

Statistic | DM (t/ha) | LAI | ||||
---|---|---|---|---|---|---|

Forst | Dornburg | Wendhausen | Forst | Dornburg | Wendhausen | |

n | 60 | 58 | 58 | 60 | 58 | 58 |

min | 2.2 | 3.4 | 4.3 | 2.3 | 2.9 | 3.0 |

max | 11.8 | 17.4 | 13.8 | 4.4 | 7.4 | 5.4 |

mean | 6.8 | 10.3 | 7.7 | 3.3 | 5.3 | 4.2 |

median | 6.7 | 10.4 | 7.7 | 3.2 | 5.1 | 4.3 |

SD | 1.8 | 2.6 | 1.9 | 0.5 | 1.1 | 0.5 |

CV | 26.2% | 25.7% | 24.6% | 15.8% | 20.8% | 12.9% |

**Table 3.**Model performance for DM and LAI prediction. Minimum, maximum and median values of 100 model runs with different randomly selected calibration (80%) and validation (20%) samples.

Parameter | R²_{p} | nRMSE_{p} (%) | ||||
---|---|---|---|---|---|---|

Min | Max | Median | Min | Max | Median | |

DM | 0.39 | 0.78 | 0.62 | 10.2 | 21.8 | 14.9 |

LAI | 0.86 | 0.96 | 0.92 | 5.5 | 9.5 | 7.1 |

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## Share and Cite

**MDPI and ACS Style**

Wengert, M.; Piepho, H.-P.; Astor, T.; Graß, R.; Wijesingha, J.; Wachendorf, M.
Assessing Spatial Variability of Barley Whole Crop Biomass Yield and Leaf Area Index in Silvoarable Agroforestry Systems Using UAV-Borne Remote Sensing. *Remote Sens.* **2021**, *13*, 2751.
https://doi.org/10.3390/rs13142751

**AMA Style**

Wengert M, Piepho H-P, Astor T, Graß R, Wijesingha J, Wachendorf M.
Assessing Spatial Variability of Barley Whole Crop Biomass Yield and Leaf Area Index in Silvoarable Agroforestry Systems Using UAV-Borne Remote Sensing. *Remote Sensing*. 2021; 13(14):2751.
https://doi.org/10.3390/rs13142751

**Chicago/Turabian Style**

Wengert, Matthias, Hans-Peter Piepho, Thomas Astor, Rüdiger Graß, Jayan Wijesingha, and Michael Wachendorf.
2021. "Assessing Spatial Variability of Barley Whole Crop Biomass Yield and Leaf Area Index in Silvoarable Agroforestry Systems Using UAV-Borne Remote Sensing" *Remote Sensing* 13, no. 14: 2751.
https://doi.org/10.3390/rs13142751