Combining multiple UAV-Based indicators for wheat yield estimation, a case study from Germany

Figures & data

Figure 1. Three-dimensional view of one of the study fields.

Table 1. Plot characteristics.

Plot	Total acreage	Crop	Soil type	Plot quality index^a
Plot 1	3.20 ha	Wheat	Silty clay	34–45
Plot 2	6.15 ha	Wheat	Silty clay	44–48
Plot 3	5.2 ha	Wheat	Silty clay	36–44

^aPlot quality according to German soil quality indexing system, which is based on factors like climatic conditions, slope, shadow from forest etc. and ranges from 0–100, 100 being the highest quality soil in Germany.

Figure 2. Methodological steps for wheat yield estimation based on UAV.

Figure 3. Multi rotor UAV.

Figure 4. RedEdge-MX camera.

Table 2. Spectral wavelength information of the RedEdge-MX camera.

Band	Band Name	Wavelength (nm)	Bandwidth (nm)
1	Blue	475 nm	32 nm
2	Green	560 nm	27 nm
3	Red	668 nm	14 nm
4	Red-Edge	717 nm	12 nm
5	NIR	842 nm	57 nm

Figure 5. Wheat yield map compiled from combine harvester machine.

Figure 6. Crop height for the wheat growing season.

Table 3. Selection vegetation indices equation and their application using UAV bands.

Vegetation Index	Equation	Reference
Normalized difference vegetation index (NDVI)	$NDVI=\frac{P_{NIR}-P_{RED}}{P_{NIR}+P_{RED}}$	C. J. J. R. s. o. E. Tucker (1979)
Normalized difference red edge index (NDRE)	$NDRE=\frac{P_{NIR}-P_{RED-Edge}}{P_{NIR}+P_{RED-Edge}}$	Gitelson and Merzlyak (1994)
Chlorophyll red-edge index (CIred-edge)	$C{I}_{red-edge}=\frac{P_{NIR}}{P_{RED-Edge}}-1$	Gitelson et al. (2003)
Simplified canopy chlorophyllcontent index (SCCCI)	$SCCCI=\frac{\frac{P_{NIR}-P_{RED-Edge}}{P_{NIR}+P_{RED-Edge}}}{\frac{P_{NIR}-P_{RED}}{P_{NIR}+P_{RED}}}$	Barnes et al. (2000)
Green chlorophyll vegetation index (GCVI)	$GCVI=\frac{P_{NIR}-P_{Green}}{P_{NIR}+P_{Green}}$	Gitelson et al. (2003)
Enhanced vegetation index 2 (EVI2)	$EVI2=2.4\frac{P_{NIR}-P_{RED}}{P_{NIR}+P_{RED}+1}$	Jiang et al. (2008)

Table 4. Definitions and equations of precision evaluation metrics used in this study.

Name	Equation
R squared (R^2)	$R^2=1-\sum i=1n{y}_i-{\widehat{y}}_{i}2{\displaystyle {\sum }_{i=1}^n{\left(y_i-\overline{y_i}\right)}^2{ }^{\prime }}$
Root Mean Squared Error (RMSE)	$RMSE=\sqrt{\frac{1}{n}\sum _{i=1}^n{\left(y_i-{\hat{y}}_i\right)}^2}$

Figure 7. Results of the multiple and linear regression models a) R² and b) RMSE.

Table 5. Validation results MLR between actual wheat yield data and combined NDRE_May20, SR_June16 with CH_June16.

yield_1	Coef.	St.Err.	t-value	p-value	[95% Conf	Interval]	Sig
ndre_20	17.914	0.538	33.32	0	16.858	18.969	***
csm_16	1.242	0.068	18.39	0	1.109	1.374	***
sr_16	−1.994	0.618	−3.22	0.001	−3.208	−0.78	***
Constant	6.389	3.269	1.95	0.051	−0.028	12.806	*
Mean dependent var	5.736		SD dependent var			1.069
R-squared	0.75		Number of obs			1722.000
Adj R-squared	0.74		Root MSE			0.53
F-test	715.492		Prob > F			0.000
Akaike crit. Aich et al. (2017)	1152.935		Bayesian crit. (BIC)			1171.264

*** p < 0.01, ** p < 0.05, * p < 0.1.

Figure 8. Results of the quantile regression model.

Table 6. Quantile regression result between actual wheat yield data and combined NDRE_May20, SR_June16 with CH_June16.

yield	Coef.	St.Err.	t-value	p-value	[95% Conf	Interval]	Sig
ndre_20	18.754	0.782	23.99	0	17.22	20.289	***
csm_16	1.131	0.086	13.21	0	0.963	1.3	***
sr_16	−1.009	0.602	−1.68	0.094	−2.19	0.173	*
Constant	−2.023	3.079	−0.66	0.511	−8.068	4.022
ndre_20	17.515	0.4	43.82	0	16.73	18.3	***
csm_16	1.075	0.099	10.89	0	0.881	1.269	***
sr_16	−2.822	0.784	−3.60	0	−4.361	−1.283	***
Constant	8.93	4.346	2.05	0.04	0.398	17.463	**
ndre_20	16.393	0.512	32.02	0	15.388	17.398	***
csm_16	1.056	0.065	16.18	0	0.928	1.184	***
sr_16	−2.638	0.636	−4.14	0	−3.887	−1.388	***
Constant	8.804	3.461	2.54	0.011	2.009	15.599	**
Mean dependent var	5.736		SD dependent var			1.069
Pseudo r-squared 0.25	0.578		Number of obs			1722.000
Pseudo r-squared 0.50	0.544		Number of obs			1722.000
Pseudo r-squared 0.75	0.556		Number of obs			1722.000

*** p < 0.01, ** p < 0.05, * p < 0.1.

Figure 9. Estimated coefficients with 95% confidence intervals for NDRE_May20 , SR_June16 and CH_June16.

Figure 10. a) comparison of model-predicted wheat yield with actual yield; b) scatter plot of predicted wheat yield with actual yield.

Figure 11. MLR model residuals plot.

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