Evaluating the contribution of Sentinel-2 view and illumination geometry to the accuracy of retrieving essential crop parameters

Figures & data

Figure 1. Land cover distributions in Bothaville and Harrismith (orange and red squares), Free State province (dark grey), South Africa (adopted from Kganyago 2022). The insert maps are projected to UTM (Universal Transverse Mercator) with WGS-84 (World geodetic System 1984) Datum. The land cover dataset was obtained from the Department of Forestry, Fisheries and the Environment (https://egis.environment.gov.za/gis_data_downloads, accessed 20 March 2021).

Figure 2. The schematic representation of the methods used in this study. Five experimental scenarios, i.e. Spectral bands (SB), SB and Angles (SB + Angles), Spectral vegetation indices (SVIs), SVIs and Angles (SVIs + Angles), and All variables (Avar) were used for crop biophysical and biochemical variable (BV) retrieval using two test datasets, i.e. cross-validation test dataset and an independent held-out test (i.e. unseen) dataset.

Figure 3. Spatial (per-pixel) variation of Sentinel-2 illumination and view angles over the two study sites, i.e. Bothaville (a–c) and Harrismith (d–f). (a) and (d) show per-pixel Sun Zenith Angle (SZA), (b) and (e) show per-pixel mean View Zenith Angle (VZA), and (c) and (f) show per-pixel mean Relative Azimuth Angle (RAA).

Figure 4. Summary statistics Sentinel-2 illumination and view angles in Bothaville (a–c) and Harrismith (d–f). The red line indicates the mean value for each geometric variable over 50,000 randomly sampled pixels.

Table 1. The various experimental scenarios were designed by excluding and including view and illumination geometry from commonly used radiometric inputs (i.e. spectral bands and vegetation indices).

Scenario	Input variables	Description of input variables
SB (p = 10)	Spectral Bands	Only spectral bands (defined in Section 3.1.2) were used.
SB + Angles (p = 13)	Spectral Bands and Angles	Spectral bands combined with the cosine of view/illumination geometries (Angles), i.e. Sun Zenith Angle (SZA), mean View Azimuth Angle (VAA), and the Relative Azimuth Angle (RAA).
SVIs (p = 10)	Spectral Vegetation Indices	Only the spectral vegetation indices were used.
SVIs + Angles (p = 13)	SVIs and Angles	SVIs combined with the Angles, i.e. SZA, VAA, and mean RAA, were used.
Avar (p = 23)	All Variables	All input variables (described above) were used.

Table 2. The red-edge indices from Sentinel-2 MSI data.

Index	Equation	Reference
Normalized Difference Index	$NDI45=\frac{R_{705}-R_{665}}{R_{705}+R_{665}}$	Delegido et al. (2011)
Meris Terrestrial Chlorophyll Index	$MTCI=\frac{R_{740}-R_{705}}{R_{740}-R_{665}}$	Dash and Curran (2005)
Modified Chlorophyll Absorption Ratio Index	$MCARI=[(R_{705}-R_{665})-0.2\times \left(R_{705}-R_{560}\right)]\times \left(\frac{R_{705}}{R_{665}}\right)$	Daughtry et al., (2000)
Red-Edge Inflection Point Index	$REIP=700+40\times (\frac{(R_{665}-R_{783})/2-R_{705})}{(R_{740}+R_{705})}$	Guyot and Baret, (1988)
Sentinel-2 Red-Edge Position Index	$S2REIP=705+35\times (\frac{((R_{665}-R_{783})/2-R_{705})}{(R_{740}+R_{705})}$	Frampton et al., (2013)
Inverted Red-Edge Chlorophyll Index	$IRECI=\frac{R_{783}-R_{665}}{R_{705}+R_{740}}$	Frampton et al., (2013)
Red-edge Chlorophyll Index (CIrededge)	$C{I}_{red-edge}=\frac{R_{NIR}}{R_{RE}}-1$	Gitelson et al., (2003)
Red Edge Relative Indices (RERI) @ 705 nm	$RER{I}_{\left[705\right]}=\frac{R_{705}-R_{665}}{R_{865}}$	XU et al. (2019)
Red Edge Relative Indices (RERI) @ 783 nm	$RER{I}_{\left[783\right]}=\frac{R_{783}-R_{705}}{R_{865}}$	XU et al. (2019)
Simple Sentinel-2 LAI Index	$SeLI=\frac{R_{865}-R_{705}}{R_{865}+R_{705}}$	Pasqualotto et al., (2019)

Table 3. The amount of spectral variability explained by the geometric variables based on multiple linear regression.

		B2	B3	B4	B5	B6	B7	B8	B8A	B11	B12
Bothaville	Adj. R^2	0.32	0.36	0.30	0.35	0.35	0.34	0.35	0.36	0.43	0.37
	p-Value	<2.2e-16	<2.2e-16	<2.2e-16	<2.2e-16	<2.2e-16	<2.2e-16	<2.2e-16	<2.2e-16	<2.2e-16	<2.2e-16
Harrismith	Adj. R^2	0.35	0.32	0.37	0.25	0.19	0.21	0.28	0.36	0.47	0.42
	p-Value	<2.2e-16	2.709e-15	<2.2e-16	9.297e-12	1.076e-08	1.624e-09	2.718e-13	<2.2e-16	<2.2e-16	<2.2e-16

Adj. R² denotes Adjusted R².

Table 4. The performance of various Sentinel-2 input variables in retrieving various crop parameters using Random Forest (RF) with two test datasets, i.e. cross-validation data pooled from the two sites and independent test data from Harrismith (in brackets).

		SB	SVIs	SB + Angles	SVIs + Angles	Avar
LAI	R^2	0.59 (0.49)	0.52 (0.58)	0.69 (0.66)	0.67 (0.67)	0.66 (0.67)
	RMSE	0.57 (0.65)	0.62 (0.62)	0.50 (0.55)	0.51 (0.53)	0.52 (0.55)
	RRMSE	0.01 (0.02)	0.01 (0.02)	0.01 (0.02)	0.01 (0.02)	0.01 (0.02)
	MAE	0.41 (0.48)	0.44 (0.44)	0.34 (0.37)	0.36 (0.36)	0.36 (0.37)
	%Bias	0.00 (−0.03)	0.00 (−0.04)	0.00 (−0.03)	0.00 (−0.03)	0.00 (−0.04)
LCab	R^2	0.71 (0.49)	0.74 (0.59)	0.72 (0.49)	0.76 (0.61)	0.74 (0.58)
	RMSE	7.16 (7.18)	6.75 (6.31)	7.01 (7.06)	6.57 (6.16)	6.69 (6.43)
	RRMSE	0.01 (0.03)	0.01 (0.03)	0.01 (0.03)	0.01 (0.03)	0.01 (0.03)
	MAE	5.68 (5.57)	5.30 (4.88)	5.56 (5.32)	5.24 (4.75)	5.57 (4.95)
	%Bias	− 0.01 (0.00)	−0.01 (−0.01)	0.00 (0.00)	0.00 (0.00)	0.00 (0.00)
CCC	R^2	0.69 (0.69)	0.67 (0.67)	0.72 (0.69)	0.72 (0.72)	0.72 (0.72)
	RMSE	33.48 (26.48)	34.52 (27.86)	32.07 (26.63)	32.37 (25.98)	32.36 (24.83)
	RRMSE	0.02 (0.04)	0.02 (0.04)	0.02 (0.04)	0.02 (0.04)	0.02 (0.03)
	MAE	23.31 (20.96)	23.88 (19.38)	22.60 (20.16)	22.39 (18.19)	22.68 (18.12)
	%Bias	0.00 (0.00)	−0.01 (−0.06)	0.00 (−0.02)	−0.01 (−0.04)	−0.01 (−0.03)

The bold values indicate the best (i.e. lowest) RMSE achieved by the input variable scenario for each biophysical/biochemical variable (BV).

Figure 5. Scatterplots for the best Random Forest (RF) models for retrieving various BVs using various Sentinel-2 covariates, cross-validation test dataset pooled from Bothaville and Harrismith (i.e. a–c) and an independent held-out (i.e. 30%) dataset from Harrismith (i.e. d–f). SB + Angles achieved the best LAI and CCC predictive accuracy with cross-validation test datasets (i.e. a and c), while SVIs + Angles resulted in superior predictive accuracy for LC_ab with both test datasets (i.e. b and e), and for LAI with the Independent held-out (i.e. 30%) dataset (i.e. d). Avar achieved superior predictive accuracy for CCC with the independent held-out dataset (i.e. f).

Figure 6. Spatial distribution of crop biophysical and biochemical variables for Bothaville (a–c) and Harrismith (d–f). The LAI and CCC maps in (a) and (c) were achieved with SB + Angles, while LC_ab in (b) and (e) SVIs + Angles. Avar was used to map CCC in (f).

Figure 7. Top 10 important variables (high to low) for retrieving LAI, LC_ab, and CCC using each experimental scenario identified with Random Forest (RF) and fivefold cross-validation with 100 iterations.

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Data availability statement

The data that support the findings of this study are available from the corresponding author, MK, upon reasonable request.