Fusion of Sentinel-2 Phenology Metrics and Saturation-Resistant Vegetation Indices for Improved Correlation with Maize Yield Maps

Abstract

To authors’ knowledge, no previous studies thoroughly focused on determining the single optimal combination of vegetation index and phenology metric for maize yield assessment based on ground truth yield map from combine harvester. Therefore, the main objective of this study was to evaluate correlation between all combinations of eight vegetation indices and seven phenology metrics with maize yield. A specific focus was put on evaluating saturation-resistant vegetation indices and utilizing Sentinel-2 images, including novel vegetation indices such as Inverted Difference Vegetation Index (IDVI), Three Red-Edge Vegetation Index (NDVI_3RE) and Plant Phenology Index (PPI). Twelve parcels located in Eastern Croatia were observed during 2022 and 2023, with a total area of ground truth data of 67.61 ha. The analysis of vegetation indices and phenology metrics indicated varying strengths of correlation with maize yield, with the combination of NDVI_3RE and Senescence producing the highest Pearson correlation coefficient (0.506). However, the relationship of optimal combination of vegetation index and phenology metric with maize yield based on combined dataset which included parcels 1–12 on individual parcels varied notably and is likely indicative of interannual weather variations. Overall, the reduced saturation effect in red-edge-based index suggests that it may be more suitable for maize yield prediction.

1. Introduction

Remote sensing is key for acquiring data in precision agriculture, enabling non-destructive monitoring of crop health, growth dynamics, and yield potential [1,2]. Among the most widely used metrics derived from spectral data are vegetation indices, which utilize the differential reflectance of plant canopies in the visible and near-infrared spectral bands to estimate biophysical parameters such as leaf area index (LAI), chlorophyll content, and biomass [3,4]. However, a major limitation of many traditional vegetation indices, such as the Normalized Difference Vegetation Index (NDVI), is their tendency to saturate under high-density vegetation conditions [5]. This saturation effect occurs when the canopy reaches a level of density where increases in LAI or chlorophyll no longer produce proportional changes in spectral reflectance, leading to marginal differences in index values [6]. Saturation is particularly problematic in the context of yield prediction, as crops in later phenological stages often develop dense canopies with high LAI [7]. Since these stages are critical for determining crop yield, the inability of conventional vegetation indices to accurately track vegetation dynamics during this period introduces significant uncertainty into yield models [8]. For instance, in crops like maize, wheat, and rice, NDVI frequently saturates well before peak biomass is achieved, limiting its usefulness for mid- to late-season yield forecasting [9,10]. To address this challenge, saturation-resistant vegetation indices have been developed, incorporating modifications that enhance their dynamic range and sensitivity across varying canopy densities. Most well-known indices include the Enhanced Vegetation Index (EVI), which introduced a soil adjustment factor and a blue-band correction to reduce atmospheric and background noise [11]. and the Wide Dynamic Range Vegetation Index (WDRVI), which applied a weighting coefficient to the near-infrared and red bands to linearize their relationship with LAI [12]. Moreover, some of new saturation-resistant vegetation indices, such as Inverted Difference Vegetation Index (IDVI) [13], Three Red-Edge Vegetation Index (${\mathrm{NDVI}}_{3\mathrm{RE}}$) [14] and Plant Phenology Index (PPI) [15], showed promising results from initial studies but are under researched in terms of evaluating correlation with crop yield. The application of these indices is particularly valuable in high-yielding agricultural systems, where precise monitoring of crop vigor during advanced growth stages is essential for accurate yield prediction [16]. By mitigating saturation effects, these indices enable more robust correlations between spectral data and agronomic parameters, improving the reliability of yield forecasts and supporting data-driven decision-making in crop management [17]. As such, the continued refinement and validation of saturation-resistant vegetation indices remain an important research frontier in agricultural remote sensing, with significant implications for food security and sustainable intensification.

Accurate and cost-effective crop yield prediction is essential for optimizing agrotechnical operations in subsequent growing seasons [18]. While yield monitor data from combine harvesters provides high-resolution spatial yield variability, their acquisition is often notably expensive, limiting widespread adoption, particularly for smallholder farms or large-scale regional assessments [19]. In contrast, freely available Sentinel-2 satellite images offer a globally accessible alternative for yield modeling, provided that the most predictive spectral and temporal features are identified [20]. A critical challenge lies in determining the optimal combination of vegetation indices and phenology metrics, as these must collectively capture both crop vigor through spectral reflectance [21] and growth stage dynamics through phenological timing [22]. Phenology metrics, such as the start of season (SOS), peak of season (POS), and end of season (EOS), are crucial because they align spectral signals with key developmental phases, ensuring that yield models account for the physiological processes driving final productivity [23]. Without proper phenological alignment, vegetation indices risk misinterpretation, as the same index value may correspond to different growth stages with distinct yield implications. By integrating the most responsive vegetation index with relevant phenology metrics, Sentinel-2 images can model yield patterns [24], enabling improvement of agrotechnical operations, such as fertilization and crop protection for future seasons. Thus, identifying this optimal combination is required for utilizing open-access satellite images as a scalable tool for precision agriculture [25].

Maize (Zea mays L.) represents one of the globally most significant crops, and serving as fundamental components of food security and livestock feed [26]. The accurate prediction of its yield is particularly challenging yet crucial due to their distinct physiological characteristics and growth patterns that demand specialized remote sensing approaches [27]. Specifically for maize, conventional vegetation indices like NDVI frequently saturate during critical reproductive stages when yield potential is determined, necessitating the use of saturation-resistant indices coupled with phenological metrics during high LAI growth stages [28]. The five-day temporal resolution of Sentinel-2 is particularly valuable for capturing these crop-specific phenological transitions, while its red-edge bands enable development of more physiologically relevant vegetation indices [29]. Optimizing these sensor-crop-specific approaches allows for overcoming the limitations of expensive yield monitor data while providing actionable insights for precision nutrient management, which is particularly critical given the increasing climate variability affecting these staple crops. Despite advances in remote sensing for agriculture, significant validation challenges persist in identifying the optimal combination of vegetation indices and phenology metrics for robust yield prediction. A primary limitation lies in the scarcity of high-quality, spatially representative ground truth data, as yield monitor measurement, while precise, are often restricted to commercial farms and may not align with Sentinel-2 pixel resolutions [30]. Additionally, the dynamic interaction between crop phenology and spectral reflectance introduces uncertainties, as the same vegetation index value may correspond to different growth stages due to variations in planting dates, genotypes, or environmental stresses [31]. For maize, these challenges are especially notable due to its distinct canopy architectures and physiological responses, which cause rapid LAI saturation [32].

To narrow the research gap in determining optimal combination of vegetation index and phenology metric for maize yield assessment, the main objective of this study was to evaluate correlation between all combinations of eight vegetation indices and seven phenology metrics with maize yield. A specific focus was put on evaluating saturation-resistant vegetation indices and utilizing Sentinel-2 images alongside yield map collected from combine harvester, achieving high spatial resolution for both datasets.

2. Materials and Methods

The workflow of the study included four fundamental steps: (1) yield map acquisition and preprocessing; (2) calculation of eight vegetation indices for each point of yield map, with a focus on saturation-resistant vegetation indices; (3) phenology analysis for each point of yield map and for all eight vegetation indices, resulting in seven phenology metrics; and (4) correlation analysis between maize yield and combinations of vegetation indices and phenology metrics.

2.1. Study Area Parcels and Yield Map Acquisition

The study area consisted of twelve maize agricultural parcels in the Eastern Croatia near Koška, with six observed during year 2022 and six observed during year 2023 (Figure 1). The total area of used maize parcels was 67.61 ha, among which 42.03 ha and 25.58 ha were represented by parcels observed in 2022 and 2023, respectively. Yield maps were acquired using Claas Lexion 6900 combine harvester (Harsewinkel, Germany), equipped with Quantimeter yield sensor and Claas Connect software v1.0 (Harsewinkel, Germany) [33] for yield mapping. Preprocessing of yield maps was performed by removing empty entries and zero yield values, after which an outlier removal based on a Median Absolute Deviation (MAD) method, retaining only values within ±3 MAD from the median (

Table 1. Description of twelve study parcels and yield map properties after preprocessing.

Year	Parcel ID	Area	Harvesting Date	Yield Samples (Raw)	Yield Samples (Preprocessed)	Mean Yield	CV
2022	Parcel 1	2.94 ha	22 October 2022	396	356	4.631 t ha−1	0.218
	Parcel 2	32.42 ha	19 October 2022	2882	2660	7.128 t ha−1	0.197
	Parcel 3	1.02 ha	20 October 2022	137	128	5.874 t ha−1	0.179
	Parcel 4	2.08 ha	18 October 2022	342	342	8.208 t ha−1	0.460
	Parcel 5	2.02 ha	18 October 2022	276	249	6.283 t ha−1	0.220
	Parcel 6	1.55 ha	18 October 2022	205	204	3.452 t ha−1	0.374
2023	Parcel 7	2.20 ha	14 October 2023	170	165	8.392 t ha−1	0.237
	Parcel 8	4.43 ha	14 October 2023	302	293	8.388 t ha−1	0.188
	Parcel 9	11.40 ha	13 October 2023	1094	1056	7.866 t ha−1	0.193
	Parcel 10	2.40 ha	13 October 2023	341	332	4.266 t ha−1	0.352
	Parcel 11	2.37 ha	13 October 2023	304	275	4.907 t ha−1	0.159
	Parcel 12	2.78 ha	13 October 2023	260	235	5.264 t ha−1	0.156

). Mean maize yield per ground truth agricultural parcel ranged from 3.452 to 8.392 t ha⁻¹. Due to relative differences in total preprocessed number of yield samples per parcel, further processing was performed for both individual parcels and their combination, including all available yield samples from twelve parcels. According to the Ministry of Agriculture, Forestry and Fishery of the Republic of Croatia [34], optimal sowing dates for maize in the study area are between 10 April and 25 April, which requires 150–200 kg ha⁻¹ of nitrogen fertilization for achieving yield of 8–10 t ha⁻¹.

A wet humid continental climate (Dfb class per Köppen climate classification) with mild summer is present in the study area. Gleysols and Luvisols are present soil classes in the study area per World Reference Base (2006) Soil Groups [35] with dominantly flat topography. Based on SoilGrids data [36], clay loam soil texture class was present on all study area parcels (

Table 2. Description of auxiliary data on soil organic carbon and soil texture parameters from twelve study parcels.

Year	Parcel ID	Soil Organic Carbon Content (g kg−1)	Clay Content (%)	Silt Content (%)	Sand Content (%)	Soil Texture Class (per USDA Classification)
2022	Parcel 1	344.0	24.4	43.0	32.6	Clay Loam
	Parcel 2	374.1	29.5	33.0	37.5	Clay Loam
	Parcel 3	301.0	25.6	38.2	36.2	Clay Loam
	Parcel 4	340.0	26.8	38.8	34.4	Clay Loam
	Parcel 5	308.0	29.0	34.1	36.9	Clay Loam
	Parcel 6	353.0	27.6	37.4	35.0	Clay Loam
2023	Parcel 7	337.0	27.6	39.0	33.4	Clay Loam
	Parcel 8	322.5	25.0	41.4	33.6	Clay Loam
	Parcel 9	412.0	30.3	30.7	39.0	Clay Loam
	Parcel 10	376.8	26.5	38.1	35.4	Clay Loam
	Parcel 11	355.3	29.1	33.8	37.1	Clay Loam
	Parcel 12	346.3	28.9	35.0	36.1	Clay Loam

). According to the same source, mean soil organic carbon stock in the study area is 55 t ha⁻¹. While SoilGrids represent state-of-the-art data source from digital soil mapping, these values can contain bias, particularly due to its 250 m spatial resolution [37]. Mean monthly air temperature for both years were slightly higher than the long-term average during 1899–2023 during maize vegetative period based on Croatian Meteorological and Hydrological Service data, while monthly precipitation in September for 2022, as well as April and May for 2023 was notably higher than the long-term average (Figure 2).

2.2. Calculation of Vegetation Indices

Eight vegetation indices were derived from Sentinel-2 Level-2A bottom-of-atmosphere surface reflectance imagery (

Table 3. Eight vegetation indices evaluated for correlation with maize yield in the study.

Vegetation Index	Abbreviation	Formula	Reference
Difference Vegetation Index	DVI	$\mathrm{DVI}=\mathrm{NIR}-\mathrm{R}$	[39]
Normalized Difference Vegetation Index	NDVI	$\mathrm{NDVI}={\displaystyle \frac{\mathrm{NIR}-\mathrm{R}}{\mathrm{NIR}+\mathrm{R}}}$	[40]
Enhanced Vegetation Index	EVI	$\mathrm{EVI}=2.5 \times {\displaystyle \frac{\mathrm{NIR}-\mathrm{R}}{\mathrm{NIR}+6\mathrm{R}-7.5\mathrm{B}+1}}$	[11]
Enhanced Vegetation Index 2	EVI2	$\mathrm{EVI}2=2.4 \times {\displaystyle \frac{\mathrm{NIR}-\mathrm{R}}{\mathrm{NIR}+\mathrm{R}+1}}$	[41]
Wide Dynamic Range Vegetation Index	WDRVI	$\mathrm{WDRVI}={\displaystyle \frac{0.2\mathrm{NIR}-\mathrm{R}}{0.2\mathrm{NIR}+\mathrm{R}}}$	[12]
Inverted Difference Vegetation Index	IDVI	$\mathrm{IDVI}={\displaystyle \frac{1+\left(\mathrm{NIR}-\mathrm{R}\right)}{1-\left(\mathrm{NIR}+\mathrm{R}\right)}}$	[13]
Three Red-Edge Vegetation Index	${\mathrm{NDVI}}_{3\mathrm{RE}}$	${\mathrm{NDVI}}_{3\mathrm{RE}}={\displaystyle \frac{{\mathrm{RE}}_3-(0.3{\mathrm{RE}}_1+0.7{\mathrm{RE}}_2)}{{\mathrm{RE}}_3+(0.{3\mathrm{RE}}_1+0.7{\mathrm{RE}}_2)}}$	[14]
Plant Phenology Index	PPI	$\mathrm{PPI}=-\mathrm{K} \times \ln \left({\displaystyle \frac{{\mathrm{DVI}}_{\max }-\mathrm{DVI}}{{\mathrm{DVI}}_{\max }+0.09}}\right)$	[15,42]

B—bottom-of-atmosphere surface reflectance in blue band (Band 2), R—bottom-of-atmosphere surface reflectance in red band (Band 4), ${\mathrm{RE}}_1$—bottom-of-atmosphere surface reflectance in first red-edge band (Band 5), ${\mathrm{RE}}_2$—bottom-of-atmosphere surface reflectance in second red-edge band (Band 6), ${\mathrm{RE}}_3$—bottom-of-atmosphere surface reflectance in third red-edge band (Band 7), NIR—bottom-of-atmosphere surface reflectance in near-infrared band (Band 8), K—gain factor based on vegetation structure.

), filtered over the study area bounds using Google Earth Engine. Vegetation index time-series per point were calculated using all available images in an observation year per maize parcel, including all images sensed between 1 January 2022 and 31 December 2022 for parcels 1–6, and all images sensed between 1 January 2023 and 31 December 2023 for parcels 7–12. Cloud and shadow masking were applied using the scene classification layer (SCL) and probabilistic cloud/snow masks, retaining only pixels with cloud probability < 5%, no cirrus (SCL ≠ 10), and no cloud shadows (SCL ≠ 3). SCL layers, as well as cloud probability maps (MSK_CLDPRB) and snow probability maps (MSK_SNWPRB) were available as a part of Level-2A preprocessing of Sentinel-2 images [38]. Vegetation index values were extracted at yield sample points at 10 m spatial resolution. Pixels with invalid values (−9999) were excluded, and duplicate entries (same ID and date) were removed.

Vegetation indices for evaluation with maize yield data were selected with a focus on minimizing saturation effects in high-biomass conditions. Vegetation indices were selected based on their frequency in agricultural remote sensing studies [4,8,43], resistance to saturation and sensitivity to crop physiological and structural changes [7,13,14,15]. The NDVI and DVI were included as a baseline due to their extensive application in crop monitoring, despite their known tendency to saturate in dense canopies [44]. To address NDVI’s limitations, EVI introduced a soil adjustment factor and atmospheric resistance, improving sensitivity in high-biomass conditions based on blue band [11]. Similarly, the two-Band EVI2 provided a simplified alternative to EVI by omitting the blue band while retaining some saturation resistance [41]. EVI2 is also extensively used for quantifying vegetation phenology in various satellite mission products under National Aeronautics and Space Administration (NASA), such as Moderate Resolution Imaging Spectroradiometer (MODIS) Land Cover Dynamics (MCD12Q2) [45] and Visible Infrared Imaging Radiometer Suite (VIIRS) Global Land Surface Phenology (GLSP) products [46]. WDRVI applied a weighting coefficient to the NIR band to extend dynamic range and reduce saturation [12]. Among three novel vegetation indices, the IDVI was selected as a linear alternative to NDVI, emphasizing absolute NIR reflectance rather than normalized ratios to maintain sensitivity across growth stages [13], the NDVI_3RE enhances discrimination in high LAI crops where traditional NDVI underperforms utilizing red-edge bands from Sentinel-2 [14], while the PPI was designed specifically to track photosynthetic activity and vegetation phenology [15,42].

2.3. Phenology Analysis and Correlation Analysis of Maize Yield and Combinations of Vegetation Indices and Phenology Metrics

Phenological metrics were extracted from time-series vegetation index data using the phenofit package [47] in R v4.3.2 [48]. The phenology analysis was performed per parcel, separately for each yield sample point and per vegetation index. Phenological curves were fitted using the Beck logistic model implemented in phenofit. This model was selected for its ability to smooth noise in remote sensing data while preserving key phenological transitions [49]. This approach minimized noise from temporal gaps in Sentinel-2 data while providing physiologically meaningful metrics for yield correlation. Key phenological transition dates, including SOS, POS, EOS, Greenup, Maturity, Senescence, and Dormancy, were derived from the fitted curves according to procedure described in [47]. Based on [50,51,52], SOS represented the onset of rapid vegetation activity marked by a sustained increase in VI; Greenup represented the period immediately following SOS characterized by accelerated growth and increasing photosynthetic activity; Maturity represented the end of the greenup phase when vegetation reaches its maximum greenness; POS represented the time of maximum VI value, representing the height of vegetation productivity; Senescence represented the onset of vegetation aging or reduced photosynthetic activity; EOS represented the point of cessation of active vegetation growth; and Dormancy represented the period with minimal vegetation activity, associated with winter or dry season conditions. The corresponding vegetation index values at these transition points were calculated using logistic growth parameters.

The correlation analysis between evaluated combinations of vegetation indices and phenology metrics and ground truth maize yield data was performed based on second degree polynomial function, using Pearson correlation coefficient to quantify their relationship. The optimal combination of vegetation index and phenology metric was determined based on the highest Pearson correlation coefficient according to combined dataset of yield samples from parcels 1–12. The relationships between optimal vegetation index and phenology metric with maize yield per parcel were further explored, as well as relationship between optimal vegetation index with all evaluated phenology metrics and optimal phenology metric with all evaluated vegetation indices.

3. Results and Discussion

3.1. Optimal Combination of Vegetation Index and Phenology Metrics for Maize Yield Assessment

The analysis of vegetation indices and phenology metrics indicated varying strengths of correlation with maize yield, with the combination of NDVI_3RE and Senescence producing the highest Pearson correlation coefficient (

Table 4. Pearson correlation coefficients between maize yield samples from a combined datasets using parcels 1–12 with all evaluated combinations of vegetation indices and phenology metrics.

Vegetation Index	SOS	Greenup	Maturity	POS	Senescence	Dormancy	EOS
DVI	0.256	0.351	0.237	0.241	0.218	0.362	0.256
NDVI	0.125	0.259	0.299	0.409	0.356	0.288	0.118
EVI	0.278	0.319	0.212	0.216	0.207	0.432	0.287
EVI2	0.263	0.344	0.199	0.211	0.195	0.429	0.281
WDRVI	0.271	0.173	0.342	0.342	0.367	0.127	0.267
IDVI	0.289	0.337	0.316	0.326	0.297	0.333	0.287
NDVI3RE	0.329	0.060	0.413	0.471	0.506	0.151	0.283
PPI	0.198	0.107	0.237	0.235	0.204	0.169	0.214

The highest Pearson correlation coefficient per phenology metric was bolded.

). These results are combined from all evaluated individual parcels, for which the results are provided in

Table A1. Pearson correlation coefficients for evaluated combinations of vegetation indices and phenology metrics per parcel during the year 2022.

Parcel ID	Vegetation Index	SOS	Greenup	Maturity	POS	Senescence	Dormancy	EOS
Parcel 1	DVI	0.313	0.375	0.329	0.305	0.312	0.412	0.321
	NDVI	0.314	0.404	0.434	0.398	0.426	0.259	0.333
	EVI	0.306	0.367	0.325	0.310	0.301	0.412	0.314
	EVI2	0.283	0.345	0.308	0.289	0.280	0.369	0.286
	WDRVI	0.238	0.373	0.183	0.186	0.203	0.235	0.209
	IDVI	0.335	0.475	0.351	0.355	0.429	0.209	0.313
	NDVI3RE	0.465	0.317	0.487	0.486	0.460	0.255	0.468
	PPI	0.323	0.167	0.348	0.338	0.322	0.296	0.349
Parcel 2	DVI	0.261	0.320	0.315	0.370	0.327	0.280	0.264
	NDVI	0.282	0.368	0.281	0.357	0.296	0.274	0.289
	EVI	0.276	0.333	0.285	0.354	0.320	0.274	0.289
	EVI2	0.253	0.358	0.284	0.365	0.317	0.312	0.266
	WDRVI	0.204	0.061	0.248	0.283	0.318	0.080	0.202
	IDVI	0.409	0.231	0.438	0.465	0.461	0.074	0.405
	NDVI3RE	0.283	0.067	0.329	0.356	0.392	0.145	0.258
	PPI	0.308	0.091	0.347	0.378	0.364	0.082	0.313
Parcel 3	DVI	0.284	0.538	0.373	0.380	0.368	0.531	0.311
	NDVI	0.534	0.317	0.572	0.573	0.575	0.303	0.532
	EVI	0.390	0.567	0.431	0.410	0.388	0.598	0.452
	EVI2	0.265	0.649	0.355	0.377	0.383	0.662	0.328
	WDRVI	0.278	0.344	0.268	0.270	0.281	0.366	0.274
	IDVI	0.819	0.661	0.830	0.849	0.849	0.719	0.838
	NDVI3RE	0.297	0.257	0.333	0.356	0.334	0.239	0.271
	PPI	0.393	0.052	0.452	0.447	0.442	0.012	0.400
Parcel 4	DVI	0.226	0.468	0.283	0.282	0.264	0.477	0.237
	NDVI	0.520	0.668	0.739	0.767	0.745	0.598	0.513
	EVI	0.361	0.660	0.278	0.325	0.328	0.642	0.363
	EVI2	0.492	0.700	0.353	0.432	0.417	0.697	0.494
	WDRVI	0.553	0.278	0.706	0.708	0.691	0.298	0.548
	IDVI	0.228	0.398	0.172	0.117	0.129	0.416	0.241
	NDVI3RE	0.578	0.319	0.650	0.666	0.633	0.232	0.541
	PPI	0.142	0.038	0.170	0.206	0.221	0.088	0.124
Parcel 5	DVI	0.363	0.352	0.361	0.357	0.340	0.356	0.373
	NDVI	0.218	0.155	0.219	0.235	0.229	0.163	0.210
	EVI	0.311	0.204	0.328	0.331	0.319	0.221	0.307
	EVI2	0.227	0.258	0.278	0.286	0.268	0.236	0.222
	WDRVI	0.265	0.101	0.308	0.262	0.242	0.086	0.267
	IDVI	0.412	0.402	0.456	0.464	0.427	0.313	0.416
	NDVI3RE	0.469	0.278	0.480	0.468	0.434	0.351	0.455
	PPI	0.321	0.146	0.362	0.364	0.356	0.170	0.316
Parcel 6	DVI	0.318	0.583	0.169	0.167	0.173	0.560	0.351
	NDVI	0.543	0.241	0.634	0.605	0.598	0.359	0.548
	EVI	0.237	0.402	0.369	0.396	0.437	0.438	0.202
	EVI2	0.235	0.424	0.339	0.375	0.434	0.407	0.224
	WDRVI	0.488	0.048	0.494	0.546	0.357	0.365	0.490
	IDVI	0.482	0.776	0.474	0.507	0.356	0.802	0.490
	NDVI3RE	0.533	0.325	0.574	0.605	0.578	0.438	0.491
	PPI	0.350	0.368	0.457	0.454	0.471	0.409	0.342

The highest Pearson correlation coefficient per phenology metric and parcel was bolded.

for year 2022 and

Table A2. Pearson correlation coefficients for evaluated combinations of vegetation indices and phenology metrics per parcel during the year 2023.

Parcel ID	Vegetation Index	SOS	Greenup	Maturity	POS	Senescence	Dormancy	EOS
Parcel 7	DVI	0.324	0.218	0.383	0.398	0.369	0.101	0.332
	NDVI	0.306	0.154	0.412	0.475	0.400	0.124	0.319
	EVI	0.316	0.272	0.407	0.414	0.377	0.095	0.331
	EVI2	0.321	0.307	0.421	0.425	0.383	0.120	0.339
	WDRVI	0.305	0.120	0.553	0.576	0.358	0.348	0.326
	IDVI	0.377	0.324	0.431	0.441	0.418	0.177	0.384
	NDVI3RE	0.475	0.263	0.538	0.556	0.552	0.276	0.452
	PPI	0.307	0.544	0.411	0.406	0.371	0.269	0.324
Parcel 8	DVI	0.261	0.323	0.318	0.335	0.294	0.206	0.267
	NDVI	0.193	0.454	0.507	0.378	0.222	0.431	0.196
	EVI	0.288	0.389	0.268	0.296	0.241	0.303	0.282
	EVI2	0.317	0.480	0.337	0.348	0.329	0.254	0.315
	WDRVI	0.374	0.126	0.579	0.587	0.505	0.267	0.395
	IDVI	0.257	0.344	0.350	0.359	0.316	0.222	0.272
	NDVI3RE	0.421	0.351	0.522	0.538	0.524	0.241	0.406
	PPI	0.322	0.304	0.345	0.363	0.341	0.039	0.320
Parcel 9	DVI	0.273	0.451	0.349	0.371	0.347	0.439	0.280
	NDVI	0.260	0.523	0.398	0.457	0.383	0.480	0.269
	EVI	0.300	0.518	0.299	0.319	0.292	0.492	0.301
	EVI2	0.301	0.528	0.358	0.380	0.344	0.488	0.299
	WDRVI	0.405	0.136	0.472	0.464	0.455	0.276	0.408
	IDVI	0.225	0.477	0.271	0.305	0.282	0.461	0.234
	NDVI3RE	0.534	0.347	0.619	0.638	0.638	0.361	0.503
	PPI	0.253	0.461	0.277	0.307	0.298	0.462	0.260
Parcel 10	DVI	0.232	0.452	0.228	0.241	0.213	0.360	0.226
	NDVI	0.381	0.362	0.280	0.162	0.238	0.159	0.398
	EVI	0.273	0.479	0.216	0.222	0.231	0.400	0.265
	EVI2	0.294	0.493	0.257	0.248	0.251	0.378	0.312
	WDRVI	0.303	0.258	0.216	0.234	0.331	0.197	0.287
	IDVI	0.176	0.486	0.289	0.310	0.269	0.375	0.183
	NDVI3RE	0.398	0.248	0.446	0.468	0.488	0.297	0.369
	PPI	0.170	0.375	0.272	0.281	0.262	0.185	0.175
Parcel 11	DVI	0.333	0.109	0.320	0.329	0.329	0.081	0.334
	NDVI	0.117	0.223	0.213	0.259	0.216	0.237	0.136
	EVI	0.314	0.048	0.328	0.327	0.330	0.062	0.320
	EVI2	0.330	0.023	0.336	0.331	0.335	0.074	0.336
	WDRVI	0.092	0.238	0.199	0.162	0.379	0.108	0.068
	IDVI	0.346	0.145	0.334	0.340	0.345	0.073	0.349
	NDVI3RE	0.066	0.124	0.061	0.066	0.044	0.111	0.081
	PPI	0.323	0.131	0.324	0.330	0.329	0.037	0.324
Parcel 12	DVI	0.105	0.122	0.178	0.189	0.154	0.095	0.097
	NDVI	0.094	0.136	0.156	0.242	0.212	0.161	0.121
	EVI	0.214	0.118	0.234	0.251	0.247	0.061	0.207
	EVI2	0.100	0.167	0.152	0.178	0.147	0.158	0.089
	WDRVI	0.337	0.167	0.239	0.376	0.067	0.237	0.288
	IDVI	0.162	0.130	0.203	0.211	0.190	0.118	0.162
	NDVI3RE	0.446	0.047	0.427	0.437	0.463	0.212	0.416
	PPI	0.221	0.154	0.257	0.254	0.245	0.117	0.222

The highest Pearson correlation coefficient per phenology metric and parcel was bolded.

for year 2023. This observation justifies the notion of previous studies to use maximum vegetation indices as proxy metrics for crop yield [53,54], but more clearly proves that not all frequently used vegetation indices interact with evaluated phenology metrics in the same way. The Dormancy stage exhibited the strongest association with EVI and EVI2, suggesting that late-season photosynthetic activity is critical for yield prediction. These results indicate the necessity of determining the optimal vegetation index per phenology metric in studies which require the analysis of specific growth stages [55], with EVI/EVI2 and NDVI_3RE being providing the most suitable options for yield modeling during dormancy and late vegetative growth stages in this study, respectively. While previous studies usually considered phenology growth stages from the agronomical perspective, there is an agreement that late vegetative growth stages, corresponding to POS and Senescence, are critical for maize yield assessment [56,57]. Overall superiority of NDVI_3RE in maize yield assessment suggests that red-edge-based indices, which are less affected by saturation and atmospheric interference [58], are better suited for tracking yield-related variability during latter maize growth stages.

NDVI produced relatively high correlation during POS and Senescence among evaluated vegetation indices, but it produced uneven correlation across maize growth season, which suggests that this may be due to saturation effect in dense vegetation, limiting its sensitivity during late growth phases [7]. While NDVI is the most frequently used vegetation index in yield prediction and agricultural studies overall [4], the results from this study indicate that its correlations were generally weaker than those of EVI, EVI2, WDRVI and IDVI, except during peak vegetation index values during Maturity, POS and Senescence. This reinforces the notion that saturation-resistant vegetation indices, particularly those incorporating red-edge bands or correction factors may outperform NDVI in yield modeling [14].

While the combination of NDVI_3RE and Senescence resulted in the highest Pearson correlation coefficient with maize yield based on combined dataset which included parcels 1–12, its performance on individual parcels varied notably (Figure 3). While a near-linear relationship was achieved with maize yield at some instances (parcels 8, 9, 10 and 12), saturation effect was still present as NDVI_3RE initially increases with yield but then plateaus or even declines at higher yield levels, particularly at parcels observed during 2022 (parcels 1, 2, 4, 5, 6 and 7). This pattern, while varying in intensity, is indicative of saturation effect [59], as NDVI_3RE was generally less sensitive to changes in biomass or canopy structure at higher productivity levels. This effect was not strongly related to mean values or variations in maize yield per parcel from Table 1, nor to value ranges of NDVI_3RE at Senescence. More notable observation was higher frequency and intensity of saturation effect on parcels observed during 2022, which might indicate that it is more susceptible to annual weather variations [60]. However, this observation should be explored in future studies, with a focus on interannual weather variations at less localized study areas.

3.2. Relationships Between Optimal Vegetation Index with Evaluated Phenology Metrics for Maize Yield Assessment

NDVI_3RE achieved a positive correlation with yield at SOS, Maturity, POS, Senescence and EOS, while the saturation effect was more pronounced at SOS and EOS (Figure 4). Scatterplots for separate parcels using the same data are presented in Figure S1. The strongest correlation was observed at Senescence and POS, indicating that peak vegetation vigor is a critical yield determinant, confirming the observations of previous studies, which frequently adopted either vegetation index at POS or maximum vegetation index as crop yield proxy metrics [53,54]. The strong correlation at Senescence suggests that prolonged greenness, which indicates extended photosynthetic activity, contributes positively to grain filling and yield formation [61]. Notably, NDVI_3RE during Dormancy produced a very low correlation, likely due to the limited vegetation activity in this phase, where variations in NDVI_3RE may be driven more by soil reflectance, cover crop presence, or residue rather than maize productivity. As early-season metric, Greenup may be more indicative of initial crop vigor [62], which did not translate into higher final yields due to potential stress events or management interventions. During Greenup, early vegetative growth was also highly susceptible to environmental conditions such as temperature and soil moisture [63], which may have influenced yield potential in complex ways not directly reflected in NDVI_3RE.

3.3. Relationships Between Optimal Phenology Metrics with Evaluated Vegetation Indices for Maize Yield Assessment

NDVI_3RE, WRDVI and NDVI produced the strongest positive correlations with maize yield at Senescence (Figure 5), confirming that extended photosynthetic activity and canopy greenness contribute to higher maize yield correlation [64]. Since the red-edge bands used in NDVI_3RE were particularly sensitive to changes in leaf chlorophyll content, it was robust indicator of vegetation condition during late growth stages when NDVI began to saturate, which was also noted through the use of normalized difference red-edge index (NDRE) in a previous study [57]. The strong correlation suggests that maize plants with prolonged greenness and sustained photosynthetic activity at Senescence contribute to higher yields, likely due to extended carbon assimilation supporting grain filling. Meanwhile, all other evaluated vegetation indices produced weaker or inconsistent relationships and were not as responsive to senescence-driven changes in vegetation. The lower correlation suggests that while EVI-based indices capture biomass well [65], their sensitivity to structural rather than physiological traits may limit their capability of correlating with maize yield at Senescence. Also, lower correlation of PPI at Senescence suggests that, while it may be useful for monitoring vegetation at higher latitudes [42], it is less effective for assessing maize yield potential.

3.4. Study Limitations and Future Considerations

To authors’ knowledge, no previous studies thoroughly focused on determining the single optimal combination of vegetation index and phenology metric for maize yield assessment based on ground truth yield map from combine harvester. Instead, a focus was frequently put on multivariate statistics using machine learning methods for crop yield prediction, which usually combined several vegetation indices and achieved very high prediction accuracy with coefficient of determination (R²) higher than 0.9 [43,57,66]. However, for research topics which require a single proxy metric for crop yield, especially cropland suitability studies [67,68,69], it is important to use a single metric to overcome the lack of reliable ground truth crop yield data for land management purposes. While this study identified optimal combinations of vegetation indices and phenology metrics for maize yield assessment, further validation across different environments and crop management practices is needed. Moreover, a more thorough analysis with more crop yield ground truth data over more than two consecutive years and narrower geospatial region, preferably at neighboring parcels, would produce a more robust result. The results from this study strongly suggested that no single vegetation index is optimal across all phenological stages, but NDVI_3RE consistently showed strong yield correlations, particularly during late growth phases. However, it should be noted that the results from this study were created based on ground truth yield data from a restricted study area, with local variation of climate, soil and topography conditions [70,71], which likely produced a degree of variability in ground truth maize yield. Therefore, this study improved present knowledge of the optimal combination of vegetation indices and phenology metrics for maize yield assessment but does not guarantee the same results at different study areas in terms of relevant abiotic conditions for maize cultivation. While used phenology metrics provided a consistent, globally applicable framework for monitoring crop development, their interpretation in terms of ground-based growth stages (such as BBCH codes [72]) requires careful consideration. Remote sensing captures canopy-level phenology, which may not perfectly align with discrete crop-stage transitions recorded in field observations. This discrepancy presents a trade-off in large-scale agricultural studies, as while satellite data enable scalable and repeatable analyses across regions, they lack the precision of field-level growth-stage records. Future work combining Sentinel-2 time series with targeted ground observations could overcome these limitations. Nevertheless, the approach used in this study provides practical advantages for yield prediction in data-sparse regions, where satellite-derived phenology may serve as a reliable proxy for crop development. Importantly, the metrics used here are derived entirely from open-access Sentinel-2 data, ensuring reproducibility and transferability to other agricultural systems.

The observed correlations of vegetation indices with maize yield indicate that a single indicator approach may not be sufficient for yield prediction, necessitating alternative modeling strategies. The presence of saturation effects urged the importance of integrating multiple spectral bands and considering additional data sources, such as environmental covariates [73,74], to improve prediction accuracy. Furthermore, machine learning approaches that can capture nonlinear patterns may enhance the utility of vegetation indices for yield forecasting [75]. Present yield indicators based on vegetation indices and phenology metrics can be further improved with the inclusion of dates in which each of phenology stages occurred, potentially serving as additional covariates in yield prediction models using machine learning. The reduced saturation effect in red-edge-based indices suggests that they may be more suitable for yield prediction, especially in environments characterized by high biomass accumulation. The superior performance of NDVI_3RE aligns with previous research indicating that indices using the red-edge spectrum provide enhanced sensitivity to variations in chlorophyll content and canopy structure [14], making them more robust indicators of crop performance under diverse yield conditions. Future studies should assess the scalability of these findings across different agroecological zones to validate the robustness of red-edge-based indices in diverse cropping systems. The additional possibility of using the interpretable machine learning approach in crop yield analysis is to model the effect of abiotic environmental conditions on yield, effectively interpreting non-linear relationships with such conditions, which may benefit future cropland suitability studies [69]. To mitigate saturation effects and enhance yield estimation accuracy, future research should also explore the integration of synthetic aperture radar (SAR) data, which may further improve the sensitivity of spectral indices to yield variations.

4. Conclusions

The results of this study noted highly varying relationships between maize yield and various vegetation indices when combined with phenology metrics, highlighting both their predictive potential and still present limitations due to saturation effects. Across the evaluated vegetation indices, saturation was evident in all evaluated indices, while NDVI_3RE proved to be most resistant to it for maize yield assessment. Specific conclusions based on correlation analysis of evaluated combinations of vegetation indices and phenology metrics with maize yield based on yield maps from combine harvester are:

• The analysis of vegetation indices and phenology metrics indicated varying strengths of correlation with maize yield, with the combination of NDVI_3RE and Senescence producing the highest Pearson correlation coefficient (0.506).
• There is an agreement with previous studies that late vegetative growth stages, corresponding to POS and Senescence, are critical for maize yield assessment.
• The relationship of optimal combination of vegetation index and phenology metric (NDVI_3RE and Senescence) with maize yield based on combined dataset which included parcels 1–12 on individual parcels varied notably.
• The higher frequency and intensity of saturation effect on parcels observed during 2022 than 2023, which might indicate that it is susceptible to annual weather variations.
• No single vegetation index is optimal across all phenological stages, but NDVI_3RE consistently showed strong yield correlations, particularly during late growth phases.
• The reduced saturation effect in red-edge-based index suggests that it may be more suitable for yield prediction, especially in environments characterized by high biomass accumulation.