Comparison of PlanetScope and Sentinel-2 Spectral Channels and Their Alignment via Linear Regression for Enhanced Index Derivation

Abstract

Prior research has shown that for specific periods, vegetation indices from PlanetScope and Sentinel-2 (used as a reference) must be aligned to benefit from the experience of Sentinel-2 and utilize techniques such as data fusion. Even during the worst-case scenario, it is possible through histogram matching to calibrate PlanetScope indices to achieve the same values as Sentinel-2 (useful also for proxy). Based on these findings, the authors examined the effectiveness of linear regression in aligning individual bands prior to computing indices to determine if the bands are shifted differently. The research was conducted on five important bands: Red, Green, Blue, NIR, and RedEdge. These bands allow for the computation of well-known vegetation indices like NDVI and NDRE, and soil indices like Iron Oxide Ratio and Coloration Index. Previous research showed that linear regression is not sufficient by itself to align indices in the worst-case scenario. However, this paper demonstrates its efficiency in achieving accurate band alignment. This finding highlights the importance of considering specific scaling requirements for bands obtained from different satellite sensors, such as PlanetScope and Sentinel-2. Contemporary images acquired by the two sensors during May and July demonstrated different behaviors in their bands; however, linear regression can align the datasets even during the problematic month of May.

1. Introduction

1.1. Research Questions

Multispectral imagery [1], acquired from satellite sensors such as PlanetScope [2,3,4,5,6,7,8,9,10,11] and Sentinel-2 [12,13,14,15,16,17,18], provides essential data for observing and analyzing the Earth’s surface. Imagery acquisition through sensors at varied spatial and temporal resolutions necessitates rigorous comparative analysis to ensure data accuracy and consistency. Such validation facilitates the necessary alignment for their contemporary utilization, supplemented by interchangeable experience derived from comprehensive literature review. This paper presents a comparative analysis of PlanetScope and Sentinel-2 bands, focusing on contemporary acquisitions and the calibration of bands useful to correctly align soil and vegetation indices over the “Riserva San Massimo” [19,20] rice farm in Northern Italy before its computing. Previous research [2,3,4,11,21,22] has highlighted the importance of alignment between vegetation indices derived from PlanetScope and Sentinel-2 data, particularly during specific periods of the year. Building upon these findings, this study explores the application of linear regression as a technique to align individual bands before computing indices and investigate their shift in processed surface reflectance values [1]. This approach aims to enhance the comparability and reliability of data derived from these two satellite sensors.

1.2. PlanetScope and Sentinel-2: Key Factors

PlanetScope and Sentinel-2 have been widely studied during the last year [4,17,23,24,25,26] and a lot of new research papers have been published to assess PlanetScope’s capabilities to improve Sentinel-2 imagery and to be used on their own [6,15,23,27,28,29,30,31,32,33,34]. It has been demonstrated that PlanetScope is useful for multiple uses in precision agriculture [17,30,35], in land cover assessment, in change detection, in geology, and in various other fields. Previous research conducted by the same authors, which was documented in several papers [2,3,4], identified miscalibration issues within the Riserva San Massimo test site and outlined potential solutions [4]. The primary objective of the research was to leverage the Sentinel-2 experience of PlanetScope images to assess PlanetScope imagery for VRA precision agriculture in rice farming. PlanetScope provides significant improvements over Sentinel-2 in both spatial resolution (~3 m vs. 10 m best) and temporal resolution (~daily vs. 5 days). This makes it highly valuable for applications demanding fine spatial detail and very frequent monitoring. Sentinel-2 offers superior spectral resolution (more bands, including SWIR) and wider area coverage per pass (swath width), which is advantageous for broader-scale land cover classification, vegetation health assessments using specific indices (e.g., involving SWIR), and mineral mapping. Its data are also freely available.

1.3. Research Development

Previous research had shown that the Red, RedEdge, and NIR bands could be inconsistent during certain periods of the year [2,3]; however, calibration could be performed effectively even in the worst-case scenarios [4], demonstrating anyway which linear regression at the index level is not sufficient, particularly in relation to indices like NDVI and NDRE [2,3,4,11,21,22]. In order to conduct a more in-depth investigation, an analysis was performed utilizing five key spectral bands: Blue, Green, Red, RedEdge, and near-infrared (NIR). These bands were subjected to comparative assessment across two distinct temporal acquisitions, each featuring contemporaneous PlanetScope and Sentinel-2 imagery. One set of images exhibited low Root Mean Square Error (RMSE) [36], while the other demonstrated high RMSE. Subsequently, a linear regression analysis was applied to each of the five band pairings for both dates to evaluate the feasibility and efficacy of implementing calibration via linear regression. The focus on contemporary acquisitions allows for a more accurate representation of current conditions and minimizes the potential impact of temporal variations on the data. Analyzed bands are fundamental for calculating widely used vegetation indices such as NDVI [37,38,39] (Normalized Difference Vegetation Index), which measures the health and the vigor of vegetation, and NDRE [38,39] (Normalized Difference Red Edge Index), which is sensitive to chlorophyll content and can be used to assess plant stress. Additionally, these bands enable the computation of soil indices like Iron Oxide Ratio [40,41,42], which provides information about soil composition, and the Coloration Index [43,44], which can be used to identify different soil types. The outcomes of this research contribute to a deeper understanding of the scaling requirements for bands acquired from different satellite sensors. The study’s emphasis on linear regression [45,46,47] for band alignment [6,27,28,48] offers a potential solution for achieving greater accuracy and consistency in data derived from multispectral imagery [1]. This, in turn, can lead to more reliable and informed decision-making in various fields. For example, in agriculture, accurate and consistent data can be used to optimize irrigation and fertilization practices, leading to increased yields and reduced environmental impact [35,49,50,51,52,53,54,55]. In environmental monitoring, reliable data can be used to track changes in land cover and vegetation health, providing early warnings of potential environmental problems. In land use planning [15,56,57,58], accurate data can be used to make informed decisions about land development and conservation. In conclusion, precision fertilization [55], soil organic matter analysis [59], weed identification [60] and agricultural drought analysis [61], which require all spectral channels compared in this paper, can benefit from Remote Sensing analysis and improve future research and development efforts (like Time Series Analysis [62]) in Earth observation, potentially leading to the development of new and improved techniques for data analysis and interpretation.

1.4. Literature Review on Prominent Soil and Vegetation Indices Which Benefit Alignment

Prior investigations have focused on the alignment of indices such as Normalized Difference Vegetation Index (NDVI) [37,38,39,57,58,59,61,62,63,64] and Normalized Difference Red Edge (NDRE) [4,38,39,64,65,66] for primary use in precision agriculture [2,3,4,38,39]. This methodology is also extensible to other indices relevant to soil analysis, offering a broader scope of application. Spectral analysis has been extended to five bands to include other indicators: the Iron Oxide Ratio [17,40,41,42,64,67,68,69,70] and Coloration Index [43,59,60,71,72,73].

Table 1. Comparing use and characteristics of important indices which are influenced by this research.

Index	Applications	Band	Detection Capability
NDVI ${\displaystyle \frac{\mathrm{N}\mathrm{I}\mathrm{R}-\mathrm{R}\mathrm{e}\mathrm{d}}{\mathrm{N}\mathrm{I}\mathrm{R}+\mathrm{R}\mathrm{e}\mathrm{d}}}$	Assessing vegetation presence, density, vigor, and overall health. Widely used in agriculture, forestry, and ecological monitoring.	Red, NIR	Quantifies the “greenness” of vegetation. Strongly correlated with chlorophyll content, leaf area index (LAI), and photosynthetic activity. Can saturate in dense vegetation.
NDRE ${\displaystyle \frac{\mathrm{N}\mathrm{I}\mathrm{R}-\mathrm{R}\mathrm{e}\mathrm{d}\mathrm{E}\mathrm{d}\mathrm{g}\mathrm{e}}{\mathrm{N}\mathrm{I}\mathrm{R}+\mathrm{R}\mathrm{e}\mathrm{d}\mathrm{E}\mathrm{d}\mathrm{g}\mathrm{e}}}$	Assessing vegetation health, chlorophyll content, and nitrogen status, particularly useful in mid-to-late growth stages or dense canopies.	Red Edge, NIR	Sensitive to chlorophyll concentration deeper within the canopy. Less prone to saturation than NDVI in dense vegetation. Often used as an indicator of plant stress or nitrogen levels.
Iron Oxide Ratio ${\displaystyle \frac{\mathrm{R}\mathrm{e}\mathrm{d}}{\mathrm{B}\mathrm{l}\mathrm{u}\mathrm{e}}}$	Highlighting areas with surface iron oxide (Fe3+) staining (e.g., hematite, goethite). Used in geological mapping and mineral exploration.	Red, Blue	Identifies surfaces exhibiting strong red reflectance relative to blue reflectance, characteristic of reddish iron oxide minerals or weathered lateritic soils.
Coloration Index ${\displaystyle \frac{\mathrm{R}\mathrm{e}\mathrm{d}-\mathrm{G}\mathrm{r}\mathrm{e}\mathrm{e}\mathrm{n}}{\mathrm{R}\mathrm{e}\mathrm{d}+\mathrm{G}\mathrm{r}\mathrm{e}\mathrm{e}\mathrm{n}}}$	Identifying areas dominated by reddish/yellowish coloration, often associated with ferric iron (Fe3+) minerals like limonite, jarosite, goethite. Used in hydrothermal alteration mapping.	Red, Green	Detects surfaces where red reflectance significantly exceeds green reflectance, indicating the presence of various ferric iron minerals common in altered or weathered zones.

provides a brief comparison, including the required spectral channels (bands).

The insights gained from this research emphasize the importance of considering specific scaling requirements for bands obtained from different satellite sensors like PlanetScope and Sentinel-2 [56,74].

1.5. Examples of Indirect Relationships Between Indices and Their Use for Revealing Information

NDRE outperforms NDVI in later growth stages and dense canopies, where NDVI tends to saturate. Although NDRE primarily measures vegetation health, it is indirectly influenced by soil properties, including moisture and organic matter. Soil texture, particularly fine particles like silt and clay, supports higher NDRE values due to better water and nutrient retention. Factors such as atmospheric conditions, soil background, and crop type must be considered for accurate interpretation of NDRE. While NDRE enhances understanding, it should be considered as one part of a larger set of data for comprehensive analysis. Indirect relationships with vegetation indices [75,76,77], like NDRE, can be utilized for many purposes, especially with ground truth and in correlation with other geological data: various factors in addition to geology, including climate, slope, aspect, and human activity, affect vegetation, requiring the integration of extensive data. Rocks type can influence vegetation [78] and NDRE values: areas with consistently lower NDRE might indicate nutrient-poor soils [79] derived from rocks like granite or quartzite. Areas with consistently higher NDRE (within the same vegetation type) could suggest more fertile soil [80] derived from rocks like basalt or shale. Sharp boundaries in NDRE patterns, especially if they align with known geological contacts or lineaments, can be suggestive of changes in rock type. Mineralization Zones [40,42,81,82] can influence NDRE (through plant stress): some types of mineralization (e.g., copper, zinc, gold deposits) can lead to elevated concentrations of heavy metals in the soil. These heavy metals can be toxic to plants, causing stress and altering their chlorophyll content. Areas with anomalously low NDRE values, particularly if they occur within a relatively uniform vegetation type and are localized, could be indicative of plant stress due to heavy metal contamination. The Red Edge region is particularly sensitive to changes in chlorophyll content, making NDRE potentially more sensitive to this type of stress than NDVI [38,39]. Mapping Alteration Zones [82,83] could be carried out through analyzing NDRE variations: hydrothermal alteration [82,84], a process associated with certain types of ore deposits, can modify the mineral composition of rocks, often resulting in the formation of clay minerals and other alteration products. These altered rocks frequently exhibit different weathering characteristics and soil properties compared to unaltered rocks. NDRE can be used to identify drainage patterns and soil moisture [85] because vegetation typically flourishes in regions with elevated soil moisture, such as along drainage channels or areas with shallow groundwater. Higher NDRE values can sometimes reveal drainage patterns, as denser and healthier vegetation along watercourses will exhibit a higher NDRE signal [86]. This phenomenon can assist in delineating geological structures that govern drainage, such as faults and fractures. Additionally, areas of consistently higher NDRE within relatively uniform terrain may indicate zones of elevated soil moisture, potentially influenced by geological factors such as impermeable layers or springs. Although topography and other elements significantly impact drainage [78], NDRE alone is not a definitive indicator of subsurface geology but rather provides valid clues. NDRE can also be used to monitor surface disturbances and reclamation: mining activities, landslides, and other factors can significantly transform the soil cover, frequently leading to vegetation loss. By employing NDRE in a multitemporal context [58] (comparing images of the same region at different time points), it is feasible to observe alterations in vegetation, which serve as indicators of the extent of disturbances. Iron oxides (like hematite and goethite) have strong reflectance in the red portion of the spectrum and low reflectance in the blue: this is relevant in a fertilization/herbicide context. This ratio highlights areas with iron oxide concentrations, which are common in many geological environments, including weathered rocks, gossans (indicators of sulfide mineralization), and certain types of soils. It is a simple but effective way to identify potential areas of iron mineralization [81]. This ratioing technique is particularly valuable as it helps to mitigate the effects of illumination differences that can arise due to variations in terrain and shadowing. By normalizing the data in this way, the relative spectral differences between the red and blue reflectances, which are more indicative of the surface material composition, are enhanced. CI is used to delineate zones with different colors. In a geological setting, it can be used to differentiate rocks or areas with distinct colors, for instance, related to iron oxides. The Coloration Index serves as a valuable tool in geological remote sensing for the differentiation of rock types based on color variations (and search for hematite/geothite) [59]. Its principle lies in exploiting the differential reflectance of geological materials in the visible spectrum, with positive values often indicating the presence of iron oxides. Currently, the Coloration Index plays a significant role in preliminary geological surveys, mineral exploration (especially for iron), and soil studies [59,60,71,72,73]. Case studies demonstrate its utility in mapping iron-rich zones using various satellite and airborne sensors.

1.6. Evaluation of Band Calibration Through RMSE and MAE

Image processing algorithms are commonly evaluated using the Root Mean Square Error (RMSE) and the Mean Absolute Error (MAE) metrics [36].

RMSE is a widely used metric for evaluating the accuracy of predictions or measurements. When RMSE is assessed globally by analyzing it pixel by pixel for a single band, each pixel’s error is calculated by comparing the values from each sensor. The errors are then squared, averaged, and the square root of this average is taken to obtain the RMSE. This process ensures that large errors have a greater influence on the RMSE value, making it an effective measure of overall accuracy. This metric is particularly useful for identifying pronounced deviations in image datasets.

MAE quantifies the average magnitude of errors in a set of predictions, without considering their direction (i.e., whether they are positive or negative). The MAE is determined by computing the average of the absolute differences between predicted values and actual values. Due to the fact that it does not involve squaring the error terms, large errors do not disproportionately influence the MAE. This attribute renders MAE particularly valuable in datasets containing outliers that are not necessarily indicative of the model’s overall performance, as observed in this application. In Formulas (1) and (2), PS_Band(i,j) represents each pixel in the specified position (i,j) within the matrix of pixels for PlanetScope’s band; similarly, S2_Band(i,j) denotes each pixel in the specified position (i,j) within the matrix of pixels for Sentinel-2’s band.

$${\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}}_{Band}=\sqrt{{\displaystyle \frac{1}{\mathrm{n}}}{\sum }_{\mathrm{i},\mathrm{j}}{\left(\mathrm{P}\mathrm{S}\_\mathrm{B}\mathrm{a}\mathrm{n}\mathrm{d}\left(\mathrm{i},\mathrm{j}\right)-\mathrm{S}2\_\mathrm{B}\mathrm{a}\mathrm{n}\mathrm{d}\left(\mathrm{i},\mathrm{j}\right)\right)}^2})$$

(1)

$${\mathrm{M}\mathrm{A}\mathrm{E}}_{Band}={\displaystyle \frac{{\sum }_{\mathrm{i},\mathrm{j}}\left|{\mathrm{P}\mathrm{S}\_\mathrm{B}\mathrm{a}\mathrm{n}\mathrm{d}}_2\left(\mathrm{i},\mathrm{j}\right)-{\mathrm{S}2\_\mathrm{B}\mathrm{a}\mathrm{n}\mathrm{d}}_1\left(\mathrm{i},\mathrm{j}\right)\right|}{\mathrm{n}}}$$

(2)

RMSE and MAE are essential metrics in this research, evaluated for each pair of images, with RMSE focusing on the magnitude of significant errors and MAE providing an equitable assessment of average error magnitude. Both metrics are crucial for a thorough understanding of algorithm performance and error distribution in image processing tasks.

2. Materials and Methods

2.1. Riserva San Massimo Test Site

The “Riserva San Massimo” [19,87,88,89,90], located in Gropello Cairoli (PV), within the Lombardy Park of the Ticino Valley, represents a notable example of integrating environmental conservation with sustainable agriculture. Figure 1 illustrates maps framing the rice farm in Italy (1a) with its varieties (1b). Reference system used: WGS84 UTM-32N.

Classified as a Site of Community Importance (SCI IT2080015) [91] and partly as a Special Protection Area (SPA) [92], the reserve covers approximately 800 hectares. It includes wetland forests (particularly black alder), natural springs, water meadows, and agricultural fields primarily used for cultivating authentic Carnaroli rice. The rice varieties grown include Cammeo, LunaCL, Rosa Marchetti, and Vialone. This research was conducted in collaboration with the esteemed agronomic consulting team led by Dr. Agr. P.A. Barbieri and Dr. Agr. G.L. Rognoni [93,94], who oversees the rice farming operations for the reserve, providing numbered crops as used for field management (with their borders and variety): essential knowledge which validates this work belongs to their experience and research activities with “Ente Risi” [95]. This site exemplifies successful sustainable agriculture and ecological preservation. The implementation of Variable Rate Application (VRA) technology optimizes the distribution of fertilizer, leading to cost reduction, decreased environmental impact, and potentially improved crop yields. This research pertains directly to the enhancement of the fertilization process for the “Riserva San Massimo” rice farm, which has been consistently monitored over the years using Sentinel-2 data by the agronomic consulting team referenced above. The farm now seeks further improvement through the utilization of PlanetScope imagery, owing to its superior spatial and temporal resolution.

2.2. Variable Rate Application to Precision Farming at “Riserva San Massimo”

During fertilization (Figure 2), a specialized fertilizer spreader (Figure 2c) is used, interfaced with hardware that manages the tractor’s semi-autonomous driving capabilities (Figure 2a,b). The spreader accurately disperses granular fertilizer according to the prescription map (Figure 2a), which details the specific dosage for each section of the field.

This precise calibration ensures maximum deviations of only 1% from the prescribed amounts provided by the agronomist. This implementation of Variable Rate Application (VRA) technology proves its effectiveness in precision agriculture, enabling the careful application of fertilizers and thereby optimizing crop yields, reducing costs, and minimizing environmental impact. The main frame (Figure 2a) displays the prescription map, where different colors indicate varying requirements (blue signifies no additional fertilizer needed, for example). By following the prescribed path, the exact amount of fertilizer can be applied to each tile.

This fieldwork is closely associated with the ability to create accurate prescription maps, as the 1% error rate demonstrates that the more precise a prescription map is, the better the results will be. Transitioning to higher spatial resolution reduces edge effects and ensures the precise distribution of fertilizer. By leveraging Sentinel-2 data and calibrating PlanetScope bands to match Sentinel-2, the accuracy of derived indices is enhanced, thereby improving the effectiveness of chemical product applications. The observations captured in the images demonstrate the effective management of crop tillering, a practice guided by the expertise of the managers and field workers at “Riserva San Massimo” rice farm.

2.3. Sentinel-2

The Copernicus Sentinel-2 project [12,13,14,16,18,96,97,98,99] utilizes two polar-orbiting satellites, Sentinel-2A and Sentinel-2B, which are positioned in sun-synchronous orbits 180° apart. Recently, Sentinel-2C has become operational [98]. The Sentinel-2 mission offers high-resolution optical imagery in 13 spectral bands via Multispectral Instruments (MSI). Imagery resolution ranges from 10, to 20 to 60 m. Sentinel-2 images are processed into two types: top of atmosphere (TOA), affected by atmospheric conditions, and bottom of atmosphere (BOA), which shows surface reflectance without atmospheric interference. The MSI [12,13,100,101] captures data across visible, near-infrared (NIR), and shortwave infrared (SWIR) bands, providing detailed and accurate Earth observations with a revisit time of 5 days for most global regions.

Use of Sentinel-2 [102] images is under license: Copernicus Sentinel satellite—Open Access compliant, CC BY-SA 3.0 IGO

2.4. PlanetScope

Planet Labs operates the PlanetScope [5,6,7,8,9,10,103] constellation of over 200 Earth observation satellites called Doves and SuperDoves [104,105,106]. These satellites capture images of the Earth’s surface at a 3 m resolution. SuperDove sensors capture 8-band images used in this research, which include surface reflectance data and rectified data. PlanetScope provides almost daily revisit times, enabling frequent and consistent monitoring of the Earth’s surface. Use of PlanetScope [107] images is under license: ©Planet Labs PBC, CC BY-NC-SA 2.0

2.5. Choice of Images

Figure 3 represents a detailed view of some rice crops (through standard colors, RGB images) for the dataset used: PlanetScope [7] (spatial resolution 3 m) and Sentinel-2 [108] (spatial resolution 10 m at its best as in the figures) contemporary acquisitions for dates 11 May 2022 (Sentinel-2 at 10:16, PlanetScope at 10:13) and 15 July 2022 (Sentinel-2 at 10:15, PlanetScope at 9:53). Notably, for the first date, images were captured at intervals of 3 min, while for the second date, they were taken at intervals of 22 min. This allows for a comparison of images with similar lighting, which is crucial for the radiometric approach. The reference system used is WGS84 UTM-32N. From the agronomist’s experienced perspective, the timeframes chosen are associated with the rice growth stage (mixed bare soil and sparse vegetation) in May and with full vegetation coverage (fertilization) in July.

These images use standard color bands: Blue, Green, and Red.

• Sentinel-2: B2 (Blue): 492.7 (65) nm; B3 (Green): 559.8 (35) nm; B4 (Red): 664.6 (30) nm. All these bands have 10 m of spatial resolution.
• PlanetScope: Band 2 (Blue): 490 (50) nm; Band 4 (Green): 565 (36) nm; Band 6 (Red): 665 (31) nm. All these bands have 3 m of spatial resolution.

Color Infrared images (CIR) [109] in Figure 4 highlight sparse vegetation coverage during May and full vegetation coverage during July with strong red color over rice crops.

Sentinel-2 images, Level-2A products, exhibited the following attributes: atmospherically corrected surface reflectances in cartographic geometry. Granules were ortho-images in UTM-32N/WGS84 projection. PlanetScope images, acquired by Superdove Sensor, exhibited the following attributes: 8 bands, calibrated surface reflectance [112], rectified assets, and radiometrically harmonized with Sentinel-2 [9,23,103]. In previous research [4] (paragraph 2.4), the harmonization of PlanetScope with Sentinel-2 was discussed: the Red, Green, Blue, and near-infrared bands of PlanetScope sensors are harmonized and normalized to align with those of Sentinel-2 (RedEdge is not harmonized). As demonstrated in this paper, it is, however, essential to ensure the alignment of harmonized bands. PlanetScope also utilizes UTM-32N/WGS84 projection. Images were selected through an extensive study spanning three years (2021–2023). The analysis of images to identify the optimal pair of multispectral images from Sentinel-2 included 73 images for 2021, 71 images for 2022, and 73 images for 2023. Similarly, for PlanetScope, the analysis comprised 222 images for 2021, 345 images for 2022, and 739 images for 2023. Several images were identified as dates on which concurrent acquisitions by Sentinel-2 and PlanetScope occurred. Through detailed research and analysis [2,4], it was found that the RMSE, applied to images pixel by pixel, varies over different timeframes. In some periods, indices showed similar values (low RMSE in July, during fertilization), while in other periods, RMSE was very high, indicating significant differences between images (high RMSE in May). This phenomenon was examined using two datasets from different dates representing each case. Previous research [2,3,4,11] indicated that aligning indices directly is feasible but does not provide insights into the underlying causes. The solution involves aligning bands directly to understand previously undiscovered differences.

2.6. Band Alignment Through Linear Regression and Nearest Neighbor Sentinel-2 Oversampling

Linear regression [4,45,46,47] is employed to model a linear relationship between a dependent variable that needs prediction and one or more independent variables that serve as predictors. A linear relationship between dependent and independent variables is applied to corresponding pixels of PlanetScope and Sentinel-2. The latter’s NIR, Red, Green, and Blue bands (10 m resolution) and RedEdge band (20 m) are oversampled and aligned [113,114,115,116] to PlanetScope’s 3 m pixel size through the Nearest Neighbor Algorithm [2,116,117]. This implies that the dependent variable changes proportionally with changes in the independent variables. In the context of this study, linear regression was executed using the “fitlm” [47] function in MATLAB R2024b. This function is particularly favored for fitting linear models due to its versatility in model specification, its ability to accommodate categorical predictors, and its comprehensive statistical output. The implementation of “fitlm” [4] necessitates the use of two matrices: one containing the predictor variables and the other containing the variable to be predicted.

The OLS (Ordinary Leath Squares) method was utilized to regress and align the values of individual bands from the PlanetScope sensor to those of the Sentinel-2 sensor. Given the requirement to calibrate PlanetScope responses to those of Sentinel-2, a key objective was to establish the linear equation that could take PlanetScope spectral band values as input and generate output values akin to those of Sentinel-2. Prior studies [11,22] have demonstrated that a buffer zone of 10 m from the borders of rice crops is essential for effectively mitigating edge effects. Consequently, this zone was excluded from linear regression application. In essence, linear regression, as implemented in this study, served as a tool to predict Sentinel-2-like values from PlanetScope data. Linear regression [4,11,47] and the incorporation of a buffer zone to minimize edge effects highlight the methodological rigor applied in this research. An example of linear regression as applied in this paper is reported on the Matlab Website [45] and in a previous paper by the same authors [4].

The selection of the five spectral channels for analysis was meticulously conducted to enable the calculation of indices as highlighted in paragraph 1.4. The selection was examined by comparing the sensors’ central wavelength, full width at half maximum (FWHM), and resolution [7,9,10,14,97,100,103,118]. Alignment was conducted through Sentinel-2 (minimal difference between Sentinel-2A and Sentinel-2B were not considered) and PlanetScope bands reported in

Table 2. Spectral channels used during alignment.

Bands	Sentinel-2	PlanetScope
Blue	Band 2—Blue	Band 2—Blue
Green	Band 3—Green	Band 4—Green
Red	Band 4—Red	Band 6—Red
Red Edge	Band 5—RedEdge 705	Band 7—RedEdge
NIR	Band 8—NIR	Band 8—NIR

. Figure 5 illustrates the process used to align the bands.

PlanetScope offers Green and Green I channels; only the former is compatible with Sentinel-2. Sentinel-2 provides multiple Red Edge channels, but only the one with a central wavelength at 705 nm is compatible. Following PlanetScope guidelines regarding NIR compatibility, interoperability is radiometrically ensured with Band 8a Narrow NIR in Sentinel-2, which has a resolution of 20 m compared to 10 m of Band 8 Standard NIR. Sentinel-2 [119,120,121,122,123] utilizes two distinct near-infrared (NIR) bands: the broader Band 8 (B8: ~842 nm center, ~115 nm width, 10 m resolution) and the narrower Band 8a (B8a: ~865 nm center, ~21 nm width, 20 m resolution). A key difference is that B8a’s narrow bandwidth is specifically positioned to avoid the atmospheric water vapor absorption feature around 820 nm, which affects the broader B8. This design gives B8a a significant advantage in retrieving surface reflectance measurements that are less sensitive to variations in atmospheric water vapor content, albeit at a coarser 20 m resolution. It is inaccurate to consider B8 and B8a spectrally “nearly identical” due to their substantial differences in central wavelength, bandwidth, and spatial resolution. Furthermore, Sentinel-2 B8a was intentionally designed for spectral consistency with the NIR band of the Landsat 8/9 OLI sensor [124,125,126] (Band 5: ~865 nm center, ~28 nm width, 30 m resolution), facilitating synergistic data use and long-term monitoring efforts between the missions. While B8 might be used for geometric alignment due to its resolution, B8a provides distinct spectral information crucial for specific atmospheric and vegetation studies and cross-sensor comparisons with Landsat 8/9. It is also plausible and often a suitable choice for geometric alignment to use B8 band aerosol correction algorithms (like Sen2Cor [127,128,129]), which typically use other bands (e.g., coastal aerosol, blue, SWIR) to estimate aerosol optical thickness (AOT) and then apply corrections across all bands, including B8 and B8a. The inherent susceptibility might differ slightly due to wavelength, but the corrected products aim to minimize these effects for both. In conclusion, B8a is particularly suitable for applications that demand high radiometric accuracy for detailed vegetation assessment, despite its reduced resolution of 20 m. Conversely, Band B8, which has a resolution of 10 m, is frequently utilized for diverse analytical purposes. This research is endorsed by expert agronomists who employ Band B8, and this study aligns with that selection for comparative analysis.

2.7. Spectral Profiles of Original Bands (Before Resampling)

In remote sensing, a spectral profile (or spectral signature) is the quantitative measure of how electromagnetic radiation (EMR) interacts with a material across wavelengths. This graph shows an object’s reflectance, absorption, or emittance based on incident EMR wavelength [28,130]. Different materials like vegetation, soil, water, minerals, and urban surfaces have unique interactions with EMR at various wavelengths, creating distinct spectral profiles for identification. Healthy vegetation reflects strongly in NIR but absorbs red and blue visible light for photosynthesis. Spectral profiles are generated from data measured by remote sensing instruments, which capture the intensity of EMR reflected or emitted from Earth’s surface in specific bands. Each pixel’s digital number or radiance/reflectance value in each band contributes to the spectral profile, plotted with wavelength on the x-axis and radiance or reflectance on the y-axis. An ideal Spectral Response Function (SRF)/spectral profile would be a perfect rectangle, meaning the sensor maintains equal sensitivity across the entire band and zero sensitivity outside it [23]. In practice, SRFs usually appear as bell-shaped curves. Comparing the SRFs of bands in various sensors is crucial for understanding how they average incoming radiation within a band, potentially resulting in variations in measured reflectance values for the same target. Overlapping SRFs between sensors can aid in data integration and comparison. Plotting the SRFs of corresponding bands from different sensors enables a visual and quantitative assessment of their overlap and shape, which helps predict how similar or different the measured values will be for spectrally varying targets. Five fields far from each other, to limit spatial autocorrelation [131,132], were chosen to be compared through their spectral profiles before analysis to compare their scaling: three Carnaroli Rice, one Luna CL, and one Cammeo. Figure 6 shows where these crops are placed through the rice farm and Figure 7 shows the electromagnetic spectrum [133] with frequencies/wavelength/color association. Figure 8 and Figure 9 illustrate the spectral profiles for the 11 May 2022 pair of images while Figure 9 and Figure 10 illustrate the spectral profiles for 15 July 2022. Certain varieties exhibit similar spectral profiles, such as the Carnaroli crops during both the growing stage and fertilization period. Additionally, Luna CL and Cammeo display comparable behaviors, although there are slight differences between them. When comparing these graphs for the same crops, it is clear that each sensor responds differently to similar frequencies (which correspond to the bands). A statistical introduction is required to deepen the analysis.

Spectral profiles are presented in this research using boxes and mean lines and are centered over EMR Figure 7 frequencies. A box and whiskers plot summarizes the distribution of data through its quartiles: it is constructed using five key statistical values: the minimum value, the first quartile (Q1), the median (Q2), the third quartile (Q3), and the maximum value [134,135,136,137].

The rectangular box represents the interquartile range (IQR), which includes the middle 50 percent of the data values. The bottom edge of the box corresponds to the first quartile (the 25th percentile), indicating that 25% of the pixel values fall below this point. The top edge of the box represents the third quartile (the 75th percentile), meaning that 75% of the pixel values are below this point. A line passing inside the box indicates the median (the 50th percentile), which is the middle value of the dataset. Vertical lines, known as whiskers, extend from the top and bottom edges of the box to a length 1.5 times the interquartile range (IQR). Data points beyond these whiskers are considered outliers. The interquartile range (IQR), represented by the height of the box in the box plot, is a measure of the spectral variability within the selected area of interest for a particular band.

A large IQR suggests dispersion of pixel values, indicating spectral heterogeneity. This might occur in areas where ground cover is not uniform, such as pixels on the boundary between different land cover types or an area containing mixed materials. Conversely, a smaller IQR indicates clustering of pixel values around the median, suggesting a spectrally homogeneous area.

By examining the shape and size of the boxes across different spectral bands in a spectral profile, it is possible to understand how the distribution of pixel values changes with the wavelength. For example, a particular band might exhibit a large IQR and a high median value, indicating variability in reflectance but a tendency towards higher reflectance in that part of the electromagnetic spectrum. Comparing these box plots across all bands provides information about the spectral characteristics of the chosen area of interest.

Mean line plot displays the average spectral reflectance for a selected area of interest across the different bands of the image. It calculates the mean pixel value for each band within the defined area and connects these mean values with a line, creating a graphical representation of the overall trend in spectral response across the electromagnetic spectrum for the chosen feature or region. Mean lines provide a view of the spectral signature, highlighting the average reflectance values for each band and allowing for an assessment of the general spectral characteristics of the area.

Outliers refer to pixel values for a specific band within a selected area of interest that lie outside the normal distribution of values for that band. These values can provide further insight into the data and might indicate mixed pixels, shadows, or unique surface materials that are spectrally distinct from the surrounding area.

Outliers can be attributed to several factors. One cause is the occurrence of mixed pixels, especially in imagery with coarser spatial resolution. A mixed pixel covers an area containing more than one type of land cover or material, resulting in a combination of spectral signatures that deviate from purer pixels representing a single land cover type. Outliers can also represent rare or unusual surface conditions, noise, or errors in the data that need consideration during analysis steps.

The data indicates that in May, there is a significant number of outliers in the higher values for RedEdge and NIR, and a substantial number of outliers in the lower values for Blue, Green, and Red. Conversely, in July, a large number of outliers are observed in the lower values for RedEdge and NIR, while Blue, Green, and Red exhibit a considerable number of outliers in the higher values. Additionally, the number of outliers in July is smaller compared to May: this may be a factor contributing to the higher RMSE and MAER observed in previous research during May [2,3,4,11,21,22]. Band data are available from the producers websites [7,12]. Comparing spectral profile of images acquired the same day it is possible to verify the different scaling for the same frequencies: 11/05/2022 (Figure 8 Sentinel-2 and 9 PlanetScope) and 15/07/2022 (Figure 10 Sentinel-2 and Figure 11 PlanetScope).

3. Results

Summary of Presented Data for each calibration through Linear Regression:

• Histograms: The top row displays histograms of the band values. The leftmost plot displays the original distributions for Sentinel-2 and PlanetScope, showing differences in the range and frequency distribution of values between the two sensors. The middle and rightmost plots present the distributions after applying linear regression-based calibration to the PlanetScope data. In each case, the calibrated PlanetScope distribution is more closely aligned with the Sentinel distribution compared to the original data.
• Scatter Plot: The bottom left plot presents a scatter plot illustrating individual data points of Sentinel-2 band values against original PlanetScope band values. Each case demonstrates a strong linear relationship, with data points clustering along a diagonal trajectory, indicating that a linear model is an appropriate choice for calibration.
• Linear Regression Model: Information about the fitted linear regression model is given, where Y represents the predicted Sentinel-2 value and X represents the original PlanetScope value.
• The RMSE and MAE values before and after linear regression are shown.
• Raster difference between PlanetScope and Sentinel-2 (as reference): Red pixels indicate areas where PlanetScope values are significantly higher than Sentinel-2 values; blue pixels represent regions where Sentinel-2 values surpass those of PlanetScope. Green and yellow markers denote areas with similar values, based on the magnitude of the difference. The color bar indicates the values of the difference between the surface reflectances measured by the two sensors. Black lines outline “Riserva San Massimo” rice crop boundaries.

Each scatter plot clearly illustrates a strong linear correlation between the two datasets, justifying the selection of a linear model for calibration. The statistical results of the linear regression model confirm this strong relationship. The extremely high R-squared value indicates that the linear models effectively capture the relationship between the two sensors’ band measurements for this specific date and crop type. The highly significant p-values for both the intercept and slope coefficients, as well as the overall model F-statistic, provide strong statistical evidence that the fitted linear relationship is not due to random chance. The F-statistic compares the amount of variance explained by the regression model to the amount of variance that remains unexplained (the residual variance). A larger F-statistic indicates that the variance explained by the model is considerably greater than the unexplained variance, lending support to the rejection of the null hypothesis. The RMSE of the model represents the residual error after fitting the linear relationship. Crucially, the comparison of pre- and post-calibration error metrics provides quantitative evidence of the calibration’s effectiveness. The significant reduction in both RMSE and MAE demonstrates that the linear calibration substantially reduced the systematic differences between the Sentinel-2 and PlanetScope band values. Based on the provided data, the linear regression calibration appears successful in reducing the discrepancy between the Sentinel-2 and PlanetScope bands. The oversampling of data from Sentinel-2 impacted the results. PlanetScope data were downsampled to a 10 m resolution during the research to understand this effect, producing comparable outcomes. After optimally aligning the PlanetScope images using these techniques, it is possible to generate prescription maps within acceptable limits. The methodology is scientifically evaluated, employing standard statistical techniques to quantify the relationship and assess the improvement. By examining the spectral profiles in Figure 8, Figure 9, Figure 10 and Figure 11 and comparing them with the histogram prior to linear regression, it becomes evident that the corresponding bands exhibit varied responses to the same input. Therefore, alignment is essential and can lead to improved calibration.

3.1. Calibration for Red Band (May and July)

Calibration effectively reduced discrepancies between the original PlanetScope Red band data and the Sentinel reference data for both analyzed dates comparing May acquisitions (Figure 12 and Figure 13) with July acquisitions (Figure 14 and Figure 15). The calibration significantly lowered RMSE and MAE values. Differences in the derived linear models and post-calibration performance metrics between the two dates indicate that optimal calibration parameters may vary over time, suggesting that temporal variations should be considered in operational calibration procedures. Difference rasters offer key information about the starting conditions and effectively pinpoint locations with considerable change (comparing Figure 13 and Figure 15). High R-squared values confirm the strong linear relationship between the datasets, supporting the use of a linear model for this application.

Most of the differences are observed over crops because, in areas with woodlands, the scale appears quite similar between the two sensors in the red channel. The histograms differ significantly between the two periods. In July, vegetation is dense, while in May, it is sparse, and during the rice farming season, the conditions vary: sometimes the crops are wet, sometimes they are not, and at times there is barren land. The variability assessed by the agronomist is critical for understanding as it represents the most challenging period for calibration assessment. The red pixel values of Sentinel-2 consistently exceed those of PlanetScope. Most of the crops exhibit a good alignment even before the LR.

3.2. Calibration for Green Band (May and July)

Even the Green calibrations, similar to the Red band, exhibit significant reductions in RMSE and MAE values post-calibration, affirming that the linear regression model successfully minimizes discrepancies comparing May acquisitions (see Figure 16 and Figure 17) with July acquisitions (see Figure 18 and Figure 19). High R-squared values in both cases indicate a strong linear relationship between the datasets. Temporal variations observed in both calibrations suggest the necessity of considering time-specific calibration parameters for optimal performance: an examination of the Difference Rasters (Figure 17 and Figure 19) reveals this observable evidence especially over crops.

Certain southern crops exhibit significantly higher Sentinel-2 values compared to the corresponding PlanetScope values; this phenomenon is partially observable in the red channel as well. There are no notable differences between these crops, except for their placement at different elevations, as illustrated in Figure 32 (discussion paragraph, considered as a future field of research).

3.3. Calibration for Blue Band (May and July)

The calibration minimized discrepancies between the original PlanetScope Blue band data and the Sentinel reference data for both dates, with significant reductions in RMSE and MAE comparing May acquisitions (Figure 20 and Figure 21) with July acquisitions (Figure 22 and Figure 23). Differences in the linear models suggest the need for periodic reassessment of calibration parameters due to temporal fluctuations: even in this case difference rasters are evidence of this behavior (compare Figure 21 and Figure 23). High R-squared values confirm a strong linear correlation, validating the use of a linear model for calibration.

The same southern crops that exhibit higher Sentinel-2 values compared to the corresponding PlanetScope values in the red and green channels demonstrate similar behavior in the blue channel.

3.4. Calibration for NIR Band (May and July)

Calibration results for the NIR band acquisitions in May (Figure 24 and Figure 25) and July (Figure 26 and Figure 27) show improved data accuracy post-calibration, with high R-squared values indicating strong correlations between datasets (see Figure 24 and Figure 26). The differences in coefficients suggest that calibration parameters need periodic adjustment to maintain accuracy as even Difference rasters demonstrate clearly comparing Figure 25 and Figure 27.

The near-infrared (NIR) band displays different characteristics compared to the visible bands of Red, Green, and Blue. For NIR, PlanetScope values are generally higher than those of Sentinel-2. For the July data, all pixel values in Sentinel-2 are higher than those in PlanetScope (thanks to the difference raster comparison in Figure 25 and Figure 27).

The near-infrared (NIR) bands exhibit the most significant differences, consistently showing higher values in PlanetScope compared to Sentinel-2. This discrepancy may be attributed to the difference between Sentinel bands 8 and 8a. However, this linear regression indicates that it is possible to address this issue, as the dependency is clearly linear.

3.5. Calibration for RedEdge Band (May and July)

The calibration for the RedEdge band shows better error reduction and consistency compared to the NIR band, especially between the analyzed dates: May acquisitions (Figure 28 and Figure 29) and July acquisitions (Figure 30 and Figure 31). Adjusting calibration parameters based on seasonal variations is essential for accurate remote sensing and even in this case difference rasters (Figure 29 and Figure 31) highlight areas of significant variability. The RedEdge band (as for RGB bands) originally has higher Sentinel-2 values, while the NIR band has higher original PlanetScope values.

RedEdge behaves similarly to Red, Green, and Blue, with PlanetScope pixel values exceeding those of Sentinel-2.

3.6. Differences Between Histograms

The linear regression models for the bands show variations between the two dates, with different intercept and slope values. This reinforces the observation regarding temporal variability in the sensor relationship seen also in previous research [2,4,11]. RMSE and MAE values are consistently reduced: the post-calibration RMSE and MAE values for the calibration on 15 July 2022 are lower than those for the calibration on 11 May 2022. This indicates that the calibration performed for July images was more effective. Additionally, the R-squared values are high for both dates, suggesting that the linear model is well suited for describing the relationship between the original and reference band data. Discrepancies in the scaling of bands between the two sensors were identified through the comparison of their spectral profiles, the difference rasters, and their linear regression, leading to inconsistencies in indices observed during prior research [2,4]. These differences arise due to variations in the way each band’s data are represented and measured. To mitigate this problem, linear regression can be employed as a preprocessing technique to align the bands. This method was implemented through Matlab 2024 b [45,46,47,138] in the current research. This alignment ensures that the data across all bands are on a consistent scale. It is important to note that this technique is most effective when applied to bands that are considered compatible by their producers, as compatibility indicates that the bands share similar characteristics and are suitable for comparison. Shifts are observed across all bands, but they do not have the same consistency for each band: Red, Green, Blue, and RedEdge have Sentinel-2 values higher than PlanetScope, while the NIR band shows Sentinel-2 values lower than PlanetScope before linear regression. These shifts are unevenly distributed across the bands and result in ineffective compensation across indices. Consequently, applying linear regression directly to the index yields inefficient results [4]. Calibrating directly indices necessitates several improvements in calibration and employs various techniques such as histogram shifting and histogram matching [4]. In contrast, aligning bands requires only linear regression. It is crucial to assess these results to determine the most appropriate methodology for each specific case [4].

4. Discussion

The research compared five bands from Sentinel-2 and PlanetScope over the “Riserva San Massimo” rice farm, analyzing their characteristics and spectral profiles across crops.

The data reveal that in May, the RedEdge and NIR bands have more high-value outliers, while the Blue, Green, and Red bands have more low-value outliers. Conversely, in July, the RedEdge and NIR bands show more low-value outliers, and the Blue, Green, and Red bands have more high-value outliers. Additionally, the number of outliers in July is smaller compared to May. This highlights the effectiveness of using linear regression (OLS) to align the Blue, Red, Green, RedEdge, and NIR bands. Linear regression models the relationship between two variables by fitting a linear equation to the observed data. Therefore, it is crucial that pixel sizes are uniform and spatially aligned. Sentinel-2 offers Blue, Green, Red, and near-infrared (NIR) bands at a spatial resolution of 10 m, as well as RedEdge at 20 m. In contrast, PlanetScope provides all its bands at a spatial resolution of 3 m. Pixels were aligned ultimately using Nearest Neighbor Resampling [116,117] with posting vectors through Matlab [113,114] to limit spatial correlation [131,132]. Throughout the research, various approaches and resampling algorithms [113,114,115,116,139,140,141] were utilized (linear, cubic, spline, makima [142], …), yielding comparable outcomes. Consequently, the simplest algorithm was retained. In this context, resampling ensured that the values from different bands were consistent with each other before alignment. The research findings demonstrate the effectiveness of linear regression as an alignment technique for the five studied bands. Applying this method resulted in the successful alignment of all five bands, thereby enabling more precise calculations of crucial vegetation and soil indices. The advantages of this approach will be quantified relative to previous research methodologies described [4,11,21,22]. Furthermore, the robustness of the linear regression technique was particularly evident in its ability to maintain alignment accuracy even during the month of May (where thte highest values of RMSE and MAE were found, except for the NIR band). This period is typically characterized by heightened discrepancies between indices [2,4,21,22], which can pose significant challenges for alignment procedures. However, linear regression consistently produced reliable results, underscoring its adaptability and effectiveness across diverse environmental conditions and temporal variations. The research revealed notable disparities in histogram indices between the months of May and July. These temporal fluctuations were consistent with the differences observed in single bands during the same timeframe. This observation suggests a correlation between the variations in histogram indices and the changes in individual band values. The shifts found in histogram indices are directly influenced by the underlying variations in the individual band values across the two months [2,4,21,22]. Further investigation is needed to understand the relationship between these measurements and the factors driving temporal changes. Research should focus on spatial autocorrelation for image pairs. Future studies could enhance our understanding of ecosystem dynamics by exploring the link between single band values and histogram indices.

Examples of improvements can be realized through the following:

• Analyzing the specific contributions of individual bands: Examining how each spectral band contributes to the indices.
• Investigating seasonal and interannual variations: Tracking how the relationship between single band values and histogram indices changes throughout the year and across multiple years to capture the effects of seasonal cycles.
• Identifying driving factors: Determining the key environmental factors (e.g., temperature, precipitation, soil moisture) that influence the observed variations in single band values and histogram indices.
• Evaluation of DTM impact on previous factors: Figure 32 shows that the southern crops are at a higher elevation than others, indicating a need for further assessment of water supply and management differences.

From an agronomist’s perspective, which includes expertise in rice farms and the development and utilization of prescription maps in the field, it is crucial to evaluate each acquisition by considering any operations performed on crops. Proper tillering and familiarity with operator machinery are vital for creating accurate prescription maps based on the available equipment. This approach should be tailored to research aimed at improving the use of satellite images, utilizing PlanetScope images as opposed to Sentinel-2 images. Although Sentinel-2 has lower spatial and temporal resolution, it offers more bands and a more accurate spectral profile. The availability of satellite images is assessed after acquisition, compared to other technologies such as field spectrometers and drones used for on-site data collection. In numerous instances, including this one, reconstructing water management and field operations for each crop becomes challenging when analysis is conducted months or years later. A novel approach for a test site could involve meticulously tracing each operation to facilitate evaluation even after extended periods. Moreover, it is crucial for agronomists to understand that sparse vegetation during May represents a critical issue that can only be analyzed using higher resolution sensors, such as SkySat [4], as demonstrated by previous research conducted by the same authors, and drone imagery. Conversely, in July, the land is fully covered by vegetation, yielding homogeneous measurements.

5. Conclusions

5.1. Main Findings

This research compares Sentinel-2 and PlanetScope imagery over a rice farm, analyzing band characteristics and spectral profiles. Findings indicate temporal variations in outlier distribution across bands between May and July, with fewer outliers in July. Spectral profiles demonstrate that PlanetScope and Sentinel-2 operate on different values scales. Linear regression proved effective for aligning the Blue, Red, Green, RedEdge, and NIR bands, necessitating uniform pixel sizes and spatial alignment, achieved via Nearest Neighbor Resampling. The robustness of linear regression (OLS) was confirmed even during May, a period of higher index discrepancies. Disparities in histogram indices between May and July are at least partially correlated with single band value scale changes. Future research should investigate spatial autocorrelation and the link between single band values and histogram indices, considering environmental factors and DTM impact. From an agronomic perspective, evaluating crop operations is vital for prescription map accuracy, favoring PlanetScope’s higher resolution despite Sentinel-2’s spectral advantages. Reconstructing past field operations poses a challenge, suggesting a need for meticulous record-keeping. High-resolution sensors like SkySat and drones are essential for analyzing sparse vegetation in May, while July’s dense vegetation yields homogeneous measurements. This paper presents an alternative method to previous calibration techniques that directly calibrated indices and obtained optimal results. This calibration approach can be used effectively when corresponding bands between sensors are available and there is no need for a proxy index. The future aim is to assess these methodologies using long-term data to identify the most appropriate approach for different situations.

5.2. Future Perspectives

Building on these results, several promising avenues can be pursued: advancement in vegetation and soil monitoring; integration with other remote sensing technologies; integration with vectorial database (Geoportale Lombardia [143], Carta Geologica e progetto Carg [144], …); and enhanced calibration techniques. Further research could examine improved calibration techniques that extend beyond linear regression, the spatial autoregressive model [132], including non-linear models or hybrid approaches used in previous studies. Previous studies indicate that indices can be aligned using together linear regression, histogram shifting, and histogram matching (in this order), even in scenarios like non-contemporary acquisition and during suboptimal timeframes [4]. Linear regression alone is not able to overcome the worst-case scenario over indices [4], which when applied on single bands, help to analyze the variations in sensor acquisition, allowing for the identification of whether there is a shift, a minor variance, or significant diversity.