Modeling Wheat Height from Sentinel-1: A Cluster-Based Approach ^†

Abstract

Crop height is a key indicator of plant development and growth dynamics, offering valuable insights for temporal crop monitoring. However, modeling its variation across phenological stages remains challenging due to canopy structural changes. This study aimed to predict wheat height throughout the growth cycle by integrating radar remote sensing data with a phenology-informed clustering approach. The research was conducted in three wheat fields in Umbria, Italy, from 30 January to 10 June 2024, using in-field height measurements, phenological observations, and Sentinel-1 acquisitions. Backscatter variables (VH, VV, and CR) were processed using two speckle filters (Lee 7 × 7 and Refined Lee), alongside additional radar-derived parameters (entropy, anisotropy, alpha, and RVI). Fuzzy C-means clustering enabled the classification of observations into two phenological groups, supporting the development of stage-specific linear regression models. Results demonstrated high accuracy during early growth stages (tillering to stem elongation), with R² values of 0.76 (RMSE = 6.88) for Lee 7 × 7 and 0.79 (RMSE = 6.35) for Refined Lee. In later stages (booting to maturity), model performance declined, with Lee 7 × 7 outperforming Refined Lee (R² = 0.51 vs. 0.33). These findings underscore the potential of phenology-based modeling approaches to enhance crop height estimation and improve radar-driven crop monitoring.

1. Introduction

Understanding crop development through remote sensing constitutes a fundamental objective within the domain of precision agriculture, aiming to support optimized field monitoring and informed management decisions. The retrieval of crop biophysical parameters from Synthetic Aperture Radar (SAR) data presents a valuable opportunity in this context, offering cloud-independent monitoring capabilities and enabling the continuous assessment of vegetation dynamics [1]. Among these parameters, plant height serves as a critical indicator of vegetative development and above-ground biomass accumulation. However, its accurate estimation from SAR observations remains a significant challenge due to the inherently complex and non-linear interactions between microwave signals and canopy structural characteristics [2].

Various methodological approaches have been explored for estimating crop height using SAR data. Among machine learning techniques, Random Forest algorithms have demonstrated considerable efficacy in the estimation of wheat height, often employing VV backscatter either alone or in conjunction with polarimetric features [3,4,5]. Furthermore, the study by Nduku et al. [6] underscored the enhanced predictive capacity achievable through the integration of Sentinel-1 and Sentinel-2 datasets, reporting superior performance when employing Random Forest Regression and Support Vector Machine models. Despite their conceptual simplicity, linear regression models have also been investigated as feasible alternatives for modeling the relationship between SAR backscatter and field-based crop height observations [7,8].

Although it is well documented that phenology can significantly influence SAR backscatter, this factor is frequently not explicitly accounted for in existing modeling frameworks. Clustering techniques—used to group observations based on feature similarity or distance—can address this limitation by organizing data into more homogeneous subsets, potentially improving both model performance and interpretability [9]. Traditional clustering approaches, such as K-Means, assign each observation exclusively to a single group, resulting in crisp partitions based on Euclidean distance. In contrast, fuzzy clustering algorithms allow for soft assignment, making them more suitable for these purposes.

Hence, this research proposes a methodology for estimating wheat height from SAR-derived parameters by partitioning the dataset into phenologically similar clusters using fuzzy C-Means clustering. Within each cluster, wheat height is then predicted using multiple linear regression, with the goal of enhancing model accuracy and capturing variability due to phenological development.

2. Materials and Methods

The experimental study was carried out across three agricultural fields managed by the “Foundation of Agricultural Education in Perugia” (Figure 1), located in Casalina, Deruta, Italy, near the Tiber Valley (158 m a.s.l., 42°56′16″ N, 12°23′34″ E). The target crop was soft wheat (Triticum aestivum L., var. Vivendo), sown between 2 and 6 November 2023, and harvested from 23 to 29 June 2024.

To capture within-field variability in crop development, two representative sampling locations were selected in each field using historical vegetation vigor maps and soil texture data. These points were positioned in zones characterized by contrasting canopy vigor. Around each sampling point, within a 5 m buffer, the average height of ten wheat plants was measured, alongside assessments of phenological stage and canopy vigor. Phenological stages were classified according to the BBCH scale [10]. At each sampling location, six soil moisture sensors were installed at a depth of approximately 20 cm to continuously monitor volumetric water content every 15 min throughout the growing season.

To complement ground-based measurements, eleven Sentinel-1 images were acquired from the Copernicus Data Space Ecosystem [11] between 30 January 2024 and 10 June 2024. Among the available acquisition tracks (Ascending 117, Descending 22, and Descending 95), Ascending 117 was selected due to its optimal overpass time (~17:30 local time), which helps minimize signal interference from dew. Both Ground Range Detected (GRD) and Single Look Complex (SLC) products were collected and processed using ESA SNAP software [12].

Containing only amplitude information, GRD images were subjected to standard pre-processing steps [13], including orbit correction, thermal noise removal, and radiometric calibration to convert digital numbers (DNs) to sigma nought (σ₀) backscatter coefficients. Speckle noise was mitigated using two filtering techniques (Lee 7 × 7 and Refined Lee). The images were then ortho-rectified using the SRTM three arcsecond Digital Elevation Model (DEM).

SLC products, which retain both amplitude and phase information, underwent the following more advanced pre-processing workflow [14]:

• Application of precise orbit file;
• TOPSAR splitting;
• Radiometric calibration to convert integer DN to complex values;
• TOPSAR debursting;
• Generation of polarimetric coherence matrix (C2);
• Multi-looking (four range × one azimuth);
• Polarimetric speckle filtering (Refined Lee 5 × 5);
• Ortho-rectification.

The linear σ₀ values were converted to decibels (dB) using the following logarithmic transformation:

σ₀ (dB) = 10 ∗ log₁₀ σ₀

(1)

For both vertical–horizontal (VH) and vertical–vertical (VV) polarization channels. Additionally, the cross-ratio was computed as follows:

σ₀ (CR) = σ₀ (VH) − σ₀ (VV)

(2)

Polarimetric decomposition was performed using a modified Cloude–Pottier algorithm to derive entropy (H), anisotropy (A), and the alpha angle (α) [15]. The dual-polarization Radar Vegetation Index (RVI) was also calculated using the following formula [16]:

RVI = 4 ∗ σ₀ VH/(σ₀ VH + σ₀ VV)

(3)

All derived SAR variables had a spatial resolution of 10 m × 10 m. To streamline analysis and optimize computational efficiency, a spatial subset of the area of interest (AOI) was used. SAR-derived parameters were extracted at each sampling location using spatial overlays in QGIS.

To explore the relationship between SAR parameters and wheat height, a fuzzy C-Means (FCM) clustering algorithm was implemented in Python v. 3.11.5. Unlike hard clustering approaches, FCM assigns each observation a membership score across clusters, minimizing the weighted within-cluster variance [17]. This soft assignment strategy may take into account the gradual progress of phenology, which rarely follows strict boundaries but rather exhibits overlapping structural traits across growth stages. Following clustering, linear correlation analyses were performed between wheat height and individual SAR variables within each group. Parameters showing statistically significant correlations (p < 0.05) were selected to build multiple linear regression models for height estimation, tailored to each cluster. Model performance was evaluated using the coefficient of determination (R²) and root mean square error (RMSE), enabling the assessment of predictive accuracy across phenologically subgroups.

The temporal evolution of SAR backscatter throughout the wheat growth cycle reflects the dynamic interplay between soil and vegetation contributions. VV polarization is particularly sensitive to soil moisture and surface roughness, especially during early growth when vegetation cover is minimal, whereas VH polarization becomes more responsive as the crop canopy develops, being influenced by structural complexity [18]. In the early stages, such as tillering, backscatter is dominated by soil signals due to sparse vegetation. As the crop enters stem elongation, increased vertical biomass (e.g., stems and leaves) causes signal attenuation, typically resulting in minimum backscatter around the booting stage [19]. Later stages, including heading and flowering, introduce more complex scattering mechanisms due to reproductive structures like ears and awns. These lead to volume and double-bounce scattering effects, making the SAR response more randomized and difficult to interpret using simple backscatter metrics alone. Polarimetric decomposition metrics help to contextualize these dynamics. Entropy (H), which quantifies the randomness of scattering, increases with canopy density, indicating the transition from surface-dominated to volume-dominated scattering. The alpha angle (α), representing the dominant scattering mechanism, shifts from low values (surface scattering) to higher ones typical of volume scattering as vegetation becomes more structurally complex [20].

3. Results and Discussion

The application of fuzzy C-Means (FCM) clustering enabled the identification of two distinct phenological clusters: the first spanning from tillering to the end of stem elongation and the second encompassing stages from booting to maturity. The correlations between wheat height and SAR observables within each cluster (

Table 1. R² values of the regression between wheat heights and SAR parameters, using Lee 7 × 7 (L) and Refined Lee (RFL) filters to remove speckle on backscatter (VH, VV, and CR) coefficients. Values in the red box are significant (p < 0.05).

Cluster Group	VH		VV		CR		H		A		α		RVI
	L	RFL	L	RFL	L	RFL	L	RFL	L	RFL	L	RFL	L	RFL
Tillering–End of Stem Elongation	0.02	0.007	0.54	0.62	0.45	0.48	0.57	0.52	0.56	0.51	0.51	0.59	0.37	0.37
Booting–Development of Fruit	0.41	0.31	0.49	0.17	0.05	0.07	0.0003	0.03	0.004	0.1	0.01	0.12	0.0009	0.0009

) align with known scattering dynamics. During the early growth phase, variables such as VV backscatter, entropy, anisotropy, and alpha exhibit high R² values with plant height, while VH backscatter shows weaker correlations—likely due to the limited structural complexity of the canopy at this stage. In contrast, during the later phenological stages only VV and VH backscatter maintain a significant relationship with height. This is attributed to the increased canopy complexity, which induces a more diffuse and variable SAR response, diminishing the explanatory power of physically derived polarimetric parameters.

These trends are further supported by multiple regression models (Figure 2), which demonstrate strong predictive performance during the early development stages, but a marked decline in accuracy during later phases, where only VV and VH backscatter remain statistically significant. This suggests that polarimetric indicators are effective at capturing structural development in the early growth phases, but their sensitivity diminishes as volumetric scattering and canopy heterogeneity dominate in the mature wheat crop.

To assess the spatial dimension of these relationships, multiple linear regression models were used to generate plant height maps for four key dates throughout the wheat growing season (Figure 3). These maps highlight spatial variability in crop height and facilitate comparison between different speckle filtering methods. Specifically, maps derived using the Refined Lee filter exhibit high pixel-level variability, resulting in a speckled appearance and limited spatial continuity. In contrast, maps produced with the Lee 7 × 7 filter show a stronger smoothing effect, leading to a more spatially coherent representation of height dynamics across the season.

4. Conclusions

This study confirms the applicability of SAR data to the agricultural context, specifically for predicting wheat height. Furthermore, it demonstrates the potential of fuzzy C-means clustering to partition height data according to phenological stages, enhancing predictive performance particularly during the early growth phases. The method was applied to a limited area; therefore, further experiments are required in the coming years to validate the proposed approach and assess its robustness in agricultural scenarios different to the one investigated.