Soil Organic Carbon Estimation Using Dual-Interval Synergistic Selection and Overlap-Constrained Ridge Regression

1. Introduction

Soil organic carbon (SOC) is a key indicator in soil quality assessment, the maintenance of farmland productivity, and research on carbon cycling in terrestrial ecosystems. Its content directly affects soil fertility, aggregate stability, and water and nutrient retention capacity, and is closely associated with soil degradation monitoring, cultivated land quality assessment, and sustainable agricultural management [1,2]. Although conventional chemical analysis methods are reliable, they are labor-intensive, costly, and time-consuming, making them unsuitable for the rapid analysis of large numbers of samples [3]. Visible and near-infrared (Vis-NIR) spectroscopy has been widely used for soil property prediction because it is rapid, non-destructive, and suitable for multi-attribute estimation [4,5]. In SOC studies, Vis-NIR spectra capture information related to organic matter, moisture, mineral composition, and soil color. However, SOC-related spectral responses are typically distributed across multiple interrelated wavelength regions and are further influenced by moisture, particle composition, iron oxides, and background reflectance [6,7,8,9]. Consequently, spectral modeling remains challenging because of high dimensionality, strong collinearity, and noise [10].

To address the modeling problems caused by high-dimensional spectral variables, various variable selection and feature compression methods have been proposed. According to the selection unit, Vis-NIR variable selection methods can be broadly divided into wavelength point selection (WPS) and wavelength interval selection (WIS) [11]. WPS selects discrete wavelengths, whereas WIS operates on continuous spectral intervals. In practical prediction tasks, different feature selection strategies usually need to be combined with regression models to form a complete spectral modeling workflow. Typical WPS methods include competitive adaptive reweighted sampling (CARS), successive projections algorithm (SPA), uninformative variable elimination (UVE), variable importance in projection (VIP), and iteratively retains informative variables (IRIV) [12,13,14,15,16]. These methods can reduce the input dimensionality, remove redundant variables, and improve modeling efficiency to some extent. However, for continuous spectral signals such as Vis-NIR spectra, wavelength point selection may weaken the structural information of continuous absorption regions, and the selected variables may be susceptible to local noise and sample fluctuations [17,18]. In addition, WPS methods generally use the contribution of individual wavelength points as the main selection criterion, providing relatively limited utilization of the continuous structure of adjacent wavelengths and the potential complementary information among different spectral regions. Therefore, relying solely on discrete wavelength selection may be insufficient to fully characterize the complex and continuous spectral response patterns of SOC.

WIS methods use continuous wavelength intervals as the basic selection unit, which is more consistent with the broad, overlapping, and continuously distributed absorption characteristics of near-infrared spectra. Representative WIS-related benchmark models include interval partial least squares regression (iPLSR), synergy interval partial least squares regression (siPLSR), and moving window partial least squares regression (MWPLS) [19,20]. These models divide the full spectrum into several continuous intervals and select effective spectral regions for modeling, thereby preserving local absorption structures while achieving variable compression. This helps improve model interpretability. Nevertheless, existing WIS modeling strategies still have room for improvement. On the one hand, because iPLSR, siPLSR, and MWPLS mostly use partial least squares regression (PLSR) as the core regression model, their interval selection results and prediction performance may be affected, to some extent, by the choice of regression model. On the other hand, existing interval-based methods generally emphasize local optima obtained from a single interval or a limited combination of intervals, and the synergistic relationships among intervals across different spectral regions remain insufficiently explored [21,22,23]. In addition, during interval combination, how to control redundant information caused by interval overlap and how to balance search efficiency with model performance improvement remain issues worthy of further investigation.

The overall goal of this study was to develop an interval-based spectral modeling framework for soil organic carbon prediction that can preserve continuous spectral structures while more effectively exploiting complementary information across different spectral regions. The novelty of this study is reflected in three aspects. First, unlike conventional wavelength point selection methods that operate on discrete bands, the proposed framework uses continuous sliding-window intervals as the basic selection unit, thereby preserving local spectral structure. Second, unlike existing interval-based methods that mainly focus on single intervals or limited local combinations, the proposed sicRidge framework introduces a cross-region dual-interval synergistic search strategy to identify interval combinations with complementary predictive contributions. Third, an overlap constraint is incorporated into the interval-combination process to reduce redundant interval pairs and improve the efficiency of interval screening under a unified Ridge regression framework. Based on this design, this study systematically compares sicRidge with full-spectrum Ridge regression, WPS-Ridge benchmark models, and WIS-related benchmark models to evaluate whether cross-region interval synergy can improve SOC prediction under the current dataset.

2. Materials and Methods

2.1. Soil Samples and Spectral Data Acquisition

A total of 168 soil samples were used in this study, including 118 samples collected from Xiangshan County, Ningbo City, Zhejiang Province, China, and 50 samples collected from Yongxiu County, Jiujiang City, Jiangxi Province, China. The Xiangshan samples were collected on 27 December 2025, and the Yongxiu samples were collected on 28 December 2025, all from citrus orchards. The sampling depth was 0–20 cm, and each sample represented a single-point sample. In the subsequent modeling analysis, samples from the two counties were pooled into a combined dataset and then partitioned into the calibration set and prediction set.

After collection, all samples from the two sampling batches were processed using the same laboratory protocol. Specifically, the samples were oven-dried at 105 °C, ground, passed through a 2 mm sieve, and then stored in sealed bags before laboratory determination and spectral acquisition. The soil samples were sent to the Qiuyin Soil Testing Laboratory on 30 December 2025 for the determination of soil organic carbon content. Soil organic carbon was measured using the potassium dichromate external heating method. For analytical quality control, each sample was determined in triplicate, and the mean value of the three measurements was used as the final SOC reference value for subsequent spectral modeling. The allowable relative error among repeated measurements was set at 2%; when the error exceeded 2%, the sample was remeasured. The measured SOC values were used directly as the reference values for subsequent spectral modeling. The descriptive statistics of SOC content are shown in Table 1.

Table 1. Descriptive statistics of soil organic carbon content.

In this study, a portable spectrometer (OFS2500, Oceanhood, Shanghai, China) was used to acquire Vis-NIR spectral information from the soil samples in December 2025. The instrument operates over a wavelength range of 342–2504 nm, covering the visible to near-infrared regions. Its built-in interpolation algorithm outputs spectral wavelengths at 1 nm intervals, generating a total of 2163 spectral variables. Considering that the spectral regions at both ends are generally affected by weakened instrumental edge response, relatively low signal-to-noise ratio, and strong noise interference, their stability and interpretability are relatively poor. Therefore, before subsequent modeling, the low-quality bands at both ends were removed, and only spectral variables within the range of 400~2500 nm were retained for analysis. In terms of instrument performance, the OFS2500 has a spectral resolution of 2.5 nm and a signal-to-noise ratio of 500:1 in the range of 342~900 nm, and a spectral resolution of 8 nm with a signal-to-noise ratio of up to 2000:1 in the range of 900~2504 nm.

For spectral measurement, each soil sample was placed in a 10 cm diameter Petri dish and spread evenly to form a sample layer of approximately 5 mm thickness. Spectral acquisition was conducted in a dark box to avoid interference from external light sources. During measurement, the spectrometer probe was positioned 2 cm above the sample surface, and the integration time was set to 2500 us. To maintain measurement stability, white and dark reference corrections were performed every 15 min throughout the experiment. The laboratory temperature was maintained at 27 °C during spectral acquisition. Before each scan, the soil sample was re-mixed to reduce random variation. Each sample was scanned three times, and the averaged spectrum was used as the representative spectrum of that sample. The raw spectral curves of the soil samples are shown in Figure 1a.

Figure 1. Raw and preprocessed spectra of soil samples at different preprocessing stages: (a) raw spectra; (b) spectra after standard normal variate transformation (SNV); (c) spectra after standard normal variate transformation and first derivative preprocessing (SNV + FD); and (d) spectra after standard normal variate transformation, first derivative preprocessing and Savitzky–Golay smoothing (SNV + FD + SG).

2.2. Spectral Preprocessing and Dataset Partitioning

Because the raw spectra were affected by scattering effects, baseline drift, and noise from low-quality bands at both ends of the spectral range, the effective spectral range was first selected from the raw spectra. Multiple preprocessing methods were then applied to extract stable spectral features and provide reliable inputs for subsequent interval modeling. Specifically, the raw spectra were first truncated from 342~2504 nm to 400~2500 nm, retaining 2101 bands. Standard normal variate (SNV) transformation [24], first derivative (FD) preprocessing [25], and Savitzky–Golay (SG) smoothing [26] were then sequentially applied.

Among these preprocessing steps, SNV was used to reduce the effects caused by particle size, sample surface conditions, and scattering differences. FD preprocessing was applied to enhance local variation features in the spectral curves and reduce baseline drift. In the present study, the first derivative was calculated along the wavelength axis using the first-order finite difference, and the last derivative value was repeated once to retain the original spectral dimensionality. Because FD preprocessing may amplify high-frequency noise, SG smoothing was further applied after FD preprocessing to reduce noise effects. The SG smoothing procedure used a window length of 11 bands and a polynomial order of 2. The spectral curves at different preprocessing stages are shown in Figure 1b–d. In the present study, the SNV + FD + SG sequence was adopted as the preprocessing scheme under the current dataset based on preliminary comparative screening within the calibration set.

In the subsequent modeling process, based on the spectral matrix after SNV + FD + SG preprocessing, the variables were further standardized using the mean and standard deviation of the calibration set to ensure that the inputs of the calibration set and prediction set were on the same scale.

To ensure the objectivity and reproducibility of model evaluation, the calibration set and prediction set were divided using a fixed stratified hold-out strategy based on the sorted SOC reference values. First, all samples were sorted in ascending order according to the SOC values. Then, every four consecutive samples in the sorted sequence were grouped together, and the first sample in each group was assigned to the prediction set, whereas the remaining three samples were assigned to the calibration set. Using this strategy, 126 samples were assigned to the calibration set and 42 samples to the prediction set. This partitioning strategy ensured that the calibration set covered the full distribution range of the target variable, while the prediction set was used as an independent hold-out set under the current data distribution.

2.3. Selection of the Full-Spectrum Reference Model and Construction of Feature Selection Benchmark Models

To determine a full-spectrum reference model suitable for the current dataset, this study first compared several spectral regression models under the full-spectrum condition, including Ridge regression [27], partial least squares regression (PLSR) [28], Random Forest [29], support vector regression (SVR) [30], and least squares boosting (LSBoost) [31]. Model selection was performed exclusively within the calibration set by cross-validation, and the regressor with the best cross-validation performance was adopted for the subsequent wavelength-selection and interval-selection procedures. The prediction set was kept completely independent during model selection and was used only for the final hold-out evaluation of the selected model.

To compare the modeling effects of different feature selection strategies, several WPS methods were further introduced as benchmark methods, including CARS [15], SPA [12], UVE [13], VIP [14], and IRIV [16]. The feature subsets obtained by each WPS method were combined with Ridge regression to construct the CARS-Ridge, SPA-Ridge, UVE-Ridge, VIP-Ridge, and IRIV-Ridge benchmark models, respectively. These models were used to compare the effects of discrete wavelength point selection strategies under a unified regression framework.

This study also compared several WIS-related benchmark models to evaluate the effectiveness of continuous interval selection and combination search strategies in sicRidge. The existing WIS-PLS-related methods used in this study included iPLSR [20], siPLSR [19], and MWPLS [32]. Considering that different regression models may affect the results, Ridge regression-based WIS benchmark models, namely iRidge, siRidge, and MWRidge, were further constructed based on the existing WIS partitioning strategies. It should be noted that iRidge, siRidge, and MWRidge are benchmark model names constructed in this study rather than existing standard algorithm names. Their purpose was to minimize the influence of differences between PLSR and Ridge regression when evaluating interval selection effects.

2.4. Construction of the Synergistic Interval-Constrained Ridge Regression Spectral Modeling Framework

To exploit complementary information across spectral regions while preserving continuous spectral structures, we constructed a synergistic interval-constrained Ridge regression framework (sicRidge). The framework uses the preprocessed Vis-NIR spectral matrix as input and continuous wavelength intervals as the basic selection unit. Its main steps include sliding-window candidate interval generation, dual-interval synergistic search, overlap constraint filtering, and final Ridge regression modeling. Unlike WPS methods, which focus on the selection of discrete wavelength points, and existing WIS methods, which mostly emphasize a single interval or limited interval combinations, sicRidge aims to identify cross-region interval combinations with complementary contributions and low redundancy within the calibration set. Modeling and comparison are then performed under a unified Ridge regression framework. The prediction set was used only for the final hold-out validation of the model and was not involved in candidate interval generation, interval combination selection, determination of the number of intervals, parameter optimization, or variable standardization, thereby ensuring the relative objectivity of model evaluation. The overall workflow of the proposed sicRidge framework is illustrated in Figure 2.

Figure 2. Conceptual workflow of the proposed sicRidge framework for SOC prediction from Vis-NIR spectra.

The detailed interval search procedure, parameter optimization strategy, and comparison of results under different numbers of intervals in sicRidge are further presented in Section 3.

2.5. Model Evaluation Metrics

To comprehensively evaluate the prediction per