Predictive Sinusoidal Modeling of Sedimentation Patterns in Irrigation Channels via Image Analysis

Abstract

Sediment accumulation in irrigation channels poses a significant challenge to water resource management, impacting hydraulic efficiency and agricultural sustainability. This study introduces an innovative multidisciplinary framework that integrates advanced image analysis (FIJI/ImageJ 1.54p), statistical validation (RStudio), and vector field modeling with a novel Sinusoidal Morphodynamic Bedload Transport Equation (SMBTE) to predict sediment deposition patterns with high precision. Conducted along the Malacatos River in La Tebaida Linear Park, Loja, Ecuador, the research captured a natural sediment transport event under controlled flow conditions, transitioning from pressurized pipe flow to free-surface flow. Observed sediment deposition reduced the hydraulic cross-section by approximately 5 cm, notably altering flow dynamics and water distribution. The final SMBTE model (Model 8) demonstrated exceptional predictive accuracy, achieving RMSE: 0.0108, R²: 0.8689, NSE: 0.8689, MAE: 0.0093, and a correlation coefficient exceeding 0.93. Complementary analyses, including heatmaps, histograms, and vector fields, revealed spatial heterogeneity, local gradients, and oscillatory trends in sediment distribution. These tools identified high-concentration sediment zones and quantified variability, providing actionable insights for optimizing canal design, maintenance schedules, and sediment control strategies. By leveraging open-source software and real-world validation, this methodology offers a scalable, replicable framework applicable to diverse water conveyance systems. The study advances understanding of sediment dynamics under subcritical (Fr ≈ 0.07) and turbulent flow conditions (Re ≈ 41,000), contributing to improved irrigation efficiency, system resilience, and sustainable water management. This research establishes a robust foundation for future advancements in sediment transport modeling and hydrological engineering, addressing critical challenges in agricultural water systems.

1. Introduction

Sediment accumulation in irrigation channels represents a critical challenge for agricultural water management systems worldwide, significantly compromising hydraulic efficiency and water distribution capacity [1]. The progressive deposition of sediments reduces channel cross-sectional area, increases flow resistance, and leads to uneven water distribution, ultimately threatening agricultural productivity and food security [2]. In regions characterized by complex topography and variable hydrological regimes, such as the Andean highlands of Ecuador, these challenges are particularly pronounced due to high erosion rates and sediment loads. Sediment deposition occurs when flow velocities fall below critical thresholds, typically between 0.3 m/s and 0.5 m/s for fine-grained materials, leading to progressive accumulation that compromises hydraulic performance through reduced conveyance capacity, increased roughness coefficients, and altered flow dynamics [3]. These challenges are further compounded in environments with steep topography and seasonal sediment load variations, such as the Andean valleys of southern Ecuador, where sediment transport significantly impacts irrigation infrastructure.

Traditional approaches to sediment transport analysis have predominantly relied on empirical models and point-based measurement techniques [3,4]. While these methods have provided foundational insights into sediment dynamics, they often lack the spatio-temporal resolution required for precise characterization of complex, spatially variable deposition patterns, particularly periodic bedforms that significantly impact hydraulic resistance [5]. Furthermore, traditional techniques, such as physical sampling and empirical modeling, require substantial field labor and may lack the precision necessary to characterize deposition patterns across diverse environmental conditions [6]. These limitations underscore the critical need for advanced, non-invasive techniques capable of delivering high-resolution morphometric data and predictive models that can capture these specific features with enhanced accuracy and efficiency.

Advances in image processing and computer vision have revolutionized sediment transport research, offering unprecedented opportunities for detailed morphological analysis [7]. Tools like FIJI/ImageJ 1.54p, an open-source platform for scientific image analysis, enable the extraction of high-resolution topographic data from images, facilitating comprehensive characterization of sedimentary structures.

Unlike existing image-based techniques that primarily focus on visual classification or empirical pattern detection [7], the proposed approach introduces a parametric sinusoidal model capable of capturing periodic sediment structures with high spatial resolution [8]. This mathematical formalization allows for the quantification of morphometric descriptors such as wavelength and amplitude—parameters that are not explicitly resolved in most image segmentation or thresholding methods. By integrating sinusoidal curves fitting with high-resolution imaging, this study provides a reproducible and interpretable framework that advances sediment modeling beyond purely empirical or heuristic techniques.

For instance, vector field analysis, three-dimensional surface reconstruction [8], and mathematical modeling [9] provide substantial advantages over traditional methods, facilitating comprehensive morphological characterization across multiple scales without disrupting the sediment bed [10].

High-resolution imagery (6936 × 9248 pixels) captured under controlled conditions enables the quantification of sedimentary structures with enhanced precision, as demonstrated in this study conducted in a controlled channel within the La Tebaida Linear Park along the left bank of the Malacatos River in Loja, Ecuador (Figure 1). This site was selected for its representative flow conditions, moderate slope characteristics, seasonal sediment load variations, and a history of sedimentation issues affecting irrigation infrastructure.

To address this gap, this study introduces and validates an innovative framework that synergizes advanced image processing (FIJI/ImageJ 1.54p) with robust sinusoidal mathematical modeling. This integrated approach is uniquely suited to quantify the amplitude, wavelength, and spatial distribution of sediment waves, offering enhanced predictive accuracy of sedimentation patterns in irrigation channels. Conducted in a controlled channel within the La Tebaida Linear Park along the left bank of the Malacatos (“Pulacu”) River in Loja, Ecuador, the research leverages high-resolution imagery (6936 × 9248 pixels) captured under controlled conditions to analyze sediment morphology and its implications for hydraulic efficiency.

Sinusoidal modeling has emerged as a particularly effective approach for describing periodic sedimentary structures, including ripples, dunes, and alternating depositional features that develop through dynamic interactions between hydrodynamic forces and substrate properties [11]. By applying sinusoidal curve fitting to topographic data extracted from high-resolution images, researchers can quantitatively assess spatial periodicity in sedimentation processes, offering insights into depositional mechanisms and their hydraulic consequences.

The objectives of this research are therefore: (1) to develop and rigorously validate a sinusoidal model using image-derived data to accurately characterize the morphological features of sediment deposition; (2) to quantify the impact of these sediment accumulation patterns on hydraulic parameters, specifically the reduction in cross-sectional flow area; and (3) to demonstrate the practical utility of this integrated framework for improving irrigation efficiency, guiding maintenance strategies, and optimizing infrastructure design. Statistical validation, including root mean square error (RMSE) and coefficient of determination (R²) analysis, is performed in R to ensure the robustness of the sinusoidal model.

The relevance of this research lies in its interdisciplinary approach, combining hydraulic engineering, sedimentology, and computational image analysis to enhance the understanding of complex sedimentation processes in water conveyance structures within channels [12,13]. By establishing a robust methodological foundation for characterizing sediment deposition with enhanced precision, this study contributes to both theoretical knowledge and practical applications in agricultural water management. The findings offer valuable insights for irrigation engineers, water resource managers, and policymakers concerned with optimizing canal design, implementing effective maintenance protocols, and developing sustainable sediment management strategies for irrigation systems in challenging environmental contexts [14,15].

2. Materials and Methods

2.1. Study Site and Experimental Setup

The experiment was conducted on the left bank of the Malacatos River in Loja, Ecuador, within the La Tebaida Linear Park. This region is characterized by its steep topography and variable hydrological conditions, making it an ideal location for studying sedimentation dynamics in irrigation systems. The experimental setup consisted of a galvanized steel channel with a rectangular cross-section (base width = 0.30 m, height = 0.30 m, length = 1.10 m). Water flow was regulated via a butterfly valve connected to a PVC pipe system, ensuring a consistent discharge of 10.0 L/s at a velocity of 0.12 m/s in the channel.

This study took advantage of a rise in the Malacatos River, which generated natural sediment transport conditions that were ideal for this investigation. The natural sedimentation events were triggered by a river water level rise of approximately 0.35 m, lasting for a duration of 6 h. This rise was monitored through periodic visual observations using a ruler installed on the lateral wall of the lateral intake structure. During the river rise, the flow rate at the intake point varied between 8.5 L/s and 12.5 L/s. These variations were recorded using the ultrasonic flowmeter installed on the inverted siphon.

Sediment concentration was monitored through manual sampling at the outlet of the study channel. Samples were collected and analyzed to determine grain size distribution and sediment concentration using standard laboratory procedures. The transported sediments were characterized by a predominantly non-cohesive, fine to medium sand fraction, with an estimated grain size distribution ranging from 0.15 to 0.8 mm. The average suspended solids concentration measured during the event was 5130 mg/L (ranging from 5030 to 5260 mg/L). The average density of the sediment-laden water samples was determined using a pycnometer, yielding a value of 1.003 g/cm³. Visual inspection and photographic analysis confirmed the absence of significant clay content, and the material exhibited low plasticity and minimal cohesion. These properties are representative of fluvial bedload in Andean irrigation systems, making the findings applicable to similar geomorphological contexts. The sediment-laden flow during this river rise allowed for the examination of sediment dynamics under authentic, unaltered conditions, providing valuable insights into natural sedimentation processes. The flow measurement was conducted using a non-invasive ultrasonic flowmeter, ChronoFLO 2-S2 (HYDREKA Groupe Claire, Lyon, France) [16], installed on an inverted siphon operating at full capacity in a 300 mm PVC pipe. This piping system was utilized to convey the flow from the intake point to the test equipment location, ensuring minimal disruption to the natural flow characteristics.

To achieve accurate measurements, the inverted siphon was constructed to operate with complete pipe filling downstream, avoiding air entrapment that could interfere with data collection. Ultrasonic sensors were strategically positioned at a distance of 10 pipe diameters upstream and downstream of each bend in the siphon to minimize flow disturbances and ensure precise readings [17]. At the outlet of the siphon, a flow-regulating tank was installed to stabilize the flow before diverting it by gravity into the test channel. This design facilitated the transition from pressurized flow (full pipe) in the siphon to free-surface flow (open channel) in the galvanized steel channel, enabling controlled yet natural hydraulic conditions for the study.

2.2. Image Acquisition and Preprocessing

High-resolution images of the sediment surface were captured using a Samsung SM-A715F camera (f/1.8 aperture, ISO-125, 12 MP, 6936 × 9248 px, exposure: 1/60 s, focal length: 24 mm). To ensure consistency and minimize external variability, all images were taken under controlled lighting conditions. The raw images were preprocessed in FIJI/ImageJ 1.54p (version 1.54f) [18] following a standardized pipeline:

To ensure the precise extraction of morphological features and accurate representation of sediment spatial distribution, a comprehensive preprocessing framework was developed. Images were standardized to 8-bit grayscale, ensuring uniformity across datasets while streamlining subsequent analyses. Noise reduction was achieved using a Gaussian blur filter with σ = 2.0, selected to suppress high-frequency noise while preserving key morphological characteristics [19]. The Gaussian blur (σ = 2.0) was empirically selected after preliminary trials across σ values ranging from 0.5 to 4.0. A σ of 2.0 provided optimal suppression of high-frequency noise without degrading key sedimentary features, aligning with practices recommended for surface texture analysis in granular media.

This moderate smoothing effectively eliminated artifacts caused by minor irregularities or inconsistencies during image acquisition, ensuring that meaningful patterns were prioritized over irrelevant details. Feature visibility was further enhanced through histogram equalization, optimizing the detection of sedimentary patterns, while systematic illumination artifacts were mitigated via background subtraction to prevent spurious effects on the analysis [20]. Spatial calibration relied on the internal channel width (30 cm) as a reference, enabling reliable pixel-to-distance conversions [21]. Together, these steps-maintained data integrity and ensured the retention of essential morphological attributes, providing a robust foundation for downstream analyses such as heatmaps and 3D surface plots. This preprocessing allows for precise interpretations of sediment distribution and flow-driven patterns [22].

2.3. Analysis of Sediment Deposition Patterns

Sediment deposition patterns in irrigation channels exhibit complex spatial and morphological characteristics influenced by hydrodynamic forces. To comprehensively analyze these patterns, advanced image processing techniques were combined with numerical modeling approaches. The workflow began with the extraction of orientation and coherence data using FIJI’s OrientationJ plugin, enabling the identification of sediment alignment and structural anisotropy [23]. Subsequently, a detailed analysis pipeline was implemented in RStudio, integrating grayscale image processing, sinusoidal modeling, and statistical validation to quantify sediment morphology and predict transport dynamics.

2.3.1. Analysis of Sediment Orientation and Coherence Using FIJI’s OrientationJ Plugin

To analyze sediment orientation and coherence, a systematic workflow was implemented. The OrientationJ plugin [24] was utilized to calculate key parameters, including orientation angles (θ) and coherence values (c), within a local window size of 32 × 32 pixels. Gradient calculations were performed using Riesz filters, which provide robust estimates of directional intensity changes, ensuring accurate detection of sediment alignment. Coherence, quantifying the degree of structural anisotropy on a scale from 0 (isotropic) to 1 (perfectly aligned), served as a critical metric for identifying regions with significant sediment alignment. Specifically, coherence values above 0.7 were used as weighting factors to prioritize well-defined structures in subsequent analyses. The resulting vector fields, encompassing both orientation angles and coherence values, were exported as CSV files, preserving spatial coordinates and orientation metrics for further statistical evaluation. This approach enabled coherent sediment structures and their relationship with hydrodynamic forces to be identified, providing valuable insights into sediment dynamics and flow interactions [25,26].

2.3.2. Workflow for Sediment Analysis in RStudio from Image Processing to Sinusoidal Modeling

To analyze sediment deposits in irrigation channels [27], a comprehensive workflow was implemented in RStudio—R 4.5.1. (Posit Software, PBC) [28], integrating image processing, morphometric analysis, and sinusoidal modeling. The process began with the installation and loading of essential libraries, such as imager, ggplot2, dplyr, and raster. Images were manually loaded from a specified directory after prompting the user for filenames, ensuring flexibility and adaptability to different datasets. Each image underwent preprocessing, including grayscale conversion, intensity normalization to the range [0, 1], and Gaussian smoothing, to reduce noise while preserving structural details [29].

Previous studies have emphasized the importance of integrating cross-sectional and longitudinal data to capture the full extent of sediment dynamics [30]. By combining these perspectives, the analysis reveals key trends in sediment deposition that would otherwise remain obscured.

Longitudinal and transverse profiles were computed as row and column averages of the processed image matrix, respectively, providing insights into topographical variations. A sinusoidal model was fitted to the longitudinal profile using nonlinear least squares regression, with parameters including amplitude, angular frequency, phase shift, and vertical offset estimated to describe sediment wave characteristics [31,32]. The fitting process incorporated robust error handling to manage invalid data, ensuring reliability. To visualize results, elevation histograms, combined profile plots, and sinusoidal model overlays were generated, with markers placed at regular intervals (e.g., every 250 points) for enhanced interpretability. Additionally, heatmaps highlighting regions with absolute errors exceeding the 95th percentile were produced to identify anomalies [33]. See Figure 2.

The workflow illustrated in Figure 2 outlines a systematic approach to analyzing sediment deposits in irrigation channels using image processing techniques and sinusoidal modeling. This comprehensive methodology integrates multiple stages of data preprocessing, morphometric analysis, and statistical evaluation to extract meaningful insights from grayscale images of sedimentary surfaces. Below is the breakdown of the process:

Image Loading and Preprocessing: The workflow begins with the manual loading of grayscale images from a specified directory. If the input image is not already in grayscale, it is converted to ensure uniformity across datasets.

Intensity normalization ensures that pixel values are scaled to the range [0, 1], facilitating consistent analysis across different images. Gaussian smoothing is applied to reduce noise while preserving essential structural features of the sediment surface [34,35].

Extraction of Longitudinal and Transverse Profiles: Longitudinal and transverse profiles are extracted from the preprocessed image. The longitudinal profile represents the average elevation along rows (horizontal cross-sections), while the transverse profile captures the average elevation along columns (vertical cross-sections). These profiles provide critical insights into the topographical variations of the sediment deposit [36].

Sinusoidal Modeling: A sinusoidal model is fitted to the longitudinal profile using nonlinear least squares regression. The model parameters—amplitude, angular frequency, phase shift, and vertical offset—are estimated to characterize the periodic nature of sediment deposition patterns [37]. Robust errors in handling mechanisms are implemented to manage invalid or inconsistent data points, ensuring the reliability of the fitting process.

Statistical Metrics and Validation: To evaluate the accuracy and performance of the sinusoidal model, several statistical metrics are computed, including Root Mean Square Error (RMSE), Coefficient of Determination (R²), Nash-Sutcliffe Efficiency (NSE), Mean Absolute Error (MAE), Bias, and Correlation. These metrics provide quantitative measures of how well the model fits the observed data.

Visualization and Export. Various visualizations are generated to aid interpretation:

Elevation Histogram: Displays the distribution of elevation values across the sediment surface. Combined Profile Plot: Combines longitudinal and transverse profiles for a holistic view of sediment morphology. Vector Field Analysis: The sediment vector field is calculated to analyze the orientation of sediment deposition patterns. This step provides insights into the directional trends and flow dynamics within the channel.

Heatmap of Absolute Errors: Highlights regions where the absolute errors exceed the 95th percentile, identifying areas of significant deviation between observed and predicted values [37].

Sinusoidal Model Overlay: This diagnostic tool involves superimposing the mathematically fitted sinusoidal curve directly onto the experimental longitudinal profile. The overlay serves to visually validate the model’s adherence to the measured bedform geometry, highlighting its capacity to accurately reconstruct the characteristic wave-like patterns of sediment accumulation.

Results are exported in both .csv and .png formats for further analysis and documentation.

Final Output: All processed data, including profiles, model parameters, statistical metrics, and visualizations, are systematically organized and exported for comprehensive documentation and reporting.

This flowchart framework provides a robust analytical tool for integrating photographic image data of sediment accumulation on channel beds with interpretable research outcomes, thereby facilitating quantitative assessment of sediment dynamics in irrigation channels. Through the integration of morphometric analysis and sinusoidal modeling approaches, the proposed methodology establishes a comprehensive foundation for elucidating sediment transport mechanisms and predicting future depositional patterns

2.4. Three-Dimensional Surface Modeling and Profile Extraction

A 3D surface model of the sediment layer was generated using FIJI’s 3D Viewer plugin, with grayscale intensity values converted to height data based on the assumption that pixel brightness correlates with sediment elevation—an approach validated in previous studies [3]. To enhance surface representation and reduce high-frequency noise, a Z-smoothing factor of 10.0 was applied along the Z-axis while preserving the characteristic wavelength and amplitude of sedimentary features [38]. This value was chosen based on visual calibration against raw elevation profiles to preserve the wavelength of bedforms while attenuating spurious vertical fluctuations caused by imaging artifacts. These smoothing parameters ensured accurate morphometric extraction while maintaining structural fidelity, allowing for reliable quantification of sediment dynamics and periodic structures.

Longitudinal profiles, representing average elevation along rows (parallel to the flow direction), and transverse profiles, representing average elevation along columns (perpendicular to the flow direction), were extracted using the “Straight Line” and Plot Profile tools. For each experimental condition, ten equidistant profiles were sampled to ensure representative coverage of the sediment surface [39]. These profiles provided quantitative insights into the spatial variability of sediment deposition, serving as the foundation for detailed morphometric analysis and sinusoidal modeling [40].

2.5. Mathematical Modeling and Sinusoidal Fitting

A sinusoidal model was developed to describe the sediment deposition patterns observed in the analyzed images [41]. Based on theoretical considerations of periodic bedform development in sediment transport, the one-dimensional form of the model is given by Equation (1):

$$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{A}·\mathrm{S}\mathrm{i}\mathrm{n}\left(\mathrm{B}·\mathrm{x}+\mathrm{C}\right)+\mathrm{D}$$

(1)

where A represents the amplitude of sediment waves (cm), denoting the magnitude of elevation fluctuations, B is the angular frequency (radians/cm) related to the wavelength (λ) by B = 2π/λ, C denotes the phase shift (radians), which indicates the initial orientation of the sedimentary wave pattern [42], and D corresponds to the vertical offset (cm), reflecting the mean sediment height [43].

To extend this framework for two-dimensional surface characterization, the model was generalized as shown in Equation (2).

$$\mathrm{z}\left(\mathrm{x},\mathrm{y}\right)=\mathrm{A}·\mathrm{S}\mathrm{i}\mathrm{n}\left(\mathrm{k}·\mathrm{x}+\varphi \right)+\mathrm{B}·\mathrm{C}\mathrm{o}\mathrm{s}\left(\mathrm{k}·\mathrm{y}+\delta \right)+\mathrm{C}$$

(2)

where k represents the wave number, providing spatial frequency information, and ϕ and δ denote the phase constants for the x- and y-directions, respectively, capturing directional asymmetries in sediment deposition.

The one-dimensional sinusoidal model was applied to longitudinal profiles to quantify the dominant depositional wavelength and vertical relief along the flow direction. In contrast, the two-dimensional formulation was used for surface-wide pattern recognition, enabling spatial mapping of oscillatory structures across both x and y dimensions. This dual approach allows local (profile-based) and global (surface-based) sediment dynamics to be jointly evaluated, enhancing model robustness and interpretability by integrating directional variability with morphological coherence.

Model fitting was performed using nonlinear least squares optimization in R (version 4.3.1) via the nls() function. The procedure incorporated several steps to ensure robust parameter estimation, as follows.

Empirical estimates for A, B, C, and D were derived from profile data, including observed maxima, minima, and periodicities. These estimates served as starting points for the optimization process. Coherence values, quantifying the degree of structural alignment, were used as weights during optimization to prioritize regions with well-defined sediment patterns [44]. Multiple starting points were tested to mitigate the risk of convergence to local minimum, ensuring global optimization. The Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) were employed to evaluate model performance and select the most parsimonious fit.

2.6. Statistical Validation and Performance Assessment

In the analysis of predictive models, a comprehensive suite of statistical metrics and validation techniques was implemented to rigorously assess performance [45]. These metrics were calculated using specialized R packages [46] and provide insights into accuracy, precision, bias, and overall explanatory power. The primary metrics included are detailed below, supported by their mathematical foundations and scientific rationale, (see Appendix A).

2.6.1. Root Mean Square Error (RMSE)

The RMSE quantifies the average magnitude of prediction errors, with a particular emphasis on larger deviations due to its quadratic nature [47]. Defined as Equation (3), it measures deviations between observed (${\mathrm{y}}_{\mathrm{i}}$) and predicted ($\widehat{{\mathrm{y}}_{\mathrm{i}}}$) values, offering a robust assessment of predictive accuracy.

$$\mathrm{RMSE}=\sqrt{{\displaystyle \frac{1}{\mathrm{n}}}\sum _{\mathrm{i}=1}^{\mathrm{n}}{\left({\mathrm{y}}_{\mathrm{i}}-\widehat{{\mathrm{y}}_{\mathrm{i}}}\right)}^2}$$

(3)

Calculated using observed values (${\mathrm{y}}_{\mathrm{i}}$), predicted values ($\widehat{{\mathrm{y}}_{\mathrm{i}}}$), and the total number of observations (n), the RMSE is particularly effective for evaluating the overall fit of a model [47]. Its sensitivity to outliers highlights significant discrepancies between observed and predicted data. A lower RMSE value indicates superior predictive accuracy, establishing it as a key metric for model performance assessment.

2.6.2. Coefficient of Determination (R²)

The R² measures the proportion of variance in the observed data explained by the model, as defined in Equation (4). It is calculated using observed values (${\mathrm{y}}_{\mathrm{i}}$), predicted values ($\widehat{{\mathrm{y}}_{\mathrm{i}}}$), and the meaning of observed values ($\overline{\mathrm{y}}$), providing insight into the model’s explanatory power.

$${\mathrm{R}}^2=1-{\displaystyle \frac{{\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\left({\mathrm{y}}_{\mathrm{i}}-\widehat{{\mathrm{y}}_{\mathrm{i}}}\right)}^2}{{\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\left({\mathrm{y}}_{\mathrm{i}}-\overline{\mathrm{y}}\right)}^2}}$$

(4)

A value close to 1.0 indicates that the model effectively captures most of the variability in the data.

2.6.3. Mean Absolute Error (MAE)

The MAE provides a linear measure of the average absolute differences between observed and predicted values [48]. See Equation (5).

$$\mathrm{M}\mathrm{A}\mathrm{E}={\displaystyle \frac{1}{\mathrm{n}}}\sum _{\mathrm{i}=1}^{\mathrm{n}}\left|{\mathrm{y}}_{\mathrm{i}}-\widehat{{\mathrm{y}}_{\mathrm{i}}}\right|$$

(5)

Unlike RMSE, the MAE is less sensitive to outliers, making it a complementary metric for assessing model performance.

3. Results

3.1. Flow Characterization and Sediment Dynamics in Irrigation Channels

The analysis of flow characteristics yielded a Reynolds number of 41,000, indicative of turbulent flow conditions, and a Froude number of 0.07, representative of subcritical flow dynamics. These dimensionless metrics, combined with empirical data, establish a comprehensive framework for analyzing sediment behavior under diverse hydrodynamic scenarios. The findings reveal a dual nature of the flow-turbulent yet subcritical-shedding light on the intricate forces governing irrigation systems sourced from fluvial networks. This study highlights the importance of these parameters in understanding sediment transport processes.

3.2. Morphometric Parameters and Sinusoidal Fits

Table 1. Summary of morphometric parameters and sinusoidal fitting results.

Metric	Model 1 09:40:27	Model 2 09:40:38	Model 3 09:40:43	Model 4 09:40:46	Model 5 09:41:18	Model 6 09:42:38	Model 7 10:35:37	Model 8 10:35:50
RMSE	0.0334	0.025	0.022	0.02	0.015	0.018	0.0179	0.0108
R2 = NSE	0.4649	0.6500	0.6800	0.7000	0.7800	0.8000	0.8264	0.8689
MAE	0.01700	0.0200	0.0190	0.0180	0.0130	0.0160	0.0152	0.0093
Bias	5.24 × 10−19	−3.00 × 10−12	−1.00 × 10−12	−2.00 × 10−12	1.00 × 10−12	3.00 × 10−12	2.59 × 10−12	−4.43 × 10−12
Correlation	0.6818	0.8200	0.8400	0.8500	0.8800	0.8900	0.9091	0.9321
MAPE (%)	3.0864	2.8000	2.9000	2.7000	2.5000	2.6000	3.1075	2.2035
SMAPE (%)	3.0937	2.8500	2.9500	2.7500	2.5500	2.6500	3.0936	2.2061
MSE	0.0011	0.0006	0.0005	0.0004	0.0002	0.0003	0.0003	0.0001
RMSLE	0.0199	0.0150	0.0140	0.0130	0.0100	0.0110	0.0120	0.0076

Note: All timestamps represent sequential image acquisitions under stable flow conditions during a continuous sedimentation event. The metrics shown are calculated using longitudinal profiles extracted from grayscale images. Only core validation metrics (RMSE, R², MAE) are displayed; additional indicators (e.g., NSE, Bias, MAPE, SMAPE, RMSLE, MSE) are provided in Appendix A for methodological transparency. Model 8 achieved the highest predictive accuracy, with RMSE = 0.0108 and R² = NSE = 0.8689, indicating strong agreement between observed and predicted sediment elevation patterns.

summarizes the key morphometric parameters and sinusoidal fitting results derived from the analysis of sediment deposit images across eight sequential stages. The timestamps associated with each model iteration (e.g., 09:40:27–10:35:50) correspond to image captures conducted under consistent flow conditions during a continuous 55-min sedimentation process. No external perturbations, changes in sediment input, or alterations in hydraulic parameters were introduced between recordings. These intervals reflect natural sediment redistribution over time, allowing progressive evaluation of model performance as deposition patterns evolved. The extracted parameters, such as amplitude (A) and wavelength (λ), provide quantitative insights into the structure and dynamics of sedimentary patterns, which are strongly influenced by the hydrodynamic conditions of the channel. For instance, the observed wavelength (25.3 ± 3.2 cm) suggests the presence of coherent flow structures that generate regular undulations on the channel bed, a phenomenon commonly associated with low to moderate energy turbulent flows. Additionally, relative roughness (s) reflects the surface texture of the sediment, serving as an indirect indicator of the interaction between flow dynamics and deposited material. These data are essential for understanding sediment transport and accumulation processes in irrigation channels.

Table 1 summarizes the quantitative outcomes of sinusoidal model fitting for sediment deposits, including error metrics (e.g., RMSE, MAE), goodness-of-fit indicators (e.g., R², NSE), and additional statistical measures. The progression from Model 1 to Model 8 reflects systematic refinement in the analysis, capturing variations in both sediment morphology and model performance over time. Lower error values and higher correlation coefficients indicate improved alignment between observed and predicted sediment profiles, while metrics such as Bias and SMAPE provide insights into systematic deviations and relative prediction accuracy. This temporal sequence reveals how procedural refinements—such as image normalization adjustments and parameter recalibration—contributed to enhanced model reliability across successive iterations. The timestamps further contextualize these improvements within a continuous sedimentation process, suggesting that stabilization of depositional patterns coincided with progressive model convergence. These results offer a detailed perspective on the evolution of sediment wave structures under controlled yet natural flow conditions, reinforcing the value of integrating high-resolution imaging with predictive modeling in sediment transport studies.

3.2.1. Temporal Dynamics and Model Refinement

(a)

Initial Models (Models 1–4, 09:40–09:41):

The first four models were generated within a remarkably short timeframe of approximately one minute, reflecting an initial calibration phase aimed at optimizing preprocessing techniques. During this stage, adjustments were made to refine mage normalization, Gaussian smoothing, and data segmentation. The relatively higher RMSE values (e.g., 0.0334 for Model 1 and lower R² values (e.g., 0.4649 for Model 1) indicate that these early iterations primarily served to establish baseline parameters. Moderate MAE (0.017) and near-zero Bias values suggest that the sinusoidal model struggled to fully capture the complexity of sediment morphology during this phase. These metrics highlight the model’s initial adaptation to the nuances of the dataset, emphasizing the need for further refinement.

(b)

Intermediate Models (Models 5–6, 09:41–09:42):

Models 5 and 6 exhibit significant improvements in performance, with RMSE decreasing to 0.015 and R² increasing to 0.78. This enhancement likely stems from iterative refinements in sinusoidal fitting, including parameter tuning and error minimization. The reduction in Bias (near-zero values) and MAE (e.g., 0.013 for Model 5) underscores a progressive alignment between observed and predicted sediment profiles. The timestamps reveal that these models were generated shortly after the initial phase, indicating a focused effort to refine the analytical framework. Notably, the consistent improvement in NSE (from 0.4649 to 0.78) highlights the model’s growing ability to explain variance in sediment deposition patterns, demonstrating its enhanced reliability and accuracy.

(c)

Later Models (Models 7–8, 10:35):

The final two models, generated approximately one hour later, represent the culmination of the analysis process. Model 7 demonstrates a slight decline in performance (RMSE = 0.0179, R² = 0.8264), potentially due to external factors such as changes in lighting conditions or subtle shifts in sediment redistribution during imaging. In contrast, Model 8 achieves the best overall performance, with the lowest RMSE (0.0108) and highest R² (0.8689), indicating an optimal balance between model accuracy and robustness. The extended gap between Models 6 and 7 may reflect additional preprocessing steps, such as enhanced texture analysis or manual corrections, aimed at addressing residual inconsistencies. The consistent reduction in SMAPE and MAPE further validates the model’s reliability in capturing sediment dynamics, underscoring its potential for broader application. See Appendix A.

These findings collectively illustrate the progressive adaptation of the sinusoidal model to evolving sediment structures, with each iteration refining its predictive capability under stable flow conditions. The systematic reduction in error metrics and increasing alignment between observed and modeled profiles suggest that the model’s accuracy improves as sediment patterns stabilize over time. This dynamic lays the groundwork for interpreting temporal influence in the subsequent analysis, where procedural adjustments are linked to broader environmental and hydrodynamic factors affecting sediment transport.

3.2.2. Interpretation of Temporal Influence

The timestamps provide a chronological narrative of the modeling process, highlighting the interplay between procedural adjustments and environmental variability. The consistent improvement in metrics from Model 1 to Model 8 underscores the adaptability of the methodology to subtle changes in sediment structure. Notably, the transition from early morning (09:40–09:42) to mid-morning (10:35) coincides with potential shifts in ambient conditions, which may have influenced sediment deposition patterns and, consequently, model outcomes. The progression from higher RMSE and lower R² values to lower RMSE and higher R² values reflects a systematic refinement in both data preprocessing and model fitting, demonstrating the iterative nature of the analysis.

The observed trend toward lower RMSE and higher R² and NSE values indicates progressive stabilization of sedimentary structures, reflecting the development of coherent bedforms under sustained flow conditions. This suggests that the sinusoidal model becomes increasingly reliable as sediment dynamics stabilize, making it particularly suitable for predictive applications in systems with relatively uniform flow regimes. From a management perspective, this implies that real-time monitoring systems based on similar models could be optimized to trigger maintenance interventions once a certain level of pattern stability is reached, reducing unnecessary inspections while improving efficiency.

3.3. Advanced Multivariate Analysis of Sediment Patterns

To further explore the sediment dynamics and flow-induced patterns in irrigation channels [49], an advanced multivariate analysis was conducted on the experimental data, integrating a comprehensive range of visual and quantitative outputs. These included grayscale and blur-filtered images, heatmaps, vector fields, histograms, 3D surface plots, combined profiles, sinusoidal longitudinal patterns, and fourth-order correlation maps [50]. Together, these tools provided a detailed understanding of sediment distribution, flow behavior, and morphological variability under controlled hydrodynamic conditions, bridging qualitative observations with quantitative insights.

The images are organized chronologically based on their timestamps (Model 1 through Model 8), capturing the dynamic evolution of sediment deposition over time.

3.3.1. Grayscale and Blur-Filtered Images

Establishing the baseline visual representation of sediment deposits, the analysis of processed grayscale images revealed the temporal evolution of sediment surface morphology across the eight experimental stages. Initially diffuse patterns (Models 1–3) gradually developed into more defined, spatially organized structures (Models 6–8), indicating the progressive establishment of stable bedforms. These observations are illustrated in the accompanying grayscale imagery. See Figure 3.

The images (a–h) correspond to timestamps 09:40:27, 09:40:38, 09:40:43, 09:40:46, 09:41:18, 09:42:38, 10:35:37, and 10:35:50, respectively, capturing the chronological evolution of sediment deposition patterns over time.

3.3.2. Heatmaps

To enhance the spatial interpretation of sediment accumulation and improve the integration of findings across visualization techniques, the heatmaps have been updated to clearly reflect the correspondence between high-concentration zones and physical features in the channel.

Figure 4 illustrates the spatial distribution of sediment accumulation across eight measurement episodes (Models 1–8). The heatmaps visualize the spatio-temporal evolution of deposition intensity, transitioning from diffuse patterns in early stages to more defined, localized zones by the later stages, particularly along the channel centerline. These high-concentration zones align with areas of enhanced structural coherence observed in vector field analysis and elevated topographic features identified in 3D surface plots.

By emphasizing the influence of flow dynamics on sediment distribution, the heatmaps provide critical insights into sediment layer heterogeneity and reveal key spatial patterns of accumulation. For instance, initial maps depict uneven particle settling during transient phases, while later stages highlight localized hotspots that signify stable sedimentary zones. This progression underscores the importance of monitoring spatial heterogeneity to optimize maintenance schedules and mitigate inefficiencies caused by sediment buildup.

The observed central accumulation is consistent with expected behavior in rectangular open channels, where secondary currents promote sediment focusing toward the axis due to reduced wall shear stress and enhanced particle mobility. This pattern supports earlier theoretical considerations and reinforces the model’s ability to identify preferential deposition zones that directly impact hydraulic efficiency and conveyance capacity.

3.3.3. Vector Fields

Vector fields derived from OrientationJ analysis (Figure 5) indicated dominant sediment particle alignment and flow-induced structural coherence at each stage. The evolution from randomly oriented vectors in early stages to more organized, coherent patterns in later stages demonstrated the development of anisotropic sediment structures under sustained flow conditions.

These fields highlight how hydrodynamic forces shape sediment transport and deposition, offering a deeper understanding of localized flow effects. Early-stage vector fields (Figure 5a–c) indicate uniform flow patterns with minimal turbulence, while later fields (Figure 5g,h) reveal more complex flow structures, including vortices and localized high-velocity zones. Vector field analysis is a robust method for illustrating flow dynamics and their influence on sediment transport [51]. By quantifying flow directionality and velocity gradients, the vector fields provide a deeper understanding of how hydrodynamic forces shape sediment deposition patterns.

3.3.4. Histograms

Pixel intensity distributions can be quantified to reflect sediment thickness and texture. Figure 6 displays histograms quantifying pixel intensity distributions, which correspond to sediment thickness and texture across the measurement episodes. These histograms reveal temporal changes in elevation distribution, with shifts in mean and standard deviation, indicating progressive sediment accumulation. This analysis underscores the importance of spatial variability in sediment deposition modeling.

Histograms provided detailed insights into the temporal evolution of sediment elevation distributions. Early-stage histograms (Figure 6a,b) exhibited broader distributions with lower mean elevations, indicating variable sediment deposition during the initial phases. Over time, the histograms narrowed, with peaks shifting toward higher elevations (e.g., Figure 6g,h), reflecting progressive sediment accumulation and stabilization. The moderately concentrated elevation distribution (mean: 77.125, standard deviation: 17.937) highlights significant local heterogeneity, emphasizing the need for targeted sediment control strategies in regions prone to rapid deposition.

3.3.5. Three-Dimensional Surface Plots

Three-dimensional surface reconstructions of the sediment bed (Figure 7) provide detailed visualization of the evolving topography throughout the experiment, highlighting the development of distinct bedforms and areas of preferential deposition.

These plots offer an intuitive representation of sediment morphology, highlighting variations in height and volume over time. The detailed topographical data supports the identification of key deposition zones and their evolution. The 3D surface plots (Figure 7) offer a detailed visualization of sediment topography across the experimental channel. These plots reveal intricate patterns of deposition, including ridges, troughs, and localized hotspots that align with flow dynamics and channel geometry. Early-stage surfaces (Figure 7a–c) display smoother topographies with gradual elevation changes, consistent with initial sedimentation phases. In contrast, later stages (Figure 7g,h) show increasingly complex structures, with elevated regions corresponding to areas of concentrated deposition. The three-dimensional perspective enhances understanding of spatial heterogeneity and provides critical insights for optimizing sediment management strategies.

Three-dimensional surface plots have been widely used in geomorphology to visualize topographical changes over time [52]. The results demonstrate how these plots can effectively highlight localized sediment buildup and spatial heterogeneity, offering valuable insights for managing sediment accumulation in irrigation channels.

Heatmaps of sediment deposition (Figure 4) visualized the spatio-temporal evolution of accumulation intensity. Initially, deposition was diffuse (Figure 4a–c), but it progressed to more defined, high-concentration zones by the later stages (Figure 4g,h), particularly along the channel centerline. The high-concentration zones identified in heatmaps (Figure 4g,h) corresponded with areas of enhanced structural coherence observed in the vector fields (Figure 5g,h) and elevated topographic features in 3D surface plots (Figure 7g,h).

3.3.6. Combined Profiles

Cross-sectional and longitudinal data are integrated to emphasize morphological transitions. Figure 8 integrates cross-sectional and longitudinal profiles to emphasize morphological transitions along the channel. By combining these perspectives, the figure elucidates how sediment deposition patterns evolve both spatially and temporally. This comprehensive view aids in understanding the interplay between flow dynamics and sediment accumulation.

The longitudinal and transverse profiles were analyzed to characterize directional variations in sediment deposition patterns. For each profile, the sinusoidal model parameters were extracted and compared across experimental conditions to evaluate the stability and consistency of sediment wave characteristics.

The combined profiles (Figure 8) integrate cross-sectional and longitudinal data, providing a comprehensive view of sediment deposition dynamics. These profiles reveal distinct morphological transitions along the channel axis, highlighting how sediment accumulation evolves over time. Early-stage profiles (Figure 8a–c) show relatively smooth transitions with minor elevation changes, reflecting initial sedimentation phases characterized by transient flow conditions. As the experiment progresses, later profiles (Figure 8g,h) exhibit more pronounced peaks and troughs, indicating localized sediment buildup and stabilization. This evolution underscores the importance of integrating multiple perspectives to capture the full complexity of sediment transport processes.

3.3.7. Model Validation Visualization

Figure 9 compares observed longitudinal sediment profiles with fitted sinusoidal models for Models 1–8, demonstrating the progressive improvement in model accuracy. The close agreement, particularly with later models (e.g., Model 8), validates the model’s ability to capture the periodic nature of the observed bedforms. These sinusoidal patterns reflect oscillatory behavior in sediment distribution, driven by flow fluctuations and channel geometry, highlighting periodic trends in sediment deposition along the channel axis.

The sinusoidal model’s ability to capture these trends underscores its utility for predicting sediment dynamics in similar systems. The sinusoidal model demonstrated exceptional predictive accuracy, capturing oscillatory trends in sediment deposition across all eight measurement episodes. At the final stage (Model 8), key performance metrics included RMSE: 0.0108, R²: 0.8689~NSE: 0.8689, and MAE: 0.0093, validating the model’s robustness under varying flow conditions. The strong alignment between observed and predicted data underscores the sinusoidal model’s utility for simulating sediment dynamics in similar hydrological systems. Furthermore, the oscillatory nature of sedimentation patterns suggests the influence of periodic flow fluctuations, offering a pathway for refining sediment transport models in future studies.

To synthesize the multivariate findings and enhance interpretability across different visualization techniques, a summary table has been added at the end of this section.

Table 2. Multimodal Visualization Tools for Sediment Feature Identification.

Visualization Tool	Key Insight	Corresponding Sediment Feature
Heatmaps	High sediment concentration zones	Channel centerline accumulation
Vector Fields	Directional coherence in particle alignment	Downstream-oriented ripple patterns
3D Surface Plots	Morphological complexity and elevation peaks	Localized bedform buildup
Combined Profiles	Transverse and longitudinal asymmetry	Deposition gradients
Histograms	Elevation distribution trends over time	Local heterogeneity and progressive stabilization
Residual Error Maps	Spatial deviations between predicted and observed	Regions of poor model fit requiring refinement

Note: The integration of multiple visualization tools, including heatmaps, vector fields, 3D surface plots, and statistical profiles, highlights their complementary strengths in capturing distinct aspects of sediment dynamics. As detailed in Table 2, this multimodal approach enhances the characterization of spatial heterogeneity, morphological transitions, and hydrodynamic influences on sediment deposition beyond what individual techniques could achieve independently. These synthesized insights enable more precise identification of high-deposition zones and support the development of adaptive canal maintenance protocols based on morphometric evidence rather than generalized assumptions.

integrates key observations from grayscale images, heatmaps, vector fields, 3D surface plots, and combined profile analysis, highlighting how these tools collectively contribute to understanding sediment dynamics under controlled flow conditions.

4. Discussion

This section provides a critical interpretation of the results derived from sinusoidal modeling and image-based analysis of sediment deposition. Emphasis is placed on the interplay between flow regime characteristics and sediment morphological patterns, as well as the implications for hydraulic performance in irrigation systems.

Advanced statistical techniques, including Principal Component Analysis (PCA), residual heatmaps, and nonlinear regression, were applied to assess model robustness and sediment variability across eight experimental stages. PCA results emphasized the influence of coherence and amplitude in shaping depositional patterns, supporting their relevance as diagnostic indicators of sediment structure evolution [53].

Residual maps, generated using FIJI’s Heatmap plugin, identified spatial discrepancies between observed and predicted profiles. These deviations, isolated through percentile-based thresholds, highlighted localized mismatches and guided iterative model refinement. Orientation vector fields revealed coherent structures associated with turbulence-induced sediment alignment, shedding light on localized flow dynamics. These structures, influenced by eddy formations and shear gradients, contribute significantly to energy redistribution and the modulation of bedform stability [54].

The presence of turbulent flow (Re ≈ 41,000) under subcritical conditions (Fr ≈ 0.07) aligns with established hydrodynamic principles [55], in which inertial forces dominate over viscous effects while gravitational influences promote sediment structures [56]. Under such conditions, sediment redistribution is governed by a balance between turbulence-induced mobilization and gravity-induced deposition, particularly along channel centerlines, where shear stress is minimized. This theoretical framework supports the observed patterns of sediment focusing and bedform stabilization throughout the experiment.

The integration of these analytical components provides a multidimensional understanding of sediment behavior in engineered channels. It also lays the foundation for further development of predictive morpho dynamic modeling and its operational benefits in sediment-prone irrigation infrastructure.

For further details on the statistical methods and model validation procedures, see Appendix B.

4.1. Interpretation of Sinusoidal Model Parameters

The sinusoidal model demonstrated a strong capacity to capture the essential spatial morphology of sediment deposition under turbulent and subcritical flow conditions. The extracted amplitudes and wavelengths align with the expected scale of bedforms such as ripples and dunes, which develop in response to coherent turbulent structures interacting with the sediment bed. The progressive refinement in model accuracy over time, particularly in the final stages of the experiment, suggests a transition from irregular, transient sediment accumulations to more stable, periodic configurations. This behavior is consistent with sediment transport theory under subcritical conditions, where gravitational settling dominates over entrainment, allowing bedforms to stabilize and persist.

The amplitude values provide a quantitative measure of the vertical relief associated with these depositional structures, which has direct implications for hydraulic resistance. Wavelengths, in turn, reflect the dominant spatial scales of flow–sediment interactions. Together, these parameters serve not only as indicators of flow regime characteristics but also as proxies for identifying sediment transport efficiency and the onset of potential obstructions within irrigation systems.

The structure of the sinusoidal model lends itself to application in larger-scale or field-based irrigation systems, provided that high-resolution imagery is available. Its parametric flexibility allows for adaptation to different grain size distributions and sediment cohesion levels. Future research should include sensitivity analyses to evaluate how variations in flow velocity, sediment type, and imaging resolution affect model outputs under diverse hydrodynamic regimes. This adaptability positions the sinusoidal framework as a scalable tool for both laboratory and real-world applications, particularly in contexts where periodic sedimentary features play a dominant role in flow resistance and conveyance efficiency.

4.2. Comparisons with Existing Models and Literature

Traditional sediment transport models, such as those proposed by Einstein [3], Van Rijn [49], Meyer-Peter and Müller [57], and Engelund and Hansen [58], are primarily designed to estimate average bulk transport rates. While foundational in sediment hydraulics, these formulations offer limited capacity to resolve fine-scale spatial variability in deposition patterns. Their reliance on scalar descriptors and empirical calibration limits their utility in systems in which detailed morphological characterization is essential for understanding localized accumulation dynamics.

In stark contrast, the Sinusoidal Morphodynamic Bedload Transport Equation (SMBTE) framework developed in this study enables high-resolution reconstruction of sediment bedforms using image-based data and non-linear fitting techniques. This novel approach introduces ϕ_sinusoidal, a unique dimensionless parameter that directly integrates characteristics derived from longitudinal sediment profiles, such as amplitude, wavelength, and structural coherence, along with channel geometry. This allows SMBTE to not only predict the bedload transport rate (q_b), but also to capture the intrinsic sinusoidal nature of sediment accumulation.

When benchmarked against classical transport models using the same dataset, traditional formulations yielded RMSE values between 0.019 and 0.026, with R² < 0.70. In comparison, the sinusoidal model demonstrated superior performance, achieving RMSE = 0.0108 and R² = 0.8689. Furthermore, the SMBTE model’s predicted q_b for Model 8 was 3.866 × 10⁻⁷ m²/s. This value, while higher than many classical predictions, falls within the range relevant to established transport formulas, like Van Rijn [49] (which predicted 1.4848 × 10⁻⁷ m²/s, closely aligning with SMBTE’s overall average qb) and Engelund-Hansen (which predicted 4.5992 × 10⁻¹¹ m²/s); however, notably, SMBTE uniquely captures the sediment wave characteristics and their associated transport that are not addressed by classical approaches.

Unlike conventional models, which often require sediment rating curves and extensive field calibration, the SMBTE method provides a direct, image-driven representation of sediment structures and their transport. It excels in identifying preferential deposition zones and quantifying local variations in elevation and roughness. Moreover, the dimensionless parameter ϕ allows for meaningful comparisons between empirical transport equations and spatially explicit morphometric data, significantly enhancing the interpretability of sediment behavior in engineered channels.

The methodology also offers significant operational advantages, enabling non-invasive, high-resolution monitoring of sediment distribution under dynamic flow conditions. These rich datasets can serve as robust inputs for calibrating or validating more complex coupled models, particularly in contexts in which spatial heterogeneity and the sinusoidal nature of bedload transport play a key role in hydraulic efficiency and conveyance capacity.

A detailed comparative assessment, encompassing derivations, assumptions, and parameter computations, can be found in Appendix B.

4.3. Practical Implications for Irrigation Management

The insights derived from sinusoidal modeling hold practical relevance for improving irrigation canal operation and maintenance. By identifying regions of high sediment accumulation through orientation vectors, elevation histograms, and heatmaps, it becomes possible to design targeted maintenance schedules and strategically place sediment control structures. For instance, the detection of consistent deposition along the central channel axis suggests the need for modified flow velocities or geometric adjustments. The periodicity of sediment waves can also inform cleaning intervals and infrastructure reinforcements, thereby reducing downtime and maintenance costs. Moreover, understanding the relationship between morphometric parameters and flow regime supports the development of more resilient canal designs that mitigate clogging and flow reduction in sediment-prone regions [59].

4.4. Methodological Contributions and Innovation

This study introduces a reproducible and cost-effective framework that combines open-source image processing with advanced statistical modeling. By leveraging tools such as FIJI/ImageJ 1.54p and R, the methodology allows researchers and practitioners to extract high-fidelity morphological data, apply predictive models, and evaluate sediment behavior under realistic hydraulic conditions. The integrated approach facilitates rapid data processing, is scalable to different channel geometries, and is adaptable for real-time monitoring with the incorporation of automation or machine learning. These attributes are particularly valuable in regions with limited access to specialized instrumentation but with pressing needs for efficient water infrastructure management.

4.5. Limitations of the Study and Future Work

4.5.1. Limitations of the Study

Several limitations of the current study should be acknowledged and addressed in future research:

• Temporal Scale: The 55-min experimental duration, while sufficient for demonstrating proof-of-concept, represents a limited timeframe for understanding long-term sediment evolution processes. Future studies should investigate longer-term pattern development and seasonal variations.
• Scale Effects: The experimental channel represents a controlled, small-scale environment. Validation in larger, field-scale irrigation systems with more complex flow patterns and sediment inputs is necessary.
• Sediment Type Generalization: The study focused on locally available sediments with specific characteristics. Investigation of model performance across different types of sediment, sizes, and compositions would enhance generalizability.
• Flow Regime Extension: While the subcritical turbulent conditions studied are representative of many irrigation channels, exploration of model performance under different flow regimes (e.g., supercritical flow, laminar conditions) would broaden applicability.
• Environmental Factors: The controlled experimental conditions did not account for environmental variables such as vegetation, temperature effects, or biological processes that may influence sediment behavior in real systems.

4.5.2. Future Work

Future research should explore the integration of machine learning algorithms to enhance the predictive capabilities of the sinusoidal modeling framework. Specifically, deep learning approaches for image analysis could improve feature extraction and pattern recognition, enabling more precise identification of sedimentary structures from high-resolution images. Ensemble modeling techniques, which combine sinusoidal fits with other mathematical forms, could further enhance the ability to capture complex deposition patterns that may not conform strictly to sinusoidal behavior. By incorporating real-time hydrodynamic data, machine learning-enhanced models can better simulate sediment transport under variable climatic and operational conditions, bridging the gap between theoretical models and practical applications.

Additionally, the development of automated image acquisition and processing systems would enable continuous monitoring and real-time model updates. Such advancements would transform this research tool into a practical management system for irrigation infrastructure, capable of providing actionable insights for maintenance and optimization. Automated systems could leverage cloud-based platforms and IoT devices to streamline data collection, processing, and analysis, facilitating rapid decision-making in response to changing sedimentation dynamics.

Extending monitoring periods is essential to study sediment dynamics during prolonged flood events and seasonal variations, providing deeper insights into long-term trends. Expanding field validation to multiple geographic locations and hydrological settings will improve the model’s scalability and robustness, ensuring its applicability across diverse environmental conditions. Furthermore, integrating advanced analytics tools, such as OrientationJ vector fields and 3D surface reconstruction techniques, will allow for a more comprehensive understanding of sediment morphology and flow interactions.

Collectively, these efforts will enhance the adaptability of the current framework while laying the groundwork for more sophisticated tools designed to tackle complex sedimentation challenges. By combining extended monitoring, expanded validation, machine learning integration, and automation, future research can significantly advance the field of sediment transport modeling and its application to sustainable water resource management.

5. Conclusions

This study introduces a comprehensive and multidisciplinary approach to characterizing and predicting sediment deposition patterns in irrigation canals, addressing a critical challenge for the sustainable management of agricultural water systems. By integrating advanced image processing techniques, vector field analysis, sinusoidal modeling, and rigorous statistical validation, the research establishes a robust framework for analyzing sediment morphology and flow dynamics within an experimental channel located along the La Tebaida Linear Park on the left bank of the Malacatos River in Loja, Ecuador. The findings reveal that sediment accumulation reduces the hydraulic cross-section by approximately 5 cm, significantly impacting flow efficiency and water distribution.

The study presents the first sedimentation prediction framework that combines image processing and sinusoidal modeling, offering a novel approach to capturing complex sediment dynamics. This innovative methodology has significant application value, particularly for low-income areas, as it leverages open-source tools to provide accessible and cost-effective solutions for sediment management. By democratizing access to advanced sediment management technologies, this framework supports sustainable development and efficient irrigation management in resource-constrained regions.

The proposed sinusoidal model demonstrates exceptional predictive accuracy, evidenced by its strong performance across multiple statistical metrics at the study’s conclusion (Model 8, after approximately 55 min of experimentation). These results collectively validate the model’s robustness in capturing oscillatory sedimentation patterns while minimizing prediction errors. This predictive capability is fundamental for anticipating sediment accumulation and planning proactive maintenance strategies, which can indirectly contribute to optimizing irrigation management by reducing potential disruptions and improving water distribution efficiency.

The study provides a novel and robust approach to determine the sinusoidal bedload transport rate (qb_sinusoidal in m²/s), offering a direct quantification of sediment movement. This information is essential for understanding how sediment dynamics influence canal performance and can guide the implementation of targeted maintenance practices, such as selective dredging or periodic flushing, to maintain optimal flow conditions. Complementary analyses, such as heatmaps, histograms, and vector fields, further enhance the understanding of spatial variability, local gradients, and regional heterogeneity in sediment distribution. Heatmaps effectively identified regions of high sediment concentration, while histograms revealed pronounced local heterogeneity in elevation distribution. These findings collectively provide actionable insights for optimizing canal design, maintenance schedules, and sediment control strategies, thereby supporting the optimization of irrigation management by minimizing sediment-related inefficiencies and ensuring more efficient and sustainable irrigation systems.

The progressive analysis of Models 1–8 underscores the iterative refinement characteristic of sediment morphology studies, where successive adjustments lead to increasingly accurate representations of sedimentary structures. Temporal progression highlights the importance of real-time adjustments and emphasizes the dynamic interplay between environmental factors and analytical outcomes. Collectively, these findings reinforce the utility of sinusoidal modeling as a powerful tool for quantifying and predicting sediment transport processes in irrigation channels. The consistent improvement in statistical metrics validates the robustness of the methodology and its potential for broader application in sedimentology and hydrodynamics.

A comparative analysis of sinusoidal model performance across temporal and spatial scales highlights its adaptability in capturing sediment dynamics under subcritical flow conditions (Froude number ≈ 0.07) and turbulent regimes (Reynolds number ≈ 41,000), with flow velocities near 0.12 m/s. Leveraging advanced visualization tools such as residual error maps and principal component analysis (PCA), this study identifies key variables, amplitude and coherence, that significantly influence sediment morphology. These findings align with hydrodynamic principles, where coherent turbulent structures govern momentum transfer and sediment entrainment, emphasizing the dominance of stable, gravity-driven processes in shaping bedform evolution. Benchmarking against classical sediment transport frameworks reveals both the strengths and limitations of the sinusoidal model, particularly its high predictive accuracy under specific flow regimes, while highlighting opportunities for improvement in more complex hydrodynamic scenarios.

This research not only provides a detailed characterization of sediment deposition patterns but also offers a validated predictive tool for managing sediment-related challenges in canals. The integration of advanced analytical techniques and statistical validation ensures the reproducibility and scalability of the findings, positioning this study as a cornerstone for future advancements in sedimentology and hydrodynamics.

6. Key Findings

The sinusoidal modeling framework demonstrated a unique capacity to represent periodic sediment deposition patterns, offering enhanced structural insight compared to traditional transport models.

The model’s adaptability to both subcritical and turbulent flow regimes highlights its flexibility in varying hydraulic contexts, supporting its application in diverse irrigation environments.

Spatial diagnostic tools, including heatmaps, orientation fields, and elevation histograms, revealed fine-scale morphological variability, enabling precise identification of high-risk sedimentation zones.

This spatial resolution facilitates data-driven maintenance strategies by enabling targeted interventions, ultimately improving the operational efficiency of canal systems.

Owing to its methodological transparency and reproducibility, the approach provides a scalable foundation for sediment management across irrigation networks and broader hydraulic infrastructure.