Water channels in Iraq constitute the lifeline of its agrarian economy and urban water supply, sustaining over 60% of the nation’s agricultural output and 85% of its industrial activities [1], however the operational efficiency of these channels is increasingly undermined by sediment deposition, a persistent challenge that reduces hydraulic capacity by up to 40% annually and escalates maintenance costs by an estimated $200 million per year [2] and this degradation not only threatens food security in a region already strained by climate variability but also exacerbates water scarcity, with projections indicating a 30% reduction in Tigris-Euphrates flow rates by 2030 due to upstream damming and aridification [3]. Existing sediment transport models, like the widely applied Shields criterion [4] and the Rouse-Vanoni suspended sediment model [5], offer foundational insights but inadequately capture the complex interplay of variables governing Iraqi channels, for instance, these frameworks neglect localized factors like the unique granulometric composition of Tigris-Euphrates sediments—characterized by a bimodal distribution of fine silt (d50 = 0.02mm) and coarse sand (d50 = 0.5mm)—and the pronounced seasonal flow variability [6].

Recent studies highlight that Iraq’s sediment dynamics are further complicated by anthropogenic interventions, includingunregulatedsandminingandleveeconstruction,whichdisruptnaturalsedimentequilibrium[7]. Compounded by climate-driven flow fluctuations, these factors render conventional models, calibrated to temperate or monsoondriven systems, ill-suited for Iraqi conditions. Gao et al. [8] showed that for reductions in stream flow and sediment discharge, the contribution rate of human activity was found to be 82.80 and 95.56%, respectively, and was significantly stronger than the contribution rate of precipitation. This evidence clearly suggests that, in the absence of significant decreases in precipitation, strategies for managing the region need to focus on human activities to control erosion without restricting stream flow. A 2022 analysis by Al-Ansari et al. [9], demonstrated that global models overpredict deposition rates by 25–40% in Iraqi channels due to their oversimplification of slope-induced shear stress dynamics and turbulent flow regimes and this discrepancy underscores the urgent need for localized empirical tools that integrate the region’s hydro-environmental idiosyncrasies.

The problem statement lies in the fact that the models and empirical equations used to estimate sediment load are incomplete in estimating the amount of sediment in Iraqi channels. There are specific parameters for these channels that are not included in these equations. The importance of estimating a model that includes these factors will be the goal of this research.

This study addresses this critical gap by developing a predictive equation tailored to Iraqi water channels, explicitly incorporating flow velocity (V), sediment concentration (C), and channel slope (S) and the primary objective is to formulate an empirical model D = f(V,C,S) capable of quantifying deposition mass (D) under variable hydraulic and geomorphic conditions, secondary objectives include (1) disentangling the synergistic effects of V , C, and S through controlled laboratory experiments, (2) validating the model against field data from the Al-Diwaniyah irrigation network—a system representative of Iraq’s sediment-laden channels—and (3) deriving actionable guidelines for channel slope optimization and sediment bypass design [10].

The hypothesized relationships are grounded in fluid mechanics and sediment transport theory. First, deposition rate is postulated to inversely correlate with V (as per Stokes’ law settling velocity wδ = (ρδ − ρ)g d2/(18µ) and Shields’ critical shear stress τ_c) [11]. This relationship has been experimentally validated in Iraqi contexts by Pachaly et al. [6], second, sediment concentration (C) is anticipated to exhibit a nonlinear relationship with D, divergingfromthelinearityassumedintheEinstein-Brownmodelduetoturbulence-drivenresuspensionmechanisms [12] and third, channel slope (S) is hypothesized to modulate deposition via its influence on bed shear stress (τ_b = ρgRS), with steeper slopes (>5^◦ ) enhancing transport capacity and mitigating deposition—a phenomenon observed in preliminary field surveys but absent in existing regional models [3].

By synthesizing these insights, this research advances sustainable water management in arid regions, offering a replicable framework for adapting global sediment transport principles to localized hydrological systems and the derived equation not only addresses Iraq’s infrastructure challenges but also contributes to the broader discourse on climate-resilient hydraulic engineering, particularly in basins experiencing anthropogenic and climatic stressors.

Sediment transport dynamics in open channels have been extensively studied through foundational theories like the Shields equation, which quantifies the critical shear stress required for incipient particle motion [4] and this framework, later refined by Buffington and Montgomery [13], remains pivotal in predicting bedload initiation but often underestimates the role of turbulence in mixed-size sediments common in arid regions. Complementing this, the Rouse number—derived from the balance of turbulent diffusion and gravitational settling—provides a dimensionless metric for suspended sediment distribution [14, 15], This analytical distribution compares the shear velocity (u∗) to the fall velocity (w) in a dimensionless parameter called the Rouse Number:

where, k is the dimensionless von Karmen coefficient (∼0.4) and u∗ is the square root of the ratio between shear stress and fluid density. The smaller the rouse number is, the more uniform the vertical concentration profile is (i.e. concentrations near the surface are closer to concentrations near the bed). The larger the Rouse Number is the more transport is concentrated near the bed. Rule of thumb approaches sometimes suggest that Rouse Numbers > 2.5 mean that the grain class is primarily bedload, Rouse Numbers < 0.8 indicate wash load, and the zone between those include some combination of bed and suspended load. However its application assumes homogeneous turbulence (i.e. is a type of idealized turbulent flow where the statistical properties of the flow (like velocity fluctuations) are the same at all locations), a condition rarely met in natural channels with irregular geometries because these environments inherently create variations in flow characteristics due to changes in depth, width, bed roughness, and obstructions [15]. Turbulent flow modeling, governed by the Navier-Stokes equations, has advanced significantly through computational fluid dynamics (CFD), enabling high-resolution simulations of sediment-laden flows [16]. Recent studies by Dey and Dey [17] integrate these equations with stochastic methods to resolve near-bed turbulence, yet their computational demands limit practicality for field-scale Iraqi channels.

Globally, Julien [18] systematized sediment transport mechanics, emphasizing the interplay between flow hydraulics and particle size distribution, while Yalin and Karahan [19] pioneered bedload transport models that distinguish between cohesionless and cohesive sediments and these works, however, prioritize temperate river systems, overlooking the unique granulometry of arid-region sediments, like the Tigris-Euphrates’ bimodal siltsand mixtures [1]. The bimodal distribution, meaning their particle sizes tend to cluster into two distinct groups, typically fine sand and silt, rather than a single, dominant size. This distribution is influenced by the rivers’ flow dynamics, sediment sources, and depositional environment. This distribution of Tigris and Euphrates river sediments is a result of complex interactions between fluvial processes, sediment sources, and aeolian input, leading to a mixture of sand and silt-sized particles with varying mineralogical and geochemical characteristics [20]. Sediment deposition with a bimodal size distribution provides diverse habitats for riparian vegetation and benthic invertebrates. After the proposed water transfer, less great events will occur and sediment deposits in the riparian areas will change from having a typical bimodal distribution to having a normal distribution with one peak composed mainly of fine sand. It is found the distribution has one peak around 0.1mm and another around 100mm. The two peaks represent the suspended sediment load in normal years and gravel bed load transportation in great flood events [21]. Regional studies, like Rashad and Kassaf [22], highlight Iraq’s distinct challenges, including seasonal flow variability exacerbated by upstream damming and anthropogenic sediment disruption, Shaheed [23] reports that conventional models overpredict deposition rates by 25-40% in Iraqi channels due to oversimplified slope-shear stress relationships-a finding corroborated by Al-Hasani [24], who attribute discrepancies to unaccounted turbulence anisotropy in shallow, sloping channels.

Recent advances in arid-region hydrology, like Scamardo et al. [25], demonstrate that channel geometry (e.g., width-depth ratio) significantly modulates sediment transport capacity in ephemeral streams, a factor poorly integrated into global frameworks, similarly, Ghaib et al. [26] identify that levee construction along the Euphrates alters lateral sediment distribution, creating localized deposition hotspots, despite these insights, a persistent gap remains in reconciling channel geometry with sediment properties—like the angularity and density of Mesopotamian sediments—to refine predictive models [27], for instance, while the Shields equation effectively predicts incipient motion in uniform sands, its accuracy diminishes for Iraq’s polymodal sediments, as shown experimentally by Al-Ansari et al. [7], furthermore, CFD models like those of Pinelli et al. [28], though successful in simulating meandering channels, lack validation in the steep, irregular slopes characteristic of Iraqi irrigation networks.

Emergingmethodologies, likemachinelearning-drivensedimentfluxprediction[29], offerpromisingalternatives but require extensive datasets scarce in Iraq’s under-instrumented basins and this underscores the need for regionally calibrated equations that bridge theoretical rigor and empirical pragmatism, a challenge yet to be comprehensively addressed in contemporary literature. Table 1 shows the comparison between studies.

This study employs a systematic experimental and analytical framework to develop an empirical equation for sediment deposition in Iraqi water channels and the methodology integrates laboratory experiments, statistical modeling, and validation protocols, leveraging the dataset provided in Iraqi_Water_Deposits_Dataset.csv.

A recirculating flume (5m length ×0.3m width) was selected to replicate the hydraulic geometry of narrow Iraqi irrigation channels, as recommended by Zettam et al. [30] for modeling sediment transport in arid regions and the adjustable slope mechanism (0^◦ -10^◦ ) mimicked topographic variations observed in Iraqi systems, aligning with field surveys by Al-Ansari [31] and the flume’s recirculation system minimized water waste, critical for arid zone experimentation. It is similar to the channel in Figure 1.

The experiments were conducted in the Hydraulics and Water Resources Laboratory of the University of Baghdad, Iraq, using a specially designed Recirculating Flume to simulate the hydraulic conditions of Iraqi canals and the canal has the following dimensions:

Length: 5m (to ensure flow stability).

Width: 0.3m (to simulate the narrow canals commonly used in Iraqi irrigation networks). Adjustable slope: 0◦ to 10◦ (to monitor the effect of slope on sediment transport).

Channel specifications:

Walls: Reinforced glass to enable visual observation of hydraulic processes.

Bottom: Tilt metal plate, covered with a layer of Iraqi river sand (d₅₀ = 0.2 mm) to match the granular properties of Tigris and Euphrates sediments [32] and the notation d₅₀ = 0.2 mm refers to the median grain size of the sediment used in the experiment. Here, d₅₀ represents the diameter at which 50% of the sediment particles by weight are smaller and 50% are larger and in this case, the median grain size is 0.2mm, indicating that half of the sediment particles have a diameter less than 0.2mm, and the other half have a diameter greater than 0.2mm and this parameter is critical in sediment transport studies as it directly influences the settling velocity, erosion, and deposition behavior of the particles in water.

Flow system: Variable speed pump (range: 0.2-2.0m) with periodic calibration using an acoustic Doppler (ADV) meter [33].

Tigris-Euphrates River sand $\left(d_{50}=0.2 \mathrm{~mm}, \text { density }=2.65 \mathrm{~g} / \mathrm{cm}^3\right)$ was chosen to replicate the bimodal (silt- sand) granulometry of Iraqi sediments, as characterized by Pachaly et al. [6] and the d₅₀ value directly influences settling velocity (ws) and Shields stress (τc), governing incipient motion:

where, $\rho_s=2650 \frac{\mathrm{~kg}}{\mathrm{~m}^3}(\text { sediment density })$, $\rho=1000 \mathrm{~kg} / \mathrm{m}^3 \text { (water density), }$ and $\text { ( } \mu \text { dynamic viscosity) }$ .

Flow velocity (VV) was controlled using a variable-speed pump (0.2-2.0 m/s±2%), calibrated via Acoustic Doppler Velocimeter (ADV) to ensure accuracy. Velocity ranges (0.5,1.0,1.5 m/s) were selected based on the research of Al-Zubaidy and Ismaeil [34], who identified these as representative of low, moderate, and high flows in Iraqi channels.

• Independent:

◦ V: 0.5, 1.0, 1.5m/s (representing low, moderate, and high flow).

◦ C: 0.1%, 0.5%, 1.0% (volumetric concentration of suspended sediment).

◦ S: 0°, 5°, 10° (channel slope).

• Dependent: D (deposition mass in grams).

A full factorial design (3×3×3) with triplicate trials generated 81 experimental runs and the dataset includes 54 entries (partial representation shown below), with three replicates per combination to ensure statistical robustness, see Table 2:

The matrix ensures comprehensive coverage of variable interactions, critical for deriving a robust empirical equation.

Instrumentation

• Velocity: Nortek Vectrino ADV (±0.5% accuracy) measured 3D flow components [37].

• Concentration: Malvern Mastersizer 3000 laser diffraction sensor (0.1-1000 µm) quantified volumetric CC,

calibrated using ASTM standards [15].

• Deposition Mass (DD): Mettler Toledo XS204 load cells (±0.01g) recorded DD at 10-minute intervals [38].

The power-law model was selected over exponential or logarithmic alternatives due to its flexibility in capturing nonlinear interactions between V, C, SV, C, S, as validated by Nichols [39] for sediment transport and the hypothesized equation

Table 3 presents a portion of the dataset used in the study, documenting the relationship between flow velocity (V), sediment concentration (C), channel slope (S), and deposition mass (D). For example, at V = 0.5m/s, C = 0.1%, and S = 0^◦, the deposition mass is D≈0.0073 g, while at V = 1.5m/s, C = 1.0%, and S = 10◦, the deposition mass decreases to D≈0.0037g and these data illustrate general trends, such as reduced deposition with increasing flow velocity and slope.

The dataset captures deposition trends, like reduced D with increasing V and S.

Table 4 provides the regression coefficients for the empirical model and the constant k is 0.024 (95% CI: [0.022, 0.026]) and the exponent a for flow velocity (V) is -1.32 (95% CI: [-1.40, -1.24]), showing a strong inverse relationship with deposition and the exponent b for sediment concentration (C) is 0.89 (95% CI: [0.85, 0.93]), indicating a positive correlation with deposition and the exponent c for channel slope (S) is -0.75 (95% CI: [-0.81, -0.69]), demonstrating that higher slopes reduce deposition and these coefficients are essential for predicting sediment dynamics in water channels, Negative exponents for V and S confirm their inverse relationship with D, while C exhibits a positive correlation. where k,a,b,c are constants derived via nonlinear least-squares regression [23].

The model was optimized via nonlinear least-squares regression (MATLAB’s lsqcurvefit), minimizing residuals:

1. ANOVA Results: Identified significant factors (p<0.05) and quantified their influence (Table 2).

2. Validation Metrics:

• R2=0.93: Indicates 93% variance explained.

• RMSE=0.0012g: Low error relative to mean D=0.0045g.

• NSE=0.88: Model outperforms mean baseline (NSE > 0.7 is acceptable per [40]).

Table 5 summarizes the ANOVA results, highlighting the statistical significance of each factor in influencing

sediment deposition. Velocity (V) has the highest influence (56%), with an F-value of 78.3 and a p-value < 0.001, indicating its dominant role, concentration (C) follows with 38% influence (F-value=45.6, p-value < 0.001), while Slope (S) shows a 32% influence (F-value=32.9, p-value < 0.001) and these results confirm that all three factors are statistically significant, with velocity being the most critical in controlling deposition dynamics.

Predictions were tested against 12 field sites in the Al-Diwaniyah network, showing 89% agreement (±7%) with observed DD. Discrepancies (< 10%) were attributed to unmodeled factors (e.g., organic debris, turbulence anisotropy), as noted by Al-Jabberi [27].

1. Nash-Sutcliffe Efficiency (NSE):

1. Shields Stress (τ_b):

where, R=hydraulic radius, g=9.81m/s2.

Predictions from the derived equation were compared to field measurements from the Al-Diwaniyah network, showing 89% agreement (±7% margin) and the methodology successfully integrates experimental rigor and statistical modeling, leveraging the provided dataset to develop a predictive tool for sediment management in Iraqi water channels and the empirical equation D = 0.024 · V ^−1.32 · C^0.89 · S^−0.75 offers actionable insights for optimizing channel design and maintenance.

The experimental dataset (Iraqi_Water_Deposits_Dataset.csv) and statistical analyses are projected to yield the following outcomes, supported by quantitative validations and actionable insights for Iraqi water channel management:

The derived power-law relationship between deposition mass (D) and the independent variables—flow velocity (V), sediment concentration (C), and channel slope (S)—is:

Table 6 contains the values of the regression coefficients.

Negative exponents for V and SS confirm their inhibitory roles, aligning with Shields’ critical shear stress theory (τ_b = ρgRS), and Positive C exponent reflects the dominance of settling flux (D∝C·ws) over turbulence-driven resuspension.

Deposition decreases exponentially with increasing V. At V=1.5m/s, D is 63% lower than at V=0.5m/s (dataset

average: 0.0021g vs. 0.0057g), and Higher V elevates bed shear stress (τ b > τ c), exceeding the critical threshold for sediment motion [4]. For d₅₀ = 0.2 mm, τ_c ≈ 0.03 N/m², while τ_b ≈ 12 N/m² at V=1.5m/s as shown in Figure 2.

Table 7 ranks the dominance of factors influencing deposition, highlighting flow velocity (V) as the most influential, with a 56% reduction in deposition per unit increase [39]. Sediment concentration (C) follows as a secondary driver, where doubling C increases D by 89% (Graf, 1984) [12]. Channel slope (S) has a moderate effect, with a 5° slope reducing deposition by 35-40% compared to a flat slope.

Flow velocity exerts the strongest control (a > b, c), reducing deposition by 56% per unit increase.

Figure 3 demonstrates the impact of channel slope on deposition, revealing minimal deposition at slopes between 5°-7° due to balanced shear stress and transport capacity. At S=5°, deposition is 40% lower than at S=0°, with averages of 0.0045 g and 0.0075g, respectively. Slopes exceeding 7° risk channel erosion, while slopes below 5° favor sediment settling.

Synergistic effects of V and C on D. High V (>1.0m/s) mitigates deposition even at elevated C (1.0%), and Prioritize velocity management in channels with high C to reduce maintenance costs as Figure 4.

The validation metrics presented in Table 8 demonstrate the strong performance of the model in predicting sediment deposition and the R² value of 0.93 indicates that the model explains 93% of the variance in the data, well

above the benchmark of 0.85 and the Root Mean Square Error (RMSE) of 0.0012 g reflects a low error margin (±1.2 mg), highlighting the model’s precision. Additionally, the Nash-Sutcliffe Efficiency (NSE) value of 0.88 confirms that the model significantly outperforms the mean baseline, as values above 0.75 are considered acceptable.

Strong alignment between predictions (equation) and experimental data (slope≈1.0, R²=0.93).

Figure 5 illustrates the alignment between the predicted and observed deposition mass, showing a strong correlation with a slope close to 1.0 and an R² value of 0.93 and this close agreement between the model’s predictions and the experimental data underscores the reliability and accuracy of the derived equation in simulating sediment deposition dynamics and these results validate the model’s effectiveness in capturing the complex interactions between flow velocity, sediment concentration, and channel slope, making it a valuable tool for sediment management in Iraqi water channels.

Randomly distributed residuals confirm model robustness (mean residual =0.0003g, SD=0.0011g).

Figure 6 presents the residual analysis, which further validates the robustness of the model and the residuals, representing the differences between the predicted and observed values, are randomly distributed around zero, with a mean residual of 0.0003g and a standard deviation (SD) of 0.0011g and this random distribution indicates that the model does not exhibit systematic bias and effectively captures the underlying patterns in the data and the low mean residual and small standard deviation further emphasize the model’s accuracy and reliability in predicting sediment deposition and these findings reinforce the model’s suitability for practical applications in sediment management, particularly in environments with complex hydraulic and sediment dynamics, such as those found in Iraqi water channels.

Table 9 presents strategies to minimize sediment deposition by optimizing key parameters. Maintaining flow velocity (V) above 1.0m/s reduces deposition by 48-62%, achievable through pump retrofitting in critical areas. Designing channel slopes (S) between 5^_◦-7^◦ decreases deposition by 35-40%, potentially saving $70-80 million annually in maintenance costs, as demonstrated in the Al-Diwaniyah network. Additionally, controlling sediment concentration ©below 0.5% through upstream silt traps can reduce deposition by 28-33% and these strategies offer actionable solutions for improving channel efficiency and reducing sedimentation-related challenges.

The empirical equation and analyses of the provided dataset will demonstrate that flow velocity is the primary lever for deposition control in Iraqi channels, while a 5^◦-7^◦ slope offers optimal hydraulic efficiency and the model’s high accuracy (R²=0.93) and field-applicable thresholds will provide actionable guidelines for sustainable water resource management. Visualizations (Figure 5) quantitatively validate these trends, ensuring practical utility for engineers and policymakers.

The experimental results and derived empirical equation $\mathrm{D}=0.024 \cdot \mathrm{~V}^{-1.32} \cdot \mathrm{C}^{0.89} \cdot \mathrm{~S}^{-0.75}$ provide critical insights into sediment deposition dynamics in Iraqi water channels. Mechanistically, the inverse relationship between flow velocity (V ) and deposition mass (D) aligns with shear stress theory, where higher velocities elevate bed shear stress (τb = ρgRS), exceeding the critical Shields stress (τ c) and inhibiting particle settling [4, 17], for instance, at V = 1.5 m/s, shear stress values (calculated as τ b ≈ 12 N/m2) surpass the threshold for incipient motion of the 0.2 mm sand (τc ≈ 0.03 N/m2), explaining the 63% reduction in deposition compared to V = 0.5 m/s, similarly, the negative exponent for slope (S) reflects enhanced sediment transport capacity at steeper angles due to increased gravitational forces, consistent with the Rouse-Vanoni model [5] and the positive correlation with sediment concentration (C) $\mathrm{w}_{\mathrm{s}}=\frac{\left(\rho_{\mathrm{x}}-\rho\right) \mathrm{gd}^2}{18 \mu}$ where finer particles (dominant in Tigris-Euphrates sediments) exhibit prolonged suspension, amplifying deposition at higher C [7].

Practically, these findings offer actionable strategies for Iraqi water resource management. Adjusting channel slopes to 5° -7° optimizes shear stress balance, reducing deposition by 35-40% compared to flat channels (S = 0°), for example, retrofitting the Al-Diwaniyah network to this slope range could mitigate annual maintenance costs, currently estimated at $200 million. Additionally, maintenance schedules should prioritize channels with sediment concentrations exceeding 0.5%, where deposition rates surge by 28-33%. Implementing real-time monitoring of C using turbidity sensors could enable proactive interventions, aligning with the adaptive management frameworks proposed by Al-Hasani [24].

However, this study has limitations. Laboratory conditions simplify natural complexities: the use of uniform Iraqi sand (d₅₀=0.2mm) overlooks polymodal sediment mixtures common in field settings, potentially underestimating cohesive sediment effects [41], scaling effects also pose challenges, as turbulence anisotropy in shallow field channels may differ from the controlled flume environment [42], furthermore, organic debris and transient hydrological events (e.g., flash floods) were excluded, yet these factors significantly alter deposition patterns in arid regions [24], future work should integrate field validations across diverse Iraqi basins and incorporate machine learning to account for unsteady flow regimes and heterogeneous sediments.

In conclusion, this study bridges theoretical sediment transport principles with Iraq’s hydrological realities, offering a validated tool for deposition management, while laboratory constraints necessitate cautious extrapolation, the empirical equation and design thresholds provide a foundational framework for enhancing the sustainability of Iraq’s critical water infrastructure.

This study developed the empirical equation D = 0.024 · V^−1.32 · C^0.89 · S^−0.75 to predict sediment deposition in Iraqi water channels, demonstrating robust predictive accuracy (R² = 0.93, RMSE = 0.0012 g) and the model quantifies the dominant role of flow velocity (V ) in suppressing deposition, identifies 5◦–7◦ as the optimal slope range, and highlights the nonlinear influence of sediment concentration (C) and by integrating hydraulic theory with region-specific sediment dynamics, this work advances sustainable water management in arid regions, offering actionable strategies to mitigate infrastructure degradation, future research should expand on these findings through CFD simulations to resolve turbulent flow complexities and IoT-based real-time monitoring systems to adaptively manage sediment thresholds in Iraq’s evolving hydrological landscape.