MTI is a low-pressure continuous irrigation method whose discharge is controlled by soil matric potential. The inner membrane closely simulates the vascular plant tissue. It uses the soil-moisture gradient for advection (Yang et al., 2008), and it assumes a line source infiltration mechanism during irrigation (Fan et al., 2018b). Table 1 summarizes the membrane properties. The technology optimizes irrigation field water use efficiency (fWUE) since it utilizes on-demand water application (Jun et al., 2012; Kanda et al., 2019).

HYDRUS-2D was used to model the solute movement in the variably saturated soil profile zone. HYDRUS-2D robustness facilitates the simultaneous modeling of multiple independent solutes or nitrogen species whose solutes go through first-order degradation reactions (Hanson et al., 2006). Coupled water flow and solute transport equations were applied. Richard's equation (Equation 1) (Richards, 1931; Šimunek et al., 2012) was used to compute the spatially distributed soil moisture and the subsequent volumetric fluxes. For this study, we adopted the x (lateral)- z (vertical) spatial directions.

Where: θ = volumetric water content [L³.L⁻³], h = pressure head [L], S = sink term [L³.L⁻³.T⁻¹] representing root water uptake as a function of spatial position and time, x_i = spatial coordinates [L], t = time [T], and K_ij and K_ij = components of the hydraulic conductivity tensor [L.T⁻¹]. The root water uptake was determined by the Vrugt model (Vrugt et al., 2001). Chemical transport of solutes in a variably saturated zone is governed by the linear partial differential equations (Equations 2, 3).

Where: c_i and s_i = solute concentrations in the liquid [M.L⁻³] and solid [M.M⁻¹] phase respectively, q_i = ith component of volumetric flux density [L.T⁻¹], μ_w and μ_s = first order rate constants for solutes in the liquid and solid phase [T⁻¹] respectively, ρ = soil bulk density [M.L⁻³], S = sink term [L³.L.³T⁻¹] in the water flow equation, C_r = concentration of the sink term [M.L⁻³], D_ij = dispersion coefficient tensor [L².T⁻¹] for the liquid phase, k = kth chain number, n_s = number of solutes involved in the reaction, K_{d, k} = distribution coefficient of species k [L³.M⁻¹], and c_k and s_k = adsorption isotherms.

Equation 4 was applied to capture how HYDRUS simulates solute behavior in the vadose zone:

Where: S_k = the dimensionless sorbed concentration of solute k on the solid phase [M.M⁻¹] representing how much of the solute is retained or adsorbed by the soil matrix, K_{d, k} = the distribution coefficient for solute k, which quantifies the ratio of the amount of solute adsorbed to the soil to the amount dissolved in the pore water, thus reflecting soil–solute interaction [L³.M⁻¹], and C_k = aqueous concentration of solute k in the liquid phase [M.L⁻³].

Soil samples were collected from various depths of 10-,20-, 30-, 40-, and 50 cm directly at the emitter (MTI) and cm from the emitter. The observed data represented the spatial and temporal solute movement during the growing season under MTI. The soil samples were air-dried and analyzed using the Leco Carbon/Nitrogen/Sulfur analyzer (Leco TRUMAC CNS Model No: 630-300-400, Serial No: 4093, St Joseph, Michigan, USA). The tube auger was used to collect soil samples after 2-, 4-, 24-, 48- and 72 h of fertigation at 20-, 30-, 40-, and 50 cm depths respectively. Above ground (ABG) plant samples were also collected, oven-dried and analyzed for N. Upon destructive sampling for N analysis in ABG plant samples, the canola stalk, leaves and the seed were dried at 30°C and ground to pass through a 1 mm sieve. Total N concentration was determined by dry combustion using the MICRO cube equipment (Elementer Americas).

MTI is a porous line source irrigation method; thus, the modeling domain assumed a rectangular geometry (Hanson et al., 2006) (Figure 2). Since the fertigation occurred under active plant uptake, the modeling domain consisted of the area occupied by roots. The effective maximum root zone depth for canola was set at 1.0 m. The transport domain consisted of 33 cm by 100 cm, with the MTI lateral buried at a depth of 20 cm. The 33 cm by 100 cm was selected as the space occupied by the fertigating MTI lateral within a single plot consisting of 3 evenly spaced laterals. The transport domain (finite element (FE) mesh) was discretized into 5,000 nodes on the boundary curve and 200,000 FE-mesh nodes with finer grid around the Moistube lateral and coarser grid in the remaining surface. The default smoothing factor of 1.3 was adopted.

The model was calibrated by adjusting the initial soil hydraulic properties (Table 2) and dispersivity values until the model closely matched the observed N concentration values (Kanda et al., 2020a). The dataset from the second fertigation exercise was used for model validation.

Nitrogen use efficiency can be quantified using the following indices; partial factor productivity (PFP_N), agronomic efficiency (AE), physiological efficiency (PE), and recovery efficiency (RE) (Gupta and Khosla, 2012). For this study, we adopted the partial factor productivity of applied N (PFP_N) as a proxy for nitrogen use efficiency (NUE) because the output was harvestable canola grain yield. In addition, the PFP_N provides a clear indication of indigenous and applied N in a system (Dobermann, 2005). The PFP_N was computed using Equation 7 (Dobermann, 2005).

Where: Y_N = crop yield with applied N (kg.ha⁻¹), F_N = amount of (fertilizer) N applied (kg.ha⁻¹), and S_i = average initial nitrogen concentration (kg.ha⁻¹) in the soil profile (0–60 cm).

The S_i for the 100% ET_c, 75% ET_c, and 55% ET_c plots were 390.43 kg.ha⁻¹, 418.66 kg.ha⁻¹, and 432.77 kg.ha⁻¹.

The nitrogen budget was computed for each fertilizer application. The input was from the N supplied by fertigation. The outputs were N measured from grain and plant, N obtained from the soil sample directly at the MTI lateral. In addition, 10% of the applied fertilizer was set to account for volatilization (Ventura et al., 2008).

HYDRUS 2D/3D is a physical-based model (Simunek et al., 2012). The validation process was done over a split sampling approach whereby the dataset for the second fertigation session for each irrigation regime was used to assess the model's performance. The split approach enabled the training of the model using the first fertigation session's dataset to better adjust for local conditions. This enabled the model to perform the validation process with considerable accuracy and precision. The validation process maintained the “conservative” values (longitudinal dispersivity and soil hydraulic properties). The conservative and non-conservative parameters applied during model validation are summarized in Table 7.

For the field experiment data, a normality test was undertaken on the solute concentration, yield and biomass data for each respective irrigation regime using the Shapiro-Wilk normality test followed by a one-way ANOVA test. All statistical analyzes were done using R Studio© (R Core-Team, 2017).

Model evaluation was done using the following criteria: normalized root mean square error (nRMSE), Model Efficiency (EF), and percentage bias (PBIAS). The selected criteria are presented in Equations 8–10. The performance evaluation statistics were selected based on robustness (Moriasi et al., 2007).

Where O_i and P_i = observed and predicted value(s), respectively, O_i = mean observed data, and x = number of observations. nRMSE defined the simulation model's accuracy, whilst the EF statistic measured the residual variance vs the measured data variance. The statistic (EF) ranges from −∞ to 1 (Moriasi et al., 2007), however, Yang et al. (2014) asserted there exists a positive and scattered correlation between EF and the index of agreement thus when estimating soil water content, a satisfactory agreement can be considered when EF≥−1. PBIAS measured the tendency of the simulated data to either under-estimate or overestimate the observed values. Table 8 summarizes the general performance rating for the selected evaluation criteria.

Under the full irrigation regime (100% ET_c), maximum solute movement occurred at t = 2 h. The depth (D) vs. solute movement curves followed a similar trajectory under the respective times, as exhibited by Figures 4a, b. There, however, was a significant variation in N concentration at t = 24 h and t = 72 h at D = 40 cm and 50 cm, respectively (p < 0.05). The respective NH4+-N, NO3--N concentrations were 0.05 g.kg⁻¹ and 0.10 g.kg⁻¹. Maximum NH4+-N, NO3--N accumulation (~0.13 g.kg⁻¹) was uniform at D = 20 cm both directly at the emitter (E) and away from the emitter (Ae) localities. This could be attributed to the MTI lateral placement depth of 20 cm that influenced solute accumulation at the near placement depth.

Under the optimal deficit irrigation (DI) regime (75% ET_c), maximum NH4+-N, NO3--N concentration (0.17 g.kg⁻¹) was at D = 30 cm after t = 24 h (Figure 3c). Under 55% ET_c, the solute movement curves at E and Ae followed a similar trajectory. Maximum NH4+-N, NO3--N accumulation was at D = 30 cm for all irrigation regimes at localities E and Ae, albeit at different times. This implied that full irrigation (100% ET_c) and the optimal irrigation (75% ET_c) had no significant effect on solute movement both at E and Ae in the variably saturated zones (p> 0.05).

Under 100% ET_c, peak NH4+-N, NO3--N accumulation at the E scenario occurred at t = 55 h (approx.) at D = 30 cm (Figure 4a) whereas under the Ae locality, peak accumulation occurred at t = 20 h at D = 20 cm and it plateaued at NH4+-N, NO3--N -concentration of 0.12–0.13 g.kg⁻¹ (Figure 5b). There was no significant difference between the concentrations at the respective depth (p > 0.05). This observation can be attributed to the soil characteristics. However, fine-textured soils exhibit lateral movement (Fan et al., 2018a), the soil in question did not have pronounced lateral movement than the vertical movement. Active root nutrient uptake (RNU) could have also potentially influenced the lag in peak concentration at the E locality compared to Ae. Mmolawa and Or (2000b) noted a solute concentration decline under a cropped field compared to an uncropped one under drip irrigation.

For the three irrigation regimes, the solute infiltration rate was high at the initial phase (t = 1 h to approx. t = 2.5 h) at both locations (E and Ae). This could be attributed to the availability of micro and macro pores that could accommodate solutes during the initial phases of fertigation. The availability of pore space in fully irrigated plots was potentially made possible by gravity-assisted drainage. There was a significant difference (p < 0.05) in concentration at various depths under the 100% ET_c regime between localities E and Ae. The highest concentration levels were recorded at D = 30 cm and 20 cm respectively at E and Ae during t = 50 h (approx.) (see Figures 5a, b). Gravity assisted solute movement was experienced at E; thus, a high NH4+-N, NO3--N concentration at D = 30 cm, whereas the effect of lateral buried depth acted on the high NH4+-N, NO3--N concentrations at location Ae, D = 20 cm.

Under the 75% ET_c DI at the E locality, peak NH4+-N, NO3--N accumulation at D = 30 cm occurred at t = 25 h (Figure 5c), which was half the time it took for the 100% ET_c irrigation regime to reach peak salt accumulation at the same depth. Similarly, under the 55% ET_c irrigation regime, peak salt accumulation occurred at t = 25 h and D = 20 cm. The phenomenon revealed how DI potentially aided the imbibition of the nitrate solutes, thus promoting mobility. Partially dry soils imbibe solutes compared to their saturated counterparts (Youngs and Leeds-Harrison, 1990).

Under the extreme DI regime (55% ET_c), nitrate concentration levels were uniform and D = 30 cm and D = 40 cm at t = 72 h (Figure 4f). Nitrate mobility was not as pronounced because of imbibing water's unavailability—due to preferential vertical flow—to transport the solutes. Interestingly, the extreme DI regime had a high NH4+-N, NO3--N concentration accumulation at D = 40 cm and 50 cm, t = 50 h and at locality E where-as, at; locality Ae the high concentration was recorded at t = 55 h (Figures 5e, f), one would argue that preferential flow was dominant in the extreme DI regime resulting in a favored vertical movement as compared to lateral. Merdun et al. (2008) argued that there is a preferential flow for a relatively dry soil favoring vertical solute movement compared to lateral movement.

Peak NH4+-N, NO3--N concentrations were observed in the depth range of D = 20 cm and D = 30 cm at time range of 20 h to 30 h (approx.) at both localities (E and Ae) under the full irrigation regime (p> 0.05, CV > 15%) and optimal irrigation regimes (p> 0.05, CV > 15%). For both irrigation regimes, the concentration plateaued for t = 20 h. This prolonged resident time presented an opportunity for active nutrient utilization by the canola. Thus, fertigation using MTI at optimal DI conditions (75% ET_c) minimizes nutrient leaching and promotes crop beneficial nutrient uptake.

There was no significant difference (p > 0.05) between solute concentrations at localities E and Ae for the 100% ET_c and 75% ET_c irrigation regimes. However, there was a significant difference (p < 0.05) in solute concentrations at locality E between the extreme DI regime and the other two irrigation regimes (full irrigation and optimal DI). There was also a significant difference (p < 0.05) at locality Ae between the full and extreme irrigation regimes, the latter had high solute concentrations at D = 20 cm and D = 40 cm. This was attributed to drier conditions in the 55% ET_c irrigation regime. The solute movement curves at E for all irrigation regimes were generally smoother than the Ae solute curves.

The solute curves followed a similar trajectory under the 100% ET_c and 75% ET_c (Figures 9a, b). Under the 55% ET_c irrigation regime, locality E's solute movement was a near-perfect vertical line. In contrast, the movement at locality Ae was curvilinear (Figure 10e). The observed phenomenon under the 55% ET_c was attributed to the extreme deficit irrigation conditions imposed on the treatment, which presented available air spaces that could accommodate solutes.

A separate second fertigation dataset was used to validate the model. The HYDRUS 2D/3D validation results are shown in Figures 10d, e. The model successfully simulated the solute movement under the three irrigation regimes (100% ET_c, 75% ET_c, and 55% ET_c). The model showed an overestimation instance under the 100% ET_c and 75% ET_c irrigation regime with a PBIAS of −8.79% and 3.53%, respectively. The model under-estimated solute concentration across the 55% ET_c irrigation regime (PBIAS = 11.34%). Also, under the 55% ET_c model efficiency was low, thus reflecting underprediction solute movement (Table 9) likely due to delayed redistribution and reduced leaching flux in extremely dry conditions. These finding are consistent with findings by Zhang et al. (2022) who stated that in dry soil conditions, nitrate movement lags behind water movement, leading to a delayed nitrate peak in the soil profile. The nRMSE (nRMSE ≤ 26%) was within acceptable ranges. However, the model efficiency (EF) was average for the 100% ET_c irrigation regime and poor for the two DI regimes (75% ET_c and 55% ET_c). This was potentially due to the DI strategy (75% ET_c and 55% ET_c) under the heavy clay Ukulinga soils. Javadzadeh et al. (2017) revealed how HYDRUS 2D/3D poorly simulated solute movement in clay textured soils. Considering that this experiment was carried out under field conditions, the effect of the inherent heterogeneity of the Ukulinga soil profile cannot be ignored in contributing to the poor EF. Also, model fitting procedures potentially affect the model performance. Merdun (2012) also attributed the low coefficient of model efficiency (CME) of HYDRUS to parameter value determination and fitting procedures.

The relative plant root distributions and the subsequent solute (N-NH4+,N-NO3-) concentrations are shown in Figure 11. The simulation was extended beyond the t = 72 h mark to t = 168 h. It is worth mentioning that actual field measurements were done up to t = 72 h. The 100% ETc irrigation regime's solute concentration was the highest in the 0–10 cm depth profile. For the 75% ET_c irrigation regime, the solutes were concentrated in the 5–15 cm depth range. Under the 55% ET_c irrigation regime, active solute uptake went beyond the emitter placement depth. The implication is for a fully saturated soil (100% ET_c), and at optimal deficit irrigation strategies (75% ET_c), most of the applied nutrients are readily available for plant uptake. The plant actively absorbs the nutrients because active RNU happens in the canola plant's effective rooting zone depth (ERD). The active water uptake occurs in the default 40%, 30%, 20%, and 10% pattern of the top surface to the lower ends of the ERD (Steduto et al., 2009; Kanda et al., 2020a). The study observed that the root-zones for the respective irrigation regimes (100% ET_c and 75% ET_c) were concentrated in the 0–20 cm region close to the MTI lateral. This is supported by the observation made from rooting patterns from the destructive plant samples. Thus, irrigators need to take note of lateral placement depth as deep-buried lateral can potentially limit RNU. Under the 55% ET_c, solute mobility was pronounced due to preferential flow. Partially dry soils exhibit pronounced solute infiltration (Figures 10a–c).

Minute solute concentration leached beyond the emitter placement depth. The lateral movement was pronounced under the 100% ET_c and 55% ET_c irrigation regimes, a phenomenon consistent with fine-textured soils. The model also displayed a wider root distribution pattern under the 100 ET_c and 55% ET_c irrigation regimes (Figure 11). Sun et al. (2019a), in their MTI laboratory experiment, observed high solute concentrations within the horizontal distance range of 5−13 cm. Interestingly, the observed lateral spread of solute concentration was minimal under the 75% ET_c irrigation. The observation mimicked a well-drained soil scenario. Continued fertigation under extreme DI strategies (55% ET_c) promotes solute leaching, leading to salinization. For high fertilizer demand crops, full and optimal DI under MTI requires periodic flushing to prevent near-surface salinization, potentially affecting directly sown crops. Also, the two irrigation regimes present an opportunity to maintain fertilizer concentrations at the near-surface and potentially below the emitter to reduce the risk of groundwater contamination (see Figure 9 simulation).

The reduced predictive accuracy of HYDRUS 2D/3D under the 55% ET_c regime highlights a model sensitivity zone associated with low water flux. A one-at-a-time sensitivity analysis revealed that soil dispersivity (λ), sorption coefficient, and root nitrate uptake had the greatest influence on nitrate transport predictions, particularly under deficit conditions. Hydraulic parameters such as residual water content and saturated conductivity also significantly affected solute redistribution. These sensitivities suggest that nitrate transport in dry soil profiles is highly dependent on precise calibration of solute and hydraulic parameters, consistent with field-based observations of delayed nitrate mobility under arid conditions (Zhang et al., 2022). While the model captured overall trends, limitations in simulating late-time nitrate retention and vertical leaching in extreme deficit scenarios should be considered when applying HYDRUS for MTI design under water-constrained environments.

The study sought to demonstrate nitrate distribution in a silty clay loam soil profile and nitrate leaching under MTI. We further employed HYDRUS 2D/3D to simulate solute mobility under three irrigation regimes, namely, full irrigation (100% ET_c) and two deficit irrigation (DI) regimes (75% ET_c and 55% ET_c). The results revealed that under full irrigation and optimal DI strategies, maximum nutrient utilization is evidenced by high yields. These findings resonate with the study by Muhammad et al. (2022) which reducing irrigation water availability to 60% of field capacity improved nitrogen metabolism and significantly decreased nitrate leaching in maize. This study observed that passive, soil moisture-responsive water delivery under moderate deficit conditions (75% ET_c) restricted nitrate transport beyond the root zone. Additionally, Ayars et al. (2020) revealed that controlled and slow release of urea as how MTI operates, reduces nitrate loss and aligns nitrogen availability with crop demand, thereby enhancing nitrogen use efficiency (NUE). By mimicking a controlled, low-flux fertigation environment, MTI effectively supports both environmental protection goals and agronomic performance.

Under extreme DI conditions, the canola crop absorbs the fertilizer as a coping mechanism. The coping mechanism is a trade-off for yield and biomass accumulation. The nitrogen budget revealed minimal leaching and increased NUE under full irrigation regimes (100% ET_c) and optimal deficit irrigation regimes (75% ET_c). Extreme deficit methods under MTI are unfavorable for nitrogen availability for the canola crop. The study concluded that nitrate distribution under full and optimal irrigation regimes provided nutrients for the plants, whereas the extreme DI strategy promotes nutrient leaching.

This study provides the first comprehensive modeling-based analysis of nitrate movement under Moistube Irrigation using HYDRUS 2D/3D, calibrated with field observations. By simulating nitrate fluxes under varying deficit irrigation levels, we demonstrate that MTI's self-regulating discharge promotes nitrate retention within the root zone, particularly under mild deficits (e.g., 75% ETc), thus minimizing leaching risk. The integration of solute transport metrics with agronomic indicators such as partial factor productivity of nitrogen (PFP_N) offers a dual-lens perspective on both environmental and efficiency outcomes. Unlike prior MTI studies that focused primarily on wetting front dynamics, this study quantifies the leaching trajectories, identifies model sensitivity zones (through temporal residual patterns, boundary condition influence, and comparative statistical performance), and presents a validation framework for MTI-nutrient interaction modeling. These findings support MTI's role in low-emission, high-efficiency irrigation strategies and offer actionable insights for optimizing fertigation scheduling in water-scarce and nitrate-vulnerable systems.

The study therefore concluded that:

The study was carried out under a controlled environment; therefore, it is recommended that it be done under rainfed field conditions and assess the relative solute mobility for the respective irrigation regimes.