6-1- The model calibration and validation
As shown (Table 3) the NSE, SE, and MAE calculations are presented to evaluate the simulation results. The model's accuracy can be determined by how close the values of MAE and SE are to zero, and the value of NSE is to one. According to the table, the calibration phase reveals that the NO3 achieved the most favorable NSE value at 0.98, signifying an exceptional level of accuracy. In both the calibration and validation stages, the BOD parameter recorded the MAE value at 0.27, highlighting its reliable simulation across both stages. Conversely, the least favorable SE value in calibration was observed for DO at 0.24, which suggests a greater variance in calibration for this parameter. In the validation phase, DO registered the lowest SE value at 0.24, which, while lower than BOD in calibration, still indicates a credible simulation outcome.
The range of SE values computed in this simulation exemplifies the validity of the model: a lower SE signifies a stronger agreement between the simulated and observed values. Additionally, a high NSE value is emblematic of the model's adeptness at simulation, reinforcing confidence in the model's ability to emulate real-world processes accurately. This comprehensive evaluation of the model's performance, through these metrics, is crucial for verifying the reliability of its predictions and for informing potential model improvements.
Table 3
The NSE, SE, and MAE criteria values for calibration and validation of QUAL2Kw model
Parameters | Calibration | Validation |
NSE | MAE | SE | NSE | MAE | SE |
DO (mg/l) | 0.30 | 0.30 | 17.12 | 0.80 | 0.18 | 0.24 |
BOD (mg/l) | 0.97 | 0.27 | 1.31 | 0.81 | 0.27 | 1.31 |
NH4 (µg/L) | 0.87 | 9.27 | 15.91 | 0.46 | 25.52 | 22.6 |
NO3 (µg/L) | 0.98 | 58.07 | 299.10 | 0.96 | 49.36 | 210.6 |
6-2- The parameters uncertainty investigation
In the course of this study, the GLUE method was employed to create a comprehensive set of potential model parameters. A thousand different sets were generated, guided by the value ranges presented in Table 2, using the Monte Carlo technique. These parameter sets underpin the probabilistic assessment of uncertainty in the model's outputs.
Figure 4 offers a series of scatter plots that visually represent the probability distributions of stochastic variables, including upstream flow, agriculture release flow, oxidation, nitrification, and denitrification rates, following the methodology described in Eq. 7. Through the execution of the model across a spectrum of parameter values within their designated limits, the resultant graphs reveal the nature of parameter uncertainty distribution. Distributions that appear flatter suggest a higher degree of uncertainty in the model parameters, whereas more peaked distributions denote a tighter concentration of values, suggesting lower uncertainty and more precisely defined parameters. Moreover, Fig. 4 facilitates the sensitivity analysis, portraying how the BOD, DO, NH4, and NO3 rates respond to changes in the stochastic variables. The insights drawn from these analyses are critical:
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- uncertainty of the agriculture release flow is more pronounced when compared to the other parameters, indicating its significant impact on the model's predictive variability.
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- the upstream flow affects all the listed parameters, confirming its role in the river water quality.
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- DO, NH4, and NO3 are particularly sensitive to changes in the nitrification rate, suggesting that nitrification processes are key to understanding variations in these water quality indicators.
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- the sensitivity of BOD and DO to the oxidation rate underscores the importance of the river's self-purification.
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- the denitrification rate exclusively influences the NO3 parameter, pointing to the specificity of denitrification in nitrogen cycling within the river system.
These findings illustrate the interconnectedness of hydrological and biochemical processes in river systems and underline the importance of accurately determining the influential parameters for effective water quality management. The sensitivity analysis not only aids in model calibration but also in identifying key processes for targeted monitoring and management strategies.
6-3- Sensitivity Analysis
In Table 4, the sensitivity analysis results indicate that the NO3 parameter has the greatest impact on the oxidation rate (as showen by Fig. 4). Additionally, it exhibits significant sensitivity toward the upstream flow, agriculture release flow, nitrification, and denitrification rates. Conversely, the DO parameter primarily influences the quantity of all stochastic variables in the model, but is the least sensitive parameter overall.
Table 4
Sensitivity analysis for the parameters
Parameters | Upstream flow (m3/s) | Agriculture release (m3/s) | Oxidation (1/day) | Nitrogen cycle (1/day) |
Nitrification | Denitrification |
DO | 0.98 | 1.23 | 1.04 | 1.23 | 1.22 |
BOD | 1.87 | 2.45 | 1.87 | 2.73 | 2.73 |
NH4 | 25.52 | 27.31 | 33.92 | 39.18 | 33.64 |
NO3 | 307.64 | 378.89 | 431.34 | 425.91 | 430.09 |
6-4- Uncertainty bands of the qualitative parameters
Figure 5, as described, illustrates the uncertainty bands for the water quality parameters BOD, DO, NH4, and NO3 in the mountainous Abbas-Abad River. The visual representation of uncertainty in this figure is crucial in understanding how water quality varies along the river under different seasonal conditions. The blue bands that represent the uncertainty range for each parameter across the river’s length provide a visual quantification of the model's predictive variability. The variation between the green and red dashed lines, denoting the uncertainty for the wet and dry seasons respectively, reveals seasonal influences on water quality.
The observed higher values of BOD, and NO3 during the dry season suggest an intensified level of pollution, likely due to decreased dilution capacity as river flows diminish. Conversely, the concentration of DO, despite being higher in the dry season, shows a declining trend along the river's course, highlighting a degradation in water quality. This inverse relationship between BOD and DO is typical, as increased organic matter from pollution leads to higher oxygen consumption during decomposition, thus lowering DO levels. Interestingly, the NH4 concentrations are reported to be higher in the dry season only within a specific section of the river (between 4 to 6 Km from the source point), which may indicate localized pollution sources or processes affecting ammonia levels.
The broad uncertainty range for NO3, stretching from 500 to a substantial 4500 mg/L, signifies a high degree of unpredictability in nitrate concentrations, which could be influenced by factors such as agricultural runoff or wastewater discharges. On the other hand, the relatively narrower uncertainty range for DO, from 3 to 15 mg/L, though indicative of variability, suggests that the model has more confidence in predicting oxygen levels across the river.
The overall trend of increased pollution during the dry season is an important finding, as it underscores the critical impact of hydrological variability on river water quality. The reduced river flow during dry periods can exacerbate the effects of pollutant inputs, highlighting the importance of managing both point and non-point sources of pollution, especially in times of low water availability. These insights can guide targeted management interventions to mitigate pollution and protect the river ecosystem, particularly during vulnerable dry seasons.