Abstract: Hydrological simulation of a watershed is challenging due to bias in input data, measurements, and the mismatch of spatial-temporal scales between the model and the physical system. We conducted a monthly runoff simulation to evaluate the effects of uncertainty propagation in the soil and water assessment tool (SWAT). We used the Particle Swarm Optimization (PSO) algorithm to investigate the effects of the objective functions (NSE, R2, and KGE) used to calibrate the hydrologic parameters in the Karkheh River watershed. In 18 sub-basins, 37 parameters were selected based on previous studies and parameter sensitivity analysis using the Latin Hypercube sampling method to simulate runoff in 6 hydrometric stations. The results showed an acceptable correlation between the simulated and observed flows. However, the best simulation occurred at Seymareh station.
Keywords: SWAT model, runoff simulation, objective function, NSE, R2, KGE
Introduction: Simulation of hydrological processes at local, regional, and global scales has played a key role in addressing many environmental, social, and water resource management challenges. However, uncertainty in model output remains a limitation in simulating hydrological processes.
Various methods have used for hydrological modeling (Yuan et al., 2020), among of them, the Soil and Water Assessment Tool (SWAT) has widely used for assessing hydrological and pollutant impacts on water and land management (Prochnow et al., 2008; Meng et al., 2018; Kuma et al., 2023), evaluating ecosystem services (Nedkov et al., 2022; Uniyal et al., 2023), quantifying climate change impacts (Mandal et al., 2021), estimating soil erosion (dos Santos et al., 2023), evaluating management practices (Yuan and Koropeckyj-Cox, 2022), analyzing the impact of land use and cover changes on river runoff (Martínez-Mena et al., 2020; Liu et al., 2024), simulation the hydrological characteristics of the watershed (Akbari et al., 2022 and Gasirabo et al., 2023).
Many parameters in the model structure are generally determined through calibration due to the high cost of field measurements. The spatial-temporal variations of parameters cause significant amounts of uncertainty in the results of water resources simulation and management; therefore, they must be calibrated to ensure accurate hydrological modeling (Akoko et al., 2021).
In this research, SWAT was used to simulate runoff in the Karkheh watershed. Three objective functions NSE, R2 and KGE were applied through PSO algorithm to calibrate the model. Then, the effect of aforementioned-objective functions was evaluated.
Methodology: The Karkheh Basin, located in western Iran (Figure 1), has an area of about 50,764 km2. Approximately 80% of the basin area is in the Zagros Mountains, which produce almost all the surface runoff of the basin. Karkheh River, the third river in Iran, flows in the largest reservoir dam in Iran and the Middle East; it has four main branches, including Gamasyab, Qarasu, Siamareh, and Kashkan. The Karkheh basin has a Mediterranean climate with cool, humid winters and hot, dry summers. The average annual rainfall varies from 150 mm/year in the lower dry plains to 750 mm/year in the mountainous parts (Masih, et. al., 2011).
Monthly temperature and precipitation data from 8 meteorological stations (Dehloran, Kermanshah, West Islamabad, Malayer, Borujerd, Khorramabad, Ilam, and Ahvaz), the map of land use, soil, and DEM of the region, and monthly discharge statistics from 6 hydrometric stations (Pol-Chehr, Doab-e-Vaisian, Ghorbaghistan, Seymareh, Pol-e-Dokhtar, and Pay-Pol) were applied to SWAT to build and calibrate the hydrological model of the Karkheh basin.
Particle Swarm Optimization (PSO) moves a collection of individuals called particles in steps throughout a region. It evaluates each particle's objective function at each step and decides on its new velocity until it takes optimum values. The modified PSO algorithm, introduced by Shi and Eberhart (1998), to the velocity update formula, can be presented by Eqns 1-2.
where Xi = [Xi,1, Xi,2, ..., Xi,D] represents each individual particle; Vi=[Vi,1, Vi,2, ..., Vi,D] represents the velocity of each particle Pbest is the best position of each partticle; and Gbest is the best location of the total swarm., the experiences are augmented by two factors c1 and c2 and two random numbers generated between [0,1] while the motion is multiplied by an inertial factor varying between [wmin, wmax].
To control and evaluate the ability of hydrological models to simulate a quantity, some criteria are usually used. In this study, the criteria of determination coefficient (R2), Nash-Sutcliffe efficiency coefficient (NSE) and Kling-Gupta efficiency coefficient (KGE) have been used to control and evaluate the ability of hydrological SWAT model, Eqns. 3-5.
Results and Discussion: Table 2 represents the value obtained at the Pol-Chehr station for the Nash-Sutcliffe, R2, and KGE objective functions, which are 0.62, 0.62, and 0.68, respectively, and are satisfactory. The values of NSE and KGE are 0.64 and 0.60, respectively, where the R2 objective function is 0.67, which indicates good performance; they are greater than 0.5 (Van Leeuw et al., 2003). Furthermore, it is clear that, at this station, the R2 objective function is the best objective function for reflecting the proportionality of a hydrograph that can be considered.
The graph comparing the observed values with the best runoff simulations at Pol-e-Chehr station with all objective functions in Figure 7 shows that in early 2004 and 2007, less runoff was simulated, and in early 2005, more, and that the results of using all functions generally coincide.
According to Table 3, at Qoorbaghistan station, using the KGE and NSE as the objective function for model calibration has led to satisfactory results, while using R2 objective function cause no satisfactory values of the NSE and KGE criteria with amount of 0.13 and 0.35, respectively, Figure 8.
At the Doab-Visian station, the use of all three objective functions has yielded acceptable results (Table 4). Comparing the observed runoff, Figure 9 shows the best runoff simulations at this hydrometric station with different objective functions. It is observed that although the simulation values are consistent, the maximum runoff values are not well estimated.
Table 5 reveals that all the objective functions have good results at the Simareh station. The simulation results for this station are better than those obtained for the other stations studied. Comparing the observed values with the best runoff simulations of this hydrometric station with three objective functions (Figure 10) indicates the coincidence of the results.
At Pol-e Dokhtar station, the results obtained by all objective functions are good, and comparison conducted between the observed and the best runoff simulations values (Figure 11) shows that at the peak points, estimated runoff using the KGE and R2 functions are more than what projected by the NSE.
Conclusion: This research applied SWAT to estimate the runoff flowing in the Karkheh Basin, then conducted the PSO method to calibrate the SWAT model using objective functions of R2, NAS, and KGE. The results showed the most observational data and the highest band thickness at the Qoorbaghestan station, in contrast to the lowest band thickness and percentage of measured data obtained at the Doab-Visian station. The highest value of the Nash-Sutcliffe objective function for the Simireh station, 0.66, indicates that the best simulation performance belongs to this station, which is in the range of good results. Simultaneously, the values of R2 and KGE objective functions are 0.68 and 0.81, respectively, representing the best results in this study.