Sensitivity analysis of hydraulic parameters of transport heavy metals Cd, Ni, and Zn in disturbed and undisturbed loamy soil columns

Introduction
Soil contamination due to heavy metals is a global environmental issue. One vital aspect for understanding the impact of a contaminant in porous media is to describe their transport behavior using appropriate models. The governing equations for solute transport in soil consist of the convection–dispersion equation (CDE) and the mobile–immobile model (MIM). Mathematical models are usually used to evaluate solute transport in porous media. The first model used to express the transport of solutes and pollutants in porous media is CDE it provides acceptable and satisfactory results in homogeneous soils in laboratory tests. Hydrus-1D is a modeling environment for simulating water, heat, and solute movement in one-dimensional variably saturated media. Sensitivity analyses and model identification are standard approaches in modeling applications to investigate the relative importance of model components that control the system’s behavior. The sensitivity analysis is applied to identify the parameters that influence the model performance most. The sensitivity analysis is defined as the rate of variation in the model outputs due to changes in the input parameters. This study is a fundamental practice for analyzing the behavior of a model under different conditions of an application. The sensitivity analysis could be a practical and powerful tool for investigating the role and importance of model components, such as parameters and forcing data on the model responses.
 
Materials and Methods
The loamy soil samples were collected in both disturbed and undisturbed forms from a farm in the Qaramalek area with appropriate humidity located in western Tabriz, Iran, at 38º 5' 59.89'' north and 45º 12' 38.57'' east. To determine and present breakthrough curves, concentration values are required throughout the laboratory columns at different times. To simulate the CDE model, Hydrus software was used. Solute transport parameters such as diffusion coefficient (D), distribution coefficient (Kd), and dispersion coefficient (β) were estimated using soil hydraulic parameters and data related to the metal concentration of cadmium, nickel, and zinc by an inverse modeling method. A sensitivity analysis was carried out for the identification of the most influential factors on the model output. This method examines the impact of input data on a given model and its actual conditions. In line with this purpose, in each run, one input data was changed to a value equal to Positive and negative five to 15%, and the other input data was kept constant. To identify the effect of the input parameters of a given model on its output, the sensitivity analysis for the Hydrus model was utilized. The parameters of hydrodynamic dispersion coefficient (D), distribution coefficient (Kd), and spreading parameter (β) were changed between five to 15 %. Sensitivity analysis was carried out on cadmium, nickel, and zinc metals with densities equal to 50, 100, and 150 mg.l^-1 in two disturbed and undisturbed soils.
 
Results and Discussion
Examining the breakthrough curves of cadmium in disturbed and undisturbed soils shows that the fitted curves using the Hydrus model and the measured curve almost coincide with each other, which is more obvious in disturbed soils. It should be noted that the model fits better in the disturbed soil than in the undisturbed soil. This may be due to the disruption of the structure the increase in the contact surface of the particles in the disturbed soil and the presence of heterogeneity in the undisturbed soil column. The simulation results show the transport of heavy metals (Zn, Ni, Cd) and Hydrus output have the highest and the lowest sensitivity to dispersion coefficient β and diffusion coefficient (D), respectively. In general, the impact of input parameters can be reported as follows: spreading parameter (β) > distribution coefficient (Kd) > dispersion coefficient (D). Therefore, it can be observed that D has a negligible effect on the model results; and consequently, measurement errors can be ignored.
 
Conclusion
Sensitivity analysis is used to analyze model behavior under different conditions. This analysis is used to investigate the relative importance of model components that control the system’s behavior. In this research, the transfer of hydraulic parameters of heavy metals Cd, Ni, and Zn in disturbed and undisturbed loam soil columns with initial concentrations of 50, 100, and 150 mg.l^-1 was performed under the simulation of the Hydrus-1D model. The comparison of the simulated BTCs of the Hydrus-1D model and the measured data indicates a high agreement between the simulation curves and the measured data. Solute transport parameters such as hydrodynamic dispersion coefficient (D), distribution coefficient (Kd), and spreading parameter (β) were estimated using soil hydraulic parameters and data related to Cd, Ni, and Zn metal concentration by inverse modeling method. Based on the results of sensitivity analysis, the spreading parameter (β) and hydrodynamic dispersion coefficient (D) had the highest and lowest sensitivity, respectively. In other words, due to the significant effect of β changes on the output values of the model, this parameter should be measured more accurately and on the other hand, the measurement errors of parameter D can be ignored. The degree of sensitivity of the parameters was independent of the initial concentration of the elements.