Assessing the hydraulic parameter’s uncertainty of the HYDRUS model using DREAM method

Introduction
The accuracy and efficiency of the analytical and numerical models to describe water flow in soil, in unsaturated environments are affected by input data uncertainty, model structure uncertainty, and hydraulic required parameters by the model. Parameter uncertainty has an impact on the model simulation by displaying uncertainty in the simulation results. Hence, the quantitative assessment of the parameter uncertainty and its influence on the model simulation is important in reducing simulation uncertainty. The Bayesian method is a common method for uncertainty analysis that has widespread application in science and engineering to reconcile the concepts of model structure with data (assimilation of input and model outputs, and inference of the parameters). Therefore, a Markov chain Monte Carlo (MCMC) algorithm based on the Bayesian inference to improve the computational efficiency of the analysis was used. The DREAM algorithm is one of the adaptive methods, the Markov chain sampling method which is known as an effective method in used soil-water models due to searching in vast space and solving complex models with a large number of variables. In addition, one of the main problems in using Bayesian inference for hydrological models is their nonlinear relations and using them in heterogenic conditions, DREAM algorithm has been developed to use Bayesian analysis in soil-water problems. Hence, this study has taken the efficiency of the DREAM algorithm as a global optimization method and convergence parser in sampling chain paths and posterior distribution of parameters. The HYDRUS model is a hydraulic model to study the soil-water processes that include nonlinear equations. In addition, center pivot irrigation is a modern method of water management that need to study using hydraulic models under various conditions. Hence, the main purpose of this article is assessment the role of the management method and environmental prevailing conditions in the uncertainty of hydraulic parameters and model structure in estimating water flow under a center pivot irrigation system in four-year alfalfa cultivation.
 
Materials and Methods
The profile was dug at 120 cm depth. The soil profile was divided into three layers and two soil texture classes. The physical-chemical soil properties were studied in each layer. Assessment of soil properties stated that exists a heterogeneous layer in this soil profile. TDR was used to measure soil water content before, after, and during every irrigation period. Soil water content was measured from 10 June to 11 September 2018 consecutively. The van Genuchten-Mualem equation was used to estimate soil hydraulic parameters and describe water flow in the HYDRUS model. The HYDRUS model is coupled with the DREAM algorithm to evaluate parameter uncertainty and the model structure uncertainty based on measured soil water content data using TDR in every three categorized layers. In this article the p-factor, d-factor, and S and T indices were used to evaluate parameter uncertainty, the model structure uncertainty, and model performance.
 
Results and Discussion
The qualitative evaluation of soil hydraulic parameters was compiled by the posterior distributions of parameters in every three depths. The parameters had a normal distribution, the model could be recognized the value of parameters, whereas the parameters didn't have a normal distribution and had high uncertainty. The “α” parameter had high uncertainty in every three depths, in other words, in two soil texture classes, this parameter compared to other parameters had high uncertainty. Along heterogeneous soil profiles, the "α", "θs", and "n" parameters were shown high uncertainty to the Hydraulic conductivity parameter of soil saturation. The value of p-factor and d-factor were obtained equal to 83.6 and 0.13 on the soil surface and 10 and 0.14 on the subsurface soil. Reducing the p-factor index in the lower soil layers explained the overlap between measured soil water content points with estimated soil water content. So, along the soil profile could be observed high uncertainty of soil hydraulic parameters under center pivot irrigation. On the other hand, increasing the d-factor index in the sub-surface soil stated increased confidence intervals which indicate the model structure uncertainty and the poor performance of the HYDRUS model in heterogenic conditions. Also, the value of two indices of S and T were obtained 0.3 and 0.76 for the surface layer and 0.88 and 1.4 in the lower soil layers respectively. The values of S and T indices stated the ability of the DREAM algorithm to reduce parameter uncertainty and the model structure uncertainty in soil surface whereas the trend of changes in the two indices explained Asymmetry of the confidence interval with respect to the measured points and the pre-estimation of the model in the lower soil layers. Therefore, the trend of the d-factor, S and T indices showed the influence of the mathematical-physics concepts in the HYDRUS model structure in the heterogenic layer and unsaturated conditions. The research results stated the ability of the HYDRUS model in describing water flow under center pivot irrigation as a novel method of managing water sources, especially in arid and semi-arid areas. Even though, the results of the assessment indices showed decreasing model performance in the lower soil layers.
 
Conclusion
The results of soil profile indicated the effect of parameter uncertainty and the model structure uncertainty in soil moisture estimation affected by management and environmental conditions. In addition, the results showed the ability of the DREAM algorithm to simultaneously evaluate the uncertainty of the parameters and the model structure in order to increase the accuracy of the HYDRUS model under the applied conditions. Also, in this study, the DREAM algorithm indicated the role of the heterogeneous layer in parameter uncertainty and its effect on the accuracy of the model performance. The DREAM algorithm is a practical and management option to evaluate the HYDRUS model during the application of the center pivot irrigation method at the farm level. So, this is an appropriate option to study the efficiency of the HYDRUS model using modern methods in agricultural practices. Moreover, to survey the efficiency of hydraulic models under the prevailing conditions could be used the ability of the DREAM algorithm based on the Markov chain.