Abstract
Determination of soil hydrodynamic parameters at field scale is of great importance for modeling soil water dynamics and for agricultural water management. The direct estimation of those parameters is time-consuming and afflicted with serious uncertainties. Inverse modeling is known to get efficient technique for solving non-linear problems in hydrology. Levenberg–Marquardt (LM) algorithm is a gradient-based method, which has been widely used for solving inverse soil water flow problems. In the LM algorithm, sensitivity coefficients are mainly evaluated by numerical differentiation methods. However, sensitivity coefficients are difficult to be precisely calculated by numerical differentiation methods, if transient states and non-linearities are involved. In this paper, a new approach is proposed for sensitivity analysis using the complex variabledifferentiation method (CVDM) to estimate simultaneously the hydraulic and dispersive properties of unsaturated soil from in-situ experiments. In this approach, the sensitivity coefficients can be determined in a more accurate way than the traditional finite difference method. The results show that the new inverse analysis method in the present work has high accuracy, validity, uniqueness and higher inversion efficiency, compared with the previous least-squares method. The simulated and measured water contents and tracer concentration were generally close. Overall, it was concluded that the CVDM is a promising method to estimate hydro-dispersive parameters in the unsaturated zone.
Highlights
Modeling of water and solute transport in soil systems is often done by numerical simulations, based on the Richards equation
The convergence curves by using the conventional LM algorithm are shown in Fig.1(a), Fig.1(b), Fig.1(c) and Fig.1(d), in which the convergences are achieved after 23 iterations
Each optimized parameter is converged to its real value, sensitivity coefficients are not accurately calculated by using the conventional LM algorithm especially for ks parameter
Summary
Modeling of water and solute transport in soil systems is often done by numerical simulations, based on the Richards equation. To obtain reliable simulation results, exact knowledge of the soil hydraulic properties at the scale of interest is indispensable [1] This is problematic, because predictions of water and solute transport for hydrologic management decisions are generally needed at larger scales such as the field scale, whereas these proprieties are usually determined in the laboratory on small soil cores. In this algorithm, we introduce the complex variable differentiation method (CVDM) into the conventional LM algorithm, within which the sensitivity coefficients are precisely calculated, rather than using numerical differentiation method in conventional LM. Knowledge, this is the first application of the CVDM in the soil physics area with real field conditions
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