Abstract
A FORTRAN code for liquid water flow in unsaturated soil under the isothermal condition was developed to simulate water infiltration into Yolo light clay. The governing equation, that is, Richards' equation, was approximated by the finite-difference method. A normalized sensitivity coefficient was used in the sensitivity analysis of Richards' equation. Normalized sensitivity coefficient was calculated using one-at-a-time (OAT) method and elementary effects (EE) method based on hydraulic functions for matric suction and hydraulic conductivity. Results from EE method provided additional insight into model input parameters, such as input parameter linearity and oscillating sign effect. Boundary volumetric water content (θ L (upper bound)) and saturated volumetric water content (θ s) were consistently found to be the most sensitive parameters corresponding to positive and negative relations, as given by the hydraulic functions. In addition, although initial volumetric water content (θ L (initial cond)) and time-step size (Δt), respectively, possessed a great amount of sensitivity coefficient and uncertainty value, they did not exhibit significant influence on model output as demonstrated by spatial discretization size (Δz). The input multiplication of parameters sensitivity coefficient and uncertainty value was found to affect the outcome of model simulation, in which parameter with the highest value was found to be Δz.
Highlights
Sensitivity analysis is used for various reasons, such as decision-making or development of recommendations, communication, increasing understanding or quantification of system, and model development
∂ŷi/ŷi ∂aw/aw where Xi,w is referred to as normalized sensitivity coefficient for wth input parameter at ith observation point, ŷi is model dependent variable value at ith observation point, and aw is wth input parameter value
In order to avoid unnecessary redundancy, we only provide the algebra for (8) that is used for sensitivity analysis in the current study as follows: θL(k)n+1 − θL(k)n Δt
Summary
Sensitivity analysis is used for various reasons, such as decision-making or development of recommendations, communication, increasing understanding or quantification of system, and model development. Sensitivity analysis is a tool to assess the effect of changes in input parameter value on output value of a simulation model. In this aspect, the sensitivity coefficient, in a normalized form, is given in the following relation: Xi,w =. Where Xi,w is referred to as normalized sensitivity coefficient for wth input parameter at ith observation point, ŷi is model dependent variable value at ith observation point, and aw is wth input parameter value This method utilizes derivative at a single point and it can be applied as OAT method when one input parameter is varied while holding other parameters fixed.
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