Uncertainty analysis of soil parameters in soil moisture profile uncertainty using fuzzy set theory

Uncertainty is the measure of the reliability associated with a particular set of results. There are a lot of effective parameters in water movement through the unsaturated zone and obtaining measurement or estimation of them are difficult and have a kind of uncertainty.In this study, a methodology based on fuzzy set theory is presented to express imprecision of input data, in terms of fuzzy number, to quantify the uncertainty in prediction. Richards’ equation as a certain model was solved numerically .To estimate uncertainty in model; input parameters (θs, θr, Ks, α and n) were introduced as fuzzy parameters. After introducing suitable fuzzy membership functions for input parameters, at different β level cuts in input parameters, there will be boundaries for each parameter, then the mathematical operation on fuzzy sets are performed at different β- cut levels and result interval boundaries for the moisture in specific time and location. Corresponding to different β- cuts, fuzzy membership functions were derived for soil moisture at any time and depth. The results showed that uncertainty in simulating soil moisture profile is minimum in saturated phase and it is maximum in advance phase, that’s because of maximum number of parameters that taking part with maximum uncertainty in this phase. The shape of fuzzy membership function for soil moisture in specific time is varying for different depths because the rule of effective initial parameters in any time and depth are different.