Fuzzy conceptual rainfall–runoff models

A fuzzy conceptual rainfall–runoff (CRR) framework is proposed herein to deal with those parameter uncertainties of conceptual rainfall–runoff models, that are related to data and/or model structure: with every element of the rainfall–runoff model assumed to be possibly uncertain, taken here as being fuzzy. First, the conceptual rainfall–runoff system is fuzzified and then different operational modes are formulated using fuzzy rules; second, the parameter identification aspect is examined using fuzzy regression techniques. In particular, bi-objective and tri-objective fuzzy regression models are applied in the case of linear conceptual rainfall–runoff models so that the decision maker may be able to trade off prediction vagueness (uncertainty) and the embedding outliers. For the non-linear models, a fuzzy least squares regression framework is applied to derive the model parameters. The methodology is illustrated using: (1) a linear conceptual rainfall–runoff model; (2) an experimental two-parameter model; and (3) a simplified version of the Sacramento soil moisture accounting model of the US National Weather Services river forecast system (SAC-SMA) known as the six-parameter model. It is shown that the fuzzy logic framework enables the decision maker to gain insight about the model sensitivity and the uncertainty stemming from the elements of the CRR model.