EXISTING MATHEMATICAL METHODS FOR UNCERTAINTY ASSESSMENT - Modelling Uncertainty in Flood Forecasting Systems - page 32

(3.16)

where are defined as

(3.17)

(3.18)

This can be illustrated by taking a simple example of a uniform flow formula given by

(3.19)

where Q is the discharge, A is the area, R is the hydraulic radius, S is the slope of the
water surface, and N is the Manning's roughness coefficient. Assuming A, R, S and N are
uncertain parameters represented by their membership functions, the lower and upper
bounds of the membership function for Q for a given ! -cut are given by

(3.20)

(3.21)

3.2.2 Expert judgement-based qualitative method

Expert judgements play a significant role in the analysis of uncertainty. When there is
lack of data to quantify uncertainties in various parameters, expert judgement may be
used to make the best possible estimates of uncertainty. This is often the case in complex
systems involving many uncertain parameters, the PDFs or moments of some of which
cannot be determined explicitly by statistical observations due to insufficient data.