Uncertainty in the estimation of mean annual flood due to rating-curve indefinition

When rating-curves of the form Q = gamma(h + alpha)(beta) are fitted by least-squares, goodness of fit as measured by the coefficient of determination r(2) is Often close to 1, suggesting that estimated discharges have high precision. This can be illusory if (a) no account is taken of the uncertainty in estimate of the parameter alpha, and/or (b) the stage h at which discharge is to be estimated is such that log(e)(h + alpha) lies far from the mean value of this variable calculated using the data points (h,Q) that define the rating-curve. Furthermore, since the annual maximum discharges in any M year period of record are all estimated from the fitted rating-curve, they will be correlated, even if the annual maximum stages in the M years are statistically independent. The usual maximum likelihood procedures for fitting extreme-value distributions do not take account of this correlation. Expressions are given for the conditional (on the values of the M annual maximum stages) and unconditional variances of the mean annual flood (Q) over bar which take account of rating-curve uncertainties. (C) 1999 Published by Elsevier Science B.V. All rights reserved.