Abstract

An estimate of the number of floods per century that can be expected at any given point of a river would obviously be an important piece of information when any expensive flood-prevention scheme is under discussion. Gumber (1958) has discussed such an estimation for a non-tidal stretch of river, and has shown how to derive estimates from existing flow data, using his method of maxima. The object of the present paper is to put forward a method of solving the intrinsically more complex problem of estimating the probability of flooding for a tidal stretch.

The mathematical theory is first briefly presented, and a generalmethod of finding the estimate is discussed. The final section is concerned with an application of the method to the River Trent at Gainsborough.

MATHEMATICAL THEORY

It has been found necessary to use a certain number of elementary statistical concepts in the following section, and for the convenience of readers unfamiliar with such concepts an examination of them will be found in the Appendix, p. 364.

Let T denote tide-height in feet at some fixed measuring point near the mouth of the river, and let F denote flow in cusec. at a point of the river which is effectively or actually non-tidal. If it is assumed that no important tributaries enter the river between the two measuring stations, it is seen that the water height H at any point on the tidal reaches will be dependent only upon T and F.