A Total Probability Approach to Flood Frequency Analysis in Tidal River Reaches

The joint effect of tidal levels and streamflow on flood risk along river reaches is currently poorly understood and there is little help to guide those responsible for providing flood protection to communities at risk. Determining Annual Recurrence Intervals (ARIs) for river reaches with non-constant downstream boundary conditions is complicated due to an inconsistent ordering of extreme events at various locations within a river reach. To date the methods commonly used to assess such channels are approximate, lack suitable theoretical foundation and although generally conservative, may underestimate flood risk at certain regions under particular conditions. This paper outlines the manner in which joint probability problems in general should be treated and presents a methodology for determining ARIs along tidally affected reaches based on a combination of a total probability approach and water surface curves and shows some surprising results, some of which may be counterintuitive. The method, based upon numerical integration of the underlying equations, is general and is capable of including correlation between the two, should any exist. A Monte-Carlo formulation has been developed, due to the complexities once both spatial and temporal dependencies are included. A comparison with a simple approximation is discussed.