2024 – Dealing with Vertex Perplexity in Parabolic Interpolation of Design Rainfall

Richard Sharpe

Flood modelling and design flood estimation are an integral component of flood risk analysis and management. A key input to the design storms that are simulated in flood models are the rainfall depths applied for varying storm magnitude and duration. For storms more frequent than an annual exceedance probability (AEP) of 1 in 2000, these rainfall depths are estimated from rainfall frequency analyses. For rarer design storms, rainfall depths are generally interpolated between the 1 in 2000 AEP and the probable maximum precipitation (PMP). Current guidance on the interpolation procedure is to fit a parabolic curve to the rainfall depths on each end of the interpolation range, using either a log-log or log-normal scale. A complication can arise if the vertex of the fitted parabola falls within the interpolation range, resulting in unreasonable rainfall estimates that are larger than the PMP. To understand the extent of this problem, the parabolic interpolation methods have been tested on 14 catchments draining into large dams in Queensland. The vertex problem occurred in 20–30% of cases and appeared to occur when the PMP depth was less than twice the 1 in 2000 AEP depth. An alternative interpolation method was developed using the inverse cumulative distribution function for a generalised extreme value (GEV) distribution. The rainfall estimates obtained from the GEV method were similar to the parabolic methods when the parabolic methods were within their range of application. For two additional catchments, the parabolic and GEV interpolation methods also replicated estimates obtained from stochastic analyses in catchment-specific AEP of the PMP studies. As such, the GEV interpolation method produces reasonable rainfall estimates and provides a useful alternative to the parabolic interpolation method since it uses a monotonically increasing function that removes the vertex perplexity issue.