Comparative Analysis of Parameter Optimization of Theoretically Consistent IDF Models of Rainfall Intensity

In an attempt to get the best parameter estimations of the theoretically consistent IDF (Intensity Duration Frequency) models of rainfall intensity for the entire state of Baden Wuerttemberg, three well-defined optimization algorithms such as Differential Evolution (DE), Nelder Mead (NM), and TNC Truncated Newton (TNC) are taken into account for comparison.

Seven-parametric IDF model contains mean intensity µ, intensity scale parameters λ₁, λ₂ , time scale parameter α, fractal/smoothness parameter Μ, Hurst parameter Η, exponent of the expression of probability dry θ,  and tail index ξ, which are obtained by minimizing the error between empirical k-moments and model quantiles. Error metric focusing on distribution quantiles x(k,T) is thus minimized for all available scales k and a series of return periods T . Non-linear solver is chosen to perform this step as these errors are non-linear functions of the parameters.

All results are demonstrated visually, and a final decision is made on the basis of precisely fitted parameter values to the model. This crucial step will also assist us in finding the optimum design values for stormwater and floods.