A Novel Approach to Design Flood Hydrograph Plotting in Water Management

This study proposes a unified analytical framework for plotting design flood hydrographs (DFH) based on four characteristic parameters: total duration (Tt), time to peak (Tp), flood volume (W), and peak discharge (Qp) associated with specific exceedance probabilities. The objective is to improve the mathematical representation of hydrograph shapes for engineering applications and future updates of hydrological design standards. Leveraging a dataset of 150 representative cross-sections of Romanian rivers, the research employs normalized axes to facilitate a dimensionless comparative analysis. This study presents three modeling approaches: the Refined Rational Function (RRF), which significantly enhances the framework initially developed by Radu Cadariu; a [4/4] Padé approximant, transitioning from a second-degree to a fourth-degree rational framework and featuring a depressed quartic numerator and a fourth-degree denominator for superior degrees of freedom; and the plotting of non-parametric hydrographs via natural cubic spline interpolation. The results demonstrate that the RRF method extends the admissible range of the shape coefficient γ beyond the traditional interval 0.15–0.50, enabling representation of hydrographs with γ values up to 0.99. The [4/4] Padé approximant provides improved flexibility for asymmetric and multimodal hydrographs, while the natural cubic spline interpolation method ensures accurate reconstruction of atypical hydrographs with volume conservation errors below 3%. These methods offer a unified, objective framework, ensuring high accuracy and adaptability across diverse Romanian hydrological regimes.