Accurate estimation of event-scale peak discharge is essential for flood risk assessment and infrastructure design, yet conventional hydrologic modelling approaches often require extensive calibration procedures and computationally demanding optimization. This study presents a parsimonious event-based framework for estimating hourly runoff hydrographs and peak discharges through direct parameter estimation from physically consistent rainfall-runoff event pairs. The framework integrates precipitation event identification, streamflow baseflow separation, and event pairing with a process-based hydrologic model combining the Natural Resources Conservation Service Curve Number method for precipitation loss estimation and the Natural Resources Conservation Service Unit Hydrograph method for direct runoff transformation. Model parameters, including catchment lag time, peak rate factor, and seasonal Curve NumberPrecipitation relationships, are estimated directly from observed rainfall-runoff events, eliminating the need for inverse numerical optimization against an explicit likelihood or objective function. The framework is evaluated across seven catchments with varying drainage areas within the Housatonic River Basin, using a leave-one-out cross-validation approach. Results demonstrate consistent performance across catchments, with negligible bias and similar residual error characteristics between parameter estimation and evaluation datasets, indicating robust performance for unseen events. Compared with a geometric mean estimator, the proposed framework reduces the standard deviation of the logarithmic residuals by roughly 40 to 60 percent, providing a computationally efficient and physically interpretable tool for large-scale event-based peak discharge estimation.
The probabilistic characterization of compound extreme events, defined as those arising from the joint action of several (generally dependent) drivers, is a central problem in engineering hydrology and water resources. The copula-based scenarios customarily used in the literature (i.e., OR, AND, Kendall, and survival Kendall) summarize multivariate risk by tracing a single boundary in the unit hypercube and assigning to it a target probability, or equivalently a return period. Except for the rectangular OR and AND cases, the prescribed probability attaches to the bounding layer rather than to the hazardous region itself, which is then determined only implicitly. Moreover, the marginal exceedance rates of the drivers are fixed by the level of the critical layer and cannot be set independently. Here we introduce a copula-based approximation that characterizes the hazardous region directly as a full-dimensional set to which the target exceedance frequency is attached. The boundary of this set consists of linear segments meeting at a vertex at the point of maximum curvature of an equiprobability surface of the copula. Crucially, the per-variable exceedance rates are predefined by the user, so that application-specific marginal rates are reconciled with the joint target within a single region, allowing asymmetric compound occurrences (e.g., high discharge under moderate coastal water level, or the reverse) to be accommodated naturally. We develop the formulation in the frequency domain for both exchangeable and non-exchangeable copulas, provide a direct extension to higher dimensions, and demonstrate it on the symmetric and asymmetric versions of the Clayton and Gumbel copulas, taken as representative models of lower- and upper-tail dependence. The resulting construction is simple to implement and particularly suited to early-warning systems, in which a hazardous combination of drivers must be recognized as it develops.
This study introduces the Burak Diagrams by incorporating an orthogonal bias axis into the Taylor Diagram (Taylor 2001), thereby enabling multiple performance metrics to be represented as analytically derived 3D surfaces. Three Burak Diagrams are developed: BD-Clim for climatological simulations, BD-HydNSE for hydrological simulations incorporating the Nash–Sutcliffe Efficiency (NSE) , and BD-HydKGE for hydrological simulations incorporating the Kling–Gupta Efficiency (KGE) . All three diagrams share a common theoretical foundation based on the geometric decomposition of the root-mean-square difference ( RMSD or E ) proposed by Taylor (2001). BD-Clim extends the Taylor Diagram by incorporating bias ( E ) as a third axis while preserving the original representation of correlation ( R ), variability, and centered root-mean-square difference ( E^' ), with E (or RMSD ) represented as analytic surfaces. Similarly, BD-HydNSE and BD-HydKGE incorporate percent bias ( PBias ) as a third axis while preserving the original Taylor Diagram representation, with NSE and KGE represented as analytic surfaces for evaluating hydrological model performance. Interactive visualization tools for all three diagrams are developed in the R programming environment and are available on CRAN as the “burakDiagrams” package. Together, the proposed diagrams support the simultaneous interpretation of complementary performance metrics, improve insight into model behaviour, and facilitate more comprehensive intercomparison of climatological and hydrological simulations. By representing RMSD , NSE , and KGE as surfaces, the diagrams visually reveal how these metrics vary in response to changes in their underlying component metrics.
The stage-discharge rating curve is an important tool for streamflow estimation, especially in poorly gauged basins where direct streamflow measurements are often unavailable. This study presents an integrated comparative evaluation of seven rating curve models using calibration and independent testing performance, flow-stratified predictive accuracy, extrapolation under very high flows, and uncertainty behaviour of estimated flows at a gauging station in the Shilabati River basin, eastern India. The rating curve models include classical power-law, polynomial, classical segmented power-law, Bayesian segmented rating curve (BaRatin), generalised power-law model (GPLM), vertically-segmented power-law, and Gaussian Process Regression (GPR). Although all models achieve good calibration and testing performance and comparable accuracy at low and moderate flow values, major differences are observed when models’ performance is assessed at high flows, extrapolation conditions and uncertainty quantification. In this investigated site, classical models show comparatively weaker extrapolation performance, while GPLM, GPR, and vertically segmented power-law models tend to underestimate extreme discharges during extrapolation and reveal less balanced uncertainty characteristics. BaRatin shows the most favourable overall performance according to the evaluation criteria, including high-flow estimation, extrapolation and behaviour of prediction intervals. However, Diebold-Mariano tests indicate that the differences in predictive accuracy between BaRatin and other models are not statistically significant at the 5
The Epidemic-Type Aftershock Sequence model (ETAS) is a widely used self-exciting spatio-temporal point process for earthquake occurrence, in which seismicity is represented as the superposition of background events and triggered events. In many ETAS implementations, the background component is estimated non-parametrically, typically through kernel smoothing. Although flexible, this approach can limit formal inference and make it difficult to incorporate structured information, such as spatial covariates and mark-related features, into the background component. This paper proposes an ETAS formulation with a regression-based background component. The standard ETAS triggering structure and declustering logic are preserved, while the background component is modelled using a regression-based approach. This provides a more interpretable representation of background seismicity and extends the range of information that can be incorporated into ETAS models. We evaluate the proposed methodology through a simulation study and illustrate its practical usefulness with an application to an Italian earthquake catalogue. The results show that the proposed approach improves the recovery of structured background intensities while maintaining competitive estimation of the triggered component.
