Uncertainty Quantification of Theoretical Consistent Intensity Duration Frequency (IDF) Curves of Rainfall Intensity

Many water-related systems and defensive structures require the design of rainfall amounts at various durations and frequencies, commonly referred to as Intensity Duration-Frequency (IDF) curves. Usually, these curves are derived from observed data, but there is a chance that the risk has been underestimated because of various uncertainty sources. As a result, measuring the uncertainty ranges of these curves becomes essential. To do this, the regionalization of the IDF curves for BW is inspected for the propagation of possible sources of uncertainty. For each site, annual extremes are obtained for varying durations (from 5 min to 16 days), and local extreme value analysis is performed in compliance with Koutsoyiannis et al. (2021).  Following this investigation, Kriging with External Drift (KED) is used to interpolate all seven parameters of theoretically consistent IDF models for each station; this implies that no parameter remains constant across the region.  Quantiles are then retrieved for every station, duration, and given recurrence interval. The uncertainty is estimated for each of the three components of the regionalization—local parameter estimation, variogram estimation, and spatial parameter estimation—in terms of accuracy (expected error) and precision (95% confidence interval width) using bootstrapping (non-parametric) and geostatistical spatial simulations. The reason for selecting Conditional Sequential Gaussian (CSG) simulations was their capability to produce a large number of equiprobable spatial simulations. Many recent studies also demonstrated its accuracy, which is why CSG was chosen to evaluate the uncertainty from spatial simulations. Subsequently, one hundred realizations were carried out at every regionalization component to examine their ultimate impact on the regionalization of parameters and IDF curves. Afterward, combined simulations were executed for the propagation of the uncertainty from the key components to the final IDF curves.

It turned out that the primary source of uncertainty in the selected regionalization process is spatial estimation, which is followed by local estimation of rainfall extremes. More specifically, the total estimation of IDF curves was mostly insensitive to variogram uncertainty. The integration of spatial simulations with local resampling yielded accurate estimates of the overall uncertainty at sampled sites, whereas at unsampled sites, the accuracy decreased based on the density and proximity of the surrounding observations. This combination was used to simulate the total uncertainty in BW via 100 runs. The results showed that, depending on the site and duration interval, tolerance ranges should be expected to be between ± 0.9-4.2 mm/h for low-recurrence intervals (less than 5 years) and ± 2.2-5.5 mm/h for high-recurrence intervals (more than 50 years), but very short durations (5 min) are relatively more uncertain than longer durations.