Modeling Intensity-Duration-Frequency curves for the whole range of precipitation

Intensity-Duration-Frequency curves are useful in water resources engineering for the planning and design of hydrological structures such as sewer lines, culverts, drains, dams, dykes.  They provide the mathematical link between the rainfall intensity, I, over a given duration, D, that is expected to be exceeded on average, once every T years (frequency). As opposed to the common use of only extreme data to build IDF curves, here, we use all the non-zero rainfall intensities, thereby making efficient use of the available information. As a parametric model, we use the Extended Generalized Pareto Distribution (EGPD) of Naveau et al. (2016)  for the non-zero intensities. We consider three commonly used approaches for building IDF curves. The first approach is based on the scale-invariance property of rainfall, the second relies on the general IDF formulation of Koutsoyiannis et al. (1998) and the last approach is purely data-driven (Overeem et al., 2008), where the linkage of parameter and duration is empirically determined from data. Using these three approaches, and some extensions around them, we build a total of 10 models for the IDF curves. We then compare them based on their in-sample performance, parsimony in parameterization, as well as their robustness and reliability in a split-sampling cross-validation framework. We consider a total of 81 stations at 10 min resolution in Switzerland.  As a result of the marked seasonality of rainfall in the study area, we adopted a seasonal-based analysis.  The results reveal that the model based on the data-driven approach is the best model. It is able to correctly model the observed intensities across duration while being reliable and robust. It is also able to reproduce the space and time variability of extreme rainfall across Switzerland. While our study focused on Switzerland, the results can be generalized everywhere, especially for locations with high-resolution data availability. To our knowledge, our work is the first to consider using the EGPD in IDF curve modeling.

 

 

References

Koutsoyiannis, D., Kozonis, D., & Manetas, A. (1998, April). A mathematic cal framework for studying rainfall intensity-duration-frequency relationships. Journal of Hydrology, 206 (1-2), 118–135. Retrieved 2021-09-06, from https://linkinghub.elsevier.com/retrieve/pii/S0022169498000973 doi: 10.1016/S0022-1694(98)00097-3

Naveau, P., Huser, R., Ribereau, P., and Hannart, A.: Modeling jointly low, moderate, and heavy rainfall intensities without a threshold selection, Water Resour. Res., 52, 2753–2769, https://doi.org/10.1002/2015WR018552, 2016.

Overeem, A., Buishand, A., & Holleman, I. (2008, January). Rainfall depth duration-frequency curves and their uncertainties. Journal of Hydrology, 348 (1-2), 124–134. Retrieved 2021-11-30, from https://linkinghubelsevier.com/retrieve/pii/S0022169407005513 doi:10.1016/j.jhydrol.2007.09.044