Modeling Non-stationary Intensity-Duration-Frequency (IDF) Curves for the whole range of precipitation

Context

Intensity-Duration-Frequency (IDF) curves link precipitation intensity, duration, and non-exceedance frequency (or rather the return period). It is a widespread and useful tool in urban water resources engineering. IDF curves are practically used to infer high return levels of rainfall intensities for the hydrological designs of structures such as sewer lines, culverts, drains, dams, dykes, etc. They are also used to calibrate/validate stochastic weather generators (Willems, 2000 ; Ritschel et al., 2017).

Many approaches to build IDF curves exist in the literature (see Langousis and Veneziano, 2007 ; Tyralis and Langousis, 2019, for a brief review). One way is to select a particular approach (eg based on scale invariance) and to use a parametric model eg Generalized Extreme Value (GEV), or its particular case, the Gumbel distribution, for the block maxima. These distributions, although widely used, have a major drawback due to poor utilization of already scarce data, since they use only the block maxima (a very small fraction of the entire data). Recently, Haruna et al. (2022) showed that it is possible to use the Extended Generalized Pareto Distribution (EGPD) (Naveau et al., 2016) to build IDF curves. EGPD has the advantage of using all the information present in the sample of non-zero rainfall data and not only one value per block (like GEV distribution). This is in addition to being compliant with extreme value theory in both the lower and upper tails.

IDF curves are traditionally built under the assumption of stationarity. The stationarity concept assumes that the statistics of extremes do not change over time. For instance, a 100-year return level today will remain the same in the future. However, climate change has brought into question the design of infrastructures with IDF curves under this notion. In fact, recent work by Cheng and AghaKouchak (2014) showed that there could be up to 60% underestimation of extreme precipitation for short durations when non-stationarity (trend) in the data is neglected. Consequently, it is essential to start by investigating the presence of a trend in the precipitation series, and if evident, to model the IDF curves accounting for this nonstationarity.

Accordingly, the aim of this master’s internship is to build IDF curves using all the non-zero precipitation intensities while accounting for non-stationarity

Objectives

The objectives of the internship are itemized below.

• Investigate the presence of trend in long series of a dense network of daily precipitation spread all over Switzerland.
• Select the appropriate approach to build IDF curves, using EGPD as the distribution for the non-zero
• precipitation intensities.
• Incorporate/account for the non-stationarity of the series in building the IDF curves.
• Compare the extreme quantiles from the IDF curves with and without accounting for non-stationarity.

To apply :

Send CV and motivation letter to juliette.blanchet univ-grenoble-alpes.fr, abubakar.haruna univgrenoble-alpes.fr, and anne-catherine.favre univ-grenoble-alpes.fr

References

• Cheng, L. and AghaKouchak, A. (2014). Nonstationary precipitation intensity-duration-frequency curves for infrastructure design in a changing climate. Scientific reports, 4(1):1–6.
• Haruna, A., Blanchet, J., and Favre, A.-C. (2022). Modeling intensity-duration-frequency curves for the whole range of precipitation : A comparison of models [submitted].
• Langousis, A. and Veneziano, D. (2007). Intensity-duration-frequency curves from scaling representations of rainfall. Water Resources Research, 43(2). Publisher : John Wiley & Sons, Ltd.
• Naveau, P., Huser, R., Ribereau, P., and Hannart, A. (2016). Modeling jointly low, moderate, and heavy rainfall intensities without a threshold selection. Water Resources Research, 52(4):2753–2769.
• Ritschel, C., Ulbrich, U., N´evir, P., and Rust, H. W. (2017). Precipitation extremes on multiple timescales–bartlett–lewis rectangular pulse model and intensity–duration–frequency curves. Hydrology and Earth System Sciences, 21(12):6501–6517.
• Tyralis, H. and Langousis, A. (2019). Estimation of intensity–duration–frequency curves using max-stable processes. Stochastic Environmental Research and Risk Assessment, 33(1):239–252.
• Willems, P. (2000). Compound intensity/duration/frequency-relationships of extreme precipitation for two seasons and two storm types. Journal of Hydrology, 233(1):189–205.