An Extended Model in Estimating Consistent Quantiles for Intensity-Duration-Frequency Curves

Intensity-Duration-Frequency (IDF) curves describe the main statistical characteristics of extreme precipitation events. Providing information on the exceedance probability or return period of certain precipitation intensities for a range of durations, IDF curves are an important tool for the design of hydrological structures.Although the Generalized-Extreme-Value (GEV) distribution is an adequate model for annual precipitation maxima of a certain duration, the core problem of extreme value statistics remains: the limited data availability. Hence, it is reasonable to use a model that can describe all durations simultaneously. This reduces the total number of parameters and a more efficient usage of data is achieved. The idea of implementing a duration dependence directly into the parameters of the extreme value distribution and therefore obtaining a single distribution for a range of durations was proposed by Koutsoyiannis et al. (1998). However, while the use of the GEV is justified by a strong theoretical basis, only empirical models exist for the dependence of the parameters on duration.In this study, we compare different models regarding the dependence of the GEV parameters on duration with the aim of finding a model for a wide duration range (1 min - 5 days). We use a combination of existing model features, especially curvature for small durations and multi-scaling for all durations, and extend them by a new feature that allows flattening of the IDF curves for long durations. Using the quantile score in a cross-validation setting, we provide detailed information on the duration and probability ranges for which specific features or a systematic combination of features lead to improved modeling skill.Our results show that allowing curvature or multi-scaling improves the model only for very short or long durations, respectively, but leads to disadvantages in modeling the other duration ranges. In contrast, allowing flattening of the IDF curves leads to an improvement for medium durations between 1 hour and 1 day without affecting other duration regimes.

Download Full-text

Estimating IDF-Relations consistently using a duration-dependent GEV with spatial covariates

10.5194/egusphere-egu2020-18724 ◽

2020 ◽

Author(s):

Jana Ulrich ◽

Madlen Peter ◽

Oscar E. Jurado ◽

Henning W. Rust

Keyword(s):

Extreme Precipitation ◽

Probability Distributions ◽

Skill Score ◽

Exceedance Probability ◽

Ungauged Sites ◽

Extreme Precipitation Events ◽

One Step ◽

Idf Curves ◽

Intensity Duration Frequency ◽

A Site

Intensity-Duration-Frequency (IDF) Curves are a popular tool in Hydrology for estimating the properties of extreme precipitation events. They describe the relationship between rainfall intensity and duration for a given non-exceedance probability (or frequency). For a site where precipitation measurements are available, these curves can be estimated consistently over durations using a duration-dependent GEV (d-GEV, after Koutsoyiannis et al. 1998). In this approach, the probability distributions are modeled simultaneously for all durations.Additionally, we integrate covariates to describe the spatial variability of the d-GEV parameters so that we can model the distribution of extreme precipitation for a range of durations and locations in one step. Thus IDF Curves can be estimated even at ungauged sites. Further advantages are parameter reduction and more efficient use of the available data. We use the Quantile Skill Score to investigate under which conditions this method leads to an improved estimate compared to the single-site approach and to evaluate the performance at ungauged sites.

Download Full-text

Impacts of Spatial Heterogeneity and Temporal Non-Stationarity on Intensity-Duration-Frequency Estimates—A Case Study in a Mountainous California-Nevada Watershed

Water ◽

10.3390/w11061296 ◽

2019 ◽

Vol 11 (6) ◽

pp. 1296 ◽

Cited By ~ 3

Author(s):

Huiying Ren ◽

Z. Jason Hou ◽

Mark Wigmosta ◽

Ying Liu ◽

L. Ruby Leung

Keyword(s):

High Resolution ◽

Spatial Heterogeneity ◽

Time Windows ◽

Exceedance Probability ◽

Extreme Precipitation Events ◽

Climate Simulations ◽

Engineering Standards ◽

Intensity Duration Frequency ◽

Using Data

Changes in extreme precipitation events may require revisions of civil engineering standards to prevent water infrastructures from performing below the designated guidelines. Climate change may invalidate the intensity-duration-frequency (IDF) computation that is based on the assumption of data stationarity. Efforts in evaluating non-stationarity in the annual maxima series are inadequate, mostly due to the lack of long data records and convenient methods for detecting trends in the higher moments. In this study, using downscaled high resolution climate simulations of the historical and future periods under different carbon emission scenarios, we tested two solutions to obtain reliable IDFs under non-stationarity: (1) identify quasi-stationary time windows from the time series of interest to compute the IDF curves using data for the corresponding time windows; (2) introduce a parameter representing the trend in the means of the extreme value distributions. Focusing on a mountainous site, the Walker Watershed, the spatial heterogeneity and variability of IDFs or extremes are evaluated, particularly in terms of the terrain and elevation impacts. We compared observations-based IDFs that use the stationarity assumption with the two approaches that consider non-stationarity. The IDFs directly estimated based on the traditional stationarity assumption may underestimate the 100-year 24-h events by 10% to 60% towards the end of the century at most grids, resulting in significant under-designing of the engineering infrastructure at the study site. Strong spatial heterogeneity and variability in the IDF estimates suggest a preference for using high resolution simulation data for the reliable estimation of exceedance probability over data from sparsely distributed weather stations. Discrepancies among the three IDFs analyses due to non-stationarity are comparable to the spatial variability of the IDFs, underscoring a need to use an ensemble of non-stationary approaches to achieve unbiased and comprehensive IDF estimates.

Download Full-text

Assessment of the intensity-duration-frequency (IDF) curves for storms in Peninsular Malaysia based on the generalized extreme value distribution

10.1063/1.4801266 ◽

2013 ◽

Author(s):

Noratiqah Mohd Ariff ◽

Abdul Aziz Jemain ◽

Wan Zawiah Wan Zin

Keyword(s):

Extreme Value Distribution ◽

Extreme Value ◽

Peninsular Malaysia ◽

Value Distribution ◽

Generalized Extreme Value Distribution ◽

Generalized Extreme Value ◽

Idf Curves ◽

Intensity Duration Frequency

Download Full-text

Stochastic simulation of reference rainfall scenarios for hydrological applications using a universal multifractal approach

10.5194/hess-2021-580 ◽

2021 ◽

Author(s):

Arun Ramanathan ◽

Pierre-Antoine Versini ◽

Daniel Schertzer ◽

Remi Perrin ◽

Lionel Sindt ◽

...

Keyword(s):

Exceedance Probability ◽

Specific Reference ◽

Rainfall Time Series ◽

Spatial Dimensions ◽

Idf Curves ◽

Intensity Duration Frequency ◽

T Values ◽

Renormalization Constants ◽

Meteorological Models ◽

Hydrological Applications

Abstract. Hydrological applications such as storm-water management or flood design usually deal with and are driven by region-specific reference rainfall regulations or guidelines based on Intensity-Duration-Frequency (IDF) curves. IDF curves are usually obtained via frequency analysis of rainfall data using which the exceedance probability of rain intensity for different durations are determined. It is also rather common for reference rainfall to be expressed in terms of precipitation P, accumulated in a duration D (related to rainfall intensity ), with a return period T (inverse of exceedance probability). Meteorological modules of hydro-meteorological models used for the aforementioned applications therefore need to be capable of simulating such reference rainfall scenarios. The multifractal cascade framework, since it incorporates physically realistic properties of rainfall processes (non-homogeneity or intermittency, scale invariance and extremal statistics) seems to suit this purpose. Here we propose a discrete-in-scale universal multifractal (UM) cascade based approach. Daily, Hourly and six-minute rainfall time series datasets (with lengths ranging from 100 to 15 years) over three regions (Paris, Nantes, and Aix-en-Provence) in France that are characterized by different climates are analyzed to identify scaling regimes and estimate corresponding UM parameters (α, C1) required by the UM cascade model. Suitable renormalization constants that correspond to the P, D, T values of reference rainfall are used to simulate an ensemble of reference rainfall scenarios, and the simulations are finally compared with datasets. Although only purely temporal simulations are considered here, this approach could possibly be generalized to higher spatial dimensions as well.

Download Full-text

Early Forecast of Maximum Amplitude due to Aftershocks by Applying Extreme Value Statistics to a Single Continuous Seismogram

Bulletin of the Seismological Society of America ◽

10.1785/0120200365 ◽

2021 ◽

Author(s):

Kaoru Sawazaki

Keyword(s):

Maximum Likelihood ◽

Maximum Amplitude ◽

Extreme Value ◽

Maximum Likelihood Estimates ◽

Extreme Value Statistics ◽

Likelihood Method ◽

Exceedance Probability ◽

Observation System ◽

Site Factors ◽

Single Station

ABSTRACT To evaluate the exceedance probability of maximum amplitude (EPMA) due to aftershocks, I developed a forecasting scheme based on the extreme value statistics applied to a single continuous seismogram of early aftershocks. By combining the general laws of aftershock activity (Gutenberg–Richter and Omori–Utsu laws) and a ground-motion prediction equation (including source, path, and site factors), I verified that the interval maximum amplitude of a continuous seismogram of aftershocks follows the non-stationary Frechet distribution (NFD), which is one of the extreme value distributions. The parameters of NFD are written explicitly from the parameters commonly used in seismology. By optimizing the NFD parameters through the maximum-likelihood method and using the maximum-likelihood estimates and their covariance values, I derived the EPMA due to aftershocks based on the Bayesian approach. The performance of the EPMA was examined by Monte Carlo simulations and real seismograms. The numerically generated maximum amplitude was predicted well from the EPMA, which was evident even in the period of intense seismicity in which many waveforms overlap in a seismogram. This performance was also robust for real seismograms of aftershocks for the 2008 Iwate–Miyagi Nairiku, Japan, earthquake. The maximum amplitudes observed for four days were mostly within the 10% and 90% EPMA curves issued within 3 hr of the mainshock. The proposed method does not need to evaluate source, path, and site factors because these factors are included in the estimated NFD parameters. Given that the proposed method allows single-station processing, a seismic “network” is not required. Therefore, the proposed algorithm will be easily implementable in a seismic observation system installed at important facilities. Also, the NFD parameters estimated robustly in the early lapse times may provide important knowledge regarding early aftershocks.

Download Full-text