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

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

<p>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.</p><p>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.</p>

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

2021 ◽  
Author(s):  
Felix Fauer ◽  
Jana Ulrich ◽  
Oscar E. Jurado ◽  
Uwe Ulbrich ◽  
Henning W. Rust
Keyword(s):  
Extreme Value ◽  
Data Availability ◽  
Extreme Value Statistics ◽  
Statistical Characteristics ◽  
Exceedance Probability ◽  
Extended Model ◽  
Adequate Model ◽  
Extreme Precipitation Events ◽  
Idf Curves ◽  
Intensity Duration Frequency

<p>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.</p><p>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.</p><p>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.</p><p>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.</p>

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

Water ◽  
2019 ◽  
Vol 11 (6) ◽  
pp. 1296 ◽  
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.

Interpolation of Regionalized Intensity Duration Frequency (IDF) Estimates based on the observed precipitation data of Baden Wurttemberg (BW), Germany

2021 ◽  
Author(s):  
Bushra Amin ◽  
András Bárdossy
Keyword(s):  
Mean Square Error ◽  
Hydrological Cycle ◽  
Information Criteria ◽  
Regional Frequency Analysis ◽  
Mean Square ◽  
Time Duration ◽  
Ungauged Sites ◽  
Marquardt Algorithm ◽  
Idf Curves ◽  
Intensity Duration Frequency

<p>This study is intended to carry out the spatial mapping with ordinary Kriging (OK) of regional point Intensity Duration Frequency (IDF) estimates for the sake of approximation and visualization at ungauged location. Precipitation IDF estimates that offer us valuable information about the frequency of occurrence of extreme events corresponding to different durations and intensities are derived through the application of robust and efficient regional frequency analysis (RFA) based on L-moment algorithm. IDF curves for Baden Wrttemberg (BW) are obtained from the long historical record of daily and hourly annual maximum precipitation series (AMS) provided by German Weather Service from 1960-2020 and 1949-2020 respectively under the assumption of stationarity. One of the widely used Gumbel (type 1)  distribution is applied for IDF analysis because of its suitability for modeling maxima. The uncertainty in IDF curves is determined by the bootstrap method and are revealed in the form of the prediction and confidence interval for each specific time duration on graph. Five metrics such as root mean square error (RMSE), coefficient of determination (R²), mean square error (MSE), Akaike information criteria (AIC) and Bayesian information criteria (BIC) are used to assess the performance of the employed IDF equation. The coefficients of 3-parameteric non-linear IDF equation is determined for various recurrence interval by means of Levenberg–Marquardt algorithm (LMA), also referred to as damped least square (DLS) method. The estimated coefficients vary from location to location but are insensitive to duration. After successfully determining the IDF parameters for the same return period, parametric contour or isopluvial maps can be generated using OK as an interpolation tool with the intention to provide estimates at ungauged locations. These estimated regional coefficients of IDF curve are then fed to the empirical intensity frequency equation that may serve to estimate rainfall intensity for design purposes for all ungauged sites. The outcomes of this research contribute to the construction of IDF-based design criteria for water projects in ungauged sites located anywhere in the state of BW.</p><p>In conclusion, we conducted IDF analysis for the entire state of BW as it is considered to be more demanding due to the increased impact of climate change on the intensification of hydrological cycle as well as the expansion of urban areas rendering watershed less penetrable to rainfall and run-off, the better understanding of spatial heterogeneity of intense rainfall patterns for the proposed domain.</p>

Reliability of global gridded precipitation products in assessing extremes

2021 ◽  
Author(s):  
Chandra Rupa Rajulapati ◽  
Simon Michael Papalexiou ◽  
Martyn P Clark ◽  
Saman Razavi ◽  
Guoqiang Tang ◽  
...  
Keyword(s):  
Spatial Variability ◽  
Extreme Precipitation ◽  
Probability Distributions ◽  
Extreme Precipitation Events ◽  
Return Levels ◽  
Time Period ◽  
Precipitation Gauge ◽  
Global Precipitation ◽  
Surface Observations ◽  
Precipitation Events

<p>Assessing extreme precipitation events is of high importance to hydrological risk assessment, decision making, and adaptation strategies. Global gridded precipitation products, constructed by combining various data sources such as precipitation gauge observations, atmospheric reanalyses and satellite estimates, can be used to estimate extreme precipitation events. Although these global precipitation products are widely used, there has been limited work to examine how well these products represent the magnitude and frequency of extreme precipitation. In this work, the five most widely used global precipitation datasets (MSWEP, CFSR, CPC, PERSIANN-CDR and WFDEI) are compared to each other and to GHCN-daily surface observations. The spatial variability of extreme precipitation events and the discrepancy amongst datasets in predicting precipitation return levels (such as 100- and 1000-year) were evaluated for the time period 1979-2017.  The behaviour of extremes, that is the frequency and magnitude of extreme precipitation, was quantified using indices of the heaviness of the upper tail of the probability distribution. Two parameterizations of the upper tail, the power and stretched-exponential, were used to reveal the probabilistic behaviour of extremes. The analysis shows strong spatial variability in the frequency and magnitude of precipitation extremes as estimated from the upper tails of the probability distributions. This spatial variability is similar to the Köppen-Geiger climate classification. The predicted 100- and 1000-year return levels differ substantially amongst the gridded products, and the level of discrepancy varies regionally, with large differences in Africa and South America and small differences in North America and Europe. The results from this work reveal the shortcomings of global precipitation products in representing extremes. The work shows that there is no single global product that performs best for all regions and climates.</p>

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

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.

scholarly journals Machine Learning for Projecting Extreme Precipitation Intensity for Short Durations in a Changing Climate

Geosciences ◽  
2019 ◽  
Vol 9 (5) ◽  
pp. 209
Author(s):  
Huiling Hu ◽  
Bilal M. Ayyub
Keyword(s):  
Climate Change ◽  
Machine Learning ◽  
Extreme Precipitation ◽  
Circulation Model ◽  
Machine Learning Algorithms ◽  
Precipitation Intensity ◽  
Potential Threat ◽  
Drainage Systems ◽  
Idf Curves ◽  
Intensity Duration Frequency

Climate change is one of the prominent factors that causes an increased severity of extreme precipitation which, in turn, has a huge impact on drainage systems by means of flooding. Intensity–duration–frequency (IDF) curves play an essential role in designing robust drainage systems against extreme precipitation. It is important to incorporate the potential threat from climate change into the computation of IDF curves. Most existing works that have achieved this goal were based on Generalized Extreme Value (GEV) analysis combined with various circulation model simulations. Inspired by recent works that used machine learning algorithms for spatial downscaling, this paper proposes an alternative method to perform projections of precipitation intensity over short durations using machine learning. The method is based on temporal downscaling, a downscaling procedure performed over the time scale instead of the spatial scale. The method is trained and validated using data from around two thousand stations in the US. Future projection of IDF curves is calculated and discussed.

scholarly journals Web-Based Tool for the Development of Intensity Duration Frequency Curves under Changing Climate at Gauged and Ungauged Locations

Water ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 1243 ◽  
Author(s):  
Andre Schardong ◽  
Slobodan P. Simonovic ◽  
Abhishek Gaur ◽  
Dan Sandink
Keyword(s):  
Climate Models ◽  
Climatic Conditions ◽  
Web Based ◽  
Matching Algorithm ◽  
Resources Management ◽  
Ungauged Sites ◽  
Land Mass ◽  
Idf Curves ◽  
Intensity Duration Frequency ◽  
Frequency Curves

Rainfall Intensity–Duration–Frequency (IDF) curves are among the most essential datasets used in water resources management across the globe. Traditionally, they are derived from observations of historical rainfall, under the assumption of stationarity. Change of climatic conditions makes use of historical data for development of IDFs for the future unreliable, and in some cases, may lead to underestimated infrastructure designs. The IDF_CC tool is designed to assist water professionals and engineers in producing IDF estimates under changing climatic conditions. The latest version of the tool (Version 4) provides updated IDF curve estimates for gauged locations (rainfall monitoring stations) and ungauged sites using a new gridded dataset of IDF curves for the land mass of Canada. The tool has been developed using web-based technologies and takes the form of a decision support system (DSS). The main modifications and improvements between version 1 and the latest version of the IDF_CC tool include: (i) introduction of the Generalized Extreme value (GEV) distribution; (ii) updated equidistant matching algorithm (QM); (iii) gridded IDF curves dataset for ungauged location and (iv) updated Climate Models.

scholarly journals Simple scaling of extreme precipitation in North America

2017 ◽  
Vol 21 (11) ◽  
pp. 5823-5846 ◽  
Author(s):  
Silvia Innocenti ◽  
Alain Mailhot ◽  
Anne Frigon
Keyword(s):  
North America ◽  
Extreme Precipitation ◽  
Probability Distributions ◽  
Spatial Scales ◽  
Extreme Rainfall ◽  
Parameter Estimates ◽  
Infrastructure Design ◽  
Simple Scaling ◽  
Intensity Duration Frequency ◽  
Extreme Probability

Abstract. Extreme precipitation is highly variable in space and time. It is therefore important to characterize precipitation intensity distributions on several temporal and spatial scales. This is a key issue in infrastructure design and risk analysis, for which intensity–duration–frequency (IDF) curves are the standard tools used for describing the relationships among extreme rainfall intensities, their frequencies, and their durations. Simple scaling (SS) models, characterizing the relationships among extreme probability distributions at several durations, represent a powerful means for improving IDF estimates. This study tested SS models for approximately 2700 stations in North America. Annual maximum series (AMS) over various duration intervals from 15 min to 7 days were considered. The range of validity, magnitude, and spatial variability of the estimated scaling exponents were investigated. Results provide additional guidance for the influence of both local geographical characteristics, such as topography, and regional climatic features on precipitation scaling. Generalized extreme-value (GEV) distributions based on SS models were also examined. Results demonstrate an improvement of GEV parameter estimates, especially for the shape parameter, when data from different durations were pooled under the SS hypothesis.

scholarly journals Modeling of IDF curves for stormwater design in Makkah Al Mukarramah region, The Kingdom of Saudi Arabia

2018 ◽  
Vol 10 (1) ◽  
pp. 954-969 ◽  
Author(s):  
Hatem A. Ewea ◽  
Amro M. Elfeki ◽  
Jarbou A. Bahrawi ◽  
Nassir S. Al-Amri
Keyword(s):  
Saudi Arabia ◽  
Probability Distributions ◽  
Daily Rainfall ◽  
Type I ◽  
Kingdom Of Saudi Arabia ◽  
Hourly Data ◽  
Idf Curves ◽  
Intensity Duration Frequency ◽  
Negative Impacts

Abstract Reducing the negative impacts of flooding in Makkah AL Mukarramah region in the Kingdom of Saudi Arabia (KSA) is of utmost importance. In the last decade, there are huge mega infrastructure projects in KSA in general and in Makkah AL Mukarramah region in particular. These projects require adequate stormwater drainage systems. Since, the availability of rainfall and runoff data are scarce, engineers and hydrologists rely on models developed in temperature regions that are not hydrologically similar from temperate regions. This leads to inaccurate designs of stormwater facilities. Therefore, deveoping in situ Intensity-Duration-Frequency (IDF) curves is a must in this arid region. This paper aims at modeling IDF curves for Makkah Al-Mukarramah region. Maximum annual daily rainfall series of 80 storms (with sub-hourly and hourly data) from four stations are investigated through six different probability distributions. Consequently, rainfall depth-duration-frequency models and curves are derived. Results revealed that the Gumbel Type I is the optimal one. Thus, it is used to deduce the IDF curves and relations for each station and for the region as a whole. The R2 value for fitting power-lawfunction (i = a Db) to the data is very high for the IDF parameters. The R2 for the coefficient parameter, a, is between 0.9999 and 0.9988 while it ranges between 0.8754 and 0.8039 for exponent parameter, b. High correlation coefficient (more than 0.95) has been obtained. The resulting IDF models are strongly recommended for rigorous, effective and safe design of the stormwater systems in Makkah Al-Mukarramah region.

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