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McGill University Department of Civil Engineering and Applied Mechanics

McGill University Department of Civil Engineering and Applied Mechanics. Montreal, Quebec, Canada. STATISTICAL MODELING AND ANALYSIS OF EXTREME PRECIPITATION PROCESSES. Van-Thanh-Van Nguyen and Tan-Danh Nguyen Department of Civil Engineering and Applied Mechanics McGill University

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McGill University Department of Civil Engineering and Applied Mechanics

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  1. McGill UniversityDepartment of Civil Engineering andApplied Mechanics Montreal, Quebec, Canada

  2. STATISTICAL MODELING AND ANALYSIS OF EXTREME PRECIPITATION PROCESSES Van-Thanh-Van Nguyen and Tan-Danh Nguyen Department of Civil Engineering and Applied Mechanics McGill University Montreal, Quebec, Canada and OURANOS, Climate Change Consortium Montreal, Quebec, Canada

  3. OUTLINE • INTRODUCTION • OBJECTIVES • METHODOLOGY • APPLICATIONS • CONCLUSIONS

  4. INTRODUCTION • Extreme storms and floods account for more losses than any other natural disaster [both in terms of loss of lives and economic costs: Saguenay (Quebec) flood damages = CAD $800 million dollars; US average annual flood damages = US$2.1 billion dollars]. • Information on extreme rainfalls and floods is essential for planning, design, and management of water-resource systems. • Design Rainfall = the maximum amount of precipitation falling at a given point (or over a given area) for a specified duration and return period  Frequency analysis of extreme rainfall events. • Climate variability and change will have important impacts on the hydrologic cycle, and in particular extreme storm and flood events How to quantify these impacts?

  5. DOWNSCALING METHODS

  6. … • The choice of an estimation method depends on the availability of historical data: • Gaged Sites Sufficient long historical records (> 20 years?) At-site Methods. • Partially-Gaged Sites Limited data records Regionalization Methods. • Ungaged Sites Data are not available Regionalization Methods.

  7. Issues Related to Estimation of Extreme Rainfall Events: • At-site methods • Current practice: Annual maximum series (AMS) using 2-parameter Gumbel/Ordinary moments method, or using 3-parameter GEV/ L-moments method. • Regionalization methods • Current practice: GEV/Index-flood method. • Similarity (or homogeneity) of sites? • How to define groups of homogeneous sites? What are the classification criteria? • No general agreement on the choice of a suitable distribution model for extreme rainfalls. • What are the impacts of climate variability and change on annual maximum series?

  8. … • The “scale” problem • The properties of a variable depend on the scale of measurement or observation. • Are there scale-invariance properties? And how to determine these scaling properties? • Existing methods are limited to the specific time scale associated with the data used. • Existing methods cannot take into account the properties of the physical process over different scales.

  9. OBJECTIVES • To propose new modelling methods that can take into account the scaling properties of the extreme rainfall process. • To demonstrate the importance of scaling consideration in the estimation of extreme rainfalls. • To propose new regional estimation methods of extreme rainfalls for ungaged sites.

  10. METHODOLOGY • Scaling Methods (for partially-gaged and ungaged sites) • The scaling concept:

  11. Generalized Extreme-Value (GEV) Distribution. • The cumulative distribution function: • The quantile:

  12. The first three moments of GEV distribution:

  13. The Scaling GEV Distribution

  14. Estimation of Extreme Rainfalls for Partially-Gaged Sites • Rainfall data are not always available for the time and space scales of interest. • Short time interval rainfall extremes areimportantfor small watersheds, but not always available. • Daily rainfall data are widely available. • Daily scale  shorter time scales ?

  15. Methods of estimation of short-duration extreme rainfalls from long-duration extreme rainfalls • Method 1. Basic equation. where

  16. … • Method 2 Basic equation: • Parameters are estimated by the method of moments.

  17. ... Data used: • Rainfall duration: from 5 minutes to 1 day. • Raingage network: 14 stations in Quebec. • Record lengths: from 15 yrs. to 48 yrs.

  18. Observation of scaling regime : k (t) 3rd order moment. 2nd order moment. 1st order moment. t 1 hour 1 day 5 min

  19. Scaling characteristics  ( k ) k

  20. Resultson scaling regimes: • Non-central moments are scaling. • Two scaling regimes: • 5-min. to 1-hour interval. • 1-hour to 1-day interval. • The slope of the straight line is the estimate of the scaling exponentb(k). • Relationship between  (k) and k, for k = 1 to 3, are linear.

  21. Based on these results, two estimations were made: • 5-min. extreme rainfalls from 1-hr rainfalls. • 1-hr. extreme rainfalls from 1-dayrainfalls.

  22. 5-minextreme rainfalls from 1-hr extreme rainfalls.

  23. 1-hr extreme rainfalls from 1-day extreme rainfalls.

  24. Results on the estimation methods: • Extreme rainfalls estimated in two cases by two methods were in good agreement with observations. • Method 2 provided more accurate estimates than method 1, especially at the two extremes.

  25. Regional estimation of daily extreme rainfalls for ungaged sites • Homogeneous sites are defined based on the similarity of rainfall occurrences (e.g., strong correlation of the number of rainy hours). • Regional relations between statistical moments of daily extreme rainfalls and the mean number of rainy hours are developed for the homogeneous group. • Statistical moments of daily extreme rainfalls at an ungaged site are estimated using these regional relations  Distribution of daily extreme rainfalls is estimated for the ungaged site.

  26. Results on the regional estimation method • Regional estimates are comparable with corresponding at-site estimates. • Good agreement between the estimates (both at-site and regional) with the observations indicates the feasibility of the proposed regional estimation method.

  27. CONCLUSIONS • Consideration of scaling properties of hydrologic processes could lead to the development of more accurate and more reliable estimation methods. • Consideration of scaling properties of hydrologic processes could provide better understanding of the physical phenomenon studied. • The GEV distribution is suitable for regional estimation of extreme rainfalls and floods.

  28. CONCLUSIONS(Continued) • It is feasible to assess the homogeneity of extreme rainfall conditions at different locations based on the similarity of rainfall occurrences. • Problems related to the estimation of extreme rainfalls are still far from being completely solved. integrated physical-statistical approaches?

  29. ... Thank You!

  30. Slides required for presentations

  31. Common probability distributions: • Two-parameter distribution: • Gumbel distribution • Normal • Log-normal (2 parameters) • Three-parameter distributions: • Beta-K distribution • Beta-P distribution • Generalized Extreme Value distribution • Pearson Type 3 distribution • Log-Normal (3 parameters) • Log-Pearson Type 3 distribution • Generalized Gamma distribution • Generalized Normal distribution • Generalized Pareto distribution • Four-parameter distribution • Two-component extreme value distribution • Five-parameter distribution: • Wakeby distribution

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