ML18005A834
| ML18005A834 | |
| Person / Time | |
|---|---|
| Issue date: | 01/05/2018 |
| From: | Holman K, Joseph Kanney, Keeney D, Verdin A NRC/RES/DRA/FRB, US Dept of Interior, Bureau of Reclamation |
| To: | Office of Nuclear Regulatory Research |
| References | |
| Download: ML18005A834 (17) | |
Text
Developing Precipitation Frequency Estimates in Regions of Complex Terrain Kathleen D. Holman1, Andrew P. Verdin1, David P. Keeney1, and Joseph Kanney2 1 Bureau of Reclamation Technical Service Center 2 U.S. Nuclear Regulatory Commission
Outline
- 1. Motivation
- 2. Precipitation-Frequency Analyses A. Methods B. Data
- 3. Case study in Tennessee River Valley A. Self-Organizing Map algorithm B. L-moments C. Bayesian
- 4. Summary & Conclusions
Motivation Knowledge of extreme precipitation events is vital for engineering planning purposes Deterministic methods used for design projects, like Probable Maximum Precipitation, provide no information on expected return periods Precipitation-frequency analyses give the users expected return periods of extreme events
Question How do precipitation-frequency estimates developed using the L-moments algorithm compare with estimates developed using Bayesian inference?
L-Statistics System for describing probability Hosking and Wallis (1997) distribution functions based on linear location combinations of moments L-moments:
scale 1=L-location (mean) 2=L-scale (variability or dispersion) 3=L-skewness (asymmetry) skewness 4=L-kurtosis (thickness of tail)
L-moment ratios (dimensionless): kurtosis r=r/2
=L-CV= 2/1 (variability)
Available R packages for L-moments:
library(lmom) library(lmomRFA)
Bayesian Inference Bayes Rule in a modeling framework:
=
()
where = 1 , 2 , , and = , ,
- Define prior distributions for model parameters (a priori knowledge)
- Consider GEV likelihood function (can consider GNO, GLO, etc.)
- Monte Carlo, acceptance criteria, builds posterior distributions of Bayesian inference derives the posterior probability as a consequence of a prior probability and a likelihood function Available R packages for Bayesian inference:
library(rstan) library(spBayes)
Historical Data Global Historical Climatology Network:
Integrated database of daily climate summaries from land surface stations (100,000+) across the globe Includes observations from multiple sources that have been subjected to a the same fully-automated quality control process (Durre et al. 2010)
Duplication of records Exceedance of physical, absolute, climatological limits Temporal persistence Inconsistencies with neighboring observations
Tennessee River Valley Watershed GHCN-Daily gauges with 85% data availability for 10+ years period of record (POR)
Regional Frequency Approach
- 1. Identify homogeneous region(s)
- 2. Screen observations for false/erroneous records
- 3. Compute annual (or seasonal) maxima
- 4. Compute frequency distribution
- L-moments
- Bayesian inference
- 5. Estimate point precipitation frequency results
SOM Output Map Self-Organizing Map Clustering algorithm used to group stations with similar attributes Apply SOM algorithm to :
- Latitude
- Longitude
- Elevation
- Avg annual precipitation
- Avg annual max one-day precipitation Each station maps to a single SOM node Gauges mapped to same node define homogeneous regions Homogeneous regions need not be contiguous Available R packages for SOM analysis:
library(som) library(kohonen)
L-Moments RGCs Bayesian Inference RGCs L-Moments vs. Bayesian Summary Precipitation-frequency analyses provide users with expected return periods of heavy events Frequency estimates vary based on methodology
- In all but one region, L-moments best-estimates exceed Bayesian best-estimates
- Uncertainty bounds from Bayesian inference exceed L-moments Additional testing is needed to understand benefits of Bayesian over L-moments
Questions?
Katie Holman kholman@usbr.gov
+1.303.445.2571 Andrew Verdin averdin@usbr.gov
+1.303.445.3647 Joseph Kanney joseph.Kanney@nrc.gov
+1.301.415.1920 This work was funded by the U.S. Nuclear Regulatory Commission under contract NRC-HQ-60-11-I-006
Bayesian inference Prior (): the strength of our belief in without the data Posterior (l): the strength of our belief in when the data are taken into account Likelihood (l): the probability that the data could have been generated by the model with parameter values Evidence p(Y): the probability of the data according to the model, determined by summing across all possible parameter values weighted by the strength of belief in those parameter values typically unknown, can be ignored with proportionality essentially a normalizing constant does not enter into determining relative probabilities (models)
Available R packages for Bayesian inference:
library(rstan) library(spBayes)
SOM Results - At-Site Means