Jozef Pecho: POT and block-maxima analysis of precipitation extremes at selected stations in Slovakia
1. Workshop „Non-stationary extreme value modelling in climatology“
Technical university of Liberec, February 15-17, 2012
POT and block-maxima analysis
of precipitation extremes at selected
stations in Slovakia
Jozef PECHO
TUL Liberec/IAP AS CR, Prague
3. MOTIVATION
• Ph.D. thesis – Regional analysis of IDF relationship of extreme rainfalls in
Slovakia
• Long time-series of sub-daily precipitation totals are available from 8-10
MS (at least 40 years of records in the period Apr.-Oct.)
• The latest approaches/methods of regional frequency analysis, estimation
of return periods through different stationary and non-stationary extreme
value modelling haven´t been applied to the datasets of sub-daily
precipitation
• Previously published analyses of IDF relationship have been based on the
non-parametric stationary modelling using the block-maxima approach
(„at site“ local estimation)
In this presentation: comparison of two sampling procedures (POT and
„block-maxima“), stationary approach of distribution estimation (GEV, GPD),
at-site local estimation
4. INTRODUCTION
• Definition of IDF (Intensity-Duration-Frequency) relationship
• The latest approaches/methods of regional frequency analysis, estimation
of return periods through different stationary and non-stationary extreme
value modelling haven´t been applied to the datasets of sub-daily
precipitation
5. DATA OF EXTREME RAINFALLS
• Sub-daily ombrographic records (1-min rainfall data) → integration to 5,
10, 15, 20, 30, ... , 180-min, ... , 24-h precipitation totals
• There are approx. 100 MS with ombrographic records (4 selected MS with
high quality data in this presentation) in Slovakia → 1995-2009 (1960-2009)
• Data quality control have been applied (comparison with the original
ombrographic records, ombrographic vs. classic rain gauge records)
• Selected station represent different geographical conditions since they
are situated in different part of Slovakia territory
6. DATA OF EXTREME RAINFALLS
Štrbské Pleso (1354 m a.s.l.)
Sliač (313 m a.s.l.)
Košice (230 m a.s.l.)
Number of years
Hurbanovo (115 m a.s.l.)
7. METHODS
DATA INPUT
1-min rainfall data → 5, 10-min, …, 24-h totals
SAMPLING
Block-maxima Peaks-over-threshold
Annual maxima series MRL test, TC test
Data Declustering
DISTRIBUTION FITTING
Generalized Extreme Value Generalized Pareto Distribution
Maximal Likehood Estimation
Quantiles Estimation
8. METHODS
Peaks-over-threshold
Selecting an appropriate threshold is a critical problem with the POT methods. Too low a threshold is likely to violate the
asymptotic basis of the model; leading to bias; and too high a threshold will generate too few excesses; leading to high
variance. The idea is to pick as low a threshold as possible subject to the limit model providing a
reasonable approximation. Two methods are available for this: the first method is an exploratory technique carried
out prior to model estimation and the second method is an assessment of the stability of parameter estimates based on the
fitting of models across a range of different thresholds.
• Mean Residual Life test (plot) - The idea is to find the lowest threshold where the plot is nearly linear;
taking into account the 95% confidence bounds.
• Threshold choice test - The second method for trying to find a threshold requires fitting data to the GPD
distribution several times, each time using a different threshold. The stability in the parameter estimates can then be
checked
• Other methods: Dispersion Index test (DI), etc.
15. CONCLUSIONS and FUTURE
AMS (GEV) vs. POT (GPD)
According to preliminary results presenting in this study, it seems that POT(GPD) methods proved to by useful tool for T-
year estimation – in the case of maximum likelihood estimation provides more efficient T-year event estimation
Threshold specification
In this contribution two parametric POT tests were applied to sub-daily precipitation dataset – MRL and TC, after the
thresholds were divided into 5-10 classes (depends on precipitation duration)
Both methods showed an ability to determined thresholds in quite narrow intervals of values (good agreement in results)
Overall we can conclude, a different methodology should be followed in order to determine the rainfall threshold (application
for the rest of the dataset of sub-daily precipitation)
Future work
While we din´t analyses a sensitivity of DF parameter values to different thresholds in the same precipitation duration
category in this study, we would like to test this approach in the future (using wider range of methodologies for thresholds
determination as well as parameters estimation – L-moments, etc.)