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

2. PRESENTATION OBJECTIVES
MOTIVATION
INTRODUCTION
DATA OF EXTREME RAINFALLS
METHODS
RESULTS

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.

9. RESULTS – AMS
Hurbanovo Štrbské Pleso
40.0 70.0
5m 10m 15m 20m 30m 45m 60m 90m 180m 5m 10m 15m 20m 30m 45m 60m 90m 180m
35.0
60.0
30.0
50.0
25.0
40.0
20.0
30.0
15.0
20.0
10.0
10.0
5.0
0.0 0.0
1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
Sliač Košice
50.0 80.0
5m 10m 15m 20m 30m 45m 60m 90m 180m 5m 10m 15m 20m 30m 45m 60m 90m 180m
45.0
70.0
40.0
60.0
35.0
50.0
30.0
25.0 40.0
20.0
30.0
15.0
20.0
10.0
10.0
5.0
0.0 0.0
1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010

10. RESULTS – AMS (GEV)

11. RESULTS – Threshold analysis
Mean Residual Life plot Hurbanovo – 5 m
8.0
7.0
6.0
Mean Excess
5.0
4.0
3.0
2.0
2 3 4 5 6
Threshold

12. RESULTS – Threshold analysis
Threshold Choice Test Hurbanovo – 5 m
0.0 1.0 2.0 3.0 4.0 5.0
0.0 1.0 2.0 3.0 4.0 5.0

13. RESULTS – Threshold time series
5m 15 m
120 190
110
170
100
90 150
80
130
70
110
60
50 90
40
70
30
20 50
1960 1965 1970 1975 1980 1985 1990 1960 1965 1970 1975 1980 1985 1990
60 m 180 m
320 400
300
280 350
260
240 300
220
200 250
180
160 200
140
120 150
1960 1965 1970 1975 1980 1985 1990 1960 1965 1970 1975 1980 1985 1990

14. RESULTS – GPD
POT (GPD)
AMS (GEV)

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.)

16. THANK YOU FOR YOUR ATTENTION