Workshop „Non-stationary extreme value modelling in climatology“              Technical university of Liberec, February 15...
PRESENTATION OBJECTIVESMOTIVATIONINTRODUCTIONDATA OF EXTREME RAINFALLSMETHODSRESULTS
MOTIVATION•   Ph.D. thesis – Regional analysis of IDF relationship of extreme rainfalls in    Slovakia•   Long time-series...
INTRODUCTION•   Definition of IDF (Intensity-Duration-Frequency) relationship•   The latest approaches/methods of regional...
DATA OF EXTREME RAINFALLS•   Sub-daily ombrographic records (1-min rainfall data) → integration to 5,    10, 15, 20, 30, ....
DATA OF EXTREME RAINFALLS                                        Štrbské Pleso (1354 m a.s.l.)                      Sliač ...
METHODS                              DATA INPUT        1-min rainfall data    → 5, 10-min, …, 24-h totals                 ...
METHODSPeaks-over-thresholdSelecting an appropriate threshold is a critical problem with the POT methods. Too low a thresh...
RESULTS – AMSHurbanovo                                                                                                  Št...
RESULTS – AMS (GEV)
RESULTS – Threshold analysisMean Residual Life plot                                          Hurbanovo – 5 m              ...
RESULTS – Threshold analysisThreshold Choice Test                                  Hurbanovo – 5 m                0.0     ...
RESULTS – Threshold time series5m                                                 15 m120                                 ...
RESULTS – GPD                    POT (GPD)AMS (GEV)
CONCLUSIONS and FUTUREAMS (GEV) vs. POT (GPD) According to preliminary results presenting in this study, it seems that POT...
THANK YOU FOR YOUR ATTENTION
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Jozef Pecho: POT and block-maxima analysis of precipitation extremes at selected stations in Slovakia

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Jozef Pecho: POT and block-maxima analysis of precipitation extremes at selected stations in Slovakia

  1. 1. Workshop „Non-stationary extreme value modelling in climatology“ Technical university of Liberec, February 15-17, 2012 POT and block-maxima analysisof precipitation extremes at selected stations in Slovakia Jozef PECHO TUL Liberec/IAP AS CR, Prague
  2. 2. PRESENTATION OBJECTIVESMOTIVATIONINTRODUCTIONDATA OF EXTREME RAINFALLSMETHODSRESULTS
  3. 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. 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. 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. 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. 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 FITTINGGeneralized Extreme Value Generalized Pareto Distribution Maximal Likehood Estimation Quantiles Estimation
  8. 8. METHODSPeaks-over-thresholdSelecting an appropriate threshold is a critical problem with the POT methods. Too low a threshold is likely to violate theasymptotic basis of the model; leading to bias; and too high a threshold will generate too few excesses; leading to highvariance. The idea is to pick as low a threshold as possible subject to the limit model providing areasonable approximation. Two methods are available for this: the first method is an exploratory technique carriedout prior to model estimation and the second method is an assessment of the stability of parameter estimates based on thefitting 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. 9. RESULTS – AMSHurbanovo 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 2010Sliač Košice50.0 80.0 5m 10m 15m 20m 30m 45m 60m 90m 180m 5m 10m 15m 20m 30m 45m 60m 90m 180m45.0 70.040.0 60.035.0 50.030.025.0 40.020.0 30.015.0 20.010.0 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. 10. RESULTS – AMS (GEV)
  11. 11. RESULTS – Threshold analysisMean 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. 12. RESULTS – Threshold analysisThreshold 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. 13. RESULTS – Threshold time series5m 15 m120 190110 17010090 15080 13070 1106050 9040 703020 50 1960 1965 1970 1975 1980 1985 1990 1960 1965 1970 1975 1980 1985 199060 m 180 m320 400300280 350260240 300220200 250180160 200140120 150 1960 1965 1970 1975 1980 1985 1990 1960 1965 1970 1975 1980 1985 1990
  14. 14. RESULTS – GPD POT (GPD)AMS (GEV)
  15. 15. CONCLUSIONS and FUTUREAMS (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 estimationThreshold specificationIn this contribution two parametric POT tests were applied to sub-daily precipitation dataset – MRL and TC, after thethresholds 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 (applicationfor the rest of the dataset of sub-daily precipitation)Future workWhile we din´t analyses a sensitivity of DF parameter values to different thresholds in the same precipitation durationcategory in this study, we would like to test this approach in the future (using wider range of methodologies for thresholdsdetermination as well as parameters estimation – L-moments, etc.)
  16. 16. THANK YOU FOR YOUR ATTENTION

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