Modelamiento estadistico de las precipitaciones de series temporales.ppt

analalitica descriptiva

1. Statistical modelling of precipitation time series
including probability assessments of extreme events
Silke Trömel and Christian-D. Schönwiese
Institute for Atmosphere and Environment
J. W. Goethe University
Frankfurt/M., Germany

2. Gaussian assumptions

3. Statistical modelling of climate time series
Parameter P1(t):
Trends
Annual cycle
Episodic component
Modell: Gaussian distribution

4. Statistical modelling of climate time series
Parameter P1(t):
Trends
Annual cycle
Episodic component
Parameter P2(t):
Trends
Constant annual cycle
Modell: Gaussian distribution

5. Statistical modelling of climate time series
Parameter P1(t):
Trends
Annual cycle
Episodic component
Parameter P2(t):
Trends
Constant annual cycle
Modell: Gumbel distribution

6. Statistical modelling of climate time series
Parameter P1(t):
Trends
Annual cycle
Episodic component
Parameter P2(t):
Trends
Constant annual cycle
Modell: Gumbel distribution

7. Statistical modelling of climate time series
Parameter P1(t):
Trends
Annual cycle
Episodic component
Parameter P2(t):
Trends
Constant annual cycle
Modell: Weibull distribution

8. Statistical modelling of climate time series
Parameter P1(t):
Trends
Annual cycle
Episodic component
Parameter P2(t):
Trends
Constant annual cycle
Modell: Weibull distribution

9. The distance function
Gaussian distribution
PDF
Least Squares
ML
Distance function
ML

10. Different distributions and their distance functions
Gaussian distribution: Least-squares:
Random number
Pdf
Random number
Distance function

11. Different distributions and their distance functions
Weibull distribution:
Frequency
Precipitation [mm] Precipitation [mm]
Distance function
Distance function
Precipitation [mm]
Gumbel distribution:
Precipitation [mm]
Pdf

12. Analyses of a German station network
•132 time series of monthly precipitation
totals, 1901-2000
•Realization of a Gumbel distributed
random variable
Eisenbach-Bubenbach

13. Example: Eisenbach-Bubenbach [47.97
o
N, 8.3
o
E]

14. Example: Eisenbach-Bubenbach [47.97
o
N, 8.3
o
E]

15. The expected value
…of a Gumbel distributed random variable
with time-dependent location parameter a
G(t) and time-dependent scale parameter b
G(t)
Precipitation [mm]
Pdf [1/mm]

16. The expected value
…of a Gumbel distributed random variable
with time-dependent location parameter a
G(t) and time-dependent scale parameter b
G(t)
Precipitation [mm]
Pdf [1/mm]

17. Germany: Changing probability of extreme events
> 95th percentile
January
< 5th percentile
January

18. Germany: Changing probability of extreme events
< 5th percentile
August
> 95th percentile
August

19. Trend estimates by comparison
LS
January
r
Gumbel
January

20. Conclusions
•The introduced generalized time series decomposition technique
allows a free choice of the underlying PDF
•The signal is detected in two instead of one parameter of the PDF
•Statistical modeling of precipitation time series can be achieved
•The analytical description of the time series
1.allows probability assessments of extreme values for every
time step during the observation period
2. provides trend estimates taking into account the statistical
characteristics (of precipitation)