Detection of Trends in
Extreme Weather
Phenomena
Comparing the skill of the Block Maxima and Point
Process approaches
ASP 2011 Colloquim: Statistical Assessment of Extreme
Weather Phenomena under Climate Change
S
Erik Haagenson, Agata Imielska, Sara Rodríguez, Anne Sabourin, Jeremy Weiss
Australian Climate Influences
SWWA rainfall decline
January to October rainfall in SWWA with centred 15 year moving
average. Years shown in red are the five lowest on record.
Trend in winter anticyclone density 1950 2010
SWWA Precipitation
GENERALIZED EXTREME VALUE
DISTRIBUTION ANALYSIS (GEV)
100
9619 Station Precipitation Maximum May-October
S Station 9619
60
40
October)
S Maximum value from
each winter obtained
and fit to GEV
Precipitation
S Winter Season (May-
80
S 1889-2004
1900
1920
1940
1960
Year 1889-2004
1980
2000
GENERALIZED EXTREME
VALUE DISTRIBUTION
ANALYSIS (GEV)
80
0.2
0.4
0.6
0.8
1.0
40
80
Empirical
Model
Return Level Plot
Density Plot
100
f(z)
0.02
140
100
0.00
60
20
Return Level
60
0.04
0.0
trend in the location
parameter only
used to set up our
experimental design
60
40
0.0
S The best fit was with a
S This information was
Empirical
0.4
Model
0.8
S Scale and location
parameters fit with a
linear trend
Quantile Plot
100
Probability Plot
1e-01 1e+00
1e+02
Return Period
20
40
60
z
80
100
Experimental Setup

Questions :

How to simulate data ?
(Given desired GEV parameters for the seasonal maxima)

Given simulated data, what kind of experiment
should we perform ?
Data Simulation
●
●
●
Season : n = 184 days.
Number of wet days over a season :
nδ : Poisson ditribution (mean : 84 wet days)
On wet days : Rainfall X has GPD ditribution :
Seasonal maximum
●
Relation GEV/GPD parameters :
●
Experimental Design
●
Year t , simulated data has seasonal
maximum
(trend b in the GEV location parameter only)
●
Range of tested trends :
b= ( -0.1, -0.05 , -0.02 , 0 , 0.02 , 0.05 , 0.1 , 0.2 )
●
●
For each value of b :
●
simulate Nsim datasets; fit on each of those:
–
–
●
A Poisson point process model
A block maxima model.
How many times was the trend detected ?
Results
Next Steps
S Expand simulations, test over a series of
trends (expand curves)
S Develop theoretical approximations to
bound the detectability of trends to help
guide detection of trends in extreme
rainfall
References
S
S
S
S
S
S
S
S
S
Bates, B.C., Hope, P., Ryan, B., Smith, I., Charles, S., 2008. Key findings from the
Indian Ocean Climate Initiative and their impact on policy development in
Australia, Clim. Change, 89: 339-354, doi:10.1007/s10584-007-9390-9.
Bates, B.C., Chandler, R.E., Charles, S.P., Campbell, E.P., 2010. Assessment of
apparent nonstationarity in time series of annual inflow, daily precipitation, and
atmospheric circulation indices: A case study from southwest Western Australia.
Water Resources Research, 46: W00H02, doi: 10.1029/2010WR009509.
Fowler HJ, Wilby RL (2010) Detecting changes in seasonal precipitation extremes
using regional climate model projections: Implications for managing fluvial flood
risk. Water Resources Research 46:W03535 doi:10.1029/2008WR007636.
Hennesy, K.J., Suppiah, R., Page, C.M, 1999. Australian rainfall changes, 19101995, Aust. Meteor. Mag., 48:1, 1-13.
Indian Ocean Climate Initiative (IOCI) 2002, Climate Variability and Change in
Southwest Western Australia, Dep. Of Environ. Water and Catchment Prot., East
Perth, WA, Australia.
Laverty, B.M., Kariko, A.K., Nicholls, N., 1992. A high-quality historical rainfall
data set for Australia. Aust. Meteor. Mag., 40, 33-39.
Li Y, Cai W, Campbell EP (2005) Statistical modeling of extreme rainfall in
Southwest Western Australia. Journal of Climate 18: 852-863
Reyes H., Vaquera H. and Vilaseñor J. Estimation of trends in high urban ozone
levels using the quantiles of (GEV), Environmetrics, vol. 21, pp.470-481, 2010.
Zhang X, Zwiers FW, Li G (2004) Monte Carlo Experiments on the Detection of
Trends in Extreme Values. Journal of Climate 17: 1945-1952
THANK
YOU!!