1. Heiko Paeth, Institute of Geography, University of Würzburg,
Regional Dynamical Downscaling of Mediterranean Climate – Climate Change Perspectives
MedCLIVAR Workshop 2007, La Londe les Maures
Introduction
Dynamical downscaling
Extreme value statistics
Simulated extreme events
Simulated changes
Postprocessing of model data
Conclusions

2. I. Introduction industrial emissions heat stress traffic flood
biomass
burning
drought
over-
grazing
wind
extremes

3. How can we infer future changes in the frequency and intensity
I. Introduction
How can we infer future changes
in the frequency and intensity
of extreme events?
dynamical aspect (climate modelling)
statististical aspect (assessment of uncertainty)

4. II. Dynamical downscaling
low latitudes are dominated by convective rain events
the spatial heterogeneity of individual rain events is high
regional rainfall estimates are subject to large sampling errors

5. II. Dynamical downscaling
station data global model regional model statist. interpol.
day-to-day variability annual precipitation
station data are often too sparse to represent regional rainfall
global models are too coarse-grid for regional details
statistically interpolated data sets fail in mountainous areas
dynamic nonlinear regional models account for the effect of orography

6. II. Dynamical downscaling
3 x CO2
the rainfall trends predicted by the global model are barely relevant to political plannings and measures
the rainfall trends predicted by the regional model are much more detailed and of higher amplitude
more detailed fingerprint or spatial noise  added value ???

7. II. Dynamical downscaling
Temperature
differences
between
ensemble
members
at certain
time scales
measure
of internal
variability
different
initial
conditions
(stochastic)
statistical
comparison
Precipitation
variance
of the
ensemble
mean
measure
of external
variability
consideration of various ensemble members enables the statistical quantification of the human impact on climate in the climate model

8. II. Dynamical downscaling
ECHAM5/MPI-OM:
A1B (GHG)
constant LC
Land degradation:
FAO original
REMO:
A1B (GHG+LC)
ECHAM5/MPI-OM:
observed GHG
constant LC
REMO:
observed GHG
constant LC
REMO:
B1 (GHG+LC)
ECHAM5/MPI-OM:
B1 (GHG)
constant LC
Land degradation:
FAO reduced
dynamics: hydrostatic
physics: ECHAM4
sector: 30°W-60°E ; 15°S-45°N
resolution: 0,5° ; 20 hybrid levels
validation: good results

9. II. Dynamical downscaling
The main features of Mediterranean climate are well reproduced by REMO.

10. III. Extreme value statisticsf
climate parameter
The processes, which cause climate extremes, are not necessarily the same as for weak climate variations.
Hence, they usually do not obey a normally distributed random process.

11. III. Extreme value statistics
The Generalized Pareto Distribution (GPD) is a useful statistical distribution, since it is a parent distribution for other extreme value distributions (Gumbel, Exponential, Pareto).
The quantile function x(F) is given by:
= location parameter (expectation)
= scale parameter (dispersion)
= shape parameter (skewness)
The parameters of the GPD can be estimated by the method of L-moments.
Estimation of T-year return values (RVs):
cumulative GPDs T = 5a q
99% RV
43mm
dispersion parameter: threshold quantile

12. III. Extreme value statistics
uncertainty of the RV estimate is inferred from bootstrap sampling:
from fitted GPD b random samples of size N generated
from random samples b indi- vidual RVs estimated
these b RVs are normal distri-buted such that STD is a mea-sure of the standard error of the RV estimate
signal-to-noise ratio is given by MEAN/STD over b RVs 1
cGPD N
random
numbers
new samples of size N mm f
STD
90% conf. interv. RV
change in RV is significant at the 1% level, if 90% confidence inter-vals of two PDFs of RVs over b bootstrap samples do not overlap: f
present-day
climate
forced
climate RV

13. III. Extreme value statistics
100-year RV in mm
The 100-year RV estimate ranges between 200 mm and 800 mm, depending on the random sample.

14. III. Extreme value statistics
single estimate / simulation
one predicted value
without uncertainty range:
pretended precision  RV
2000
2050
99%
Monte Carlo approach
probabilistic forecast
with mean and uncertainty
range:
more objective basis for
decision makers
90%
s+=84% RV
x=50%
security
costs
s-=16%
10%
2000
2050 1%
probabilistic forecast of future rainfall changes provides a reasonable scientific basis for political plannings and measures

15. IV. Simulated extreme events
1-year return values of heavy daily rainfall
The occurrence of extreme rain events is a function of the land-sea contrast, orography, geographical latitude and seasonal cycle.

16. IV. Simulated extreme events
1-year return values of high daily temperature
The occurrence of high temperature is also a function of the land-sea contrast, orography, geographical latitude and seasonal cycle.

17. IV. Simulated extreme events
S/N ratio for
1-year RVs
of heavy
daily rainfall
The estimate of extrem values is more robust in regions and seasons with large-scale rather than convective precipitation.
The choice of long return times in the pre-sence of short time series is unappropriate.

18. V. Simulated changes extremes (1y-RV) seasonal means PRECIPITATION
2025 minus
present-day
extremes (1y-RV)
α = 5%
seasonal means

19. V. Simulated changes extremes (1y-RV) seasonal means TEMPERATURE
2025 minus
present-day
extremes (1y-RV)
α = 5%
seasonal means

20. VI. Postprocessing of model data
assessed variability
discontinuity
daily precipitation
The assessment of changes in weather extremes is very sensitive to inhomogeneities in observational data.
No problem with model data.

21. VI. Postprocessing of model data
different
initial
conditions
(stochastic)
radiation
budget and
energy
fluxes
atmospheric
and oceanic
circulation
instability
and
convection
cloud
micro-
physics
precipitation
error
nonlinear error growth
time
precipitation is the end product of a complex causal chain
each step imposes addititional uncertainty, particularly if it is based on a physical parameterization in the model

22. VI. Postprocessing of model data
observed station
time series
(local information)
REMO grid box
(50km x 50km)
climate models:
area-mean
precipitation
observations:
local
station data
comparison ?
model data
station data

23. VI. Postprocessing of model data
Weather Generator
simulated
grid-box
precipitation
(dynamical part)
local topography
(physical part)
random distribution
in space
(stochastical part)
virtual station rainfall
(result)

24. VI. Postprocessing of model data
original REMO rainfall
REMO rainfall:
- wrong seasonal cycle
- underestimated extremes
- hardly any dry spells
Weather Generator:
- statistical distribution
as observed
- individual events not in
phase with observations
rainfall from weather generator
station time series
model data
station data
model data postprocessed

25. VII. Conclusions
Regional climate models are required in order to account for the spatial heterogeneity of Mediterranean climate.
The estimate of extreme values and their changes requires appropriate statistical distributions and a probabilistic approach.
When estimating EVs from short time series, it is necessary to restrict the analysis to short return periods.
The occurrence of climate extremes is a function of land-sea contrast, orography, geographical latitude and seasonal cycle.
REMO projects no coherent changes in heavy rainfall whereas warm temperature extremes clearly tend to increase.
Systematic model deficiencies and the grid-box problem can be overcome by use of a weather generator.
The model results now need to be corroborated by available homogeneized long-term observational time series.