1. Extreme events and Euro-Atlantic atmospheric blocking in present and future climate simulations
Jana Sillmann
Max Planck Institute for Meteorology, Hamburg
International Max Planck Research School on Earth System Modelling
Paris, SAMA seminar, 20th January 2009

2. Motivation cold waves heat waves floods droughts
ournewsbrooklyn.wordpress.com
cold waves
heat waves
floods
droughts
IPCC 2007: ”Climate change may be perceived most through the impacts of extremes…”
In the last decades, mankind started to worry about climate change due to anthropogenic forcings. And as the last IPCC reported, climate change may be perceived most through the impacts of extreme events, such as cold and heat waves, flood or droughts. In the last years we had several examples for this reasoning, e.g. the Elbe flood 2002 and the heat wave 2003 in Europe, which caused enormous financial and also human losses. The impact of extreme events is also refelcted in the statistics of re-insurances, such as the German Munich Re-insurance, which reports an increase in climate related catastrophes and assosiated losses since the 1950s. However, this statitsic cannot be taken as evidences that climate extremes have increased in the last few decades, because it is biased by growing population density, higher technology standards, increasing media attention and more insured properties. Thus, the nature of climate extremes as well as their driving mechanisms should be studied scientifically to find out whether extreme events will increase under anthropogenic climate change and to be able to prevent catastrophes caused by extreme events.
So the scope of my thesis was to make use of a state-of-the-art global climate model to assess large-scale climate extreme events in present and future climate simulations and to analyse connections to large-scale atmospheric circulation patterns.
Munich Re 2005: Increase of climate related catastrophes and associated material and human losses since 1950

3. Outline Theory Questions Climate model and data
Defining extreme climate events and atmospheric blocking
Questions
Is the model able to capture observed patterns of climate extremes?
What changes in extremes can we expect under anthropogenic climate change?
Can we find associations between climate extremes and atmospheric blocking?
Can we use these associations in the statistical modeling of extreme events?
In my talk, I will first give some information about the climate model and data I have used for my analyses and define the term extreme climate event.
Then I will raise 4 major question addressed in my thesis which I will answer throughout this talk.

4. Model & Data Model & Data
Coupled general circulation model ECHAM5/MPI-OM
Atmosphere
Ocean
T63 (1.875° x 1.875°)
31 vertical levels
1.5° horizontal resolution
40 vertical levels
For my analysis I used the coupled general circulation model ECHAM5/MPI-OM, consisting of an atmosphere model ECHAM5 with a horizontal resolution of 1.8degree and 31 vertical levels which is coupled to the Max-Planck Institute ocean model with a 1.5deg horizontal resolution.
This graph shows several climate simulations preformed with the ECHAM5/MPI-OM model which are forced with observed greenhouse gas concentrations for the present climate (20C) and prescribed greenhouse gas concentrations according to the SRES emission scenarios for the future climate starting in year The present and future climate simulations are ensemble simulations each consisting of 3 ensemble members (realizations).
I concentrated mainly on the 20C and A1B scenario for my analysis of the climate extreme events.
20C, A1B and B1 – each with 3 ensemble members

5. Extreme events Definition of extreme climate events
Extreme event … very rare and very intense event with severe impacts on society and biophysical systems.
A precise definition of an extreme event is difficult to formulate and varies for the region under consideration, but in general, extreme events are defined as very rare and very intense events with severe impacts on society and biophysical systems. In particular, an extreme climate event can be classified as a pattern of extreme weather that persists for some time (e.g. few days) especially if it yields an average or total that is itself extreme. Extreme events occur on different spatial and temporal scales which is illustrated in this figure. Whereas the small scale events such as hail or storms cannot be resolved by a global climate model with a T63 resolution, larger-scale extreme events (or climate extremes) such as floods heat/cold waves as well as droughts can be simulated by a global climate model. Thus in my studies I concentrated on these large-scale extreme climate events.

6. Identification of extreme events in climate data
Methods for extreme value analysis
Indices for climate extremes ¹
Statistical modeling of extreme values
based on daily temperature and
precipitation data
describe moderate and statistically
robust extremes
easily understandable and
manageable for impact studies
There are two major approaches how to asses extreme events in climate data. On the one hand there are the indices for climate extremes developed by the Expert Team on Climate Change Detection Monitoring and Indices which are based on daily temperature and precipitation data. These indices describe in general moderate and statistically robust extremes which are meant to be easily understandable and applicable for model comparison as well as for climate impact studies.
On the other hand there is a parametric approach which involves the statistical modeling of extreme values to which I will explain more in the second part of my talk.
At this point I will focus on the indices for climate extremes, and I will present results especially for these 4 selected indices in the first part of my talk.
Yearly/monthly indices:
Minimum of daily minimum temperature
Maximum of daily maximum temperature
Maximum 5 day precipitation
Maximum number of consecutive dry days
¹ Expert Team on Climate Change Detection Monitoring and Indices

7. What changes can we expect under anthropogenic climate change?
Indices for extremes
What changes can we expect under anthropogenic climate change?
This leads me to the next question: What changes can we expect under anthropogenic climate change?
For this question I compared two 30-year time slices, one in the present climate ( ) with one in the future climate from for the A1B and B1 scenario. In the following slide however I will only show the results for the A1B scenario.

8. Changes in extremes Difference A1B scenario – present climate
Annual maximum temperature
Annual minimum temperature
[ ºC ]
Annual max. 5-day precipitation
Annual max. consecutive dry days
[ days ]
[ mm ]
On these figures you see significant difference to the 5 % significance level between the A1B scenario and the present climate time slice. On the upper panel the TXx is shown and on the lower panel the TNn. You can depict a global and overall significant warming trend, but the warming pattern differs between the two temperature indices. The maximum temperature rises the most in southern latitudes and in the summer time, whereas the minimum temperature rises predominantly in northern latitudes, especially northern America and north central Eurasia in winter time.
Now on the right side we see the changes in the precipitation based indices. The upper panel shows a general increase in the 5day precip., only around the Mediterranean Sea we can see a decrease. This decrease is concentrated on the summer months, whereas the increase in precipitation in central Europe is concentrated on the winter months or throughout the year in northern Europe.
The number of consecutive dry days are increased especially around the Mediterranean Sea and in the southern hemisphere. Since these prolonged dry periods fall together with the increasing summer temperature and decreasing precipitation, the Mediterranean region will have severe problems with heat stress and water supply in future climate.
We can see that the climate extremes change with distinct regional and seasonal patterns.
These results are already reflected in studies of observed climate extremes for the past few decades, which show similar trends but not yet as significant.
So these results can be viewed as continuance of already observed trends.

9. Winter climate of the Euro-Atlantic domain
Atmospheric blocking
Can we find associations between climate extremes and atmospheric blocking?
Winter climate of the Euro-Atlantic domain
Minimum Temperature
The next question I was interested in was whether we can find associations between large-scale atmospheric circulation patterns and climate extremes.
I focused my attention on atmospheric blocking in the North Atlantic –European domain which has a considerable impact on the European winter climate and especially the minimum temperature.
For the following analysis I prolonged the time slices to 40 years and I used the stabilization period with constant GHG forcing at the level of 2100 for future scenario A1B to increase the statistical robustness of my results.

10. Atmospheric blocking
… sustained, quasi-stationary, high-pressure systems that disrupt the prevailing westerly circumpolar flow
Height of tropopause (2 pvu *):
elevated tropopause associated with strong negative potential vorticity anomalies ( > -1.3 pvu )
At this point I will briefly define atmospheric blocking to you. In general terms atmospheric blocking is defined as sustained, quasi-stationary, high pressure system that disrupts the prevailing westerly flow. It differs from normal high pressure systems due to its long life-time. The figure illustrates an example of a blocked situation in January 1987 over the North Atlantic European domain. The blue layer indicates the tropopause between 500 and 150hPa. Dark blue areas show an elevated tropopause which are associated with strong negative potential vorticity anomalies. Due to this elevation of the tropopause, the prevailing westerly flow has to find its way around the “blocked” area. The anti-cyclonic flow conditions associated with this blocking situation lead to temperature and precipitation anomalies especially in European winter.
To capture these kind of atmospheric blocking situation in the model I am using a blocking indicator developed by Schwierz et al 2005, which is based on the potential vorticity and which tracks strong negative PV anomalies from its genesis to its lysis.
 relationship between temperature and precipitation anomalies
(Rex 1951, Trigo et al. 2004)
* [10-6m2s-1K kg-1]

11. Potential Vorticity (PV) - based blocking indicator
Atmospheric blocking
Potential Vorticity (PV) - based blocking indicator
Blocking detection method (Schwierz et al. 2004):
Identification of regions with strong negative PV anomalies between hPa
PV anomalies which meet time persistence (> 10 days) and spatial criteria (1.8*106km2) are tracked from their genesis to their lysis
To capture these kind of atmospheric blocking situation in the model I am using a blocking indicator developed by Schwierz et al 2004, which is based on the potential vorticity and which tracks strong negative PV anomalies from its genesis to its lysis.

12. Representation in present and future climate
Atmospheric blocking
Representation in present and future climate
Blocking events > 10days
DJF
model
ERA-40 re-analysis
As a first step I investigated how well atmospheric blocking is represented in the model by comparing the winter blocking events that are longer than 10days in the model with those in the ERA-40 reanalysis. We can see that the model represents the overall blocking frequency well, but the maximum of blocking frequency is shifted southward of Greenland in the model. The blocking frequency indicates the percentage of time when a particular grid point is blocked by a block with a life time greater/equal 10 days. Thus, a blocking frequency of 1 % means approx. 1 blocked day per season.
In the future scenario we can see that the blocking frequency diminishes southeast of Greenland but increases west of Greenland which indicates a northwestward shift of the blocking region.
Blocking frequency in %

13. Blocking frequency for DJF
Atmospheric blocking
European blockings
(15°W-30°E,50°N-70°N)
Blocking frequency % %
Blocking frequency for DJF
Having these information about atmospheric blocking, I want to use it to analyze the association between atmospheric blocking and extreme events by means of correlation analysis. For that I defined an area of European blockings to capture all blocking events that reach the European continent thus having the most impact on its winter climate. I averaged over this region and received a time series of blocking frequencies for this European blocking area which I correlated with the indices for extreme events at each grid point in the Euro-Atlantic domain.

14. Atmospheric blocking
Correlation of European blockings with winter (DJF) minimum temperature
I particularly applied the Spearman’s rank correlation because it does not rely on normal distributed data. In the figures you see the spearman rank correlation coefficient for European blockings and the extreme index minimum of the minimum temperature for winter. On the left side for the present climate and on the right side for the future climate. You can see clearly a negative correlation over large parts of Europe in the present climate. Due to the anti-cyclonic flow conditions associated with the European blockings cold air masses from Northeast are transported into Europe and lead to very cold nighttime temperatures indicated by TNn.
In the future climate the negative correlations remain but weaken due to the decrease in blocking frequency. Thus, indicating less cold winter nights due to decreasing blocking situations closed to Europe.
Significant Spearman’s rank correlation coefficient to the 5% significance level

15. Identification of extreme events in climate data
Methods for extreme value analysis
Indices for climate extremes
Statistical modeling of extreme values
GEV – Generalized Extreme
Value distribution
parametric approach to
characterize the distribution of
extreme events
calculation of return values
I come now to the second part of my talk which is focused on the statistical modeling of extreme events. In contrast to the indices, this is a parametric approach which characterizes the distribution of extreme events and allows extrapolation of extremes with return values far beyond the observed time period. The statistical modeling of extremes or the extreme value theory goes back to the extremal limit theorem of Fisher and Tippet in 1928, which states that the maxima of a sample of random variables converges to one of three asymptotic extreme value distributions as sample length goes to infinity. These three extreme value distributions are summarized by the General Extreme Value distribution, which I will explain briefly in the next few slides.

16. Generalized Extreme Value (GEV) distribution
Stationary GEV
Generalized Extreme Value (GEV) distribution
with parameters  (location)‏,  (scale) and  (shape)
This is the general formula for the GEV distribution, which consists of 3 parameters. The location parameter indicates where the distribution is located on the x axis, the scale parameter is a measure of the variability of the distribution and shrinks of stretches the distribution. The shape parameter distinguishes between the 3 forms summarized in the GEV distribution. If the shape parameter is negative we have a Weibull distribution (bounded tail), if it is zero we have a Gumbel distribution and if it is positive we have a Frechet distribution with a heavy tail.
So for my special example here in this talk, I fitted the GEV distribution to monthly minimum temperature extremes for the winter season (December-February) under the assumption of stationary conditions.

17. Parameters for DJF minimum temperature
Stationary GEV
Parameters for DJF minimum temperature
location
scale
shape
ERA-40
20C
Here are the results of this fit, first for the present climate for ERA40 reanalysis in the upper panel and for the 20C simulation in the lower panel. Shown are the parameters of the GEV distribution. Grid points where the fit failed are left blank. You can see a good agreement between the patterns in the re-analysis and the 20C model simulation, with a north-south gradient in the location and scale parameter. The ERA40 reanalysis show a higher location parameter (warmer temperatures) and smaller scale parameter (less variability) in northern Europe than the model, however the ERA40 reanalysis are known to have a warm bias in northern latitudes. The shape parameter is negative throughout Europe indicating a Weibull distribution typical for temperature extremes.
In the lowest panel we see now the difference between the future scenario A1B and the 20C simulation. We can depict a strong increase of the location parameter especially in the northeastern Europe which decreases towards southwest. These changes are similar to what we could see in the analysis of the indices for extreme events, especially the TNn. The scale parameter decreases especially in parts of central Europe indicating less variability in the minimum temperature extremes. There is not much change in the shape parameter only in France we can see an increase, however even there the shape parameter still remains negative.
A1B –20C

18. Non-stationary GEV
Can we use the association between extreme events and atmospheric blocking in the statistical modeling of extreme events?
stationary GEV  non-stationary GEV
COV – time dependent covariate
The next question I was interested in was whether we can find associations between large-scale atmospheric circulation patterns and climate extremes.
I focused my attention on atmospheric blocking in the North Atlantic –European domain which has a considerable impact on the European winter climate and especially the minimum temperature.
For the following analysis I prolonged the time slices to 40 years and I used the stabilization period with constant GHG forcing at the level of 2100 for future scenario A1B to increase the statistical robustness of my results.
Atmospheric blocking as covariate derived from the PV-based blocking indicator (CAB)

19. Covariate atmospheric blocking
Euro-Atlantic domain
Blocking frequency %
Atmospheric blocking events are captured by the before described PV based blocking indicator. For the statistical analyses I now took into account all blocking events over the North Atlantic and Europe in contrast to only the European blocking events to have more blocking events available and to be able to compare my result to the ERA40 re-analysis.
European blockings
Euro-Atlantic blockings

20. Statistical modeling Model selection Model choice Deviance Statistic:
nllh
353
349
348
example *
* degrees of freedom
Model choice
Deviance Statistic:
where nllh0(M0) is the neg. log-likelihood of simple model
nllh1(M1) is the neg. log-likelihood of more complex model
I now want to test whether the covariate will improve the statistical modeling of extreme temperature data or if it is sufficient to use the stationary approach. So I set up a collection of statistical models, the stationary GEV and the non-stationary GEV with the location and the scale parameter linked to the CAB. Depending on the number of parameters each model has a certain degree of freedom, which plays a role for the choice of the best model. I fit the 3 models to the minimum temperature extremes and estimate the parameters via ML. So each model has a certain likelihood attached to it, resembling the probability that the parameters of the model can most likely represent the probability distribution of the underlying data.
Based on that likelihood I can use the Deviance Statistic to test which model is is the best to represent the underlying data. In the deviance statistic, the likelihood (or more precise the negative log-likelihood) of the more complex model (with more df) is compared with the nllh of the simpler model. The deviance (D) is for a sufficient large sample, approx. C-squared distributed with a degrees of freedom. Where a is the difference between the df of the compared models. We test the validity of the simpler model relative to the more complex model at the a level of significance and reject the simpler model if the deviance is larger than ca which is the 1-a quantile of the C-squared distribution. This means if D falls above ca with a =0.1 in this study, then the more complex model explains more variations in the data than the simple model at the 10% significance level.

21. minimum temperature extremes in winter
Non-stationary GEV
Model selection for
minimum temperature extremes in winter
model
model
model
On this slide you see the result for this method. First of all for the ERA40 re-analysis in this figure. The colors indicate the model which was selected as best be the deviance statistic. You can see that in most parts of Europe the model 1 is best to represent the underlying data, thus meaning that linking the location parameter to atmospheric blocking improves the fit significantly.
This is also the case for the 20C simulation of the ECHAM model as depicted in this figure.
For the future climate simulation the area where model 1 is best diminishes and in large parts of eastern Europe the stationary GEV can represent the data best. This is due to the decreasing blocking frequency and northeastward movement of the blocking area.

22. Slope of the location parameter
Non-stationary GEV
Slope of the location parameter
ºC/blocking freq. %
An important parameter which we have to have a look to is the slope of the location parameter. In model 1, which was the predominant best model in large parts of Europe the location parameter was linearly linked to the CAB. Thus b1 in this setting represents the slope of the location parameter. The slope indicates the changes of the location parameter (in degree Celsius) with the change in blocking frequency. The figures here show the slope of the loc parameter for ERA40, 20C and A1B. We see a homogeneous pattern of a decreasing slope when blocking is implemented as covariate in the GEV. This means that with increasing blocking frequency, so to say if there is a block present in the Euro-Atlantic domain, that the location parameter, representing the mean of the minimum temperature extremes, will be decreased.

23. Grid-point example at 9ºE, 53ºW
Non-stationary GEV
Grid-point example at 9ºE, 53ºW
GEV distribution for the stationary and non-stationary model 1
This can be made clearer by a grid point example. In this figure I display the GEV distribution for the minimum temperature at grid point 9/53 (Hamburg) for the stationary model (black line) and the non-stationary model with different blocking frequencies. The non-stationary GEV with zero blocking frequency (green line) looks very similar to the stationary case but with increasing blocking frequency this curve moves towards much colder temperatures as indicated by the red line for 27% blocking frequency. And according to the distribution also the quantiles of the distribution change with increasing blocking frequencies as indicated by the dashed line for the 5% quantile of the respective distribution.

24. Return values at grid point 9ºE, 53ºW
Non-stationary GEV
Return values at grid point 9ºE, 53ºW
T-year return value … is the (1-1/T)th quantile of the GEV distribution
median
This brings us to the return values which are represented by the (1-1/T)th quantile of a distribution, in this case of course the GEV distribution. With T standing for the waiting time for a particular extreme event. E.g. for a 2 year waiting time we would consider the 0.5th or 50%quantile as the 2-year return value of a certain extreme event, accordingly for a 20-year return value we would consider the 0.95th or 95% quantile of the distribution.
At the left graph we see as grey line the time series of minimum winter temperature extremes in the 20C simulation to which the stationary and non-stationary GEV was fitted. The stationary GEV of course has stationary moments as well as stationary quantiles and return values over time as represented by dashed black line (median) and solid black line 20yr return value. In contrast, the non-stationary GEV (in this case for model1) has non-stationary quantiles over time indicated by the red line. We can see that the median as well as the 20yr return value vary with the blocking frequency at each particular time step. Thus for months with high blocking frequency the 20yr-return value is much lower as for month without blocking. We thus receive a range of possible 20-yr return values, which can happen in dependance of the blocking occurrence.
But only for month with very strong blocking events the return value of the non-stationary GEV deviates significantly from those of the stationary case..
20-year return value
90% confidence interval

25. 20-yr return values for minimum temperature extremes in winter
Non-stationary GEV
20-yr return values for minimum temperature extremes in winter
Significant differences between RV20 of stationary and non-stationary GEV distribution
ERA40
20C
A1B
This can be summarized in the following figures for ERA40, 20C and A1B. Here I show the significant differences between the 20-yr return values for the stationary GEV and the non-stationary GEV for the highest blocking event in each particular simulation. We see in each figure a significant decrease of the 20-yr return value if we consider atmospheric blocking in the GEV for large parts of Europe. The differences in magnitude are explained by the different maximum blocking frequency in each simulation (ERA40 12%, 20C 27%, A1B 16%) the association between blocking and extreme winter nighttime temperatures persists in future climate, but a smaller area in A1B were atmospheric blocking significantly influences return values, because of the decreasing blocking frequency and changing blocking location.

26. Summary
Is the model able to capture observed patterns of climate extremes?
What changes in extremes can we expect under anthropogenic climate change?
increase of temperature and precipitation extremes as well as dry periods
regional and seasonal distinguished changes of extremes in future climate

27. Summary
Can we find associations between climate extremes and atmospheric blocking?
atmospheric blocking favors extreme cold nighttime temperatures in Europe
association remains robust in future climate, but influence of blocking events diminishes due to decreasing blocking frequency
Can we use these associations in the statistical modeling of extreme events?
atmospheric blocking implemented as covariate in the GEV can explain more of the variability in the underlying data
modeling of colder return values possible

28. Outlook Improvement of the statistical modeling:
longer climate simulations (500-year control run) to further test the statistical robustness of the results
apply Generalized Pareto distribution
use other or more covariates
Usage of this methodology for statistical downscaling:
limit region of interest, e.g. to northern, southern Europe
find appropriate covariate for that region
test method with observations

29. Thank you very much!

30. Is the model able to capture observed patterns of climate extremes?
Indices for extremes
Is the model able to capture observed patterns of climate extremes?
HadEX dataset: indices for extreme events calculated on the basis of a worldwide weather observational dataset from the Hadley Centre (3.75° x 2.5° horizontal resolution) (Alexander et al. 2006)
Time coverage:
Now I come to the first question I addressed in my thesis:
Is the model able to capture observed patterns of climate extremes?
To answer this question I needed to find an appropriate observational dataset which I could compare my model results with. Since 2005 the Hadley Centre provides a dataset with indices calculated on the basis of worldwide weather stations in a rather coarse but gridded resolution with a time coverage from I used this dataset for comparison.

31. Temperature indices - global
Present climate
Temperature indices - global
Here you see the results for the temperature based indices, on the upper panels for the maximum of the maximum temperature and on the lower panels for the minimum of the minimum temperature. Left are the HadEX data and right the model data. Areas where there were no observational data available are left blank. For TXx we see a good agreement in the lower latitudes but in the higher latitudes and on the Tibetean Plateau the model shows a cold bias that can be up to 10degrees. In contrast, the TNn is very well presented by the model in comparison with the HadEX data.

32. Precipitation indices - global
Present climate
Precipitation indices - global
Here you see the precipitation based indices, on the upper panel the max. 5 day precipitation and the lower panel the max. consecutive dry days, where the HadEX data are on the left side and the model data o the right side. The overall pattern looks good for both indices but the RX5day is underestimated in some regions, e.g. southern Europe ad south east Asia. On the other hand the CDD are overestimated in these regions.
I concluded from my results that the model is able to represent the broad-scale patterns of the climate extremes, but the model bias can be substantial in some regions, which has to be kept in mind for subsequent analyses.

33. Temperature indices - regional
Present climate
Temperature indices - regional

34. Precipitation indices - regional
Present climate
Precipitation indices - regional

35. Temperature indices - global
Indices for extremes
Temperature indices - global

36. Pot. Vorticity (PV)-based Blocking indicator
Atmospheric Blocking
Pot. Vorticity (PV)-based Blocking indicator
… captures the block at the core PV-anomaly at tropopause level (Croci-Maspoli 2007)
latitude [°N]
climatological tropopause
instantaneous tropopause
PV anomaly [pvu]
PV anomaly < -1.3 pvu
tropopause = 2pvu [10-6 m2 s-1 K kg-1]
[hPa]
150
500
800
This is a north-south cross section, where the block is again indicated by the elevated tropopause, shown by the bold contour
The most striking feature is the strong negative PV anomaly just underneath the tropopause, here indicated by the dashed blue contours
Note also the positive anomalies which are located in the north and south
This strong anomalies at the tropopause level motivate for the definition of a blocking indicator which makes use of the three- dimensional information of the atmosphere
Therefore the PV field is vertically averaged between which yields to a 2D field - base field for the index

37. Atmospheric Blocking PV-based Blocking identification
Dashed = negative PV anomalies, and drawn through are positive PV anomalies
If they life longer than 5days they are captured as blocks (red contour) -> and called APV*
evolution of one blocking event
Genesis and lysis
This objective detection routine allows to calculate a long-term climatology
averaged PV-anomaly between 500 and 150hPa
(Schwierz et al. 2004, GRL)‏

38. Atmospheric Blocking PV-based Blocking identification
Dashed = negative PV anomalies, and drawn through are positive PV anomalies
If they life longer than 5days they are captured as blocks (red contour) -> and called APV*
evolution of one blocking event
Genesis and lysis
This objective detection routine allows to calculate a long-term climatology
filled contours indicate vertically-averaged PV anomalies (0.7pvu steps)‏
red = APV* blocking location
(Schwierz et al. 2004, GRL)‏

39. Atmospheric blocking
Composite maps

40. Modeling Diagnostic
Testing the method for El Nino and its impact on precipitation for winter (ONDJFM)
xCOV(t)
(mm)‏
Best model
model #
Now my question was, whether my method is working correctly and whether the inclusion of the blocking as covariate really improves my statistical modeling of the extreme events.
First I tested the method on another region with well known relationships between a large-scale circulation pattern and precipitation. I choose the El Nino and its impact on southern America. The left picture shows the well observed patterns of the association between the occurrence of El Nino during winter months and the mean precipitation.
The bottom pictures show the selected models and the slope of the parameter depending on the Elnino. You see in regions where there are dry conditions expected we have a negative slope, meaning less precipitation when during Elnino seasons, and were wet conditions are observed we see a positive slope, meaning more precip. Extremes during Elnino season.

41. Model Diagnostic at Grid Point [9E, 53N] for min.Tmin (ONDFM)‏
empirical
model
Probability Plot
Quantile Plot
empirical
model
Another way to test the method is by doing model diagnostics by means of probability or quantile plots. This method is only applicable for single grid points. So I show you one example of a grid point, approximately where Hamburg is located in the north of Germany

42. Generalized Extreme Value (GEV) distribution
Statistical modeling
Generalized Extreme Value (GEV) distribution
Block maxima approach
Daily minimum temperature data are blocked into sequences of length n, generating a sequence of block minima to which the GEV distribution can be fitted
select block size (e.g., 1 season, 1 month)‏
choose smallest event in each block (month or season)
fit GEV distribution to selected extreme events
estimation of GEV parameters for each global grid point via
Maximum-Likelihood
According to the block maxima approach the data series can be divided into blocks of a certain length, e.g. years or months and select the maxima out of each block, thus generating a new data series of block maxima. These block maxima are according to the extremal limit theorem converge to the GEV distribution. Thus the GEV distribution can be fitted to the block maxima and parameters are estimated via ML.