Temperature and probability density functions in ENSEMBLES regional scenarios ENSEMBLES Technical Report No. M. Déqué April 9 ISSN 7-8
Contents Description of the method. Experiments used.......................... Pdf of individual models...................... From weights to pdfs....................... 6 Results 9. Organization of the gures.................... 9. Overview of the capitals..................... 9
CONTENTS
Chapter Description of the method. Experiments used At the time of writing this report 6 simulations are available in the daily database of RTB with AB scenarios at km resolution: CIR, CNRM, DMI, ETHZ, KNMI, ICTP, METN, METO-Q, METO-Q, METO-Q6, MPI, OURA, SMHI (driven by dierent GCMs) and UCLM In this study we will restrict to seasonal means (DJF, MAM, JJA and SON) of m and. The scenario period is - and the reference period is 96-99.. Pdf of individual models In studying the probability density functions we are interested both in the mean and in the extremes. In this context extreme means the tail of the distribution, i.e. the last deciles; it does not mean the very rare and catastrophic events for which our approach is not suited. It is however important to work with model grid point data, if we want to extend the study to daily pdfs. The calculation, and moreover the display, of all grid points is a huge unnecessary work. In addition models do not share the same grid. If we had to work only with means, considering spatial averages per country could have been a good approach. In the case of pdf, we will consider the capital of each European country, more precisely the closest model grid point to each capital. When including non-eu countries, we have capitals in Europe (tiny countries like Vatican, San Marino, Andorra, Monaco... are not considered here). Malta is an EU country, but this island is not resolved by the km meshes, so the nearest grid point is a sea point, with a dierent climate. We have also disregarded Nicosia and Reykjavik, because some models provide
6 CHAPTER. DESCRIPTION OF THE METHOD there unrealistic due to the too close lateral boundary. Finally, we have selected model locations, which will be referred to as the nearest European capital. Each model provides an uncertain result because the model seasonal response for a variable ( or ) is the average of two -year means. This sampling uncertainty is named the natural variability, which is a non-negligible part of the uncertainty. The model response is: R = 99 n=96 (X n+6 X n ) where X n is the seasonal mean of year n. If we assume that each year is independent of the others in terms of anomaly, R is the mean of independent values. As we work at the scale of a grid point, this assumption is widely veried. Otherwise, we would be able to predict the local seasonal weather one year in advance. As X is a seasonal mean, it is nearly gaussian (even for ). According to the limit central theorem, R is gaussian with the same mean as the yearly dierences and a standard deviation divided by. In the bivariate context ( and ), we get a gaussian couple with the same correlation coecient as the yearly dierences. It is thus easy to produce for each model a pdf (monovariate or bivariate) which takes into account the only uncertainty at this stage, which is the sample variability.. From weights to pdfs As we have, like in PRUDENCE, several models, a new source of uncertainty can be considered, which is the choice of a model. The above pdfs are in fact conditional pdfs if the selected model is considered to be true. The models are a combination of a driving GCM and a driven RCM. We will consider that all GCMs are equiprobable. The weights of the RCMs have been calculated in RT with a complex procedure based on ERA driven simulations. The closest the simulation to the 96- observations, the largest the weight. We chose the rescaled weight, which make a ratio of. in each of the 6 subscores between the largest and the lowest RCM. CI w=.69 CNRM w=.6 DMI w=.6
.. FROM WEIGHTS TO PDFS 7 ETHZ w=.67 ICTP w=.76 KNMI w=.9 METN w=.6 METO-Q w=.6 METO-Q w=. METO-Q6 w=.69 MPI w=.7 OURA w=.6 SMHI w=.79 UCLM w=.9 The nal range is, between METO-Q and KNMI, which allows each RCM to contribute signicantly to the nal pdf. With the unscaled weights, KNMI and ICTP would have a contribution equivalent to all the other RCMs. Then we make the assumption that the probability of an RCM is proportional to its weight. After multiplicative combination (we assume GCM and RCM are independent) and normalization, we have 6 positive numbers p i, the sum of which is. The compounded probability, e.g. for is: 6 pdf(t) = p i pdf(t model = i) i= and similarly for or for the couple (, ). The continuous pdf is a mathematical concept that we cannot handle with computers. So we have to dene bins. Here we have considered bins for each variable, from - to +6 C and from - to +6 mm/day, according to the range of responses of the models. As the dierence between the model means is often greater than the standard deviation due to their natural variability, the nal pdf may have several modes which correspond to individual models. This is the consequence of the underlying probabilistic model: the true response is given by one of the model. To articially introduce the possibility that the response may be between two models, we have applied a gaussian lter, aka gaussian kernel method. We replace the probability in each bin by a gaussian distribution with the mean as the center of the bin and a standard deviation of σ =. K and. mm/day. These values have been visually
8 CHAPTER. DESCRIPTION OF THE METHOD adjusted to cancel out as far as possible the multimodal eect, but to avoid a pure gaussian shape for the smoothed pdf (except when all models are in agreement). The extension to the bivariate pdf is easy, but computationally expensive with bins in dimensions. For, the ltered pdf pdf(t) reads: pdf(t) = T pdf(t ) T πσ exp ( T T σ ) where T is the width of each bin.
Chapter Results. Organization of the gures Figs.. to.8 present the pdf of changes (multiplied by ) for each season (blue for winter, green for spring, red for summer and yellow for autumn). Figs..9 to.6 show similar quantities for change. There are capitals per page (in alphabetic order). Finally, since: for a given model, there is an interannual correlation between and change (e.g. the warmest summers are often the driest) models which have a larger response in may also have a larger response in and responses are not independent. Figs..7 to.8 show the bivariate density (multiplied by ). Here it is not possible to superimpose the four seasons in a same panel, so there is one capital per page.. Overview of the capitals Let us examine rst the mean of the and pdf for each capital. Note that for the sign of the response is never signicant, since there is always at least % probability that the sign is positive and at least % probability that it is negative, whatever the capital and the season. So, when one reads mean increases by. mm/day, this does not means that this increase is certain. 9
CHAPTER. RESULTS Athens: mean decreases by. mm/day in all seasons. The maximum warming is in summer and autumn (.7 K). Belgrade: mean increases by. mm/day in winter and decreases by. mm/day in summer. The maximum warming is in summer (. K). Berlin: mean increases in all seasons, with a maximum in winter (. mm/day). The maximum warming is in winter (.8 K). Bern: mean increases in autumn and winter (. mm/day). It decreases in summer (. mm/day). The maximum warming is in winter (.7 K). Bratislava: mean increases in all season except summer (. mm/day). The maximum warming is in winter (.8 K). Brussels: mean increases in autumn (. mm/day) and winter (. mm/day). The maximum warming is in winter (. K). Bucharest: mean increases in autumn (. mm/day) and decreases in spring and summer (. mm/day). The maximum warming is in summer (. K). Budapest: mean increases in autumn and winter (. mm/day). The maximum warming is in summer and winter (.8 K). Copenhagen: mean increases in all seasons with a maximum in autumn and winter (. mm/day). The maximum warming is in winter (.7 K). Dublin: mean increases in winter and autumn (. mm/day) and decreases in spring (. mm/day). The maximum warming is in autumn (. K). Helsinki: mean increases in all seasons with a maximum in autumn (. mm/day). The maximum warming is also in winter (. K). Lisbon: mean increases in winter (. mm/day) and decreases in the other seasons (maximum. mm/day in autumn). The maximum warming is in summer and autumn (.6 K) Ljubljana: mean increases in winter (. mm/day) and decreases in summer (. mm/day). The maximum warming is both in winter and summer (.8 K).
.. OVERVIEW OF THE CAPITALS London: mean increases in winter and autumn (. mm/day in winter) and decreases in spring (. mm/day). The maximum warming is winter and autumn (. K). Luxembourg: mean increases in winter and autumn (. mm/day in winter). The maximum warming is winter (.6 K). Madrid: mean increases in winter (. mm/day) and decreases in the other seasons (maximum. mm/day in autumn). The maximum warming is in summer (. K). Oslo: mean increases in all seasons, with a maximum in autumn and winter (. mm/day). The maximum warming is also in autumn and winter (.8 K). Paris: mean increases in winter (. mm/day) and decreases in spring (. mm/day) and summer (. mm/day). The warming is uniform (. K) except in spring (. K). Prague: mean increases in all seasons with a maximum in summer and autumn (. mm/day). The maximum warming is in winter (.9 K). Riga: mean increases in all seasons (. mm/day). The maximum warming is in winter (. K). Rome: mean decreases in all seasons with a maximum in autumn (. mm/day). The maximum warming is in summer (. K). Sarajevo: mean increases in winter (. mm/day) and decreases in summer (. mm/day). The maximum warming is in summer (. K). Skopje: mean decreases in spring and summer (. mm/day). The maximum warming is in summer (. K). Soa: mean increases in autumn and winter (. mm/day) and decreases in spring and summer (. mm/day). The maximum warming is in summer (. K). Stockholm: mean increases in all seasons (. mm/day). The maximum warming is in winter (.9 K). Tallinn: mean increases in all seasons (. mm/day). maximum warming is in winter (. K) The The Hague: mean increases in autumn (. mm/day) and winter (. mm/day). The maximum warming is also in autumn and winter (. K).
CHAPTER. RESULTS Tirana: mean increases in winter (. mm/day) and decreases in spring and summer (. mm/day). The maximum warming is in summer (. K). Vienna: mean increases in all seasons (. mm/day). maximum warming is in winter (.8 K). The Vilnius: mean increases in all seasons (. mm/day in autumn and winter). The maximum warming is in winter (. K). Warsaw: mean increases in all seasons (. mm/day in autumn and winter). The maximum warming is in winter (. K). Zagreb: mean increases in autumn and winter (. mm/day) and decreases in summer (. mm/day). The maximum warming is in summer (.9 K).
.. OVERVIEW OF THE CAPITALS - - 6 - - 6 - - 6 - - 6 Figure.: Probability density function ( C ) for response ( C) in Athens (top left), Belgrade (top right), Berlin (bottom left) and Bern (bottom right) for DJF (blue), MAM (green), JJA (red) and SON (yellow).
CHAPTER. RESULTS - - 6 - - 6 - - 6 - - 6 Figure.: As Figure. for Bratislava (top left), Brussels (top right), Bucharest (bottom left) and Budapest (bottom right).
.. OVERVIEW OF THE CAPITALS - - 6 - - 6 - - 6 - - 6 Figure.: As Figure. for Copenhagen (top left), Dublin (top right), Helsinki (bottom left) and Lisbon (bottom right).
6 CHAPTER. RESULTS - - 6 - - 6 - - 6 - - 6 Figure.: As Figure. for Ljubljana (top left), London (top right), Luxembourg (bottom left) and Madrid (bottom right).
.. OVERVIEW OF THE CAPITALS 7 - - 6 - - 6 - - 6 - - 6 Figure.: As Figure. for Oslo (top left), Paris (top right), Prague (bottom left) and Riga (bottom right).
8 CHAPTER. RESULTS - - 6 - - 6 - - 6 - - 6 Figure.6: As Figure. for Rome (top left), Sarajevo (top right), Skopje (bottom left) and Soa (bottom right).
.. OVERVIEW OF THE CAPITALS 9 - - 6 - - 6 - - 6 - - 6 Figure.7: As Figure. for Stockholm (top left), Tallinn (top right), The Hague (bottom left) and Tirana (bottom right).
CHAPTER. RESULTS - - 6 - - 6 - - 6 - - 6 Figure.8: As Figure. for Vienna (top left), Vilnius (top right), Warsaw (bottom left) and Zagreb (bottom right).
.. OVERVIEW OF THE CAPITALS - - - - - - - - Figure.9: Probability density function ( mm day) for response (mm/day) in Athens (top left), Belgrade (top right), Berlin (bottom left) and Bern (bottom right) for DJF (blue), MAM (green), JJA (red) and SON (yellow).
CHAPTER. RESULTS - - - - - - - - Figure.: As Figure.9 for Bratislava (top left), Brussels (top right), Bucharest (bottom left) and Budapest (bottom right).
.. OVERVIEW OF THE CAPITALS - - - - - - - - Figure.: As Figure.9 for Copenhagen (top left), Dublin (top right), Helsinki (bottom left) and Lisbon (bottom right).
CHAPTER. RESULTS - - - - - - - - Figure.: As Figure.9 for Ljubljana (top left), London (top right), Luxembourg (bottom left) and Madrid (bottom right).
.. OVERVIEW OF THE CAPITALS - - - - - - - - Figure.: As Figure.9 for Oslo (top left), Paris (top right), Prague (bottom left) and Riga (bottom right).
6 CHAPTER. RESULTS - - - - - - - - Figure.: As Figure.9 for Rome (top left), Sarajevo (top right), Skopje (bottom left) and Soa (bottom right).
.. OVERVIEW OF THE CAPITALS 7 - - - - - - - - Figure.: As Figure.9 for Stockholm (top left), Tallinn (top right), The Hague (bottom left) and Tirana (bottom right).
8 CHAPTER. RESULTS - - - - - - - - Figure.6: As Figure.9 for Vienna (top left), Vilnius (top right), Warsaw (bottom left) and Zagreb (bottom right).
.. OVERVIEW OF THE CAPITALS 9 8 8 - - - - - - - 8-8 - - - - 6 8 Figure.7: Bivariate probability density function for and response in Athens for DJF (top left), MAM (top right), JJA (bottom left) and SON (bottom right). Contours are,,, 6, 8 and C mm day.
CHAPTER. RESULTS 8 8 - - - - - - 8 - - - - - - 6 8 Figure.8: As Figure.7 for Belgrade.
.. OVERVIEW OF THE CAPITALS - - - - - - 8 8 - - - - - - 6 8 Figure.9: As Figure.7 for Berlin.
CHAPTER. RESULTS - - - - - - - - - - - - 6 8 Figure.: As Figure.7 for Bern.
.. OVERVIEW OF THE CAPITALS 8 8 - - - - - - - - - - - - 6 8 Figure.: As Figure.7 for Bratislava.
CHAPTER. RESULTS - - - - - - 8 8 - - - - - - 6 8 Figure.: As Figure.7 for Brussels.
.. OVERVIEW OF THE CAPITALS 8 8 - - - - - - 8 - - - - - - 6 8 Figure.: As Figure.7 for Bucharest.
6 CHAPTER. RESULTS 8 8 - - - - - - 8 - - - - - - 6 8 Figure.: As Figure.7 for Budapest.
.. OVERVIEW OF THE CAPITALS 7 8 - - - - - - 8 8 - - - - - - 6 8 Figure.: As Figure.7 for Copenhagen.
8 CHAPTER. RESULTS 8 8 - - - - - - 8 8 - - - - - - 6 8 Figure.6: As Figure.7 for Dublin.
.. OVERVIEW OF THE CAPITALS 9 8 8 - - - - - - 8 8 - - - - - - 6 8 Figure.7: As Figure.7 for Helsinki.
CHAPTER. RESULTS - - - - - - 8 - - - - - - 6 8 Figure.8: As Figure.7 for Lisbon.
.. OVERVIEW OF THE CAPITALS - - - - - - - - - - - - 6 8 Figure.9: As Figure.7 for Ljubljana.
CHAPTER. RESULTS 8 - - - - - - 8 8 - - - - - - 6 8 Figure.: As Figure.7 for London.
.. OVERVIEW OF THE CAPITALS - - - - - - 8 - - - - - - 6 8 Figure.: As Figure.7 for Luxembourg.
CHAPTER. RESULTS 8 8 - - - - - - 8 - - - - - - 6 8 Figure.: As Figure.7 for Madrid.
.. OVERVIEW OF THE CAPITALS - - - - - - - - - - - - 6 8 Figure.: As Figure.7 for Oslo.
6 CHAPTER. RESULTS - - - - - - 8 8 - - - - - - 6 8 Figure.: As Figure.7 for Paris.
.. OVERVIEW OF THE CAPITALS 7 8 - - - - - - 8 8 - - - - - - 6 8 Figure.: As Figure.7 for Prague.
8 CHAPTER. RESULTS 8 8 - - - - - - 8 - - - - - - 6 8 Figure.6: As Figure.7 for Riga.
.. OVERVIEW OF THE CAPITALS 9 8 - - - - - - 8 - - - - - - 6 8 Figure.7: As Figure.7 for Rome.
CHAPTER. RESULTS 8 - - - - - - - - - - - - 6 8 Figure.8: As Figure.7 for Sarajevo.
.. OVERVIEW OF THE CAPITALS 8 8 - - - - - - 8 8 - - - - - - 6 8 Figure.9: As Figure.7 for Skopje.
CHAPTER. RESULTS 8 8 - - - - - - 8 - - - - - - 6 8 Figure.: As Figure.7 for Soa.
.. OVERVIEW OF THE CAPITALS 8 8 - - - - - - 8 8 - - - - - - 6 8 Figure.: As Figure.7 for Stockholm.
CHAPTER. RESULTS 8 8 - - - - - - 8 8 - - - - - - 6 8 Figure.: As Figure.7 for Tallinn.
.. OVERVIEW OF THE CAPITALS 8 - - - - - - 8 - - - - - - 6 8 Figure.: As Figure.7 for The Hague.
6 CHAPTER. RESULTS - - - - - - - - - - - - 6 8 Figure.: As Figure.7 for Tirana.
.. OVERVIEW OF THE CAPITALS 7 8 8 - - - - - - 8 - - - - - - 6 8 Figure.: As Figure.7 for Vienna.
8 CHAPTER. RESULTS 8 8 - - - - - - 8 - - - - - - 6 8 Figure.6: As Figure.7 for Vilnius.
.. OVERVIEW OF THE CAPITALS 9 8 8 - - - - - - 8 - - - - - - 6 8 Figure.7: As Figure.7 for Warsaw.
6 CHAPTER. RESULTS - - - - - - - - - - - - 6 8 Figure.8: As Figure.7 for Zagreb.
List of Figures. Probability density function ( C ) for response ( C) in Athens (top left), Belgrade (top right), Berlin (bottom left) and Bern (bottom right) for DJF (blue), MAM (green), JJA (red) and SON (yellow)............... As Figure. for Bratislava (top left), Brussels (top right), Bucharest (bottom left) and Budapest (bottom right)...... As Figure. for Copenhagen (top left), Dublin (top right), Helsinki (bottom left) and Lisbon (bottom right)........ As Figure. for Ljubljana (top left), London (top right), Luxembourg (bottom left) and Madrid (bottom right).... 6. As Figure. for Oslo (top left), Paris (top right), Prague (bottom left) and Riga (bottom right)............. 7.6 As Figure. for Rome (top left), Sarajevo (top right), Skopje (bottom left) and Soa (bottom right)............. 8.7 As Figure. for Stockholm (top left), Tallinn (top right), The Hague (bottom left) and Tirana (bottom right)..... 9.8 As Figure. for Vienna (top left), Vilnius (top right), Warsaw (bottom left) and Zagreb (bottom right)...........9 Probability density function ( mm day) for response (mm/day) in Athens (top left), Belgrade (top right), Berlin (bottom left) and Bern (bottom right) for DJF (blue), MAM (green), JJA (red) and SON (yellow)....... As Figure.9 for Bratislava (top left), Brussels (top right), Bucharest (bottom left) and Budapest (bottom right)...... As Figure.9 for Copenhagen (top left), Dublin (top right), Helsinki (bottom left) and Lisbon (bottom right)........ As Figure.9 for Ljubljana (top left), London (top right), Luxembourg (bottom left) and Madrid (bottom right).... 6
6 LIST OF FIGURES. As Figure.9 for Oslo (top left), Paris (top right), Prague (bottom left) and Riga (bottom right).............. As Figure.9 for Rome (top left), Sarajevo (top right), Skopje (bottom left) and Soa (bottom right)............. 6. As Figure.9 for Stockholm (top left), Tallinn (top right), The Hague (bottom left) and Tirana (bottom right)..... 7.6 As Figure.9 for Vienna (top left), Vilnius (top right), Warsaw (bottom left) and Zagreb (bottom right).......... 8.7 Bivariate probability density function for and response in Athens for DJF (top left), MAM (top right), JJA (bottom left) and SON (bottom right). Contours are,,, 6, 8 and C mm day.... 9.8 As Figure.7 for Belgrade....................9 As Figure.7 for Berlin...................... As Figure.7 for Bern...................... As Figure.7 for Bratislava.................... As Figure.7 for Brussels..................... As Figure.7 for Bucharest.................... As Figure.7 for Budapest................... 6. As Figure.7 for Copenhagen................. 7.6 As Figure.7 for Dublin.................... 8.7 As Figure.7 for Helsinki.................... 9.8 As Figure.7 for Lisbon.....................9 As Figure.7 for Ljubljana.................... As Figure.7 for London..................... As Figure.7 for Luxembourg.................. As Figure.7 for Madrid..................... As Figure.7 for Oslo....................... As Figure.7 for Paris..................... 6. As Figure.7 for Prague.................... 7.6 As Figure.7 for Riga...................... 8.7 As Figure.7 for Rome..................... 9.8 As Figure.7 for Sarajevo...................
LIST OF FIGURES 6.9 As Figure.7 for Skopje..................... As Figure.7 for Soa...................... As Figure.7 for Stockholm................... As Figure.7 for Tallinn..................... As Figure.7 for The Hague................... As Figure.7 for Tirana.................... 6. As Figure.7 for Vienna.................... 7.6 As Figure.7 for Vilnius.................... 8.7 As Figure.7 for Warsaw.................... 9.8 As Figure.7 for Zagreb.................... 6