toreti imsc
A NON-PARAMETRIC APPROACH FOR THE EVALUATION OF PRECIPITATION EXTREMES SIMULATED BY CLIMATE MODELS
Andrea Toreti1 and Philippe Naveau2
1 Joint Research Centre, European Commission 2 Laboratoire des Sciences du Climat et l'Environnement (LSCE) CNRS
1
Outline
•
Overview
•
The proposed approach
•
An application to CMIP5 model data
•
Conclusions & discussion
2
Precipitation Extremes Today
50-y ret levels in winter (DJF) estimated from 1966-2005. Ensemble Mean of 8 CMIP5 model runs Source:Toreti et al., 2013
3
Tomorrow
TORETI ET ET AL.: AL.: CMIP5 TORETI CMIP5PRECIPITATION PRECIPITATIONEXTREMES EXTREMES
Ensemble mean changes (%) of 50-y ret levels 2060-2099 w.r.t. 1966-2005 Source:Toreti et al., 2013
Precipitation extremes
G.J. Babu, A. Toreti / Journal of Statistical Planning and Inference (
4
)
–
As Fig. 1 but(SON) for 5-year return Values in mm. Euro-CORDEX Estimated 5-y ret levels Fig. in 3.autumn fromlevels. 1989-2009. ERA-Interim driven runs Source: Babu and Toreti, 2016
7
Evaluation
MIP5 PRECIPITATION EXTREMES
6162 6162
Taylor diagram. 50-y ret levels in winter. CMIP5 model runs w.r.t. Aphrodite in northern Eurasia Source: Toreti et al., 2013
JOUR NU AR L NOA JO
Estimated GPD parameters for winter (DJF) precipitation extremes. Model w.r.t. observations Source: Chan et al., 2014
FIG . 4. but for1-day JJA 1-day precipitation accumulat FIG. 4. As inAs Fig.in2,Fig. but2,for JJA precipitation accumulations. for threshold and the ps units units for threshold (t) and(t)the scale 5
gauges), andisthis is simulated well simulated by both theand 12-the and gauges), and this well by both the 12-
The proposed approach Let X1 , X2 , . . . , Xn and Y1 , Y2 , . . . , Ym be two continuous random samples
Z
¯ m F¯n )2 mn 1 (G A= dHN ¯ N ( HN ) 1 ¯n + mG ¯m n F ¯N = H ; N =n+m N T = (A
I(fe ; ge ) = Efe
6
(
log
E(A))
1 A
e fe (Xe /µX 0 ) e ge (Xe /µX 0 )
!)
The proposed approach N 1 ¯ nm X (G m A= N i=1 1
Mi = nFn HN
1
N 1 F¯n )2 1 1 X (Mi N = i N nmN i=1 (N N
ni)2 i)
i ( ) N
N 1 N 1 1 X 2 V(Mi ) 1 X i 1 E(A) = N = = nmN i=1 (N i) N i=1 N 1 2 8 !2 9 N 1 < X M = ¯2 1 N2 i V(A) = + 2 2E 4 n m : N i ;
¯ i = Mi M
i
Ne X 1 ˆ e ; ge ) = 1 + I(f log Ne i=1 7
e ¯ ei /ˆ G(X µX 0 ) ¯ G(0)
Naveau et al., 2013. J. R. Stat. Soc. B 76
!
¯ =1 G(t)
(m + 1)
1
m X i=1
ni N
I{Y i /ˆµYe t} e
0
The proposed approach
The method can be applied to the entire set of X and Y values or to rescaled excesses
e Xe /µX 0 ,
8
Ye /µY0 e
e µX 0 = E(Xe |X > u)
µY0 e = E(Ye |Y > u)
is re- sponsible for CMIP, and we thank the climate modeling groups (listed in the table) for producing and making available their model output. For CMIP the U.S. Department of Energys Program for Climate Model Diagnosis and Intercomparison provides coordinating support and led development of software infrastructure in partnership with the Global Organization for Earth System Science Portals.
CMIP5 model runs over Euro-Med Model CMCC-CM (CMCC) CNRM-CM5 (CNRM) HadGEM2-CC (HadCC) HadGEM2-ES (HadES) INM-CM4 (INM) IPSL-CM5A-MR (IPSL) MIROC5 (MIROC) MRI-CGCM3 (MRI)
Institution Centro Euro-Mediterraneo sui Cambiamenti Climatici Centre National de Recherches Meteorologiques - Centre Europeen de Recherche et Formation Avancees en Calcul Scientifique Met Office Hadley Centre Met Office Hadley Centre - Instituto Nacional de Pesquisas Espaciais Institute for Numerical Mathematics Institut Pierre-Simon Laplace Atmosphere and Ocean Research Institute (The University of Tokyo), National Institute for Environmental Studies, and Japan Agency for Marine-Earth Science and Technology Meteorological Research Institute
References
Winter (DJF) autumn (SON) precipitation Benjamini Y and Y Hochbergand 1995 Controlling the False Discovery Rate: daily a practical and powerful approach to multiple testing J. Roy. Stat. Soc. B 57 289–300 OBS from E-OBS historical: 1966-2005 RCP8.5: 2020-2059 and 2060-2099 9
es. Lett. 10 (2015) 014012
CMIP5
A Toreti and P Naveau
Spearman-based spatial correlation matrix of the tail scaling factors. Winter 1966-2005
1. Spearman-based spatial correlation matrix of the tail scaling factors, estimated for the eight GCMs, μˆ 0model , and the gridded tions E-OBS, μˆ 0obs , in the winter period 1966–2005. The colors and the shape of the ellipses are associated with the correlation The last 10 column refers to the same analysis without the southern part of the domain (South of 38.25° North).
A Toreti and P Naveau
11
Environ. Res. Lett. 10 (2015) 014012
Rescaled-tail comparison of model simulations and E-OBS. Winter 1966-2005 Figure 2. Rescaled-tail comparison of model simulations during the historical winter period and E-OBS. Colors are associated with
CMIP5
CMIP5 3
2
1
0 CMCC
CNRM
HadCC
HadES
inm
IPSL
MIROC
MRI
gure 3. Boxplots of the ratio between the estimated conditional means of the excesses for the future winter time periods (2020–2059: Boxplots of the ratio between the estimated scenario the future winter time μˆ 0hist , means derived of forthe eachexcesses grid pointfor in the domain. ue; 2060–2099: green) and the historical simulations, μˆ 0conditional periods (2020–2059: blue; 2060–2099: green) and the historical simulations in winter.
of the domain seems to be affected by a significant 12 reduction, but with remarkable inter-model dif-
estimation) in the northern/central (southern) part o the region. As for the projections for the mid-21st cen
Environ. Res. Lett. 10 (2015) 014012
CMIP5
Results of the rescaled-tail comparison of the winter period 2020–2059 w.r.t. the historical simulation (1966–2005) A Toreti and P Naveau
13
Environ. Res. Lett. 10 (2015) 014012
Figure 5. As figure 4, but for 2060–2099.
CMIP5
Results of the rescaled-tail comparison of the winter period 2060–2099 w.r.t. the historical simulation (1966–2005) A Toreti and P Naveau
14
Conclusions and Discussion •
Good performance of the approach with large data samples and “not too similar tail behaviour”
•
results support the existence of a linear relationship between conditional means of rescaled excesses from models and observations.
•
Significantly different tail behaviour of models w.r.t. observations.
•
Results support an increase of heavy precipitation in future decades due to increased scaling factors. Higher uncertainties characterise the tail behaviour.
15
The European Commission’s science and knowledge service Joint Research Centre
Thank you! Toreti and Naveau, 2015. On the evaluation of climate model simulated precipitation extremes. Env. Res. Lett. 10. 014012
1 Joint Research Centre, European Commission 2 Laboratoire des Sciences du Climat et l'Environnement (LSCE) CNRS
1
Outline
•
Overview
•
The proposed approach
•
An application to CMIP5 model data
•
Conclusions & discussion
2
Precipitation Extremes Today
50-y ret levels in winter (DJF) estimated from 1966-2005. Ensemble Mean of 8 CMIP5 model runs Source:Toreti et al., 2013
3
Tomorrow
TORETI ET ET AL.: AL.: CMIP5 TORETI CMIP5PRECIPITATION PRECIPITATIONEXTREMES EXTREMES
Ensemble mean changes (%) of 50-y ret levels 2060-2099 w.r.t. 1966-2005 Source:Toreti et al., 2013
Precipitation extremes
G.J. Babu, A. Toreti / Journal of Statistical Planning and Inference (
4
)
–
As Fig. 1 but(SON) for 5-year return Values in mm. Euro-CORDEX Estimated 5-y ret levels Fig. in 3.autumn fromlevels. 1989-2009. ERA-Interim driven runs Source: Babu and Toreti, 2016
7
Evaluation
MIP5 PRECIPITATION EXTREMES
6162 6162
Taylor diagram. 50-y ret levels in winter. CMIP5 model runs w.r.t. Aphrodite in northern Eurasia Source: Toreti et al., 2013
JOUR NU AR L NOA JO
Estimated GPD parameters for winter (DJF) precipitation extremes. Model w.r.t. observations Source: Chan et al., 2014
FIG . 4. but for1-day JJA 1-day precipitation accumulat FIG. 4. As inAs Fig.in2,Fig. but2,for JJA precipitation accumulations. for threshold and the ps units units for threshold (t) and(t)the scale 5
gauges), andisthis is simulated well simulated by both theand 12-the and gauges), and this well by both the 12-
The proposed approach Let X1 , X2 , . . . , Xn and Y1 , Y2 , . . . , Ym be two continuous random samples
Z
¯ m F¯n )2 mn 1 (G A= dHN ¯ N ( HN ) 1 ¯n + mG ¯m n F ¯N = H ; N =n+m N T = (A
I(fe ; ge ) = Efe
6
(
log
E(A))
1 A
e fe (Xe /µX 0 ) e ge (Xe /µX 0 )
!)
The proposed approach N 1 ¯ nm X (G m A= N i=1 1
Mi = nFn HN
1
N 1 F¯n )2 1 1 X (Mi N = i N nmN i=1 (N N
ni)2 i)
i ( ) N
N 1 N 1 1 X 2 V(Mi ) 1 X i 1 E(A) = N = = nmN i=1 (N i) N i=1 N 1 2 8 !2 9 N 1 < X M = ¯2 1 N2 i V(A) = + 2 2E 4 n m : N i ;
¯ i = Mi M
i
Ne X 1 ˆ e ; ge ) = 1 + I(f log Ne i=1 7
e ¯ ei /ˆ G(X µX 0 ) ¯ G(0)
Naveau et al., 2013. J. R. Stat. Soc. B 76
!
¯ =1 G(t)
(m + 1)
1
m X i=1
ni N
I{Y i /ˆµYe t} e
0
The proposed approach
The method can be applied to the entire set of X and Y values or to rescaled excesses
e Xe /µX 0 ,
8
Ye /µY0 e
e µX 0 = E(Xe |X > u)
µY0 e = E(Ye |Y > u)
is re- sponsible for CMIP, and we thank the climate modeling groups (listed in the table) for producing and making available their model output. For CMIP the U.S. Department of Energys Program for Climate Model Diagnosis and Intercomparison provides coordinating support and led development of software infrastructure in partnership with the Global Organization for Earth System Science Portals.
CMIP5 model runs over Euro-Med Model CMCC-CM (CMCC) CNRM-CM5 (CNRM) HadGEM2-CC (HadCC) HadGEM2-ES (HadES) INM-CM4 (INM) IPSL-CM5A-MR (IPSL) MIROC5 (MIROC) MRI-CGCM3 (MRI)
Institution Centro Euro-Mediterraneo sui Cambiamenti Climatici Centre National de Recherches Meteorologiques - Centre Europeen de Recherche et Formation Avancees en Calcul Scientifique Met Office Hadley Centre Met Office Hadley Centre - Instituto Nacional de Pesquisas Espaciais Institute for Numerical Mathematics Institut Pierre-Simon Laplace Atmosphere and Ocean Research Institute (The University of Tokyo), National Institute for Environmental Studies, and Japan Agency for Marine-Earth Science and Technology Meteorological Research Institute
References
Winter (DJF) autumn (SON) precipitation Benjamini Y and Y Hochbergand 1995 Controlling the False Discovery Rate: daily a practical and powerful approach to multiple testing J. Roy. Stat. Soc. B 57 289–300 OBS from E-OBS historical: 1966-2005 RCP8.5: 2020-2059 and 2060-2099 9
es. Lett. 10 (2015) 014012
CMIP5
A Toreti and P Naveau
Spearman-based spatial correlation matrix of the tail scaling factors. Winter 1966-2005
1. Spearman-based spatial correlation matrix of the tail scaling factors, estimated for the eight GCMs, μˆ 0model , and the gridded tions E-OBS, μˆ 0obs , in the winter period 1966–2005. The colors and the shape of the ellipses are associated with the correlation The last 10 column refers to the same analysis without the southern part of the domain (South of 38.25° North).
A Toreti and P Naveau
11
Environ. Res. Lett. 10 (2015) 014012
Rescaled-tail comparison of model simulations and E-OBS. Winter 1966-2005 Figure 2. Rescaled-tail comparison of model simulations during the historical winter period and E-OBS. Colors are associated with
CMIP5
CMIP5 3
2
1
0 CMCC
CNRM
HadCC
HadES
inm
IPSL
MIROC
MRI
gure 3. Boxplots of the ratio between the estimated conditional means of the excesses for the future winter time periods (2020–2059: Boxplots of the ratio between the estimated scenario the future winter time μˆ 0hist , means derived of forthe eachexcesses grid pointfor in the domain. ue; 2060–2099: green) and the historical simulations, μˆ 0conditional periods (2020–2059: blue; 2060–2099: green) and the historical simulations in winter.
of the domain seems to be affected by a significant 12 reduction, but with remarkable inter-model dif-
estimation) in the northern/central (southern) part o the region. As for the projections for the mid-21st cen
Environ. Res. Lett. 10 (2015) 014012
CMIP5
Results of the rescaled-tail comparison of the winter period 2020–2059 w.r.t. the historical simulation (1966–2005) A Toreti and P Naveau
13
Environ. Res. Lett. 10 (2015) 014012
Figure 5. As figure 4, but for 2060–2099.
CMIP5
Results of the rescaled-tail comparison of the winter period 2060–2099 w.r.t. the historical simulation (1966–2005) A Toreti and P Naveau
14
Conclusions and Discussion •
Good performance of the approach with large data samples and “not too similar tail behaviour”
•
results support the existence of a linear relationship between conditional means of rescaled excesses from models and observations.
•
Significantly different tail behaviour of models w.r.t. observations.
•
Results support an increase of heavy precipitation in future decades due to increased scaling factors. Higher uncertainties characterise the tail behaviour.
15
The European Commission’s science and knowledge service Joint Research Centre
Thank you! Toreti and Naveau, 2015. On the evaluation of climate model simulated precipitation extremes. Env. Res. Lett. 10. 014012
