Supplemental Material for Northern North Atlantic Sea Level in CMIP5 Climate Models: Evaluation of Mean State, Variability, and Trends against Altimetric Observations Kristin Richter, a Jan Even Øie Nilsen, b Roshin P. Raj, b Ingo Bethke, c Johnny A. Johannessen b,d Aimée B. A. Slangen e,f and Ben Marzeion g a Institute of Atmospheric and Cryospheric Sciences, University of Innsbruck, Innsbruck, Austria b Nansen Environmental and Remote Sensing Center, Bjerknes Centre for Climate Research, Bergen, Norway c Uni Research Climate, Bjerknes Centre for Climate Research, Bergen, Norway d Geophysical Institute, Bergen, Norway e Department of Estuarine and Delta Systems, Royal Netherlands Institute for Sea Research (NIOZ), and Yerseke, Netherlands f Utrecht University, Yerseke, Netherlands g Institute of Geography, University of Bremen, Bremen, Germany (Manuscript received 12 May 2017, in final form 11 August 2017) Copyright 2017 American Meteorological Society Permission to use figures, tables, and brief excerpts from this work in scientific and educational works is hereby granted provided that the source is acknowledged. Any use of material in this work that is determined to be fair use under Section 107 of the U.S. Copyright Act or that satisfies the conditions specified in Section 108 of the U.S. Copyright Act (17 USC 108) does not require the AMS s permission. Republication, systematic reproduction, posting in electronic form, such as on a website or in a searchable database, or other uses of this material, except as exempted by the above statement, requires written permission or a license from the AMS. All AMS journals and monograph publications are registered with the Copyright Clearance Center (http://www.copyright.com). Questions about permission to use materials for which AMS holds the copyright can also be directed to the AMS Permissions Officer at permissions@ametsoc.org. Additional details are provided in the AMS Copyright Policy statement, available on the AMS website (http://www.ametsoc.org/copyrightinformation).
Supplements Computation of metrics used in the analysis Definition of weights such that sum over all weights equals 1: w i = cos(lat i )/ i cos(lat i ) (1) Area weighted mean µ w = i w i x i (2) Area weighted variance with correction factor for unbiased estimate s 2 w = s 2 w = i w i ( i w i) 2 i (w i) 2 w i (x i µ w ) 2 (3) i 1 1 i (w i) 2 w i (x i µ w ) 2 (4) i The standard deviation is the square root of s 2. Area weighted mean square error (unbiased) between fields x and y RMSE is the square root of mse. 1 mse w = 1 i (w i) 2 w i ((x i µ wx ) (y i µ wy )) 2 (5) i Area weighted correlation coefficient (unbiased) cr w = 1 1 i w i(x i µ wx )(y i µ wy ) i (w i) 2 (6) s wx s wy 1
Institution Model Name historical period CSIRO (Commonwealth Scientific and Industrial Research Organisation, Australia), and BOM (Bureau of Meteorology, Australia) Beijing Climate Center, China Meteorological Administration Canadian Centre for Climate Modelling and Analysis gridspacing lon,lat ACCESS1-0 1850 1.0, 0.6 bcc-csm1-1 1850 1.0, 1.0 CanESM2 1850 1.4, 0.9 National Center for Atmospheric Research CCSM4 1850 0.9, 0.5 Centro Euro-Mediterraneo per I Cambiamenti Climatici CMCC-CMS 1850 2.5, 1.2 Centre National de Recherches Meteorologiques CNRM-CM5 1850 1.2,0.6 / Centre Europeen de Recherche et Formation Avancees en Calcul Scientifique Commonwealth Scientific and Industrial Research Organization in collaboration with Queensland Climate Change Centre of Excellence CSIRO-Mk3-6-0 1850 1.9, 0.9 Geophysical Fluid Dynamics Laboratory GFDL-ESM-2G 1861 1.0, 1.0 GFDL-ESM-2M 1861 1.0, 1.0 Met Office Hadley Centre (additional HadGEM2-CC 1860 1.0, 1.0 HadGEM2-ES realizations contributed by Instituto Nacional de Pesquisas Espaciais) HadGEM2-ES 1860 1.0, 1.0 Institute for Numerical Mathematics inmcm4 1850 1.5, 0.6 Institut Pierre-Simon Laplace IPSL-CM5A-MR 1850 2.4, 1.2 Japan Agency for Marine-Earth Science and Technology, Atmosphere and Ocean Research Institute (The University of Tokyo), and National Institute for Environmental Studies MIROC-ESM 1850 1.4, 1.2 Max Planck Institute for Meteorology MPI-ESM-LR 1850 0.7, 0.5 Meteorological Research Institute MRI-CGCM3 1850 1.0, 0.5 Norwegian Climate Centre NorESM1-M 1850 0.9, 0.5 NorESM1-ME 1850 0.9, 0.5 Table S1: CMIP5 models used in the study. The beginning of the historical run is given in the 3rd, the grid-spacing in the area in the 4th column. The native grid of most of the models is irregular and the grid-spacing given here is considered as representative for the region, but only approximate. 2
model equal weights in or out 1/RMSE ACCESS1-0 1 2 1.01 bcc-csm1-1 1 0 0.65 CanESM2 1 0 0.73 CCSM4 1 2 1.46 CMCC-CMS 1 2 1.07 CNRM-CM5 1 2 1.32 CSIRO-Mk3-6-0 1 0 0.84 GFDL-ESM2G 1 0 0.65 GFDL-ESM2M 1 0 0.82 HadGEM2-CC 1 0 0.99 HadGEM2-ES 1 2 1.04 inmcm4 1 2 1.1 IPSL-CM5A-MR 1 0 0.8 MIROC-ESM 1 0 0.83 MPI-ESM-LR 1 2 1.26 MRI-CGCM3 1 0 0.68 NorESM1-M 1 2 1.35 NorESM1-ME 1 2 1.41 Table S2: Weights for the three different approaches to form a multi-model mean: equal weights, excluding models with RMSE larger than median RMSE (in or out), and weights computed as 1/RMSE. For easier intercomaprison, the weights presented here are normalized with the mean weight. When computing weighted multi-model means and standard deviations, the weights are normalized with the sum over all weights. 3
a) glaciers (0.49/0.28 mm/yr) b) ice sheets (0.43/0.29 mm/yr) mm/yr 6 4 2 0 2 4 6 Figure S1: Contribution from melting land ice to sea level trends for the period 1993 2012 for a) glaciers and b) the Antarctic and Greenland ice sheet. The numbers above each map represent the region-wide mean and standard deviation, respectively. 4
ACCESS1 0 (0/0.19 m) CNRM CM5 (0/0.19 m) HadGEM2 ES (0/0.22 m) MRI CGCM3 (0/0.15 m) bcc csm1 1 (0/0.12 m) CanESM2 (0/0.23 m) CCSM4 (0/0.2 m) CSIRO Mk3 6 0 (0/0.14 m) GFDL ESM2G (0/0.13 m) GFDL ESM2M (0/0.15 m) inmcm4 (0/0.17 m) IPSL CM5A MR (0/0.18 m) MIROC ESM (0/0.21 m) NorESM1 M (0/0.21 m) NorESM1 ME (0/0.21 m) ensemble mean (0/0.15 m) 0.5 0.3 0.1 0.1 0.3 0.5 m CMCC CMS (0/0.16 m) HadGEM2 CC (0/0.23 m) MPI ESM LR (0/0.22 m) observations (0/0.19 m) Figure S2: Modeled MDT from each model during the observational period 1993-2012. Ensemble mean and observations are also shown. Black/grey/white contour lines in the ensemble mean show areas where the signal-to-noise ratio (defined as the ratio of ensemble mean to ensemble standard deviation) is larger than 1/1.5/2, respectively. The numbers above each map represent the region wide mean and root mean square, respectively. 5
ACCESS1 0 (2.88/1.63 cm) CNRM CM5 (2.48/0.68 cm) HadGEM2 ES (3.02/1.25 cm) MRI CGCM3 (3.88/1.72 cm) bcc csm1 1 (3.13/1.57 cm) CanESM2 (2.66/1.2 cm) CCSM4 (1.76/0.53 cm) CSIRO Mk3 6 0 (3.07/1.19 cm) GFDL ESM2G (1.75/0.52 cm) GFDL ESM2M (2.54/1.09 cm) inmcm4 (2.36/1.01 cm) IPSL CM5A MR (1.8/0.98 cm) MIROC ESM (3.19/1.4 cm) NorESM1 M (1.88/0.86 cm) NorESM1 ME (1.67/0.71 cm) ensemble mean (2.57/0.74 cm) 0 1 2 3 4 5 cm CMCC CMS (2.01/0.57 cm) HadGEM2 CC (3.36/1.43 cm) MPI ESM LR (2.88/1.5 cm) observations (2.36/0.92 cm) Figure S3: Modeled variability in terms of temporal standard deviation from each model during the period of maximum pattern correlation. Ensemble mean and observations are also shown. Black/grey/white contour lines in the ensemble mean show areas where the signal-to-noise ratio (defined as the ratio of ensemble mean to ensemble standard deviation) is larger than 1/1.5/2, respectively. The numbers above each map represent the region wide mean and root mean square, respectively. 6
ACCESS1 0 (2.77/4.26 mm/yr) CNRM CM5 (2.08/2.35 mm/yr) HadGEM2 ES (2.25/3.95 mm/yr) MRI CGCM3 (0.12/1.91 mm/yr) bcc csm1 1 (4.97/1.43 mm/yr) CanESM2 (3.1/2.13 mm/yr) CCSM4 (1.04/1.01 mm/yr) CSIRO Mk3 6 0 (2.57/2.28 mm/yr) GFDL ESM2G (2.25/1.12 mm/yr) GFDL ESM2M (4.19/2.12 mm/yr) inmcm4 (3.57/0.79 mm/yr) IPSL CM5A MR (0.92/1.84 mm/yr) MIROC ESM (1.96/1.68 mm/yr) NorESM1 M (1.61/1.13 mm/yr) NorESM1 ME (0.68/2.74 mm/yr) ensemble mean (2.26/0.84 mm/yr) 6 4 2 0 2 4 6 mm/yr CMCC CMS (1.44/1.49 mm/yr) HadGEM2 CC (2.59/1.9 mm/yr) MPI ESM LR (2.52/4.14 mm/yr) observations (1.75/1.55 mm/yr) Figure S4: Modeled trends from each model during the observational period. Ensemble mean and observations are also shown. Black/grey/white contour lines in the ensemble mean show areas where the signal-to-noise ratio (defined as the ratio of ensemble mean to ensemble standard deviation) is larger than 1/1.5/2, respectively. The numbers above each map represent the region wide mean and root mean square, respectively. 7
ACCESS1 0 (1.84/1.95 mm/yr) CNRM CM5 (2.19/1.44 mm/yr) HadGEM2 ES ( 0.68/2.81 mm/yr) MRI CGCM3 (0.38/2.25 mm/yr) bcc csm1 1 (0.63/1.98 mm/yr) CanESM2 (1.93/1.29 mm/yr) CCSM4 (1.13/0.85 mm/yr) CSIRO Mk3 6 0 (1.46/1.2 mm/yr) GFDL ESM2G (1.24/1.54 mm/yr) GFDL ESM2M (4.45/2.22 mm/yr) inmcm4 (2.06/1.87 mm/yr) IPSL CM5A MR (0.7/2.08 mm/yr) MIROC ESM (0.28/2.21 mm/yr) NorESM1 M (0.93/1.34 mm/yr) NorESM1 ME (1.56/1.24 mm/yr) ensemble mean (1.32/1.24 mm/yr) 6 4 2 0 2 4 6 mm/yr CMCC CMS (1.83/1.59 mm/yr) HadGEM2 CC (0.29/2.17 mm/yr) MPI ESM LR (1.45/2.38 mm/yr) observations (1.75/1.55 mm/yr) Figure S5: Modeled trend anomalies from each model during the period of maximum pattern correlation. Ensemble mean and observations are also shown. Black contour lines in the ensemble mean show areas where the signal-to-noise ratio (defined as the ratio of ensemble mean to ensemble standard deviation) is larger than 1. The numbers above each map represent the region wide mean and root mean square, respectively.here, anomalies are presented, i.e. the mean has been subtracted and is only shown for information. 8
a) 0.92/0.4 b) 0.96/0.29 c) 0.94/0.35 m 0.5 0.3 0.1 0.1 0.3 0.5 Figure S6: Multi-model mean of MDT with a) no weighting, b) only models with RMSE smaller than median, c) models weighted with inverse of RMSE. The numbers indicate the PCC with the observations and the standardized RMSE. Black/grey/white lines represent the signal to noise ratio of 1/1.5/2 defined as the ratio of weighted multi-model mean and weighted ensemble standard deviation of the regional maps. a) 0.66/0.77 b) 0.68/0.73 c) 0.66/0.76 cm 5 4 3 2 1 0 Figure S7: Multi-model mean of simulated variability over periods of maximum PCC with a) no weighting, b) only models with MDT RMSE smaller than median, c) models weighted with inverse of MDT RMSE. The numbers indicate the PCC with the observations and the standardized RMSE. Black/grey/white lines represent signal to noise ratio of 1/1.5/2 defined as the ratio of ensemble mean and ensemble standard deviation of the regional anomaly maps. 9
a) 0.66/0.77 b) 0.65/0.77 c) 0.66/0.76 mm/yr 6 4 2 0 2 4 6 Figure S8: Multi-model mean of simulated trend anomalies over periods of maximum PCC with a) no weighting, b) only models with MDT RMSE smaller than median, c) models weighted with inverse of MDT RMSE. The numbers indicate the PCC with the observations and the standardized RMSE. Black/grey/white lines represent signal to noise ratio of 1/1.5/2 defined as the ratio of ensemble mean and ensemble standard deviation of the regional maps. 10