Attributing Variation in Regional Climate Change Model Experiments
Chris Ferro
Climate Analysis Group
Department of Meteorology
University of Reading, UK
PRUDENCE Project Meeting, Toledo, 9 September 2004
PRUDENCE Work
Tools for diagnosing changes in probability distributionsBeniston et al. (2004, in preparation); Ferro, Hannachi & Stephenson (2004, in revision); McGregor, Ferro & Stephenson (2004, submitted)
Statistical methods for analysing extreme valuesFerro & Pezzulli (2004, in preparation); Ferro & Segers (2004, in press); presentations at 9IMSC, Royal Met. Soc. and UK Extremes
Attributing variation in climate model experimentsFerro (2004, PRUDENCE note); Ferro & Sanchez (2004?)
Land-averaged annual mean 2m air temperature interpolated to CRU grid
Tem
per
atu
re (
°C)
EC
HA
M4
RC
AO
Had
AM
3HH
IRH
AM
EC
HA
M4
HIR
HA
M
Had
AM
3HR
CA
O
EC
HA
M4
RC
AO
Had
AM
3HH
IRH
AM
EC
HA
M4
HIR
HA
M
Had
AM
3HR
CA
O
30-year control
30-year A2 scenario
Land-averaged annual mean 2m air temperature interpolated to CRU grid
ECHAM4HIRHAM
ECHAM4RCAO
HadAM3HHIRHAM
HadAM3HRCAO
Normal Linear Model
Linear models for temperature Ti j k on equivalent CO2 xk
Ti j k = i j + i j (xk – x0) + Zi j k
GCM ( i ) HadAM3H ECHAM4RCM ( j ) HIRHAM RCAO HIRHAM RCAO
Year
( k )
1961 T1 1 1 T1 2 1 T2 1 1 T2 2 1
: : : : :1990 T1 1 30 T1 2 30 T2 1 30 T2 2 30
2071 T1 1 31 T1 2 31 T2 1 31 T2 2 31
: : : : :2100 T1 1 60 T1 2 60 T2 1 60 T2 2 60
Decomposition
i j = + iG + jR + ijGR
overall mean
iG effect of GCM i
jR effect of RCM j
ijGR effect of combining GCM i with RCM j
Ti j k = i j + i j (xk – x0) + Zi j k
i j = + iG + jR + ijGR
overall CO2 response
iG effect of GCM i
jR effect of RCM j
ijGR effect of combining GCM i with RCM j
Parameter Estimates
ijGR HadAM3H ECHAM4 jR
HIRHAM +0.11 –0.11 –0.35
RCAO –0.11 +0.11 +0.35
iG –0.10 +0.10 = 10.48
ijGR HadAM3H ECHAM4 jR
HIRHAM +0.01 –0.01 +0.03
RCAO –0.01 +0.01 –0.03
iG –0.80 +0.80 = 6.24
CO2 responses (°C / ppkv): standard errors 0.09
Mean effects (°C): standard errors 0.03
Diagnostic Plots
control scenariore
sid
ual
s
Variance Decomposition
If R and GR are omitted then CO2 response is independent of RCMand the RCM difference, for each GCM, is independent of CO2.
% p-value
91.4 0.000
G 0.2 0.004
G 1.5 0.000
R 2.2 0.000
R 0.0 0.764
GR 0.2 0.001
GR 0.0 0.898
Z 4.5
Contrasts
GCM CO2 responses: ECH – HAD = 1.60°C / ppkv
RCM effects: RCA – HIR = 0.48°C (HAD) 0.91°C (ECH)
GCM effects: ECH – HAD for each RCM and year (°C)
● RCAO○ HIRHAM
Grid-point Analysis
Fit model separately at each grid point and plot maps:
Proportion of variation explained by each model term
Evolution of differences between GCMs for each RCM
Evolution of differences between RCMs for each GCM
Differences between GCM CO2 responses for each RCM
Differences between RCM CO2 responses for each GCM
Variation Explained (%)model Z
G R GR
G R GR
GCM Contrasts: ECHAM4 – HadAM3HH
IRH
AM
RC
AO
1961 1975 1990 2071 2085 2100
°C
RCM Contrasts: RCAO – HIRHAM
1961 1975 1990 2071 2085 2100
Had
AM
3HE
CH
AM
4
°C
Response ContrastsHIRHAM RCAO
HadAM3H ECHAM4
ECHAM4 –HadAM3H
RCAO –HIRHAM
°C / ppkv
Conclusions
Summary: quantify variability from different model components, assess their relative importance, synthesise output, infer climate changes and model differences.
Extensions: more models, scenarios, ensemble members and variables; non-linearity, serial dependence, multiple comparisons, random effects, multivariate responses.
Design set of experiments carefully with view to analysis!
5% Significant Effects: α + αG + αR + β + ...
GR
G
R
G + R
GR + G
GR + R
GR + G + R
GR + G
+ R + GR
