Geophysical Research Letter
Supporting Information for
Non-linearity of ocean heat uptake during warming and cooling in the FAMOUS
climate model
Bouttes, N.1, P. Good2, J. M. Gregory1,2 and J. A. Lowe2
1
NCAS-Climate, University of Reading, Reading, RG6 6BB, UK
2
Met Office Hadley Center, Exeter, EX1 3PB, UK
Contents of this file
Text S1 to S2
Figure S1 to S2
Tables S1 to S3
Introduction
The supporting information contains a description of the four ensemble members for the
ramp-up ramp-down and abrupt 4xCO2 experiments, a discussion about equation3
using negative hosing experiments, a figure showing the results from the abrupt step
experiments used for the step model predictions, a figure showing the results relative to
the negative hosing experiments, and tables of values used to quantify the results from
the step model predictions.
Text S1.
To test whether the results depend on variability we have run three additional members
for the 4xCO2 and ramp-up ramp-down experiments. They start from years 2, 3 and 100
of the control simulation. The corresponding evolution of air temperature, ocean
temperature and AMOC is plotted on Figure 1 (a, c and e) for the mean and standard
deviation.
Text S2.
Change in ocean circulation can induce changes in ocean heat uptake even in the absence
of radiative forcing changes. We consider four ‘negative hosing’ experiments, with
freshwater fluxes ranging between -0.1 and -0.4 Sv (negative fluxes indicate the net
1
removal of fresh water) spread uniformly over the North Atlantic between 50 and 70
degN. The resulting strengthening of the AMOC induces a rate of change of ocean heat
content (dH/dt) that is proportional to the AMOC change (supplementary Figure S2),
with regression coefficient -1.8x1020 J/yr/Sv. We used this regression coefficient to
predict the ocean heat change for the step down simulation starting from 4xCO2 down to
1xCO2 (1xfrom4x), given the AMOC changes in that experiment. This prediction is -1.6
x1021 J/yr over the first 100 years, which is almost an order of magnitude smaller than the
actual ocean heat content change ( -1.1x1022 J/yr) in the 1xfrom 4x simulation. This
justifies our omission of such effects in equation 3.
2
Figure S1. Evolution of (a) global mean air temperature (°C), (b) global mean ocean
temperature (°C) and (c) AMOC strength (Sv) (all variables relative to the parallel control
simulation) for the abrupt step experiments starting from 1xCO2 (solid lines) or 4xCO2
(dashed lines).
Figure S2. Change of ocean heat content (J/yr) as a function of AMOC change (Sv) for
hosing experiments.
Air temperature (°C)
Standard deviation
0.18
Ocean temperature
(°C)
0.02
AMOC (Sv)
1.11
Table S1. Standard deviation of annual means of the last 100 years (years 400-499) of
the ramp-up ramp-down simulation (stabilization phase).
Step model
Air temperature (°C) Ocean temperature AMOC (Sv)
prediction
(°C)
SR-4x
0.43
0.15
-1.34
SR-0.25x
1.21
0.28
-12.73
SR-0.5x
1.54
0.26
-14.52
SR-2xfrom4x
-0.75
-0.09
4.13
SR-1xfrom4x
0.08
-0.01
-0.67
SR-0.5xfrom4x
0.41
0.08
-4.34
SR-0.25xfrom4x
0.69
0.15
-6.15
Table S2. Time-mean error of the SR predictions of the stabilization phase (difference
between the step model prediction and the GCM simulation over the years 400-499).
3
Air temperature (°C)
Ocean temperature
(°C)
0.02
AMOC (Sv)
Std Ramp-up ramp- 0.18
1.06
down
Std SR-4x
0.06
0.02
0.36
SR-4x error
0.48
0.15
-1.30
Table S3. Intra-ensemble standard deviation (std) of annual means for the four
ensemble members for the stabilization phase (years 400-499) of the ramp-up rampdown experiments and the prediction using the 4xCO2 experiments (SR-4x), as well as
the time-mean prediction error during the stabilization phase (difference between the
prediction and GCM simulation over the years 400-499).
4