Supplementary Methods - Word file (44 KB )

Supplementary Material to: Weakening of Tropical
Pacific Atmospheric Circulation due to Anthropogenic
Gabriel A. Vecchi*, Brian J. Soden§, Andrew T. Wittenberg◊, Isaac M. Held◊, Ants
Leetmaa◊, Matthew J. Harrison◊
*University Corporation for Atmospheric Research Visiting Scientist Program at
NOAA/GFDL, Princeton, NJ, USA.
Rosenstiel School for Marine and Atmospheric Sciences, University of Miami, Miami,
NOAA/Geophysical Fluid Dynamics Laboratory, Princeton, NJ, USA
Tests for Statistical Significance:
In both the individual model ensemble members and in the observational record,
there is substantial decadal variability of SLP (the difference in sea level pressure
anomalies averaged in the region (80°E-160°E,5°S-5°N) with those averaged in the
region (160°W-80°W,5°S-5°N), which serves as a useful proxy for zonal winds across
the equatorial Pacific) arising from processes internal to the coupled system (i.e. not
forced by radiative changes, natural or anthropogenic); this variability is often larger
than that coming from the long-term trend (see Supp. Fig. 1). The statistical significance
of long-term trends should be computed against trends that may arise in the absence of
long-term forcing.
A 2,000-year integration with invariant radiative conditions from the 1860s serves
as a Control to the historical experiments, and can be used compute statistical
significance estimates. For individual ensemble members, two-sided statistical
significance from a zero trend for linear least squared trends computed from N-years of
data is estimated from the statistical distribution of the (2000-N+1) “N”-year trends
from the 2,000-year Control integration. The p=0.05 range is computed as that for
which only 5% of the trends from the Control integration have an amplitude larger than
the extremes of the range, after removing the long-term trend of the Control integration
(long term trend in Control is an order of magnitude smaller than forced trend in
historical runs).
The apparent trends in SLP that arise from internal variability in an individual
realization can be substantial, especially for short records (Supp. Fig. 2). The strong
decadal variations make estimating the long-term trend in SLP from a record shorter
than about 100 years problematic. For model records as long as 100-years there is at
least a 5% chance that individual ensemble members could show nominally positive
trends, even though the long-term forced trend is negative. However, for the record
lengths available, the modelled and observed long-term trends in SLP are significantly
different from zero, at p=0.05; and all show a weakening of SLP.
A Bootstrap method (with 100,000 Bootstrap samples) is applied to the Control
integration to estimate the significance of the ensemble-means of 3- and 5-members.
Three (and five) member ensembles are created by sampling from the entire population
of “N”-year trends in the Control simulation, with replacement, 100,000 times.
Estimates of statistical significance of ensemble-mean trends are computed from the
statistical distribution of these artificial ensemble-means.
Inter-model Comparison:
Many institutions around the World have generated model runs similar to the ones
described here for the Fourth Assessment Report of the Intergovernmental Panel on
Climate Change (IPCC-AR4), and some of the output from these models is available to
us (provided by U.S. Department of Energy Program for Climate Model Diagnosis and
Intercomparison; data available at ).
With this data we can test the inter-model robustness of our results. SLP trends from
19 models submitted to the IPCC-AR4 are explored here, which provide a total 67
ensemble members of historical simulations (19th through 20th Century). We have
excluded from analysis two models that have a large-scale time-averaged zonal SLP
gradient of the opposite sign as that observed.
As described above, the Control simulations using pre-industrial (mid-19th
Century) radiative and land use forcing, allow the estimation of the statistical
significance of observed SLP trends (removing the linear trend over the entire record
for each control run, since some models exhibited substantial drift). Shown in Suppl.
Fig. 3 are the two-sided p=0.05 range on zero trend of different lengths from the 19
Control simulations (only the GFDL-CM2.1 GCM is identified). The GFDL-CM2.1
estimates on statistical significance on SLP trends are among the more conservative.
Further, each of the observed long-term SLP trends is significantly different from zero
at p=0.05, for all of the IPCC-AR4 GCMs. Based on all of the models submitted to the
IPCC-AR4, the observed reduction in SLP since the mid-19th Century is statistically
significant at p=0.05. It should be noted that the length of the Control simulation for
each of the models differs (the range is between 250 and 940 years for the models
explored here). The utility of having a 2,000 year Control simulation with GFDLCM2.1 to estimate significance of fairly long trends (>100 years) is highlighted by the
second model from the right in Suppl. Fig. 3, for which the range for 152-year trends is
larger than that for 140-year trends – this counterintuitive finding is likely spurious and
due to the short record (351 years) relative to the trends being estimated (140 and 152
In agreement with the observed trend, a reduction in SLP since the 19th Century
is the consensus of the 67 historical simulations in the IPCC-AR4 database (Suppl. Fig.
4). The duration of the simulations of historical climate also vary (the range is between
the period 1890-2000 – 110 years - and the period 1849-2000 - 152 years), and aspects
of the radiative forcing differ between the various models; here, trends are computed for
either the period 1861-2000 or the entire available record from each model (whichever
is shorter). Significance estimates are computed for trends of corresponding length for
each model; the model that shows very large error-bars (third from the right) is a set of
experiments that are each only 110 years long. The long-term trend of each Control
simulation is removed.
There is substantial spread in the linear trends across the various ensemble
members, however there is only one ensemble member that exhibits a significantly
positive trend, contrasted with 12 ensemble members showing a significantly (at
p=0.05) negative trend. Further, 66% of the ensemble members exhibit a nominally
negative trend, and 8 of 19 models have at least one ensemble member with significant
weakening of SLP. Though GFDL-CM2.1 exhibits the strongest and one of the most
consistent responses in this particular index of the Walker Circulation, the reduction of
SLP since the mid-19th Century is the consensus of the IPCC-AR4 simulations.
Acknowledgements GAV supported by the Visiting Scientist Program at the NOAA/GFDL administered
by UCAR. We are extremely grateful to the model development teams at GFDL. Thanks to A.E.
Johansson, M.P. Vecchi, T. Knutson, T. Delworth, J. Russell and three anonymous reviewers for
comments and suggestions.
Correspondence and requests for materials should be addressed to G.A.V. (e-mail:
[email protected]).
Supplementary Figure 1: Evolution of SLP from GFDL-CM2.1 historical
integrations. Five-year running-mean SLP for: five-member ensemble mean in
upper left panel, five individual ensemble members in other panels. In each
panel, the linear-trend in SLP corresponding to each time-series is shown.
Note the substantial decadal variability in each ensemble member, and the
impact of the decadal variability on the computed trend.
Supplementary Figure 2: Statistical significance limits of single-member SLP
trends of different lengths, estimated from the 2,000-year control GFDL-CM2.1
integration. Shading indicates the two-sided p-value of a trend of a particular
value (vertical axes) computed from a SLP record of a particular length
(horizontal axes). Thick black line shows the 5-member ensemble-mean trend
from the all-forcing GCM experiment (the model trend to be detected), a vertical
dash indicates the length of the trends from the GCM. Symbols show the
observed trends from: Kaplan29 (star symbol), Hadley28 (circle symbol),
Kaplan29/Hadley28/NCEP27 blend (square symbol).
Supplementary Figure 3: Two-sided confidence intervals on zero SLP trend
from pre-Industrial IPCC-AR4 GCM control experiments. Bars show the
negative side of the two-sided p=0.05 range on single member SLP trends of
lengths corresponding to those of the three observational records. Dashed lines
show the linear trends computed from the three observational datasets:
Kaplan29 (1854-1992), Hadley Centre28 (1871-1998), and a blend of Hadley28
and Kaplan29, extended into 2005 using the NCEP gridded27 ship data (18542005). Units are Pa.year-1. Number of Control years available indicated inside
each column.
Supplementary Figure 4: Linear-trends of SLP from IPCC-AR4 models. Linear
trends of SLP for the 19th-through-20th Century simulations of 67 historical
runs of 19 models in the IPCC-AR4 database. Dots show trend value for each
ensemble member, over either the period 1861-2000 or (if the available record
was shorter) the entire model record. Bars indicate the p=0.05 limits on singleensemble member trends from a record of length corresponding to that of each
model. Only the model used in this study is identified. Units are Pa.year-1. Years
over which model trends were computed are indicated over each column.
Supplementary Figure 5: Modelled changes in equatorial Pacific oceanic
currents. GFDL-CM2.1 modelled linear trends over 1861-2000 in nearequatorial (a) zonal current (10-2 m s-1 year-1), and (b) vertical currents (10-2 m
day-1 year-1), from the five-member ensemble-mean all forcing experiment.
Positive zonal currents are west-to-east, positive vertical currents are upward
(upwelling). Note the reduction of in surface zonal currents, the upward shift of
subsurface zonal currents, and the upward shift and reduction of upward
(positive) vertical velocities.
Supplementary Figure 6: Evolution of equatorial Pacific thermocline depth and
slope. Model and observed anomalies in mean east-west slope of equatorial
Pacific thermocline (blue line) and equatorial Pacific zonal-mean thermocline
depth (black line). Left panel is from the ensemble-mean all-forcing GCM
experiment, five-year running mean. Right panel is from an observational
estimate30, thick lines are five-year running means and thin lines are annualmeans. Thermocline slope defined as the thermocline depth averaged (140°E180°E, 2°S-2°N) minus that averaged (130°W-90°W, 2°S-2°N). Thermocline
defined as the location of the maximum vertical temperature gradient.