manuscript submitted to Geophysical Research Letters
Revisiting Mountains and Stationary Waves: the1
Importance of the Zonal Mean Response2
R.H. White1,2⇤
, J.M. Wallace2, and D.S. Battisti
23
1Barcelona Supercomputing Center, Carrer de Jordi Girona, 29, 31, 08034 Barcelona, Spain42Department of Atmospheric Science, University of Washington, Seattle, WA 98195, USA5
Key Points:6
• Orography significantly alters tropospheric and stratospheric Northern Hemisphere7
winter zonal mean climate, impacting the stationary waves8
• The dominant e↵ect of orography is to amplify the pattern of wintertime station-9
ary waves forced by land-sea contrast10
• When orography is flattened stationary wave amplitudes are reduced to as little11
as 1/3 of the present day values12
⇤Marie Curie Actions
Corresponding author: R.H. White, [email protected]
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manuscript submitted to Geophysical Research Letters
Abstract13
We revisit the impact of global orography on wintertime climate using a state-of-the-art14
climate model, with sophisticated parameterization of the impacts of sub-gridscale orog-15
raphy (the Whole Atmosphere Community Climate Model, WACCM). The main impact16
of orography is to amplify the stationary waves produced by land-sea thermal contrasts,17
as evidenced by the strong spatial resemblance between the stationary wave pattern in18
a no-mountain (NM) simulation with that induced by orography. Orography amplifies19
extratropical NM stationary waves at all levels, with an amplification factor of a ⇠ 1.620
in the mid-latitudes, increasing to a > 1.9 in the high-latitude stratosphere. Orogra-21
phy also decelerates the zonal mean zonal wind poleward of 40�N throughout the tro-22
posphere and stratosphere. The e↵ect of the weakening of the zonal winds on station-23
ary waves is twofold: it amplifies the thermal forcing and it amplifies the planetary-wave24
response to a prescribed thermal forcing.25
1 Introduction26
Earth’s atmospheric stationary waves are seen in the planetary scale wave-like struc-27
ture in climatological sea level pressure or geopotential height. In the Northern Hemi-28
sphere the dominant features of the wintertime stationary waves are so prominent that29
they have been given names: the Aleutian low, the Icelandic low, and the Siberian high.30
The forcing of stationary waves is provided by planetary features that are, unsurpris-31
ingly, largely stationary: orography (Charney & Eliassen, 1949; Bolin, 1950), and zonal32
asymmetries in atmospheric heating, typically from land-sea contrasts (e.g. Smagorin-33
sky, 1953; Manabe & Terpstra, 1974; Hoskins & Karoly, 1981; Valdes & Hoskins, 1991).34
From the 1980s to 2010 numerous studies examined the relative contributions of35
‘orographic’ and ‘thermal’ forcing to the observed stationary waves. This research, col-36
lectively using linear and non-linear stationary wave models, as well as full general cir-37
culation models (GCMs), has shown that orography produces anywhere between 30%38
and 66% of the observed stationary wave amplitude, with recent estimates towards the39
lower end of this range (Held, 1983; Chen & Trenberth, 1988a, 1988b; Nigam et al., 1988;40
Valdes & Hoskins, 1989; Ting et al., 2001; Held et al., 2002; Chang, 2009). The authors’41
impression is that the value of 30% from the review of Held et al. (2002) is often taken42
as the best estimate of the role of mountains, even if it were not intended as such. The43
large range of results can be at least partially understood from di↵erences in the back-44
ground flow into which the orography was placed, including di↵erences in low-level winds45
(e.g. Valdes & Hoskins, 1989; Held & Ting, 1990; Ringler & Cook, 1995; Held et al., 2002),46
as well as model di↵erences in atmospheric dissipation strength and imposed drag (Valdes47
& Hoskins, 1989).48
Much less attention has been paid to the impact of orography on the axisymmet-49
ric flow. As Held et al. (2002) noted, the tropospheric zonal mean zonal wind structure50
is broadly similar between the Northern and Southern hemispheres (NH and SH), sug-51
gesting that the orography of the NH has relatively little impact in the troposphere, con-52
sistent with earlier modelling results (Manabe & Terpstra, 1974). Conversely, a strong53
asymmetry exists between the wintertime zonal mean stratospheric jets in each hemi-54
sphere, caused by large di↵erences in wave activity generated by land-sea contrasts and55
orography (Waugh & Polvani, 2010; White et al., 2018). Early modelling results suggest56
that orography reduces the speed of the NH winter stratosphere jet by approximately57
15% (Manabe & Terpstra, 1974), although large biases in that model existed. In a mod-58
ern GCM, White et al. (2018) found that the presence of the ‘Mongolian mountains’ of59
Asia alone reduces zonal mean stratospheric wind speeds in winter by up to 40%.60
In addition to acting as a large-scale obstruction to the flow, orography impacts61
the climate through subgrid-scale orographic drag, through the forcing of orographic grav-62
ity waves, as well as the blocking of flow (e.g. McFarlane, 1987; Shaw et al., 2009; Sig-63
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manuscript submitted to Geophysical Research Letters
mond & Scinocca, 2010; Pithan et al., 2016; Sandu et al., 2016, 2019). Including grav-64
ity wave parameterization of orographic e↵ects substantially increases zonal mean sea65
level pressure in the high latitude NH (shown in the appendix of Broccoli & Manabe,66
1992), and will thus impact the low-level zonal mean zonal wind (U). Parameterizing67
the e↵ects of orographic drag reduces tropospheric U (Sandu et al., 2016) and alters sta-68
tionary waves (van Niekerk et al., 2017; Sandu et al., 2019). The representation of such69
impacts within GCMs has improved in recent years, through both increased resolution,70
and improved parameterizations (Garcia et al., 2007; Richter et al., 2010; Garcia et al.,71
2016), although limitations and biases still exist (Sandu et al., 2019). The time there-72
fore seems ripe to re-evaluate the role that orography plays in the wintertime climate73
using a state-of-the-art climate model.74
Using NCAR’s Whole Atmosphere Community Climate Model (WACCM), we quan-75
tify the total role of orography on the observed stationary waves, including both local76
and remote changes in diabatic heating, as well as changes in SSTs due to air-sea heat77
fluxes. We present evidence for a substantial impact of orography on the zonal mean cli-78
mate in both the troposphere and stratosphere, and highlight the remarkable similar-79
ity between the stationary wave patterns from ‘land-sea forcing’ and from ‘orographic’80
forcing, o↵ering a new perspective on how orography influences the stationary waves. We81
propose that the most important impact of orography on stationary wave amplitude is82
to amplify the ‘land-sea’ stationary waves, in addition to forcing a stationary wave pat-83
tern of its own, as in the traditional view.84
2 Models and Experiments85
We use the WACCM4, an atmospheric dynamical model with 66 vertical levels, in-86
cluding a well-resolved stratosphere (Marsh et al., 2013). In addition to high resolution87
in the upper atmosphere, the WACCM has improved parameterizations of vertically prop-88
agating gravity waves and surface stress from unresolved topography (termed turbulent89
mountain stress, TMS), relative to the lower-top CAM model (Garcia et al., 2007; Richter90
et al., 2010; Marsh et al., 2013). A horizontal resolution of 1.9�x 2.5�is used.91
Mountains are known to a↵ect the ocean circulation (Kitoh, 2002; Sinha et al., 2012)92
through impacts on wind stress and freshwater fluxes (Warren, 1983; Emile-Geay, 2003).93
Here we focus on the dynamical atmospheric response to global mountain ranges and do94
not consider dynamical ocean changes. Orographic forcing can also influence SSTs through95
air-sea heat fluxes (Okajima & Xie, 2007; Chang, 2009). This influence may a↵ect the96
impact of orography on diabatic heating, in the past considered to be small (Held, 1983).97
Since the WACCM is not currently coupled to a slab ocean, we allow atmospheric changes98
to a↵ect SSTs by using simulated changes in monthly climatological SSTs from a slab-99
ocean model coupled to the CAM model with and without orography. The NH extra-100
tropical SSTs for each experiment, as well as the CTL-NM di↵erence, are shown in sup-101
plemental Fig. S1.102
To investigate the role of orography in shaping the stationary waves, two WACCM103
simulations are performed, each 30 years in length (following a one year spin-up period).104
The ‘CTL’ simulation has present-day topography, and the ‘NM’ (No-Mountain) sim-105
ulation has all topography flattened to 50m above sea level. In addition to the topographic106
height, we reduce the variables associated with subgrid-scale variability in orography, ‘SGH’107
and ‘SGH30’, to approximate values associated with regions of low orography in the CTL108
simulation (30 and 10 m respectively).109
The WACCM model reproduces tropospheric and stratospheric circulations well,110
albeit with a cold pole bias (Marsh et al., 2013). Throughout this paper we further eval-111
uate the WACCM by comparing it with the ERA-interim re-analysis data (Dee et al.,112
2011).113
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3 Results114
The stationary wave pattern can be seen in the eddy geopotential height, Z 0 = Z�115
Z, where the overbar denotes the zonal mean. Fig. 1 shows Z 0 at 60�N for ERA-I, the116
CTL and NM simulations, and the CTL-NM di↵erence. The CTL simulation reproduces117
the observed pattern from ERA-interim re-analysis data well (compare Figs. 1a and b).118
The climate in the CTL and NM simulations, and thus the climate response to orogra-119
phy (CTL-NM), is broadly similar to that found in earlier studies (e.g. Nigam et al., 1986;120
Held, 1983; Held et al., 2002). The orographic response (CTL-NM) and NM pattern are121
generally of similar magnitude.122
To provide a quantitative metric for comparing the relative contributions of orog-125
raphy and land-sea contrast, we calculate the ‘stationary wave strength’, defined as the126
longitudinal standard deviation (�) in Z. The ‘orographic contribution’ is calculated as127
(�(ZCTL)��(ZNM ))/�(ZCTL). There is substantial variation in the orographic con-128
tribution with latitude and height (see supplemental Fig. S2a), with a maximum value129
of ⇠ 85% in the high latitude stratosphere, and a latitude-weighted value in the NH mid-130
latitudes (30-70�N) of approximately 45% throughout the troposphere and stratosphere.131
In idealized simulations, the stationary response to a single mountain has a zonal132
wavenumber of around 4-6 (Hoskins & Karoly, 1981; Valdes & Hoskins, 1991; Cook &133
Held, 1992; Held et al., 2002; White et al., 2017). In contrast to these idealized studies,134
the CTL-NM response has a wavenumber, phase, and vertical structure remarkably sim-135
ilar to that in the NM simulation (compare Figs. 1c and d), with a pattern of approx-136
imately wavenumber 2 in the troposphere, and wavenumber 1 in the stratosphere. That137
is, the first order e↵ect of the mountains is to amplify the mid-latitude stationary wave138
pattern that is already present as a consequence of the land-sea contrast.139
This amplification of the land-sea stationary wave pattern (NM) in the CTL sim-140
ulation can also be seen in maps of Z 0 (Fig. 2). A comparison of Z 0 between ERA-I and141
our CTL simulation shows that the WACCM simulates the observed spatial pattern of142
stationary waves well at both 300 and 1000 mb (c.f. Fig. 2a with 2b and Fig. 2d and143
2e; colours show the eddy component, whilst black contours show the full fields). The144
NM eddy fields (Figs. 2c and f) exhibit a spatial structure similar to that of the CTL145
fields, but with muted amplitude; the first order e↵ect of orography is to greatly amplify146
this pattern.147
We calculate the Pearson correlation coe�cient between the CTL-NM and NM fields,153
with masking for points that are below the surface in the CTL simulation. At 1000, 300,154
and 30 mb respectively, the latitude-weighted correlation coe�cients for the mid-latitudes155
are 0.33, 0.60, and 0.81, thus confirming that a large component of the CTL-NM response156
is to amplify the background stationary wave pattern present in the NM simulation, par-157
ticularly above the lower troposphere. To provide a quantitative metric for the strength158
of this amplification by orography we define an ‘amplification factor’, a, as the slope of159
the linear regression between the CTL and NM fields; we can thus write Z 0CTL = aZ 0
NM+160
Z 0M , where Z 0
M is the orography-induced change in eddy geopotential height that does161
not project onto the NM pattern. The latitude-weighted mean amplification factor a ⇠162
1.6 throughout the troposphere and stratosphere. Vertical cross-sections of both the cor-163
relation coe�cient and amplification factor are shown in supplemental Figs. S2b and c.164
4 Zonal mean response to orography165
In addition to the stationary wave response, orography substantially shapes the win-166
tertime zonal mean zonal wind climatology. Figure 3 shows a pole-to-pole meridional cross-167
section of U (colours), and Z (black contours) for winter in each hemisphere, i.e. DJF168
in the NH and JJA in the SH. Fields are masked between 10�S and 10 �N to emphasise169
the discontinuity at the equator. The WACCM reproduces the general structure of the170
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Figure 1. Eddy geopotential height, Z0, at 60
�N: a. ERA-I, b. CTL, c. NM, and d. CTL -
NM
123
124
.
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Figure 2. DJF Z, full fields (black contours; zero contour bold) and zonal anomalies (Z0;
colours), at 1000 mb (left), and 300 mb (right). Top row: ERA-I; centre: CTL, and bottom
row: NM. Prominent highs and lows in the full fields are denoted with H and L respectively. At
300 mb the contour interval for the full fields for CTL and NM is 200 m, whilst at 1000 mb the
contour interval is 20 m.
148
149
150
151
152
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wintertime geopotential and zonal jets in both hemispheres well, including the di↵erence171
in strength of the NH and SH stratospheric jets (c.f. Figs 3a and b). The NM fields (Fig.172
3c) show much greater symmetry between the NH and SH, as expected. At 10 mb the173
NH wintertime stratospheric jet in the NM simulation is only ⇠ 10% weaker than its SH174
counterpart: orography thus plays a dominant role in the hemispheric di↵erences in the175
stratospheric winter jet (see also White et al., 2018).176
Fig. 3d shows the CTL-NM di↵erences in the zonal mean fields. The orographic181
impact on the NH stratospheric jet is substantial: at 10 mb the jet reaches 82 m/s in182
the NM simulation, in contrast to 39 m/s in the CTL (c.f. figures 3b and c). Consistent183
with previous understanding (e.g. Held et al., 2002), changes in the sub-tropical jet are184
small. There is, however, a significant orographically-induced weakening of tropospheric185
U north of 50�N, extending all the way down to the surface. Whilst the absolute mag-186
nitude of the near-surface changes is small relative to the stratospheric changes (⇠ 3m/s187
at 925 mb between 50-80�N), it has a profound e↵ect on the character of the low-level188
flow.189
To explore the mechanisms behind the weakening of U in CTL relative to NM, Fig.190
4 shows the Eliassen-Palm (EP) wave activity flux and its divergence (Eliassen & Palm,191
1961; Andrews & McIntyre, 1976; Edmon et al., 1980). Arrows are scaled (see caption),192
and thus should not be used to estimate divergence. The EP fluxes are calculated based193
on climatological wintertime data, that is, they show the propagation of stationary wave194
activity, and the impacts of the stationary waves on the zonal mean flow. Positive di-195
vergence of the EP fluxes signifies a strengthening of the zonal mean flow by the waves196
(Andrews & McIntyre, 1976; Edmon et al., 1980).197
The CTL simulation reproduces the ERA-I spatial pattern of stationary wave EP198
fluxes, and their divergence, relatively well (c.f. Figs. 4a and b), although the magni-199
tude of EP flux divergence in the mid-latitude troposphere is underestimated; we thus200
avoid making quantitative conclusions based on this analysis. The EP flux arrows show201
a reduction in the propagation of wave activity strength away from the surface in the202
NM simulation relative to the CTL (c.f. Figs 4b and c). Stationary wave activity is still203
present in the troposphere in the NM simulation: the land-sea forcing is su�cient to pro-204
duce substantial tropospheric wave activity at lower latitudes; however the strong EP205
flux divergence north of 40�N is absent in the NM simulation. There is also a stark ab-206
sence of wave activity (and thus divergence) reaching into the stratosphere in the NM207
simulation. Calculation of EP fluxes on daily data confirms that stationary waves dom-208
inate the stratospheric CTL-NM response, consistent with a relatively small propaga-209
tion of transient waves into the stratosphere (Li et al., 2011).210
5 Discussion216
The impact of global orography on the wintertime wind climatology is examined217
with the WACCM, a state-of-the-art climate model, revisiting the seminal work of the218
1980s and 1990s. The influence of orography on the NH mid-latitude stationary waves219
is generally comparable to land-sea thermal contrasts, with orography dominating in some220
parts of the troposphere and stratosphere. This is consistent with previous work, but sug-221
gests a larger role for orography than the most recent estimates (Held et al., 2002; Ting222
et al., 2001; Chang, 2009). We highlight the remarkable similarity between the NM sta-223
tionary wave pattern and the CTL-NM response, concluding that the first-order role of224
orography is to amplify the stationary wave pattern that would be present by virtue of225
the land-sea contrast alone. The amplification factor, a measure of how much orogra-226
phy amplifies the NM stationary wave pattern, is approximately 1.6 for the troposphere,227
and 1.8 for the stratosphere.228
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Figure 3. Wintertime (DJF for NH, JJA for SH) U (colours), and Z (black contours, contour
interval 200 m for a-c and 100 m for d; negative values dashed and 0 contour bold), for a. ERA-
I, b. CTL, c. NM, and d. CTL - NM. Wintertime fields are shown for both hemispheres; values
are masked between 10�S to 10
�N.
177
178
179
180
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Figure 4. Wintertime (JJA for SH, DJF for NH) stationary wave Eliassen-Palm flux (arrows,
m/s2) and flux divergence (colours, m/s/day) for a. ERAI, b. CTL and c. NM. The EP flux
follows the scaling of (Edmon et al., 1980) for log-pressure coordinates, and divides by the square
root of 1000/pressure to aid visualization (Taguchi & Hartmann, 2006). Wintertime fields are
shown for both hemispheres; values are masked between 10�S to 10
�N.
211
212
213
214
215
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In addition to the amplification of the stationary waves, orography has a strong229
impact on the zonal mean flow poleward of 40�N. Without orography, the NH winter-230
time polar night jet is much stronger than in observations and the WACCM CTL sim-231
ulation, and is comparable to the strength of the SH wintertime stratospheric jet. The232
strong sensitivity of the NH stratospheric winter jet to the inclusion of mountains is con-233
sistent with the concept of a positive feedback in stratospheric zonal wind: faster strato-234
spheric flow limits the waves that can propagate into the stratosphere to smaller wavenum-235
bers (Charney & Drazin, 1961); this reduces the Eliassen-Palm flux convergence in the236
stratosphere, further enhancing the zonal wind. Our results suggest that, in the absence237
of orography, very little stationary wave activity is able to propagate into the stratosphere.238
The impact of orography on zonal winds extends all the way down to the surface pole-239
ward of ⇠ 50�N.240
This profound impact of orography on the zonal mean flow can be connected to241
the orographic amplification of the land-sea stationary wave that we have highlighted.242
For low-level extratropical heating, the amplitude of the stationary wave response to a243
given diabatic heating profile is inversely proportional to the low-level mean zonal wind244
(Held & Ting, 1990). The linear model of Held and Ting (1990) shows a stationary wave245
amplitude response to low-level wind changes of the same order of magnitude that we246
see in our simulations: an amplification of ⇠1.6 for a reduction in U from, for example,247
⇠ 6 m/s (NM) to 2 m/s (M).248
In addition to the reduction in stationary wave amplitude for a fixed diabatic heat-249
ing, deceleration of the zonal mean flow allows stronger zonal temperature gradients (from250
land-sea contrast) to be maintained; in the limit of infinite zonal flow, no zonal temper-251
ature gradients could be maintained. Thus a reduced zonal flow can enhance the dia-252
batic heating pattern from land-sea contrast, leading to an amplification of the ‘thermal’253
stationary wave pattern. Supplemental Fig S1 shows that the diabatic heating patterns254
are indeed enhanced in the CTL simulation relative to NM.255
The positive feedback of stratospheric zonal wind speed, discussed above, may pro-256
vide an additional mechanism by which orography amplifies the existing stationary wave257
in the stratosphere: in the presence of orography, enhanced stationary wave EP flux con-258
vergence in the stratosphere weakens the stratospheric jet; this in turn enhances the prob-259
ability of waves generated by land-sea contrast being able to propagate into the strato-260
sphere. This mechanism di↵ers somewhat from that discussed by White et al. (2018),261
who removed individual mountain regions; this di↵erence suggests non-linear interactions262
between di↵erent orographic regions. The amplification of the NM stationary wave pat-263
tern by the orography may also be a↵ected by the location of the main orographic fea-264
tures of the NH. Both the North American Rockies and the dominant orography in Asia265
are located approximately 30� longitude upstream of the eastern edge of a continent; the266
mechanical forcing of the orography results in northerly flow and cold advection down-267
stream of the mountain range, which is thus, rather coincidentally, located such that it268
enhances the existing land-sea temperature contrast (e.g. Brayshaw et al., 2009).269
The impact of orography is reduced when SSTs are held fixed to the observed cli-270
matology in both the CTL and NM simulations (shown in Supplemental Fig. S3). The271
degree of correlation between the CTL-NM and NM patterns, and the orographic am-272
plification factor, are also reduced (although still present). This lower boundary condi-273
tion may thus be part of the reason that this amplification e↵ect has remained largely274
unnoticed up until now. In retrospect, this ‘constructive interference’ can be seen to some275
degree in earlier studies, even when SSTs were fixed to observed values in both the CTL276
and NM simulations. Held (1983), Held et al. (2002) and Chang (2009) mention a con-277
structive interference between the thermal forcing and the orography forcing between278
120E and 60W, but did not explore this further.279
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This work o↵ers a new perspective of how orography shapes Earth’s stationary waves:280
orography provides a substantial amplification of the background, land-sea generated,281
stationary wave pattern, through the impact of orography on the zonal mean flow, as282
well as forcing an additional stationary wave pattern.283
Acknowledgments284
RHW received funding from the European Unions Horizon 2020 research and innova-285
tion programme under the Marie Skodowska-Curie Grant Agreement No. 797961, from286
the National Science Foundation grant AGS-1665247, and from the Tamaki Foundation.287
DSB was supported by the Tamaki Foundation. Simulations were performed at the De-288
partment of Atmospheric Sciences at the University of Washington, and on the NCAR’s289
Cheyenne computer under grant UWAS0064.290
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Supporting Information for Revisiting Mountainsand Stationary Waves: the Importance of the ZonalMean Response
R.H. White1,2, J.M. Wallace
2, and D.S. Battisti
2
1Barcelona Supercomputing Center, Carrer de Jordi Girona, 29, 31, 08034 Barcelona, Spain
2Department of Atmospheric Science, University of Washington, Seattle, WA 98195, USA
Contents of this file
1. Figures S1 to S3
Introduction This supporting information provides additional figures to supplement the
main text.
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X - 2 :
Figure S1. Supplemental Fig. S1. DJF fields for ERA-I (top row), CTL (2nd row), NM
(3rd row) and CTL-NM di↵erence (bottom row). Left: sea surface temperature; centre: mass-
weighted average diabatic heating between 1000-850 mb; right: mass-weighted average diabatic
heating between 850-500 mb. Note the change in colour scale for the CTL-NM plots.
May 16, 2019, 9:37am
: X - 3
Figure S2. Supplemental Fig. S2. Cross-section of DJF metrics of orographic
impact on stationary waves. a. orographic contribution to stationary wave strength
((�(ZCTL)� �(ZNM))/�(ZCTL)); b. Pearson correlation coe�cient between CTL-NM and NM
fields; c. orographic amplification factor (the slope of the linear regression between the CTL and
NM fields).
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X - 4 :
Figure S3. Supplemental Fig. S3. As Fig. S2, but for simulations where SSTs are fixed to
observed values in both CTL and NM experiments.
May 16, 2019, 9:37am
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