revisiting mountains and stationary waves: the importance...

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]

–1–


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

–2–


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

.

–5–


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

–7–


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

–8–


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

–9–


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

–10–


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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–13–

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.

May 16, 2019, 9:37am

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).

May 16, 2019, 9:37am

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

revisiting mountains and stationary waves: the importance...

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