Local wave activity budgets of the wintertime Northern ...
Transcript of Local wave activity budgets of the wintertime Northern ...
Confidential manuscript submitted to Geophysical Research Letters
Local wave activity budgets of the wintertime Northern1
Hemisphere: Implication for the Pacific and Atlantic storm2
tracks3
Clare S. Y. Huang1∗, Noboru Nakamura14
1Department of the Geophysical Sciences, University of Chicago, Chicago, Illinois, USA.5
Key Points:6
• Seasonal mean budget of LWA reveals that the low-level meridional heat flux is the ma-7
jor source of LWA over both storm tracks.8
• On synoptic timescales the horizontal LWA flux convergence and diabatic heating play9
the leading roles in the LWA budget.10
• Convergence of the meridional eddy momentum flux describes the covariation of barotropic11
zonal wind and LWA over the Pacific but not the Atlantic.12
∗5734 S Ellis Ave, Chicago IL 60637
Corresponding author: Clare S.Y. Huang, [email protected]
–1–
Confidential manuscript submitted to Geophysical Research Letters
Abstract13
A recently developed finite-amplitude local wave activity (LWA) diagnostic framework quan-14
tifies eddy-mean flow interaction on regional scales. Here we examine the column budgets of15
LWA for the winter Northern Hemisphere with the ECMWF ERA Interim product, with an16
eye toward quantifying the maintenance and variability of the Pacific and Atlantic storm tracks.17
The budget is governed by (i) low-level meridional eddy heat flux, (ii) horizontal convergence18
of the LWA flux, and (iii) nonconservative (diabatic) sources-sinks. In both regions the low-19
level meridional heat flux fuels LWA on seasonal timescales but the zonal LWA flux conver-20
gence and diabatic effects dominate the synoptic variability. Cospectral analysis shows that the21
interplay between barotropic zonal wind and column-averaged LWA through the meridional22
eddy momentum flux convergence is significant over the Pacific but not the Atlantic. A first23
attempt at partitioning LWA into stationary and transient eddy contributions is also discussed.24
1 Introduction25
Migratory weather systems populate the storm track regions of Earth’s midlatitudes and26
affect the lives of billions [Chang et al., 2002; Shaw et al., 2016]. In the Northern Hemisphere,27
storm tracks are localized over the Pacific and Atlantic sectors, whereas in the Southern Hemi-28
sphere, they are more zonally spread over the Southern Ocean [Hoskins and Hodges, 2002, 2005].29
Surface orography contributes significantly to the difference in the spatial structures of the storm30
tracks through stationary Rossby waves [Hoskins and Karoly, 1981; Held and Ting, 1990; Held31
et al., 2002; Wilson et al., 2009]. Storm tracks are generally more active in winter when the32
pole-to-equator and land-sea temperature gradients enhance baroclinicity, although the mid-33
winter suppression of the North Pacific storm activity is a notable exception [Nakamura, 1992].34
Commonly used metrics of storm track activities include the Eady growth rate [Lindzen35
and Farrell, 1980], variance in highpass sea level pressure and geopotential height [Nakamura,36
1992], transient eddy kinetic energy (EKE) [Orlanski, 1998; Deng and Mak, 2006] and aggre-37
gate potential vorticity (PV) anomalies contributed from individual storms [Hoskins and Hodges,38
2002, 2005]. To elucidate the underlying dynamics with meteorological data, metrics with known39
budget components are useful since they allow breakdown of the contributions from different40
physical processes. For example, Chang [2001] applies the budgets of EKE and wave activ-41
ity flux to the Southern Hemisphere storm tracks and show that the upstream generation of42
baroclinic wave activity maintains the downstream development of wave packets.43
The wave activity flux diagnostic [Plumb, 1985; Takaya and Nakamura, 2001] is widely44
used to describe the 3D propagation of Rossby wave packets. However, its derivation assumes45
that the wave amplitude is small. While the wave activity flux is readily calculable from data,46
the budget of wave activity cannot be closed with the small-amplitude assumption: it is dom-47
inated by triple products of eddy quantities at finite amplitude, and the (small-amplitude) wave48
activity itself becomes unreliable as the background PV gradient is reversed [Solomon and Naka-49
mura, 2012].50
Recently, Huang and Nakamura [2016] (hereafter HN16) introduced finite-amplitude lo-51
cal wave activity (LWA) to describe eddy-mean flow interaction on regional scales. LWA gen-52
eralizes the small-amplitude theory to eddies of arbitrary amplitude with a simple, closed bud-53
get. Both LWA and its eddy forcing terms are calculable from meteorological data, and the54
residual of the budget quantifies the net nonconservative processes. HN16 demonstrate that55
LWA captures the life cycle of anomalous wave events (see their Figs. 8 and 9). In this study,56
we analyze the column budget of LWA with the European Centre for Medium-range Weather57
Forecasts (ECMWF) ERA-Interim product [Dee et al., 2011] for the Northern Hemisphere win-58
ter to study the maintenance and variability of the Pacific and Atlantic storm tracks. A method59
will be introduced to decompose LWA into stationary and transient eddy contributions. As we60
will see, the transient component of LWA is consistent with, but better-behaved than, the small-61
amplitude transient wave activity defined by Plumb [1986]. We will also perform spectral anal-62
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ysis of the forcing terms for synoptic to intraseasonal timescales over the two oceans to de-63
lineate the frequency dependence of the LWA budget.64
2 The local finite-amplitude wave activity (LWA)65
2.1 Definition of LWA66
LWA extends the finite-amplitude wave activity (FAWA) theory of Nakamura and Zhu67
[2010], formulated based on the conservation of quasigeostrophic PV (QGPV) on isobaric sur-68
face in a rotating, stratified atmosphere. FAWA measures the net ‘exchange’ of QGPV sub-69
stance across latitude circles by eddies. HN16 introduce LWA as the longitude-by-longitude70
contribution to FAWA. In spherical coordinates the interior LWA is defined as71
A∗(λ, φ, z, t) = −a
cos φ
∫ ∆φ
0qe(λ, φ, φ′, z, t) cos(φ + φ′)dφ′ z > 0, (1)72
where a is the radius of the planet, (λ, φ, z) defines longitude, latitude and pressure pseudo-73
height [z ≡ −H ln(p/p0) where p is pressure, p0 = 1000 hPa and H = 7 km is assumed].74
qe(λ, φ, φ′, z, t) ≡ q(λ, φ + φ′, z, t) − qREF(φ, z, t) is an ‘eddy’ component of the QGPV q, de-75
fined as the departure from a zonally symmetric, Lagrangian-mean reference state qREF(φ, z, t)76
at equivalent latitude φ [see Supporting Information (SI) sections 1-2 for details]. In the above77
φ′ is latitude relative to φ and used to describe the meridional displacement of QGPV from78
the reference state qREF(φ, z, t). ∆φ(λ, φ, z, t) is the meridional displacement of the QGPV con-79
tour q = qREF from the latitude circle at φ. (See HN16 Fig.1.) By definition, A∗ is positive80
definite and its zonal average recovers FAWA. Unlike previous studies with the FAWA formal-81
ism (e.g. Nakamura and Solomon [2010], Wang and Nakamura [2015], hereafter NS10 and WN15,82
respectively), the equivalent latitude and the reference state in this study are defined in a hemi-83
spheric domain, with the assumption that the effect of inter-hemispheric exchange of QGPV84
on the mid-latitude dynamics is insignificant.85
This paper focuses on the horizontal distribution of the density-weighted column aver-86
age of LWA and its fluxes, which we evaluate by the averaging operation87
〈(·)〉 ≡
∫ ∞0 e−z/H(·)dz
H. (2)
2.2 Comparison between instantaneous 〈 A∗〉 and 〈EKE〉88
LWA measures the meridional displacement of the QGPV substance. Unlike EKE, it is89
not a measure of how energetic eddies are locally: the two metrics quantify different aspects90
of eddies. To illustrate, Fig.1 compares daily snapshots of 〈A∗〉 and 〈EKE〉, together with the91
500hPa geopotential height (Z500) contours. During this period (December 14-17, 2010) there92
were a persistent anticyclone over the central Pacific (30−60◦N, 180◦) and a cyclone form-93
ing over the Gulf of Alaska (45−60◦N, 160◦W). 〈A∗〉 attains maxima at the centers of both94
features, where the zonal flows are most obstructed. This is consistent with the theoretical ex-95
pectation that LWA negatively covaries with the zonal flow (HN16, see also Fig.10 of SI). 〈EKE〉,96
in contrast, attains maxima around the features where the Z500 contours are densest (i.e. where97
the geostrophic flow is most energetic).98
2.3 Budget equations of LWA and zonal wind99
The column budget equations for the interior zonal wind u and LWA A∗ read:100
∂
∂t〈u〉 cos φ︸ ︷︷ ︸
zonal windtendency
≈ −1a∂Fu
∂λ︸ ︷︷ ︸zonal windzonal flux
convergence
−1
a cos φ∂
∂φ′
⟨ueve cos2(φ + φ′)
⟩︸ ︷︷ ︸
meridional eddymomentum
flux convergence
+ Gu︸︷︷︸ageostrophic
Coriolistorque
+ ˙〈u〉 cos φ︸ ︷︷ ︸residual
, (3)
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Confidential manuscript submitted to Geophysical Research Letters
∂
∂t
⟨A∗
⟩cos φ︸ ︷︷ ︸
LWA tendency
≈ −1a∂FA
∂λ︸ ︷︷ ︸zonal LWA
fluxconvergence
+1
a cos φ∂
∂φ′
⟨ueve cos2(φ + φ′)
⟩︸ ︷︷ ︸
meridional eddymomentum
flux divergence
+f cos φ
H
(veθe
∂θ/∂z
)z=0︸ ︷︷ ︸
low-level eddymeridional heat
flux
+˙⟨
A∗⟩
cos φ︸ ︷︷ ︸residual
,
(4)
where (u, v, θ) define the zonal and meridional wind velocities and potential temperature. The101
subscript e denotes the departure from the reference state (‘eddy’), Fu and FA are the column-102
averaged zonal fluxes of zonal wind and LWA, Gu is the Coriolis torque of the ageostrophic103
meridional wind (see Appendix A for the full expressions), f is the Coriolis parameter, θ(z, t)104
is the area-weighted average of potential temperature over the Northern Hemisphere, and u and105
˙A∗ represent non-conservative contributions. (See SI sections 3-5 for derivations and compu-106
tation.) The above equations generalize Eqns. (29) and (27) of HN16 for spherical coordinates.107
The zonal LWA flux FA includes advective fluxes [the first two RHS terms of (A.3)] that are108
cubic (or higher) in eddy products. The second RHS term of (4) represents the local transfer109
of barotropic momentum to and from the zonal wind. The third term is the upward wave ac-110
tivity input from the surface. The zonal convergence of the last term in (A.3), together with111
the second and third RHS terms of (4) make up the column average of the 3D Eliassen-Palm112
(EP) flux convergence. The last term of (4) represents nonconservative sources-sinks of LWA,113
including diabatic heating, dissipation through mixing, radiative and Ekman damping. The bud-114
get of surface wave activity associated with the meridional displacement of low-level poten-115
tial temperature will not be analyzed in this study. The main contribution to the column av-116
erage quantities over the oceans comes from the upper troposphere, where eddy amplitudes117
are greatest, even with the density-weighing that decreases with height (2) (HN16).118
The tendency terms in (3)-(4) are negligible upon time averaging over a season (December-119
February in this study). Denoting such time averaging by [(·)], (4) becomes:120
0 ≈ −1a∂[FA]∂λ
+1
a cos φ∂
∂φ′
[⟨ueve cos2(φ + φ′)
⟩]+
f cos φH
[(veθe
∂θ/∂z
)z=0
]+
[˙⟨
A∗⟩]
cos φ. (5)
This steady-state budget describes the balance between the flux convergence (the first three121
RHS terms) and sources-sinks of LWA (the last term), which will be evaluated in Fig.3 be-122
low.123
We also examine the frequency dependence of the budget by computing the cospectra124
(i.e. the in-phase signal of cross-spectra) between the LHS and each of the RHS terms of (3)125
and (4). We apply this spectral analysis after averaging each term in the equations over the126
respective domain (Fig.3). See Appendix B for the definition of the domains of averaging. The127
cospectrum of two quantities A and B will be denoted by Cosp(A,B) in the figure legends. The128
overall impact of nonconservative processes on LWA is estimated as the residual of the bud-129
get. No further breakdown of the nonconservative processes will be attempted. The residual130
also contains analysis errors (sampling errors, non-QG effects, truncation errors, etc.), which131
will not be quantified in this study. As we will see, the residual has nontrivial contributions132
to the LWA budget.133
3 Results134
3.1 Climatology of local wave activity in the boreal winter135
Figure 2a shows the December-January-February climatology (1979-2015) of the col-136
umn averaged LWA 〈A∗〉 cos φ (shades) and zonal wind 〈u〉 cos φ (contours). 〈A∗〉 cos φ is large137
at the poleward flanks of barotropic zonal jets over the storm track regions. Note that this seasonal-138
mean LWA includes contributions from both stationary and transient eddies. Decomposition139
of LWA and its fluxes into stationary and transient eddy contributions is not straightforward140
partly because the definition of LWA [(1)] requires a reference state based on the Lagrangian141
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mean that does not commute with the Eulerian time mean. Nevertheless, having confirmed that142
the time mean of qREF does not deviate much from qREF computed from the Eulerian time mean143
of q at midlatitudes (See SI sections 6-7), we estimate the stationary eddy component of LWA144
by applying (1) to the time mean of QGPV field, i.e., 〈A∗([q])〉 (Fig.2b). The peaks at the east145
of the Mongolian Pleateau and Norwegian Sea arise largely from topography-induced merid-146
ional excursion of the QGPV contours at the lowest level (z = 1 km).147
The climatology of transient component of LWA is computed as the difference between148
the total and the estimated stationary component of LWA (Fig.2c), i.e. [〈A∗(q)〉]−〈A∗([q])〉.149
Its longitudinal extent over the North Pacific is consistent with other common metrics of storm150
tracks [e.g. Chang et al., 2002 Fig.2]. Over the Atlantic, where the barotropic jet is tilted north-151
eastward, the LWA maxima are found at both flanks of the jet, namely, over Quebec and west-152
ern Europe.153
One may question whether a zonally symmetric reference state is suitable to analyze wave154
dynamics over the northeast-tilted Atlantic storm track. As a comparison, we show in Fig.2d155
the climatology of transient wave activity proposed by Plumb [1986] [his Eq. (2.20)], which156
is based on a zonally-varying basic state for small-amplitude waves. Our estimated transient157
LWA (Fig.2c) has a spatial structure consistent with Plumb’s transient wave activity (Fig.2d),158
which implies that the obtained LWA structure, especially the relative minimum over the At-159
lantic, is not a consequence of a particular choice of the reference state. Rather, it is an in-160
trinsic property of wave activity that it is suppressed along the jet axis, as derived in HN16.161
This comparison also demonstrates the strength of the finite-amplitude LWA formalism: its162
magnitude is well-constrained by the wind field and much smoother, while the small-amplitude163
wave activity is plagued with spuriously large values in regions where the gradient of time-164
mean QGPV vanishes.165
3.2 Climatology of wave activity budgets166
As a first estimate of how the LWA budget is maintained, Fig.3 shows the climatology167
of the terms on the RHS of (5). The positive (poleward) low-level meridional heat flux (Fig.3c)168
is the major source of wave activity for both storm tracks. Over the North Pacific, its peaks169
are localized to the storm track entrance – from the Sea of Japan to the Kuroshio extension170
– and along the Alaska current. In contrast, large values of low-level poleward heat flux span171
over the majority of the Atlantic north of 40◦N. Much of this signal is due to the quasi-stationary172
zonal asymmetry in the low-level potential temperature forced by the underlying SST distri-173
bution and the associated meridional flow.174
Over the Atlantic, the low-level poleward heat flux is largely balanced by the zonal di-175
vergence of the LWA flux (blue in Fig.3a). Note that the region with large low-level heat flux176
(Fig.3c) is marked by relatively weak LWA (Fig.2a), indicating that LWA is moved away from177
the source region by the zonal flux into the downstream regions of convergence over Europe178
(red in Fig.3a). The meridional momentum flux convergence (blue in Fig.3b) also partially com-179
pensates the zonal flux convergence on the southern flank of the storm track, but the degree180
of this compensation is relatively small.181
Over the Pacific, there is considerable spatial variation in the balance of RHS terms of182
(5). In the source regions (e.g. the Sea of Japan and the Alaska current) a strong cancellation183
is still observed between the low-level poleward heat flux (Fig.3c) and the zonal divergence184
of the LWA flux (Fig.3a) as in the Atlantic. In the Central Pacific, where the low-level pole-185
ward heat flux is relatively weak, the zonal convergence of the LWA flux as a gain, as well186
as the meridional convergence of the eddy momentum flux associated with the equatorward187
radiation of LWA (Fig.3b) and the negative residual (Fig.3d) as losses, all contribute to the LWA188
budget. The magnitude of the residual is quite significant, being comparable to or greater than189
that of the momentum flux convergence. Assuming that the negative residual represents a lin-190
ear damping of LWA, the ratio of the area averaged residual to that of the column LWA gives191
a mean damping timescale of ∼ 12 days. Since this is much shorter than the typical radiative192
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damping timescale in the troposphere (∼30 days), it may be related to Ekman damping or en-193
strophy dissipation (mixing) by wave breaking.194
The residual (Fig.3d) over the continental regions is largely negative, which suggests that195
friction over land surfaces promotes the demise of LWA. Exceptions are found on the lee side196
of mountains (e.g. the Mongolian Plateau and the Rockies). Over the oceans, the residual is197
generally weakly negative. However, there are pockets of weakly positive values over the At-198
lantic Ocean and the Norwegian Sea, hinting that the underlying warm ocean is providing ap-199
preciable diabatic sources of LWA (primarily through latent heat of condensation) that over-200
ride the effect of surface damping. We suspect that this partial cancellation causes the aver-201
age residual less negative over the Atlantic than over the Pacific.202
3.3 Synoptic to intraseasonal variability203
Much of the weather-related LWA variability occurs over synoptic to intraseasonal timescales,204
which is filtered out in the seasonal mean in the foregoing analysis. To delineate wave activ-205
ity budget on these timescales, we compute the cospectra of LWA tendency [the LHS of (4)]206
with each term on the RHS and compare it with the power spectrum of LWA tendency (Fig.4).207
Note that the sum of the cospectra resembles the power spectrum. The solid lines indicate the208
budget over a regular square box domain including both land and ocean grids, while the shad-209
ing indicates the budget change if the domain shrinks to oceanic regions only (Appendix B210
and SI section 8).211
Comparing Figs.4a and 4b, one sees that the variance in the Atlantic is more than twice212
larger than that in the Pacific but the spectral shapes are largely similar between the two re-213
gions. The power spectrum of LWA tendency maximizes around 0.15-0.25 cpd (4-7 days); over214
half of that is explained by the in-phase components of the zonal LWA flux convergence (blue)215
with a similar spectral shape. Cospectra with the meridional eddy momentum flux divergence216
(cyan) are an order of magnitude smaller than those with the zonal flux convergence (blue)217
for both regions, indicating that the LWA budget is dominated by the zonal passage of syn-218
optic weather systems in and out of the regions. Even though the low-level poleward heat flux219
dominates the LWA budget in the seasonal mean (Fig.2), it plays only a minor role in the LWA220
tendency except at low frequencies (< 0.05 cpd, red). The heat flux cospectrum over the At-221
lantic is broader than that over the Pacific, which is more right-shewed. Somewhat surprisingly,222
the residual (green) contributes to the LWA tendency much more than the heat flux over syn-223
optic timescales. Its contribution is comparable to the zonal advective flux convergence (blue)224
over the land-oceanic domain, while a bit smaller over oceanic domain. This suggests that there225
is significant diabatic forcing of wave activity in both regions.226
Given that the meridional eddy momentum flux divergence accounts for only a small frac-227
tion of LWA tendency, to what extent do LWA and the zonal wind covary through this term228
[(3) and (4)]? Figures 4c and 4d compare the cospectra of the meridional eddy momentum flux229
convergence with the LWA tendency (blue), with the zonal wind tendency (green), the cospec-230
tra of LWA tendency and the zonal wind deceleration (red), and the power spectrum of the zonal231
wind tendency (black) for the two storm track regions. The power spectrum of the zonal wind232
tendency peaks at around 0.05 cpd in both regions. Over the Pacific, the close alignment of233
blue, green, and black curves on synoptic timescales indicates that the convergence of the merid-234
ional momentum flux accomplishes barotropic conversion between 〈A∗〉 and 〈u〉 as suggested235
by (3) and (4), and it accounts for most of the zonal wind tendency. This is not the case with236
the Atlantic, where the meridional eddy momentum flux divergence has a negative contribu-237
tion to the LWA tendency and it accounts for much less fraction of zonal wind tendency. In-238
terestingly, the cospectra between the LWA tendency and the zonal wind deceleration (red) are239
positive throughout the frequency domain shown and deviate significantly from the other three240
curves at higher frequencies in both regions, particularly when the domain includes only oceanic241
regions: that is, the negative covariation of LWA and zonal wind is robust regardless of the242
contribution from the meridional eddy momentum flux divergence. Such covariation is espe-243
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cially robust at the diffluent regions of the jets (See SI section 9). The implication is that the244
processes other than the meridional eddy momentum flux divergence, such as the zonal ad-245
vective flux convergence, maintain negative covariation of LWA and the zonal wind.246
Regression of LWA on various climate oscillation indices resembles the leading patterns247
of zonal wind distributions corresponding to the particular oscillation (See SI section 10). How-248
ever, the weak correlations suggest that exchange between LWA and the zonal winds is not249
the main mechanism governing such variability.250
4 Summary251
There has hitherto been no formal attempt to close the local angular momentum-wave252
activity budget for the midlatitude atmosphere. We have applied the column budget of finite-253
amplitude LWA, a density of angular pseudomomentum, to the winter storm tracks over the254
North Pacific and the North Atlantic using meteorological data. The regional budget of LWA255
is simpler than the budget of small-amplitude wave activity. The latter is often hard to close256
without large nonlinear terms and only the wave activity fluxes (but not the wave activity it-257
self) are used for diagnosis in this context [Plumb, 1985; Takaya and Nakamura, 2001; Chang,258
2001].259
Complementary to EKE, LWA maximizes where waves attain greatest cross-stream dis-260
placement of QGPV and weak zonal wind speeds (Fig.1). We have proposed an approximate261
partitioning of LWA into transient and stationary eddy contributions by decomposing the QGPV262
fields used in (1). The estimated transient eddy LWA climatology has spatial distribution con-263
sistent with that of Plumb’s small-amplitude transient wave activity [Plumb, 1986] with zonally-264
asymmetric basic state.265
The climatology of seasonal-mean LWA flux convergence gives a first estimate of how266
the LWA budget is maintained. In both storm track regions, the low-level poleward heat flux267
is a major source of LWA. The balancing mechanisms are nevertheless different. Over the At-268
lantic the loss is primarily through the zonal divergence. Over the Pacific, the LWA input by269
the heat flux is localized to the western and northeastern ends of the ocean basin, where it is270
largely balanced by the zonal LWA flux divergence. However, over the Central Pacific, the flux271
convergence is largely balanced by the loss through the residual (damping).272
On synoptic timescales, the area-averaged LWA tendency is closely associated with the273
convergence of the zonal LWA flux in both regions, corresponding to the transient passage of274
weather systems. However the residual term representing the net diabatic source has a com-275
parable magnitude whereas the low-level poleward heat flux plays a relatively small role. Whilst276
LWA and the zonal wind covary negatively at all scales, the barotropic conversion of zonal277
momentum plays only a limited role for this and is only significant over the Pacific.278
Future studies will compare interannual variability of LWA and fluxes over the two oceans.279
Also, since the net nonconservative sources and sinks of LWA are only inferred from the resid-280
ual of the budget in this study, more direct assessment of the diabatic sources of LWA in re-281
lation to the storm track maintenance [Hoskins and Valdes, 1990] will be performed with the282
aid of general circulation models. Nevertheless, this work provides a promising framework to283
delineate tendency of longitudinally localized wave activity with arbitrary amplitudes, which284
is potentially useful for comparing wave responses in models in climate change scenarios.285
A: Abbreviation in the flux equations313
The expressions for the column-averaged zonal fluxes in (3)-(4) are:314
Fu ≡⟨uREFue + u2
e
⟩(A.1)
315
Gu ≡ 〈 f ve cos φ〉 −1a∂ 〈ψ〉
∂λ(A.2)
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120°E 150°E 180° 150°W 120°W
5.0
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90
30°N
40°N
50°N
60°N
70°N
120°E 150°E 180° 150°W 120°W
5.0
5.05.25.2
5.2
5.3
5.3
5.3
5.5
5.5
5.5
5.75.8
5.8
Shaded: <LWA>cosφ | Contours: Z500 | 2010/12/16
0
15
30
45
60
75
90
30°N
40°N
50°N
60°N
70°N
120°E 150°E 180° 150°W 120°W
5.0
5.05.25.2
5.2
5.3
5.3
5.3
5.5
5.5
5.5
5.75.8
5.8
Shaded: <LWA>cosφ | Contours: Z500 | 2010/12/17
0
15
30
45
60
75
90
Figure 1. Left column: Daily mean of 〈A∗〉 cos φ (shaded) and 500hPa geopotential height in km (contour)
over the Pacific. The four panels correspond to, from top down, December 14, 15, 16 and 17, 2010, respec-
tively. Right column: Same as left except that the shading indicates 〈EKE〉. Here EKE= 12 u′2 + v′2, where u
and v are the zonal and meridional wind velocities, whereas the overbar and prime denote the zonal mean and
departure from it, respectively. The red box indicates where a blocking event happens.
286
287
288
289
290
FA ≡⟨uREF A∗
⟩−
acos φ
⟨∫ ∆φ
0ueqe cos(φ + φ′)dφ′
⟩+
12
⟨v2
e − u2e −
RH
e−κz/Hθ2e
∂θ/∂z
⟩(A.3)
See SI sections 3-5 for further details.316
B: Computation of area-weighted average317
The land-ocean mask is retrieved from the ERA-Interim database as an invariant, with318
the same resolution (i.e. 1.5◦×1.5◦) as the other variables. The latitude range for area-weighted319
average for both oceans are [30◦, 75◦N]. The longitude range of Pacific is chosen to be [120◦E, 240◦E]320
and that of Atlantic is chosen to be [270◦W, 30◦E]. The results for land-ocean domain (solid321
lines in Fig.4) include all grid-points within the regions mentioned above. The results for oceanic322
domain only (the bound of shades in Fig.4) include only oceanic grid-points based on the land-323
sea mask. See SI section 8 for further sensitivity analysis.324
C: Treatment of data325
The budget terms in (3)-(5) are computed from 6-hourly temperature and wind fields on326
37 pressure levels from the European Centre for Medium-Range Weather Forecasts ERA-Interim327
datasets [Dee et al., 2011] for 1979-2015 with a horizontal resolution of 1.5◦×1.5◦. Data are328
–8–
Confidential manuscript submitted to Geophysical Research Letters
30°N
40°N
50°N
60°N
70°N
30°N
40°N
50°N
60°N
70°N
60°E 60°E120°E 180° 120°W 60°W 0°60°E 60°E0
0
5 5
5
10
10
10
1015 15
15
20
2025
Climatology: DJF Seasonal mean <LWA> cosφ | Contour: <U>cosφ
8
14
20
26
32
38
44
50
30°N
40°N
50°N
60°N
70°N
30°N
40°N
50°N
60°N
70°N
60°E 60°E120°E 180° 120°W 60°W 0°60°E 60°E0
0
5 5
5
10
10
10
1015 15
15
20
2025
Climatology: <LWA> of DJF Seasonal mean QGPV | Contour: <U>cosφ
0
3
6
9
12
15
18
21
30°N
40°N
50°N
60°N
70°N
30°N
40°N
50°N
60°N
70°N
60°E 60°E120°E 180° 120°W 60°W 0°60°E 60°E0
0
5 5
5
10
10
10
1015 15
15
20
2025
Climatology: Estimated transient component of <LWA> cosφ | Contour: <U>cosφ
4
9
13
18
22
27
31
30°N
40°N
50°N
60°N
70°N
30°N
40°N
50°N
60°N
70°N
60°E 60°E120°E 180° 120°W 60°W 0°60°E 60°E0
0
5 5
5
10
10
10
1015 15
15
20
2025
Climatology: Plumb (1986) transient wave activity for DJF | Contour: <U>cosφ
8
14
20
26
32
38
44
50
Figure 2. (Shaded) Seasonal (DJF) climatology of (a) 〈A∗〉 cos φ, (b) estimated stationary-eddy component
of 〈A∗〉 cos φ in DJF, (c) estimated transient component of 〈A∗〉 cos φ taken as the difference of (a) and (b),
and (d) small-amplitude quasigeostrophic transient LWA computed with a zonally varying reference state
based on Plumb [1986]. In (d) a weak horizontal smoothing is applied to the seasonal-mean QGPV field
before computing the horizontal gradient. The color scale in (d) has been adjusted to be comparable to that
of (a)-(c) for comparison. Values exceeding the color range are indicated in brown. Contours indicate the
barotropic zonal wind 〈u〉. Both quantities have the unit [ms−1]. Regions masked by the gray stipples, where
the topography is higher than 1 km (i.e. zs > 1 km), have been excluded from analysis.
291
292
293
294
295
296
297
298
first interpolated vertically onto 49 equally spaced (1 km) pseudo-height levels as in NS10.329
The interpolated fields are then used to compute QGPV, wave activity and the fluxes at each330
pseudoheight level as functions of longitude and latitude. Evaluation of ue and θe involves com-331
putation of the reference state (uREF , θREF) from qREF . See SI section 4 for the details. Sim-332
ilar to WN15, the column average [(2)] in the discrete data is performed over all the ‘interior’333
(i.e. not at the boundaries) points. The lower boundary condition at z = 0 is replaced by the334
weighted mean values on the two lowest levels (z = 0 and 1 km), which will be referred to335
as ‘low level’ hereafter. See SI section 5 for the evaluation of the low-level meridional heat336
flux and the sensitivity to the choice of the lower boundary conditions.337
Acknowledgments338
This research is supported by NSF Grant AGS-1563307. The ECMWF ERA-Interim data [Dee339
et al., 2011] were downloaded from http://apps.ecmwf.int/datasets/data/interim-full-daily/levtype=sfc/.340
Helpful comments by two anonymous reviewers are gratefully acknowledged.341
–9–
Confidential manuscript submitted to Geophysical Research Letters
30°N
40°N
50°N
60°N
70°N
30°N
40°N
50°N
60°N
70°N
60°E 60°E120°E 180° 120°W 60°W 0°60°E 60°E
(a) Zonal LWA Flux Convergence [x 10**{-5} m/s**2]
-21
-14
-7
0
7
14
21
30°N
40°N
50°N
60°N
70°N
30°N
40°N
50°N
60°N
70°N
60°E 60°E120°E 180° 120°W 60°W 0°60°E 60°E
(b) Meridional Eddy Momentum Flux Divergence [x 10**{-5} m/s**2]
-21
-14
-7
0
7
14
21
30°N
40°N
50°N
60°N
70°N
30°N
40°N
50°N
60°N
70°N
60°E 60°E120°E 180° 120°W 60°W 0°60°E 60°E
(c) Low Level Meridional Heat Flux [x 10**{-5} m/s**2]
-21
-14
-7
0
7
14
21
30°N
40°N
50°N
60°N
70°N
30°N
40°N
50°N
60°N
70°N
60°E 60°E120°E 180° 120°W 60°W 0°60°E 60°E
(d) Residual [x 10**{-5} m/s**2]
-21
-14
-7
0
7
14
21
Figure 3. The December-February climatology (ERA-Interim 1979-2015) of vertical column-average (with
cosine weighting) of (a) zonal LWA flux convergence, (b) meridional momentum flux divergence, (c) low-
level meridional heat flux, and (d) residual [see (5)]. The color scales for (b) to (f) are the same, with values
greater than the maximum given by the color bar is displayed in brown, while that less than the minimum
given by the color bar is displayed in green.
299
300
301
302
303
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0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.91
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Cosp
ect
ral densi
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1e 9
Pacific 1979-2015 (Nov 15 - March 15)
(a)
PowerSpec(d<LWA>/dt)
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cycle per day
(d)
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