Sponge layer feedbacks in middleatmosphere models
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Shepherd, T. G., Semeniuk, K. and Koshyk, J. N. (1996)
Sponge layer feedbacks in middle-atmosphere models.
Journal of Geophysical Research, 101 (D18). pp. 2344723464. ISSN 0148-0227 doi: 10.1029/96JD01994 Available at
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JOURNAL OF GEOPHYSICAL
RESEARCH, VOL. 101, NO. D18, PAGES 23,447-23,464, OCTOBER 27, 1996
Sponge layer feedbacks in middle-atmosphere models
T. G. Shepherd,K. Semeniuk,and J. N. Koshyk
Departmentof Physics,Universityof Toronto,Toronto,Ontario, Canada
Abstract. Middle-atmospheremodelscommonlyemploy a spongelayer in the
upper portion of their domain. It is shownthat the relaxationalnature of the
spongeallowsit to coupleto the dynamicsat lowerlevelsin an artificialmanner. In
particular,the long-termzonallysymmetricresponseto an imposedextratropical
local forceor diabatic heatingis shownto inducea drag forcein the spongethat
modifiesthe responseexpectedfrom the "downwardcontrol"argumentsof Haynes
et al. [1991]. In the caseof an imposedlocal forcethe spongeacts to divert a
fraction of the mean meridional mass flux upward, which for realistic parameter
valuesis approximatelyequal to exp(-Az/H), whereAz is the distancebetween
the forcingregionand the spongelayer and H is the densityscaleheight. This
sponge-induced
upper cell causestemperaturechangesthat, just belowthe sponge
layer, are of comparablemagnitude to thosejust below the forcing region. In
the caseof an imposedlocal diabatic heating, the spongeinducesa meridional
circulationextendingthrough the entire depth of the atmosphere.This circulation
causestemperaturechangesthat, just below the spongelayer, are of oppositesign
and comparablein magnitudeto those at the heating region. In both cases,the
sponge-induced
temperaturechangesare essentiallyindependentof the heightof the
imposedforceor diabatic heating, providedthe latter is located outsidethe sponge,
but decreaseexponentiallyas one movesdown from the sponge.Thus the effect of
the spongecan be made arbitrarily small at a given altitude by placing the sponge
sufficientlyhigh; e.g., its effect on temperaturestwo scaleheightsbelow is roughly
at the 10% level, providedthe imposedforce or diabatic heating is located outside
the sponge. When, however,an imposedforce is applied within the spongelayer
(a highlyplausiblesituationfor parameterizedmesospheric
gravity-wavedrag),
its effect is almost entirely nullified by the sponge-layerfeedbackand its expected
impact on temperatures below largely fails to materialize. Simulations using a
middle-atmospheregeneral circulation model are described,which demonstrate
that this sponge-layerfeedbackcan be a significanteffectin parameterregimesof
physicalinterest. Zonallysymmetric(two dimensional)middle-atmosphere
models
commonlyemploya Rayleighdrag throughoutthe model domain. It is shownthat
the long-termzonally symmetricresponseto an imposedextratropical local force
or diabatic heating, in this case,is noticeablymodifiedfrom that expectedfrom
downward control, even for a very weak drag coefficient.
Haynes et al. argued that the long-term mean response
in the meridional circulation or temperature is exclu-
1. Introduction
sively "downward."(In this paper, "heating"is underHayneset al. [1991]haveconsidered
the zonallysym- stoodto includeboth positiveand negativevalues.)In
metric responseof the middle atmosphereto an imposed particular, an equal and opposite force is induced in
extratropical quasi-steadyforce F, conceivedto be as- the boundarylayer througha slight adjustmentof the
sociatedwith the upward propagationand breaking of surfacewinds, which leadsto a steadymean meridional
Rossbyand gravity waves. Assumingthat the diabatic
heating acts to relax temperaturesback to someradiatively determined temperature field and that there is
a relaxational frictional boundary layer at the ground,
circulationextendingbetweenthe surfaceand the level
of the imposedforce. In the verticalbranchesof this circulation, temperatures are pulled away from radiative
equilibrium by adiabatic heating.
It is also instructive to consider the zonally symmet-
Copyright 1996 by the American Geophysical Union.
Paper number 96JD01994.
0148-0227/96/ 96JD-01994509.00
ric responseto an imposed extratropical quasi-steady
diabatic heating Q, conceivedto be associatedwith a
changein the radiatively determinedtemperature due
to changesin concentrationof radiatively active con23,447
23,448
SHEPHERD ET AL.: SPONGE LAYER FEEDBACKS
stituents. AlthoughHayneset al. [1991]did not ex- F or diabaticheatingQ. (The caseof a diffusivesponge
plicitly consider this problem, their arguments would
imply that the long-term mean responsein this case
is exclusivelylocal, with a modification of the temperature in the vicinity of the imposedheating and no mean
layer is briefly consideredin section 6 and is found to
give a similar response.)The problemis first studied
through idealized numerical simulations in section 2.
The results suggesta departure from the "downward
meridionalcirculation. (This thought experimentwas controlled"response,including significanttemperature
discussed
by Mcintyre [1992,section6]; seealsoHolton changesabove the level of the imposed force or diaet al. [1995,section3].)
batic heating. In section3 an asymptotic analysisof
Of course, any realistic middle-atmospheremodel is the long-term responseis performed,extendingthe resubject to forcing and diabatic heating throughout its sults of Haynes et al. [1991];this analysisprovides
domain. The point of the thought experiments de- information on parameter dependences. Two experscribed above is to identify the expected responseto iments with a middle-atmospheregeneral circulation
a local changein forcing or diabatic heating. Evidently, model are described in section 4, which demonstrate
this responsemust involve other changesin forcing or that sponge-layerfeedbacksin middle-atmospheremoddiabatic heating in the long-term limit, in order for els can be important, in practice. The caseof a uniform
the model to reach a steady state balance. If these Rayleigh drag, relevant to many two-dimensionalmodinducedchangesare complex (involving,for example, els, is consideredin section 5; a noticeable departure
O(1) changesin the wave-inducedforcing), then the from the downward controlled responseis also found in
imposedF or Q cannot really be regardedas given and this case,evenfor a very weak drag coefficient.The rea simplecause-and-effect
understandingof the response sults are summarizedin section6, and someconclusions
cannot be obtained. A key assumptionof the scenario are drawn in section 7.
proposedby Hayneset al. [1991]is that suchcomplex feedbacksare second-ordereffects and the dominant responseinvolves induced changesin two model
componentsthat are relaxational and therefore easy to
understand,namely, boundary layer frictional drag and
radiative heating. Both kinds of induced changesare
highly plausibleon physicalgrounds.
Yet many middle-atmosphere models have mechanical drag processesin addition to boundary layer friction that
are also relaxational.
Two-dimensional
mod-
els commonlyinclude a Rayleigh drag throughout the
model domain, and three-dimensionalmodelscommonly
includea Rayleigh drag or diffusivespongelayer in the
upper portion of the model domain. In both casesthe
drag acts primarily as a surrogate for missinggravitywave drag, in order to produce a reasonableclimate.
Yet its responseto perturbations can be expected to be
quite differentfrom that of gravity-wavedrag, in that a
Rayleigh or diffusivedrag is relaxational and will thus
(like a spring)react with whateverstrengthis required
to opposean applied force. In contrast, the strength
of middle-atmospheregravity-wave drag is determined
by the tropospheric gravity-wave sources;changesin
local wind conditionswill changewhere the drag is deposited,but not its total amount. (There could be a
small feedbackon the troposphericflow and therefore on
the strength of the gravity-wave sources,but for middleatmospheredrag this shouldbe a second-order
effect.)
Therefore it is quite possible, as noted by Haynes et
al. [1991],that middle-atmosphere
modelswith a relaxational drag could respondto an imposedlocal force
or diabatic heating in an unphysicalmanner.
The purpose of this paper is to explore this possibility. In particular, we considerthe long-term zonally
symmetric responseof a middle-atmospheremodel with
a Rayleigh-dragspongelayer (in additionto a frictional
boundarylayer) to an imposedextratropicallocalforce
2. Idealized
Numerical
Solutions
We wish to considerthe problem of the zonally sym-
metric, balancedresponseto an imposed(switchon)
extratropical local forceor diabatic heating, in the presence of a lower frictional boundary layer, an upper
spongelayer, and Newtonian coolingtoward a reference
state. For mathematical tractability it is advantageous
to considerthe limit of small perturbations, with the
reference
stateat rest. Hayneset al. [1991]haveshown
that such an idealization captures the essentialnature
of the dynamical responsein the extratropical middle
atmosphere. (The tropics have a different character;
see,e.g., Dunkerton[1989].)
We thus considerthe zonally averagedprimitive equations, linearized about a state of rest, under the assumption that the zonal flow remainsin geostrophicand hy-
drostaticbalance[see,e.g., Andrewset al., 1987]:
Ou
Ot 2•laV
- F- r(z)u,
(1)
OT
Ot
+ Sw = Q -aT,
2f•l•OU
/20T
Oz_
-aHR (1-/•2)•
0/•'
(2)
(3)
(•[(1
1/2V
] +•oo
a•zz
(•(pow)
0/•
-/•2)
- O. (4)
In the above,u, v, and w are the zonal, meridional, and
verticalvelocities,respectively;
po(z) and To(z) are referenceprofilesof densityand temperature,respectively;
T is the departure of the temperature from the referenceprofile;$ = dTo/dz + nTo/H is a measureof the
staticstability,wheren = R/cp; R is the gasconstant,
and Cpis the specificheat at constantpressure;H is
SHEPHERD ET AL.: SPONGE LAYER FEEDBACKS
23,449
the (constant)densityscaleheight;f• and a are the ro- (westward)forceF < 0, with Q = 0 (Figure 1). The
tation rate and radius of the Earth, respectively;z is a initial (transient)response
is shownin Figure la, the
log-pressure
vertical coordinate;and p = sin•b,where sponge-free
response
after I yearis shownin Figure lb,
•bis latitude. The nondivergence
condition(4) allows and the responseafter I year in the presenceof the
the introduction of a meridional mass stream function
spongeis shownin Figure lc. We considerthe sponge!b defined by
free, downwardcontrolledresponse(Figure lb) to be
the true response,and differencesbetweenFigures lb
I
0•b
1
v- ,
w. (5) and lc to be a spurioussponge-layerfeedback.
p0(1-/_•2)1/20Z
poa
The initial response(Figure la) is as predictedby
We have included a force term in the zonal momen-
the theory of Eliassen[1951]: the force acts locally
to decelerate the atmosphere but also drives a pole-
tum equation(1) consisting
of an imposed(switchon) ward mean meridional circulation which returns equaforceper unit massF togetherwith a Rayleighdrag torward, partly above but mainly below the forcing
with a coefficientr(z) that is zero exceptin the lower
frictionalboundarylayer and the upper spongelayer.
In a similarway we haveincludedadiabatic heatingin
the temperatureequation(2) consistingof an imposed
(switchon) heatingQ togetherwith NewtonJancooling
on a timescale1•c•; makingQ • 0 in a certain region
is thus equivalentto changingthe radiative equilibrium
temperaturethere. It is appropriateto identify (v, w)
in (1)-(5) with the transformedEulerian meancirculation (•*, t•*) in the zonally averagedequationsof motion [Andrewset al., 1987]. In the steadystate limit,
(v, w) can alsobe identifiedwith the diabatic circula-
region (Figure la, top). This meridionalcirculation
tion. The mass stream function • is taken to be zero
at •b -- 0ø, •b -- 90ø, and at the top and bottom of the
grows in magnitude, the latter must correspondingly
causesadiabatic heating that leadsto a quadrupolepat-
tern of temperaturetendenciesOT/Ot (Figure la, middle). The net effectis to spreadthe zonalwind tendenciesOu/Ot (Figure la, bottom) out in sucha way that
the combined wind and temperature tendencies are in
thermal wind balance(3). The responseis elliptic and
therefore nonzero everywhere, but it is most pronounced
in the vicinity of the forcing.
As the temperature perturbation grows in time, the
c•T term in (2) becomesincreasinglyimportant. Since
c•T will have the same sign as OT/Ot, as the former
decrease,with the sum of the two balancing-Sw (the
model.(As shownby Haynesand Shepherd
[1989],this mean meridional circulation being essentiallyprescribed,
lower boundary condition involves an approximation, on thesetimescales),until eventuallyOT/Ot shutsoff.
but its effectsare unimportant for middle-atmosphere This local saturation of the responseoccurs on a timeapplications.)
scaleof order 1/a and leavesa quasi-steadylocal balWe solve(1)-(5) numericallyoverthe northernhemi- ance between adiabatic heating and diabatic heating.
sphereusingfinite differenceson a height-latitudegrid. (If the forcingregionis "tall" then the saturationtime-
Parameter valuesare To -- 240 K, a --- 1/(5days),
scale may be considerablylonger; see Haynes et al.
H - 7 km, N •' -- 10-4 s-2, po(0)-- 1.225kg m-g, and [1991].) As describedby Haynes et al. [1991],the
• -- 2•r d-1. The modeltop is placedat z - 80 km, meridional cells then "burrow" both upward and downand the imposedforce and diabatic heating are Gaus- ward, away from the forcingregion, with the massflux
sian distributions in z and •b centered at 40 km and of the lower cell slowly increasing at the expense of
45øN, with half widths of Az - 5 km and A•b -- 10ø. the upper cell. The cells eventually run into the upTheir maximumstrengthsare, respectively,-10 m s-1 per and lower boundaries. In the presence of relaxd-1 and I K d-1. The verticalgridspacing
is 0.4 km, ational drag processesnear those boundaries,the negawhile the horizontal grid spacing is 0.9ø. The plane- tive zonal wind accelerationdriven by the equatorward
tary boundarylayer and spongelayer (when applied) meridional circulation inducespositive drag forces.
are represented
by a Rayleighdrag with r(z) givenby
When the drag is purely at the lower boundary, as
envisaged
by Hayneset al. [1991],the upper cell dies
away,leavingonly the lowercell (Figure lb, top). The
1
65km<z<80km
__
2 days
1 - cos[•r(z- 60)/5]
60km<z<
__
4 days
=
0
__
6 days
__
65km
__
60km
associatedtemperature changeis located exclusivelybetween the ground and the forcing region, in a dipole
pattern (Figure lb, middle), and is maintainedby the
5km<z<
I + cos(•rz/5)
__
0km<z<
5km.
meridional circulation. Becauseof the decreasingdensity with height, a constant mass flux translates into
an exponentially decreasingtemperature changeas one
movesdown from the forcinglevel. The positivemeridional temperature gradient below the forcing region
(6)
The numericalsolutionsare carried forward for I year. leads,through (3), to a negativechangein the zonal
The model has not yet reacheda steady state by then, wind both below and above the forcing region, flanked
but the resultsare indicativeof the long-termresponse. by positive values, with no vertical shear above the forcWe first consider the case of a localized
switch-on
ing (Figurelb, bottom).
23,450
SHEPHERD ET AL.' SPONGE LAYER FEEDBACKS
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Figure 1. Numericalsolutionsof (1)-(5) for an imposednegativeGaussianforceF < 0 centered
at 40 km and 45øN,with a maximumstrengthof -10 m s-1 d-1 The modellid is at 80 km,
andthesponge
begins
at60kin,ramping
uptoa constant
value
•)fr - 1/(2days)
between
65
and 80 kin; densityscaleheightH - 7 kin; and a - 1/(Sdays). (a) Instantaneous
response,
(b) modelresponse
after I yearwith no spongelayer,and (c) modelresponse
after I year with
the spongelayer. Shownfor eachresponseare the meridionalmassstreamfunction•h (top), the
temperatureperturbationT (middle),andthe zonalwindperturbationu (bottom). In Figurela,
the tendenciescqT/c?t
(middle)and cqu/c?t
(bottom) are shown.Contourintervalsare as follows'
Figurela (top), 0.5 kg m-1 s-i; Figureslb and lc (top), 2.0 kg m-1 s-i; Figurela (middle),
0.1 K d-i; Figureslb and lc (middle),2.0 K; Figurela (bottom),0.4 m s-1 d-i; Figureslb
and lc (bottom),20 m s-1.
When, however,the relaxational drag is alsoexerted
through an upper spongelayer, a positive force is inducedat the top as well as at the bottom of the model,
and the upper cell can persistindefinitely. The long-
force is imposedsufficientlyfar away from the sponge,
about three scale heights away, that the upper cell is
term response consists of meridional cells both above
verticallyelongatedquadrupole(Figurelc, middle);the
and below the forcing region, although in this casethe
constantmassflux abovethe forcinglevel translatesinto
practicallyinvisible(Figure lc, top). Yet its effectis
clearly seenin the temperature change,which is now a
SHEPHERD
ET AL.: SPONGE LAYER FEEDBACKS
an exponentiallyincreasingtemperature changeas one
movesup. The zonal wind changeis similar to the previous casebelow the forcing region but decreaseswith
height abovethe forcingregion (Figure lc, bottom).
Another way to understandthe responsein this case
is that the downwardcontrolledresponse(Figure lb)
impliesnegativezonalwind accelerations
in the sponge
layer, whichinducepositivedrag forces.The combined
responseis thus consistentwith downwardcontrol, so
longas oneconsiders
the inducedpositivesponge-drag
forcetogetherwith the imposednegativeforceF.
In termsof temperature,the sponge-layerfeedbackis
comparablein magnitudeto the presumablyreal, downwardcontrolledresponse.The temperaturechanges
below the level of the imposedforce are, in this case,essentiallyunaffectedby the sponge(compareFigureslb
and lc, middle), but if onepresumesthat all portionsof
the modelatmospherebelowthe spongeare of physical
interest (this is usually the criterion that dictates the
positionof the sponge)then onemust concludethat the
spongeinducesspurioustemperature and zonal wind ef-
fectsthat are quantitativelysignificant.
We next consider the case of a localized switch-on
23,451
case the two-cell meridional circulation can and does
persist(Figure2c, top); moreover,it is quite broad. It
might be thought that the breadth of this circulation
is a transient effect, that the circulation would even-
tually collapseonto the latitude band of the heating
region. This is not the case,however,as can be seen
from the fact that there is a strongmeridionalflowin
Figure2c (top) in both the spongelayer and the frictional boundarylayer, extendingright to the equator.
In fact,it is clearthat if thetransientcirculation
of Figure2b (top)isremoved
fromFigure2c(top),thenwhat
is left is a pair of cellsextendingthroughthe depthof
the modelatmosphere,with essentiallyverticalflow in
the drag-freeregions.Thesecellspersistindefinitely,
beingdrivenby the dragforcethat hasspunup in the
spongelayer, and there is nothingto forcethem to be
meridionally confined.
Despitethe breadth of this sponge-induced
meridional circulation,the temperaturechangeassociated
with it is in this caselargelyconfinedto its ascending
branch. The combined
temperatureresponse
(Figure
2c, middle)is a superposition
of localwarmingin the
vicinityof the imposeddiabaticheating,essentially
unchanged
fromthe sponge-free
case(Figure2b, middle),
(positive)diabaticheatingQ > 0, with F = 0 (Figure 2). The initial response
(Figure2a) is againpre- togetherwith a sponge-induced
coolingthat decreases
dictedby the theoryof Eliassen[1951]: the heating exponentially
asonemovesdownfromthe sponge.The
actslocallyto warm the atmosphere(Figure 2a, mid- maximumvalueof this sponge-induced
coolingis comdle) but also drivesa rising mean meridionalcircula- parableto the maximumvalueof the warmingbelow.
tion which returns downward on either side of the heatThereforethe presenceof an upper spongelayer is
ing region(Figure2a, top). This meridionalcirculation seento significantlyaffect the zonally symmetricrecausesCoriolisforcesthat lead to a quadrupolepattern
sponseto an imposed extratropical local force or di-
of zonalwind tendencies
Ou/Ot (Figure2a, bottom). abaticheating.It doesthis by allowinga dragforceto
The net effect is to spreadthe temperaturetendencies developin the sponge,which then drivesa circulation
OT/Ot (Figure2a, middle)out in sucha way that the extendingthrough the entire depth of the model. Alcombinedwind and temperature tendenciesare in ther- thoughthe sponge-layer
feedbackis attenuatedby the
mal wind balance.
densitydecrease
with height,it stillhasa significant
im-
As describedabove, the relaxationalheating term
actsto saturatethe temperatureresponsein the vicinity
of the imposeddiabatic heatingon a timescaleof order
1/c•, and the two meridionalcellsthen burrowupward
anddownwardawayfromthe regionof imposedheating,
pact on the temperatureresponse
just belowthe sponge,
even when the imposedforce or diabatic heating is located about three scaleheightsaway from the sponge.
The asymptotic analysisin the next sectionshowsthat
this is alwaysthe case, no matter how far away the
spongeis from the imposedforce or diabatic heating.
It shouldalso be noted that the sponge-layerfeedback
is not latitudinally confinedto the regionof the imposed
forceor diabatic heating. This effect, which is another
departurefrom downwardcontrol, is particularly evidentin the caseof the imposeddiabaticheating,where
the sponge-freecirculation vanishes.
The parameterdependences
of this sponge-layer
feedbackwill be quantifiedby meansof an asymptoticanalysis in the next section. Before doing so, we consider
onemoreidealizednumericalsolution,motivatedby the
until they hit the upper and lower boundaries. When
the drag is purelyat the lowerboundary(Figure 2b),
then any induceddrag force cannot be balancedelsewherein the atmospheric
column(as is requiredunder
steadystate conditions)and the circulationmust eventually collapse. In fact, in this casethere is somecir-
culationremainingafteroneyear (Figure2b, top), but
this is a transienteffect.The temperatureresponse
has
alreadyconfineditselfto the vicinityof the imposeddiabaticheating(Figure2b, middle),producinga dipole
barotropiczonalwind changeabove(Figure 2b, bottom).
In contrast,whenthe relaxationaldragis alsoexerted
throughan upperspongelayer(Figure2c), the Coriolis
forcesimposedat the top andthe bottomare of oppositesignwithineachcolumnandthe induceddragforces
can thereforebalanceeach other indefinitely. In this
followingconsiderations.
The availableevidence[e.g.,
Holton,1982;Garciaand Solomon,1985;Shine,1989]
suggeststhat most of the middle-atmosphere
gravitywave drag is imposed in the upper mesosphereand
mesopauseregions. It is generally accepted that this
drag is crucialfor determiningthe temperaturestruc-
23,452
SHEPHERDET AL.' SPONGE LAYER FEEDBACKS
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I
,
I IllIll Illl I,
.!./,,•----,,
••...'•._..'j
I:///
%
•
I
.....
-...
,,
'
I IIIII • I I I:
":
\ I I
6•0 '
LATITUDE
II II IIllII II IIllll•
iII1'
! '-- "\ ! !
-,
' 3•0 '
LATITUDE
L•TITUDE
60
,. ....
20
.:
',.,
,,,
i
6'0
,
LATITUDE
Figure 2. Sameas in Figure 1, exceptfor an imposedpositivediabaticheatingwith maximum
strengthof I K d-1 . In Figures2a-2c (top) the meridionalcellsare ascending
at 45øN.Contour
intervals
areasfollows:
Figure2a (top),0.1kgm-1 s-l; Figures
2band2c(top),0.02kgm-1
s-i; Figure2a (middle),0.04K d-i; Figures2b and2c (middle),0.4 K; Figure2a (bottom),0.05
m s-1 d-i; Figures2b and 2c (bottom),2.0 m s-1.
to an imposeddragforceis modifiedwhenthe
ture in the mesosphere
[e.g., Andrewset al., 1987], response
possiblydown to the middle stratospherein polar re- dragis imposedwithin the spongelayeritself.
This caseis shownin Figure 3, whichcorresponds
to
gions[Hayneset al., 1991; Garcia and Boville,1994].
However, in most middle-atmospheregeneral circula- FigureI but with the imposedforcecenteredat 73 km,
tion models the lid is no higher than the mesopause
and any spongelayer is therefore acting in the upper
mesosphere. This implies that gravity-wave drag parameterization schemesin such models will be applying
the bulk of their drag within the spongelayer. It is
thereforeinterestingto considerthe extent to whichthe
in the heart of the spongelayer. As before,the instantaneousresponse
is shownin Figure3a, the sponge-free
long-termresponse
is shownin Figure3b, andthe longterm response
in the presenceof the spongeis shownin
Figure3c. By comparingFigures3b and 3c, it is evident that the spongecompletelydistortsthe long-term
SHEPHERD ET AL.' SPONGE LAYER FEEDBACKS
23,453
b
I,
88
I
I , I
I
88
I
'
I
I
I
80
,
_j
I
i
,
60
rE40
,.
N
i
20
0
3•0 '
0
' 6'0 '
' 90
3i0
0
LATITUDE
i
i
!
60
,
0
, 3[0
'
60
LATITUOE
LATITUDE
LATITUDE
LATITUOE
80
88
68
rE40
20
0
0
i
,
3•0
i
i
6•0
,
,
go
LATITUOE
80
80
'
,
..,.
...
I
,
,
t
i
i
.:
,.
........
,:
,:
u
I
30
'
'
6•0
LATITUOE
0
0
30
LATITUOE
3'0
,
,
6•0
90
LATITUOE
Figure 3. Sameasin Figure1, exceptfor an imposed
forcelocatedwithinthe sponge
layer.
Contourintervalsare as follows:Figure3a (top), 0.01 kg m-• s-•; Figures3b and 3c (top),
0.025kg m-• s-•; Figure3a (middle),0.1 K d-•; Figures3b and3c (middle),1.5K; Figure3a
(bottom),
0.3m s-• d-•; Figures
3band3c(bottom),
20m s-•.
response.The masscirculation(Figures3b and 3c, top)
is weakenedin overall strength by about a factor of 5
and is spreadover the entire hemisphere,insteadof being confineddirectly belowthe force. The temperature
response(Figures3b and 3c, middle) is likewiseweakened,by a factorof 5 to 10 in its maximumvalues,and is
meridionallybroadenedand vertically shortened.This
suggests
that the response
to the imposedforcehasbeen
almostcompletelynullified by the sponge;in addition,
3. Asymptotic Solutions
In this sectionwe considerasymptotic solutionsof
(1)-(5) in the long-timelimit, followingHayneset aL
[1991].For consistency
with Hayneset al., wesetz = 0
at the level of the imposed force or diabatic heating.
The upper boundaryis then at zt > 0, and the lower
boundaryis at Zo < 0. The spongeand the planetary
boundarylayer are representedwith a Rayleigh-drag
givenby r(z) = •7t(z- zs)+ ',•((z- Zo)/H),
a spurious mass circulation has developed that forces coefficient
(weak)temperaturechangesoverall latitudes.
where5(.) is the Dirac delta functionand 7/(.) is the
23,454
SHEPHERD ET AL.: SPONGE LAYER FEEDBACKS
Heavisidestep functionand where 0 < zs < zt. The ing terms representthe infinite seriesof responsesof
fieldsare decomposed
into a Hough-mode
representa- the spongeto the u, inducedby the planetaryboundtion (seeappendix),in whichcase(A1)-(A4) maybe ary layer and vice versa. (A more revealingform of
combinedinto the singleequation
(10), whichshowsthis infiniteseriesof responses,
is ob-
tainedbyexpanding
thefactor[1- rl•e-(Zs-Zo)/H]
-1 in
•e-(•-•o)/•.)
0 •)_Po
1•zz
0(poOU
enN
22 0 r)
• n 4fi2a
Forreasonable
valuesof the parameters,
•ezø/Hwill
__
e.
N2F.
_2•apoH
e.R Oz
0(poQ.)
(7)
4•2a 2
'
be extremely small for a force imposedmany scale
heightsawayfrom the lowerboundary;hencethe terms
involving• will be negligiblefor practicalpurposesand
the steadystateresponse
will be givento goodapprox-
whereN 2 • RS/H is takento be constant.
Wefirstconsider
thec•e ofanimposed
forceF. (z,t) imation by
= f,•(t)J(z/H), with Q, -O. Hayneset al. [1991,
equation(3.21)] showedthat the intermediate-timeresponseconsists
of upwardand downwardpropagating
u. •
f.b.
I1+•e
(z-zS)/H
0<z<z8
(11)
o•
ez/H+ rle(z-z•)/H,Zo< z < O.
adjustments.
After a time t • b,z•/aH, the upward
Someof the parameterdependences
of r/are explored
propagatingadjustmentencounters
the spongelayer
and inducesa "spongeforce"that causesa downward in Figure 4, where it is seenthat for reasonablevalues
propagatingadjustmentjust like the originalone;the of the model parameters,r/•0 -0.5. In fact, it is easily
resultingsponge-induced
modificationto the zonalwind seenfrom (9) that r/ •0 -1 in the limit bn?/a >> 1,
•n• takes the form
8
f,b, e(•_•)/•
un • • 2a
this limit being of somerelevanceto middle-atmosphere
models. In short, r/ can be expected to be an order
unity, negative number.
The sponge-layerfeedbackthereforereducesthe zonal
wind changenearly to zero just below the sponge,with
the effectexponentiallydecreasingas one movesdown.
This explainsthe resultsseenin Figureslb and lc (bottom). The corresponding
temperature changecan be
inferredfrom (A3); in the steadystate limit, neglecting
the terms involving •,
b"z• [ Ha2 •/•
•erfc•-(t+•)[4b,(•;1)]z•]]
},(8)
wherez• - z- 2zs,b, = -e,N2H2/4fi2a2, and
1_
• i+A 1- (1-•
1•) 2exp[A(zs
- zt)/H] '
with A = [1+ (4b,•/a)]1/2. The latitudinaldistribu-
f.N2H
2{tie
(z-z•)/H
, 0<z<Zs
T.• 2•aRa
ez/H
+•e(z-z•)/H,
zo
<z<O.
tion of this spongeforce is not the same as that of the
imposedforcef,, since• dependson n. When the orig(12)
inal downwardpropagatingadjustmentencountersthe The magnitudeof the (spurious)sponge-induced
templanetary boundarylayer, an upward propagatingad- peraturechangejust belowthe spongeis seento be comwhichis givenby Hayneset al. parableto the (presumablyreal) temperaturechange
justment u,b is induced,
[1991,equation(5.4)]. In the presenceof both upper just below the imposedforce; both decreaseexponenand lower boundariesthe long-term responsethen con- tially in z as one movesdown. This explainsthe results
sistsof an infinite seriesof responsesfrom each bound- seenin Figureslb and lc (middle).
ary to the adjustmentsinduced by the other. In the
To determine the effect on the meridional mass cirsteady state limit we obtain
culation,notethat in the steadystatelimit, (A2) and
O<z<Zs
Un •
f,b, {1+•)e
(z-z•)/H
+•eZO/H
+•)•e(Z-Zs+Zo)/H,
a[1
- rl•e-(z.-zo)/H]
eZ/H
+rle(Z_Z•)/H
+•ezo/H
+rl•e_(Z•_zo)/H
, z0<z<0
(10)
where• = (a/b,?)-l. The part ofu, in (10) associated (A5) imply•bn- -(poaa/S)Tn. The ez/H factorsin
directlywith the imposedforcedoesnot containr/or T, seenin (12) are thereforeremovedwhenit comesto
•. Termsthat involver/but not • representthe sponge •b,, and we find meridionalcellsof oppositeorientation
responseto the un induced by the imposedforce, with- aboveand belowthe forcing,with a ratio in strength
out any feedbackfrom the planetary boundarylayer. givenby (againignoring
thesmallcorrections
involving
Termsthat involve• but not r/are the responseof the
planetaryboundarylayer to this sameu,, without any
feedbackfromthe spongelayer. (Note that with r/- 0,
(10) reduces
as expectedto the resultgivenby Haynes
massflux in upper cell
rle-z•/ H
(13)
mass flux in lower cell
et al. [1991,equations
(3.21)and (5.4)].) The remain1 + tie-z•/H '
SHEPHERD
ET AL.' SPONGE
LAYER
When the spongeis severalscaleheightsawayfrom the
forcinglevel, its effecton the masscirculationis thus
FEEDBACKS
i
0.0
23,455
t
I
I
•
I
i
seento be small. This explains the results seenin Fig-0.3
ures lb and lc (top). Yet even the weak upper cell
is seento have significanteffectson the temperature
structurewithin one or two scaleheightsof the sponge.
Hayneset al. [1991,p. 668a]did, in fact, brieflyconsider the case where the "surface" drag was imposed
abovethe level of the forcing. In that casethey found
a reductionin the strength of the lower cell of order
+
+
+
+
+
++
-0.8
++
+++++++++++++++
e-zS/Hforbnff/a>>1, whichis consistent
with (13).
We now consider the case of an imposed diabatic
0
heating,Qn(z,t) = qn7t(t)5(z/H), with F• = 0. The
analysisproceedsmuch as above. The sponge-induced
fieldsbehaveas if they originatedfrom a switch-onforcing at the base of the sponge;for intermediatetimes,
•
1•6
24
32
0.
beforefeedbackfrom the planetary boundary layer, the
b
sponge-induced
modificationto the zonalwindtakesthe
form
q,b,f•aR (z-zs)/H
u,, ,• r• N2H2a
$
b,•z•
Ha2
•/2
xerfc{-(t
+ ) [4b(b
+ ]
-0.8'
In the steady state limit we find
q,•b,•2f•aR
Un• N2H2o•(1
_ rl•e_(Z•_Zo)/H
)
-1
.0
0
I
2.5
•
I
5.0
•
I
7.5
10.0
1+rl
e(z-z•)/H
0<z<Zs
x
(15)
Fie
(:•-:•)/H+ rl•e-(:•-:•ø)/H Zo< z < 0
of r/ [definedin (9)] on n and
As above,the terms involving•, which reflect the feed- Figure 4. Dependence
back from the planetary boundary layer, are negligible •/a, with fixed parameters(a) •/a - 2.5 and (b) n 2. In both cases,zt - zs - 17.5 km and H - 7 kin.
for adiabatic heating imposedmany scaleheightsaway
from the lower boundary and the long-term responseis
then given, to good approximation,by
Figure 2c, top). That the sponge-induced
responsehas
a different latitudinal structure than the imposed heating is again explained by the fact that r/ depends on
q,•b,•2f•aR
{1+Fie
(:•-:•8)/H
0<z<z,
Un
• N2H2
a rle(z-z•)/HZo
<z<0
n.
(16)
This explains the results seen in Figures 2b and 2c
(bottom). The corresponding
steadystate temperature
changeis
Tn•0q,•7e(•-•)/H
q,
+ --5(z/H).
4. Experiments With a Middle-Atmosphere General Circulation Model
In this section, sponge-layerfeedbacksare examined
in a developmentalversionof the first-generationCanamodel (CMAM). The modelis
As in the caseof the imposedforce, the sponge-induced dian middle-atmosphere
temperature changeis oppositelysignedto the temper- basedon a developmentalversionof the third-generation
ature changeat the level of the imposedheating and Canadian Climate Centre (CCC) general circulation
CCC GCM is deachievesa comparablemagnitude just below the sponge model(GCM); the second-generation
(17)
(allowingfor integrationoverthe 5 function,of course). scribedby McFarlane et al. [1992]. The CMAM is
by Shepherd
[1995],and a full descripThis explains the large sponge-inducedcooling above brieflydescribed
the level of imposedheating seenin Figure 2c (middle). The meridionalmasscirculationin this caseis
entirely due to the spongeand may be calculatedfrom
• - -(poaa/S)T,; it extendsthrough the depth of
the atmospherewith a verticallyuniformmassflux (see
tion is providedby S.R. Beagleyet al. (The radiativedynamicalclimatologyof the first-generationCanadian
Middle Atmosphere Model, submitted to AtmosphereOcean,1996). Triangular spectraltruncation at wavenumber 32 (T32) and 50 vertical levels betweenthe
23,456
SHEPHERD
g::---L' ,, /,,
ET AL.' SPONGE
ground and 0.001 mbar define the model resolution,
with an approximate vertical resolution of 3 km above
the tropopause. The spongelayer consistsof Rayleigh
..::•?';•-•':••:•..
.010• "'- ....
dragwith a maximumrelaxationcoefficient
of 1.0 d-•,
0.10
acting on the horizontal wind above 0.01 mbar.
One major discrepancybetweenCMAM and observations is that the model overestimatesthe magnitude of
the southern hemisphere wintertime mesosphericzonal
jet by almost a factor of 2. This problem is com-
64
1
•-•
100
•
000
.....::....
0
LAYER FEEDBACKS
30s
32
16
associatedwith the inadequate representation of meso-
sphericgravity-wavedrag (GWD) effects. Although
somemesosphericdrag is generatedover the Antarctic
plateauin CMAM by the orographicGWD parameterizationof McFarlane[1987],thisis insufficient
to correct
0
60s
mon to many middle-atmosphere
models[e.g.,Hamilton et al., 1995; Boville, 1995]and is at least partly
90s
Latitude
the excessive zonal winds.
• ....
'.:'"'
. ......
L:Z;.c;.•;.4
,- .--.,
•0.10;..-0•
Figure 5a showsthe temporally and zona!!yaveraged
sponge-layerplus planetary boundary layer zonal momentum forcing obtained from the model in the stan-
.,o-[
,,,-"ø
-ø ;;',,,
,. '..'---'.-'
,' /1 64•.
o ......."-.....-'"
dard configurationfor a singleJune-July-August(JJA)
season(the controlrun). In an attempt to reducethe
excessive
zonal winds associatedwith this model (not
shown), a secondversionof CMAM was developed.
This versionincludesan additional forcing that can be
considereda crude surrogate for missing mesospheric
gravity-wavedrag (the wavedrag run). The additional
lOO
•
........_-.,:.
0
:)08
008
1•
o
908
LaLiLude
forcing consistsof Rayleigh drag F, which is activated
only when the local horizontal wind speedin the model
exceeds
100m s-• andwhichhasa dampingcoefficient
proportional to the excess.
Figure 5b showsthe sponge-layerplus planetary boun-
dary layer forcing for the wave drag run together with
the additional Rayleigh drag F, temporally and zonally
averagedoverthe sameJJA season.Comparisonof Figure 5a to 5b indicates that F has a maximum amplitude
97
81
of about15 m s-• d-• at approximately
60øSand 0.1
64 ß
I-d,
4õ •
mbar. The differencebetweenthe fields shownin Figures 5a and 5b is displayedin Figure 5c, which demonstrates that the drag on the zonal wind associatedwith
F (negative-valued,
dashedcontours)is accompanied
by
a decreasein the magnitude of the sponge-layerforcing
(positive-valued,
solidcontours).Thus, comparedwith
16
o
9os
the control run, a positive force is induced within the
spongelayer in the wave drag run.
This change in the sponge-layerdrag is consistent
with the argumentsof section2. From (1) the steady
LaLiLude
state zonal momentum balance in the model sponge
layer can be approximately expressedas
Figure 5. (a) Zonallyand temporallyaveragedsponge-
-2Ft/•v - F•,
(18)
layer plus planetary boundary layer zonal momentum
forcing from the Canadian middle-atmospheremodel whereFs is the forcingprovidedby the sponge.When
(CMAM) controlrun for a singleJune-July-August
sea- F is initially applied in the model, a transient picture
son. (b) Same as Figure 5a, but for a run including
surrogatemesosphericgravity-wavedrag centerednear not unlike that of Figure la (top) emerges,addingan
(60øS,0.1 mbar). (c) The differencebetweenthe fields equatorwardcomponentto the meridionalwind (i.e.,
in Figures 5a and 5b, i.e., Figure 5b minus Figure 5a. Av > 0) abovethe forcingregion. As this meridional
Contour intervals are 5 m s-• d-•.
wind changeworksits way up into the spongelayer, Fs
SHEPHERD ET AL.' SPONGE LAYER FEEDBACKS
act, (19) providesa reasonableapproximationto the
zonally averagedthermodynamic equation in CMAM.
Subtractingthe equationscorresponding
to (19) for the
respectiveexperimentsdiscussedabove and seasonally
.OOl
.OlO
,
0.10
averaging gives
-
1.0
,
T
lO
+
-
(20)
whereATi and ATy denotethe differencein temperature betweenthe control and wave drag runs at the
beginning(June1) and end (August31) of the simula-
lOO
{
lOOO
0
30S
60S
90S
Latitude
Figure 6. Zonally and temporally averagedtemperature difference
23,457
between
the CMAM
control
run and a
run includingsurrogatemesosphericgravity-wavedrag
for the June-July-August season.Contour interval is 5
K.
adjusts to smaller negative values. Thus, as shown in
Figure 5c, AFs > 0 accordingto (18) (note that/• < 0
in the southernhemisphere).
The zonally and JJA temporally averagedtemperature differenceAT betweenthe control and wave drag
runs is shownin Figure 6. Figure 6 is similar to Figure
lc (middle), althoughthe meridionalasymmetryin the
quadrupoleof the former is stronger. Possiblereasons
for the differenceinclude the use of a sophisticatedradiative coolingparameterizationin CMAM (for which
radiative relaxation times vary with latitude and altitude) as well as the existenceof secondaryfeedbacksin
CMAM, such as differencesin the amount of parameterized orographic GWD between the control and wave
drag runs. The latter effect turns out to play a significant role in the perturbed heating experiment considered later in this section.
The quadrupolepattern of Figure 6 is similar to those
seenin somepreviousGCM studies. For example, Mc-
Farlane[1987,Figure 13] studiedthe effectsof an orographic GWD parameterization on the Canadian Climate Centre first-generationGCM and found that the
additionof a localizedlowerstratosphericdrag resulted
in a quadrupoletemperature anomaly comparedwith a
run without this drag. The shapeof the quadrupolepattern suggeststhat this was a spongefeedbackand not a
transient response;the spongein his caseconsistedof a
Rayleigh "roof" drag applied at the uppermost model
level.
tion, respectively;r - 92 days is the length of the JJA
season;and the anglebracketsdenotethe seasonalaverage. SinceQs is essentiallyprescribedfor CMAM (climatologicalozonedistributionsare usedin the model),
it doesnot appearin (20). To establishthat Figure 6
is indicativeof the steady state behaviorof CMAM, it
is sufficientto showthat the dominantbalancein (20)
is betweenthe secondand third terms or, equivalently,
that either the secondor third term in (20) is much
larger than the first. (Note that it is not requiredthat
the full thermodynamicbalance(19) be closeto steady
state.)
Figure 7a showsthe first term in (20) and Figure 7b
showsthe third term in (20) ascalculatedfrom CMAM,
both terms zonally averagedand shownin kelvins per
day. Comparisonof Figure 7a to 7b indicatesthat the
term on the right-hand side of (20) is about I order
of magnitude larger than the first term on the lefthand side. This confirmsthat the upper portion of the
quadrupolepattern seenin Figure 6 is indeedassociated
with the sponge-layer
feedbackseenin Figure 5c.
A secondexperimentconsistsof perturbing CMAM
with a sourceof diabatic heating (the perturbedheating run). The heating perturbation consistsof a zonally symmetricGaussianfunctioncenteredon (60øS,60
km), with a maximum amplitude of 10 K d-1. The
model is restarted at the beginningof May and integrated through to the end of August. The first month
is discardedfor the purposeof comparisonwith the control run described earlier.
Figure 8a showsthe imposedheating perturbation,
and Figure 8b showsthe differencein temperature between the control run and the perturbed heating run.
The regionin the vicinity of the heating perturbation
showsincreasedtemperatures,as expected,while a region of reducedtemperaturesis seenabove, extending
well into the spongelayer. This aspectof the response
is similar to the responseseenin Figure 2c (middle).
In order to verify that the temperature differenceseen However,significantdifferencesare also apparent.
in Figure 6 reflectsthe steady state behavior of CMAM,
Before discussingthose differences,we first establish
it is usefulto consider(2) in the form
that the responseseen in Figure 8b reflects a steady
state responseof CMAM. The approximate relation
0---•
-•-SW-- QsqrQir,
(19) (20) againapplies,providedthe imposedheatingperturbation is added to the right-hand side. Figure 9 is
where Q8 and Qir representsolar heating and infrared analogousto Figure 7, and shows that the difference
cooling, respectively. For the special case of Newto- in total heating (Figure 9b) has valuesabout i order
nian cooling,Qir = -aT as in (2). Althoughnot ex- of magnitude larger than the differencein temperature
OT
23,458
SHEPHERD ET AL ß SPONGE. LAYER FEEDBACKS
.001••.•
010•.0
• 0.10
1.0
10
100
1000
0
LaLiLude
LaLiLude
.OOl
97
. O01
.OlO
81
.010
• O.lO
64•.
[• O.lO
48 •"
• 1.0
lO
3;8
r•
lOO
16
1.o
o_ 97
o.o ', ,'
i
0
i
I
I
i
30S
i
60S
i
i
81
64 •
-
48 •
5.0
10
32 •
16
100
0.0
0.0
1000
,'
1000
0
0
90S
30S
LaLiLude
0
90S
60S
LaLiLude
Figure 7. Zonally averagedfields appearingin (20),
Figure 8. (a) Diabaticheatingperturbation
imposed
(a) (ATy - ATi)/•, contourintervalof 0.1 K d-i, and in the CMAM perturbedheatingrun, contourinterval
(b) (AQir), contourintervalof I K d-1. Differences of 2 K d-i, and(b) zonally
andtemporally
averaged
betweenthe CMAM controlrun and the wavedrag run
are denotedby A.
temperature differencebetweenthe CMAM control run
and the perturbedheatingrun, contourintervalof 2.5
K. The temporalaverage
is overa singleJune-July-
August season.
tendency(Figure9a). This confirmsthat the response
seenin Figure 8b is a steady state response.
Yet it is clear that the sponge-layerfeedbackis not
the only feedbackin this case. In particular, the temperature increaseis spread quite broadly and attains
its maximum value over the pole. The differencein
sponge-layerdrag betweenthe two runs, shownin Figure 10a, is positiveacrossthe sponge,insteadof having
the dipolestructure(positiveto the north and negative
to the south) that one would expect from the heating
perturbation alone. It turns out that these features
are associatedwith changesin the structureof the parameterizedorographicGWD, which are shownin Figure 10b. These changesinduce their own response,includingtheir ownsponge-layer
feedback,whichtogether
with that from the heating perturbation contribute to
the temperature responseseenin Figure 8b. Such "secondary feedbacks"serveto remind us that the response
to an imposedextratropical local force or diabatic heating in a real middle-atmospheremodel may be significantly more complex than that describedin section 2.
Nevertheless,sponge-layerfeedbackscan be expectedto
be part of the response.
5. Case of a Uniform Rayleigh Drag
In sections 2-4 we have considered
the case of a ver-
tically confinedupper spongelayer, which is the situation
of most
relevance
to three-dimensional
middle-
atmosphere models. However, it is also of interest
to considerthe case of a background Rayleigh drag
throughout the domain, as is commonly used in two-
dimensional
middle-atmosphere
models[e.g.,Garciaand
Solomon,1985; Garcia et al., 1992]. Suchmodelsare
SHEPHERD
ET AL.: SPONGE LAYER FEEDBACKS
23,459
.oo!
.010 .'
81
• 0.10
•
•
1.0
•0.'••- b
•.,;
"'•--:n48
10
3;8
• lOO
o10
0.10 -
-64
m
1.0 -
-48
•
10-
-16
100-
1000
1000
0
-32 •
30S
60S
I
0
90S
I
I
I
I
30S
I
60S
0
90S
97
97
.001
OlOb
4'
1.oi
30•
I
Latitude
Latitude
0
I
60s
81
81
64 •.
64 m
48 •'
48 •
16
16
o
o
90S
o
Latitude
30S
60S
90S
Latitude
Figure 9. Zonallyaveragedfields,(a) (ATy - ATi)/•,
Figure 10. Zonally and temporally averaged difcontourintervalof 0.1 K d-•, and (b) (AQ), contour ferencesin (a) sponge-layerdrag and (b) orographic
interval of I K d -•
ß
Differences between the CMAM
control run and the perturbed heating run are denoted
by A.
still widely usedfor climate changeand impact assessment studies, becauseof their reduced computational
cost. The impact of Rayleighdrag on the long-termresponseto an imposedforceor diabatic heatinghas been
previouslyexaminedby Garcia[1987],and Hayneset al.
[1991]havesuggested
that the useof a Rayleighdrag
could lead to an underestimation
of downward
control.
Figure 11 shows the result of an idealized numeri-
gravity-wavedrag betweenthe CMAM controlrun and
the perturbed heating run. Contour interval is 2.5 m
s-1 d-1.
(Figurelb) to be the true response,and differences
betweenFigures lb and 11 to be a spuriousRayleigh-drag
feedback.ComparingFigures 11 and lb, it is clear that
the meridional mass circulation departs from a downward controlledregime in this case (it is spreadout
meridionally,particularly toward lower latitudes) and
that the total masstransport has been reduced by the
Rayleigh drag. The temperature responseis likewise
distorted and is nonzero above the level of the imposed
force. As for the zonal wind response,it is reducedby
cal calculationcorresponding
to Figure lc (namely,an
imposedlocal force centeredat 40 km), but with the
sponge-layerdrag replaced by a weak uniform back- about a factor of 2.
ground Rayleigh drag imposed throughout the model
Figure 12 showsthe samefields as in Figure 11, but
domain,with r - 1/(100days). (This is the valueused for the case of an imposed local diabatic heating as
by Garcia et al. [1992].) The instantaneous
response in Figure 2. Comparing Figures 12 and 2b, we again
and the long-term responsein the absenceof Rayleigh find the responseto depart from a downwardcontrolled
drag(with onlythe planetaryboundarylayer)are given regime in this case: there is a meridional mass circulaas beforeby Figures la and lb, respectively.As in sec- tion extendingover most of the model atmosphere.The
tion 2, we consider the downward controlled response temperature responseis not very different in terms of
23,460
SHEPHERDET AL.' SPONGELAYER FEEDBACKS
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Figure 11. Same as in Figure lc (caseof imposed
force),exceptwith the spongelayer replacedby a uniform Rayleigh drag throughout the depth of the atmosphere,with r = 1/(100 days). Contourintervalsare as
Figure 12. Same as in Figure 2c (caseof imposed
diabaticheating),exceptwith the spongelayerreplaced
by a uniformRayleighdragthroughoutthe depthof the
atmosphere,
with r = 1/(100 days). Contourintervals
in Figure lc.
are as in Figure 2c.
the maximumvalueof the warming,but it is spreadout
In thecase
oftheswitch-on
force
Fn(z,t) - fn•(t)'
longtimethe
latitudinallysothat the zonalwind response
is reduced 6(z/H) withQ• -0, aftera sufficiently
responseis given by
by about 20%.
We nowtry to understandtheseeffectsquantitatively
f•b•
1_
e(lq=X)z/2
H
by meansof an asymptoticanalysisasin section3. We
2a
A
assumer < a, whichis appropriatefor two-dimensional
middle-atmosphere
models.In this caseit is convenient
to ignorethe boundariesaltogether. We can still use
the approachof Hayneset al. [1991],thoughnotethat
it fails as r -• a. (The propagatingcharacterof the wherethe minussignin the :F is usedfor z > 0 and the
forz < 0, A- [1+ (4bnr/a)]«
> I asbefore,
solutionsdisappearswhenr - a, in whichcasethe time plussign
and
bn
bn(a
-r)/a.
This
has
the
steady
statelimit
dependence
is the samefor all z, namely,1 -e-at.)
xerfc{(t:F
z,]«},
(21)
SHEPHERDET AL.: SPONGE LAYER FEEDBACKS
23,461
doesbelow. This explains the resultsseenin Figures 2b
(middle)and 12 (middle).
6. Summary
with associatedtemperature change
1- A
Middle-atmosphere models commonly employ a spo-
nge layer in the upper portion of their domain. One
-X)z/2H
fnN2H
2 2Ae(1
, z>0
purposeof the spongeis to absorb vertically propagat-
ing waves,thereby preventingspuriousreflectionsoff
Tn
•"2•aRa1+)•e(l+X)z/2H
z<0
Without Rayleigh drag, A - 1; with Rayleigh drag,
A > 1. Without Rayleighdrag, (23) impliesthat the
temperaturechangein steadystate is proportionalto
ez/n belowthe forceand is zeroabove.With Rayleigh
drag there is a more rapid decaybelowthe force,togetherwith a temperaturechangeabovethe forceof
oppositesign,decayingmoreslowlywith Izl than the
the model lid. In this respectthe spongecan be said to
act realistically,with no feedbackon the dynamicsbelow. Yet the spongeis generally also allowed to act on
the zonally symmetric part of the flow. In this respectit
acts primarily as a surrogate for missing gravity-wave
drag. The sponge-dragcoefficientcan, of course, be
tuned so that the total spongedrag is roughly comparable to the missinggravity-wavedrag, thus producing
a reasonable climate. However, the sensitivity of this
drag to model perturbationscan be expectedto be quite
different in the two cases. Whereas the total gravitywave drag is presumably determined by the strength
temperature
changebelow[cf. Garcia,1987,Figure1].
This explainsthe resultsseenin Figureslb (middle)
and 11 (middle). As before,the latitudinalprofileof
the Rayleigh-drageffectwill be differentfrom that of of the troposphericgravity-wavesources(the middlethe imposedforce, becauseA dependson n. (When atmosphere wind profiles only determining where the
A - 1, in contrast,the steady state responseis latitu- dragis deposited,not its total amount),the relaxational
dinallylocalized;this is part of downwardcontrol.)
nature of the spongeallowsit to coupleto the dynamics
In the caseof the switch-ondiabaticheatingQn(z, t) = at lower levels in an artificial manner.
qn7-l(t)5(z/H)with F• - 0, aftera sufficiently
longtime
This possibility, which was noted by Haynes et al.
the responseis given by
[1991],has been investigatedby consideringthe problem of the long-term zonally symmetric responseto an
U n •'•
imposed extratropical quasi-steady local force or diabatic heating, extending the analysis of Haynes et al.
, (24) by including an upper spongelayer in addition to the
lower frictional boundary layer. In the case of an imposed force the sponge-free, downward controlled rewhere as abovethe minus sign in the :• is usedfor z > 0 sponse consists of a steady meridional cell extending
and the plus sign for z < 0, and vice-versafor the +. from the surface up to the level of the imposed force,
This has the steady state limit
with temperature changesconfined below the forcing
level. However, the sponge acts to divert a fraction
1+ Xe(l_X)z/2H
z>0
qnb•2f•aR
2A
Un
"'•N2H2
a 1:21
--Xe(l+X)z/2H
Z<0'
'
with associatedtemperature change
of the mean meridional mass flux upward that, for
(25)realistic parameter values, is approximately equal to
exp(-Az/H), where Az is the distancebetweenthe
forcing region and the spongelayer and H is the density scaleheight. The effect on the temperature field
is much more drastic; temperature changesare induced
below the spongelayer that are comparablein magnitude to those found below the forcing region. In the
Tn• q__?_n
5(z/H),
z= 0
(26) caseof an imposeddiabatic heating, where the spongefree temperature responseis confinedto the vicinity of
the heatingregion,the spongeinducesa meridionalcir1-4AX2e(l+•X)z/2
H' z < 0.
culation extendingthrough the entire depth of the atWithout Rayleighdrag, (26) impliesthat the temper- mosphere.This circulationcausestemperaturechanges
ature changein steadystate is confinedto the level of belowthe spongelayer that are of oppositesign and
the imposeddiabatic heating. With Rayleigh drag the comparablein magnitude to those at the heating re5 function temperature change at z - 0 is accompa- gion.
The effectsdescribedabovemay be clearlyseenin the
nied by an oppositely signed temperature change extending aboveand below. The drag-inducedtempera- idealized numerical simulations presented in Figures 1
ture changedecaysmore slowlywith Izl abovethan it and 2 and havebeenexplainedby an asymptoticanaly-
1-41X2e(l_•X)z/2
H' z > 0
23,462
SHEPHERD ET AL.: SPONGE LAYER FEEDBACKS
sisof the steadystate behavior(section3). Anotherdeparture from the downward controlled response,which
is particularly evident in Figure 2, is the fact that the
spongeresponseis not as latitudinally confinedas is the
imposedforce or diabatic heating. This feature is also
accountedfor by the asymptotics, since the extent of
the sponge-layerfeedbackdependson the spatial scale
of the imposedforce or diabatic heating.
Having demonstratedthe existenceof a sponge-layer
•,
--......
,, •:',....,!
feedback, it must be emphasized that its effect on temperatures and winds decreasesexponentially as one
movesdown from the sponge. Thus the effect of the
spongecan be made arbitrarily small, at a given alti-
•
[
[
i
i
,
•
'
LATITUOE
tude, by placingthe spongesufficientlyhigh; e.g., its effect on temperaturestwo scaleheightsbelowthe sponge
•
,
is roughlyat the 10%level(i.e., e-2 • 0.1). However,
this statement applies only when the imposed force or
diabatic heating is located outside the sponge.
When an imposed force is located within the spo-
:o
ß' -,
..
'•!•'-•'"'I •"
.
T
:
•-
/
.
_2•': ......
•
... ,,,:•:•.,.•,,:••'•
ngelayer (a highlyplausiblesituationfor parameterized
mesospheric
gravity-wavedrag), the responsebelow is
severelydistortedfrom downwardcontrol(Figure3). In
this casethe force is nearly entirely absorbedwithin the
spongelayer, and what little remains of the mass circulation is spread out over the entire hemisphere. This
suggeststhat any parameterized force acting within a
model spongewill largely fail to achieve its expected
impact on temperatures below.
Some middle-atmosphere models employ a diffusive
rather than a Rayleigh-drag sponge layer. Although
diffusion is still relaxational, there is now a constraint
that the net drag over the sphere,on a givenlevel, must
vanish. To see whether this constraint has a qualitative effect on the response,we repeated the experiment
•
z - 60 km and z -
65 km to avalueof5
x 10• m •
[
,• ,
3'•
6'•
,?
,
90
LATZTUBE
I
i
80
i
.
60
!ifil/ ii, t
,,,'•,/
ß
20
!:
shownin Figure i (corresponding
to an imposedforce),
but with the Rayleigh spongedrag -ru replaced by a
horizontaldiffusion•V2u, with • rampingup between
ß"
;
!
,,
,..
... - ......
o
o
30
,,
60
90
L^TITUDE
s-•. (This corresponds
approximately
to the diffusion
Figure 13. Same as in Figure lc (caseof imposed
usedby Hack et al. [1994].)The preciseverticaldepen- force), exceptwith the Rayleighspongedrag replaced
denceof y above60 km is the sameas in (6). Figure 13 by a strong horizontal diffusion in the spongelayer.
showsthe responseand is to be compared with Figure
lc. Evidently, the sponge-layerfeedbackis qualitatively
Contour intervals are as in Figure lc.
the same in the two cases.
That the sponge-layerfeedbacksin middle-atmosphere sociatedeffectson the temperature. That the spurious
modelscan be important in parameterregimesof prac- temperaturechangeswill be comparablein magnitude,
tical interest is demonstrated in section 4, where some just belowthe sponge,to the supposedly
real changes
at
experimentswith a middle-atmosphere
generalcircula- the levelof the imposedforceor diabatic heatingcan be
tion model are described.
arguedfrom a simplescalinganalysisunderthe highly
assumption
[seeHayneset al., 1991,section7]
The existenceof this sponge-layerfeedbackreflects plausible
that
in
the
transient
stage,
w is roughlyindependentof
the highly nonlocalcharacterof the zonally symmetric
response
problem.As Hayneset al. [1991]haveshown, heightabovethe level of the imposedforceor diabatic
any localizedforce(or diabaticheating;seesection3) heating.
The principalfocusof this paper is on sponge-layer
will induce an atmosphericresponsethat propagatesup
thesebeingrelevantto manythree-dimensionto the top of the model. The zonal wind changein the feedbacks,
upper part of the model will then induce a changein al models. In contrast, two-dimensionalmiddle-atmosthe spongedrag that drivesa downwardcontrolledcir- pheremodelscommonlyemploya backgroundRayleigh
culation through the depth of the atmosphere,with as- drag through their entire model domain (sometimes
SHEPHERD ET AL.: SPONGE LAYER FEEDBACKS
23,463
augmentedwith a regionof increaseddrag at the top). distorted). In the caseof a uniform Rayleighdrag the
Althoughthisdragis generallymuchweakerthan a spo- responseis noticeably distorted throughout the region
nge drag, it alsooccursright in the regionsof interest. of interest.
Our results have implications for the placement of
The possibilityof a spuriousRayleigh-dragfeedbackin
suchmodels(a possibilityalsonoted by Hayneset al. model lids in three-dimensionalmiddle-atmospheregen[1991])is therefore
worthconsidering.
Thisproblemhas eral circulationmodels. Although direct observational
been studiedin section5, where it is shownthat even a evidenceis lacking, it is widely believed that mesoweakRayleighdrag(r = 1/(100days),compared
with a spheric gravity-wave drag is crucial for determining
[e.g.,AnNewtoniancoolingcoefficientof r• = 1/(5 days))leads the temperaturestructurein the mesosphere
to a distortion of the responseto an imposedextrat- drewset al., 1987],possiblydownto the middlestratoropicallocal forceor diabatic heating. The effectsare spherein polar regions[Hayneset al., 1991; Garcia
modeling
clearlyseenin Figures11 and 12 (whichare to be com- and Boville,1994]. Many middle-atmosphere
GWD paramparedwith Figureslb and 2b, respectively),and are groupsare implementingcomprehensive
eterization schemes,in order to try to cure the "cold
consistent
with the earlierresultsof Garcia[1987].
It shouldbe emphasizedthat the resultsof this pa- pole" problemsthat bedevil their models. If a signifiper apply only to the extratropical middle atmosphere. cantfraction(in a mass-weighted
sense)of this GWD is
In the tropics the downwardcontrol argumentsfail to depositedin the upper mesosphereand mesopausereapply[Hayneset al., 1991;Holtonet al., 1995],andthe gions,then the argumentsof this paper would suggest
mean circulationis dominatedby nonlinear,angular- that any spongelayer must be applied above, say, 100
momentum-conserving
meridional overturningin resp- km altitude (assumingthat a 10% error in the downonseto time-dependentradiative driving [Dunkerton, wellingwould be regardedas acceptable);sincea spo1989].The wayin whichthistropicalregimeconnects
to nge layer should itself probably be at least two scale
the downwardcontrolledextratropical regime remains heights deep, this would imply a model lid above 110
to be fully elucidatedand is an important area of cur- km. This is much higher than what is currently usedin
rent research.
most middle-atmospheregeneralcirculationmodels. Of
course,it may well be that the significantGWD occurs
7.
Conclusions
lower down; it may also be that models can get away
with damping only the non-zonal-meanpart of the flow
in their spongelayer. These questionsremain open at
the present time.
Strongfeedbacksfrom physicalparameterizationsare
problematical for climate models in two distinct ways.
First, when one is developinga climate model, it is important to eliminate model errors. Second, once one Appendix
has a climate model that is regarded as acceptable,an
The Hough-mode
decomposition
of the fields[Plumb,
important use of the model is to examine the climate
1982]
takes
the
form
change induced by natural or anthropogeniceffects.
Both activities involve examining the model's response
v- v(z,
w- w(z,
to perturbations that are under the modeler's control.
Clearly, it is essentialthat this responsebe physically
realistic. Since physical parameterizations are usually
•b-- • •bn(Z,
t)(1- p2)l/2Bn(p),
the least reliable aspectof a climate model, strongfeedbacks from those parameterizations can make the perU z
turbed responsehighly unreliable.
n
n
In the extratropical middle atmosphere the kinds of
perturbations discussedabove can nearly always be
F z
r(z,
QQ(z,
understood in terms of changesto the wave-induced
forcing F or the diabatic heating Q. We have shown
that the long-term zonally symmetric responseto such wherethe functions©n(p) and Bn(p) satisfy
changesincludes a strong feedback from model drag
processesof a relaxational character. The particular
examplesthat we have consideredconsist of an upper
n
n
n
n
n
d{1-p2
d[On(p)]}--enOn(P),
dp
p2dp
spongelayer (characteristicof many three-dimensional
d
models)and a spatiallyuniformRayleighdrag (characteristic of many two-dimensionalmodels). In the case
(listedin Haynes
of the spongelayer the spuriouscomponentof the resp- and enare the Hough-modeeigenvalues
onsehasclearlyidentifiablefeatures(unlessthe imposed et al. [1991,Table1]). Notethat en< 0 and lenl>> 1.
With this decomposition,(1)-(5) take the spectral
force or diabatic heating is applied within the sponge
layer itself, in which case the responseis completely form
dp[(1- p2)l/2Sn(p)
] - On(p),
23,464
SHEPHERD ET AL.' SPONGE LAYER FEEDBACKS
Hack, J.J., B.A. Boville, J.T. Kiehl, P.J. Rasch, and D.L.
Williamson, Climate statistics from the National Center for AtmosphericResearchCommunity Climate Model
OT.
CCM2, J. Geophys.
Res., 99, 20,785-20,813, 1994.
-- +
- ate,
(A2) Hamilton, K., R.J. Wilson, J.D. Mahlman, and L.J. Umscheid,Climatology of the SKYHI troposphere-stratosphere-mesospheregeneral circulation model, J.Atmos.Sci.,
=
(A3)
Oz
2flail'
52, 5-43, 1995.
Haynes, P.H., and T.G. Shepherd, The importance of sura 0
facepressurechangesin the responseof the atmosphereto
(A4)
v. + -po (pow.)- O,
zonally-symmetricthermal and mechanicalforcing. Quart.
J.Roy.Meteor.Soc., 115, 1181-1208, 1989.
1 0•b.
•b.
v. =
,
w. - --.
(AS) Haynes, P.H., C.J. Marks, M.E. Mcintyre, T.G. Shepherd,
Po Oz
poa
and K.P. Shine, On the "downward control" of extratropical diabatic circulations by eddy-induced mean zonal
forces, J.Atmos.Sci., •8, 651-678, 1991.
Acknowledgments.
This researchhas been supported
by the Canadian MAM project, through grants from the Holton, J.R., The role of gravity wave induced drag and
diffusion in the momentum budget of the mesosphere,
Natural Sciencesand EngineeringResearchCounciland the
J. Atmos.Sci., 39, 791-799, 1982.
AtmosphericEnvironment Serviceof Canada. K.S. acknowledgesreceipt of an Ontario graduate scholarship. The au- Holton, J.R., P.H. Haynes, M.E. Mcintyre, A.R. Douglass,
R.B. Rood, and L. Pfister, Stratosphere-troposphereexthors would like to thank the referees for helpful and conOt
structive
2fv. - F. - r(z)u.,
(A1)
comments.
References
Andrews, D.G., J.R. Holton, and C.B. Leovy, Middle AtmosphereDynamics, 489 pp., Academic, San Diego, Calif.,
1987.
Boville, B.A., Middle atmosphereversionof CCM2 (MACCM2): Annual cycleand interannualvariability, J. Geophys.Res., 100, 9017-9039, 1995.
Dunkerton, T.J., Nonlinear Hadley circulation driven by
asymmetric differential heating, J.Atmos.Sci., •6, 956974, 1989.
Eliassen,A., Slowthermally or frictionally controlledmeridional circulation in a circular vortex, Astrophys.Norv.,
5(2), 19-60, 1951.
Garcia, R.R., On the mean meridional circulation of the
middle atmosphere, J. Atmos.Sci., •, 3599-3609, 1987.
Garcia, R.R., and B.A. Boville, "Downward control" of the
mean meridional circulation and temperature distribution
of the polar winter stratosphere, J. Atmos.Sci., 51, 2238-
change,Rev.Geophys.,33, 403-439, 1995.
McFarlane, N.A., The effect of orographicallyexcited gravity wave drag on the general circulation of the lower
stratosphere and troposphere, J.Atmos.Sci., •, 1775-
1800, 1987.
McFarlane, N.A., G.J. Boer, J.-P. Blancher, and M. Lazare,
The Canadian Climate Centre second-generationatmosphericgeneralcirculation model and its equilibrium climate, J. Clim., 5, 1013-1044, 1992.
Mcintyre, M.E., Atmosphericdynamics: Some fundamentals, with observationalimplications,in The Use of EOS
for Studiesof AtmosphericPhysics,edited by J.C. Gille
and G. Visconti, pp. 313-486, North-Holland, New York,
1992.
Plumb, R.A., Zonally symmetric Hough modesand meridional circulations in the stratosphere and mesosphere,
J. Atmos.Sci., 39, 983-991, 1982.
Shepherd,T.G., The Canadian MAM project, CMOS Bulletin, 23, pp. 3-12, CanadianMeteorologicaland OceanographicSociety,Ottawa, 1995.
Shine, K.P., Sourcesand sinks of zonal momentum in the
middle atmospherediagnosedusing the diabatic circulation, Quart.J.Roy.Meteor.Soc., 115, 265-292, 1989.
2245, 1994.
Garcia, R.R., and S. Solomon,The effect of breakinggravity
waves on the dynamics and chemical composition of the
mesosphereand lower thermosphere,J. Geophys.
Res., 90,
T. G. Shepherd, K. Semeniuk, and J. N. Koshyk, Department of Physics,University of Toronto, 60 St. George
Street, Toronto, Ontario, Canada M5S 1A7. (e-mail:
[email protected])
3850-3868, 1985.
Garcia, R.R., F. Stordal, S. Solomon,and J.T. Kiehl, A new
numerical model of the middle atmosphere, 1, Dynamics
and transport of tropospheric source gases, J. Geophys. (ReceivedFebruary 28, 1996;revisedJune 18, 1996;
Res., 97, 12,967-12,991, 1992.
acceptedJune 18, 1996.)