GEOPHYSICAL RESEARCH LETTERS, VOL. 25, NO.15, PAGES 2941-2944, AUGUST 1, 1998
Local heating/cooling of the mesospheredue to gravity
wave and tidal coupling
Han-Li Liu and Maura E. Hagan
NCAR High Altitude Observatory,Boulder, Colorado
0v
Abstract. Numerical experiments in this study show
that the tidal wind may have strong impacts on the
stability of the gravity wave and therefore significantly
affectsthe breaking of the gravity wave. This enhances
the local dynamicalcoolingand turbulenceheating, and
1
--]-(VT -]-V)' V (VT -]-V) -]- -Vp-]- gk
Ot
P
0 ((v+ KM)•z
0zv)
+•zz
02V
OX2
(2)
producesdescending
heating/coolingstructures,which
020
0
0
are similar to recent lidar observations.The propagat- 00
0-•
+
(v•
+
v).
v0
v,•--•
+
•zz((•,
+
KH)•zO
)+
ing phase of such structures is dependent on the descendingphase of the tidal wave and the gravity wave
Q•
(3)
breaking level. The maximum heating corresponds
cnpT
closelywith a negative or positive shear of the accelerwhere p, p, 0 and T are density, pressure,potential temated flow, dependingon the gravity wave propagation
perature,and temperature,respectively;VT = (UT(z, t), O)
direction.
1.
Introduction
Recent lidar
observations
have demonstrated
the de-
is the horizontalcomponent(zonalor meridional)of the
GSWM tidal windprofile;v = (u, w) is the gravitywave
velocityfield;g is gravityaccelerationand k = (0, 1); Q
is diabatic heating when applicable. The molecularvisvelopment of transient anomaliesin upper mesosphere cosity coefficientv is assumedto be equal to the molectemperature structures, the so-called inversion layers ular diffusioncoefficient. The eddy viscosityand diffu(e.g., [Hauchecorne
et al., 1987;Dao et al., 1995;Meri- sion coefficients,KM and KH respectively,are derived
wetheret al., 1998]). Inversionlayersare regionsof tem- from the turbulenceenergydensityand turbulencemasperature enhancementswith amplitudes that can reach ter length scale, which are calculated from the 2.5 level
20-30K or even larger, sandwichedby cooling regions second-moment
closureturbulencemodel [Mellor and
with amplitudes of about 10-30K. The altitude of inver- Yamada,1982; Yamada,1983]. This turbulencemodel
sion layer occurrencepropagatesdownward at a rate of considersthe diffusive and advective transport of tur-
1-3 km/hr, whichcorresponds
wellwith the phaseprop- bulence as well as its production and decay. Molecular
agation of the diurnal tide. However, the temperature diffusion in the horizontal direction is also included in
enhancementsare much larger than the Global Scale the equation, becausewhen the flow becomesunstable,
Wave Model (GSWM) diurnal tidal predictions,which large wavenumbercomponentsmay be generatedin the
leads to the conjecturethat gravity wave-tidal interac- horizontal as well as in the vertical direction. On the
tion might play an important role in the layer formation other hand, turbulent mixing is only consideredin the
[Meriwetheret al., 1998]. In this work, a two dimen-
vertical
direction.
sionalnonlinear numericalmodel is employedto study
Spatial discretization is on a staggeredgrid system
the propagation of a gravity wave in a diurnal tidal with secondand fourth order accuracy on vertical and
wind field and its local thermal and dynamical impacts horizontaldirectionsrespectively.Temporal integration
on the tidal structure.
is semi-implicit, with secondorder Adam-Bashforth for
2.
Numerical
non-diffusive
Model
The numerical model used in this study solves the
two dimensional nonlinear N avier-Stokesequations in a
non-rotational system:
Op
Ot
Copyright1998 by the AmericanGeophysicalUnion.
Papernumber98GL02153.
0094-8534/98/98GL-02153505.00
Euler for the diffu-
turbulence equations.
The effective computational domain has an altitude
range from 30 km to 140 km and horizontal range of
100 km.
+ V. (p(VT + v)) = 0
terms and backward
sive terms. A similar schemeis used for solvingthe
(1)
A monochromatic
wave with horizontal
wave
length of 100 km is forced at the lower boundary and
a spongelayer is imposed at the upper boundary. De-
tailed discussion
of the modelcan be foundin [Liu et
al., 1998].
We usedGSWM diurnaltidal results(e.g., [Haganet
al., 1995])in combination
with the GSWM zonalmean
zonal wind field [Haganet al., 1997]to specifythe
2941
2942
LIU AND
HAGAN'
GRAVITY
WAVE
evolving backgroundwind conditionsfor our numerical investigation. Briefly, GSWM is a 2-dimensional,
linearized, steady-state numerical tidal and planetary
wave model which extendsfrom the groundto the thermosphere.The GSWM backgroundwind field is defined
by a seriesof empirical models. In the stratosphereand
mesospherewinds are determined from zonal mean tem-
peratures [Hedin,1991]assuminggeostrophic
balance.
The semi-empiricalwinds of Groves[1985, 1987] are
usedat troposphericheightsand the empirical model of
Portnyaginand $olov'eva[1992a,1992b]is usedin the
mesopauseregion. GSWM migratingtidal forcingis attributable to the absorptionof solarradiation throughout the atmosphere and is parameterized in GSWM
[Hagan,1996]. GSWM alsoaccountsfor the effectsof
AND
TIDAL
Time=
COUPLING
12000.0see
Time=
120
15000.0sec
120[
11o
110[
1oo
80
80
70
70
60
60
5O
50
-20
-10
0
10
20
I
.
-20
-10
Tenup (K)
Time=
0
10
20
Temp (K)
18000.0sec
Time=
21000.0see
120
120[.................
110
110[
,-, 100[
100
•o
80
70
70
80
,50
60
..
-20
50
-10
0
10
20
Temp (K)
-20
-10
0
10
20
Temp (K)
ion drag, molecular and eddy viscosityand conductivity, radiative damping, and gravity wave drag on the
Figure 2. Temperaturevariationcorresponding
to Figure 1. Solid line: mean temperature change due to
diurnaltide. The readeris referredto [Hagan,1996] gravity wave heating/cooling;dash line: temperature
and [Haganet al., 1993;Hagan et al., 1995;Hagan et variation due to diurnal tide.
al., 1997]for details.
sultsfrom Experiment II are presentedin details, while
those from Experiments I and III are only summarized
Three numerical experimentshave been donefor com- due to the limit of space. In Experiment I, there is a
parative studies. In Experiment I, a monochromatic net coolingin the wave breaking region. The coolingis
wave with a horizontalphasevelocityof 33ms-• is mostly due to the dynamical processafter the gravity
forcedat the lower boundary (30 km) with the back- wave breaks. Specifically,for an upward propagating
ground wind set to zero. The amplitude of the vertical gravity wave,the horizontaladvectionterm -uOO/Ox
velocityperturbationis 0.1ms-•. In ExperimentII, the contributesto coolingwhile the vertical advectionterm
3. Results and Analysis
meridionalcomponentof the diurnaltidal wind (21ø N, -wOO/Oz contributesto heating. Under stablecondiOctober) calculatedfrom GSWM are imposedat each tions and in the absenceof backgroundwind, the amplitime step (startingfrom 2200localtime), and the wave tudesof the coolingand heatingterms are proportional
sourceis the same as that in Experiment I and assumed to the squareof waveperturbation amplitude, and they
nearly balance each other. During gravity wave breakto propagatenorthward. In Experiment III, the GSWM
ing,
the amplitudes of both terms decreasebecauseof
zonal mean wind and the zonal componentof the diurwave
saturation. The decreaseof the heating term is
nal tidal wind are used at each time step (also from
steeper
than that of the coolingterm, leading to a net
2200 local time). The gravity wavesourcehas a phase
cooling
in the breaking region. When the background
velocityof-33ms -• (westward).
In thispaper,the reand tidal wind are present, the gravity wave heat and
momentum flux are affected. In Exp II, the gravity
Time=
15000.0see
Time=
12000.0see
110[
•-. 100[
90
'•
wave first becomes unstable
120
120[ ...............
110
r- -
,-. 100
80
•
9o
'•
80
60
50
-100
-50
0
-100
50
of 88 km
gionof the diurnal tidal waveand right below the linear
critical level. From Figure 1, the gravity wavedeposits
'• 7o
'• 70
at the altitude
at 1.2x 104second
(3.3hour),in the positiveshearre-
-50
0
50
momentum in the mean flow and causes mean flow acceleration below the critical level. The model result also
,-, 100
showsthat additionalgravity wavesare generatedat the
critical layer and propagatefurther upwardalongwith
the originalwave. Suchwavesagainbecomeunstablein
the positive shearregion of the tidal wave at about 110
8O
•'
km at 1.8x 104second
(5 hour),similarto the initial
7O
• 7o
Horizontal Velocity (m sec-')
Horizontal Velocity (m sec")
Time=
Time=
18000.0see
120[
21000.0sec
110
il0[
8O
breakingat lower altitude. The strong mean flow acceleration locally enhancesthe positive tidal wind and
6O
6O
5O
5O
modifiesthe positionof its maximum. Figure 2 shows
there existsa strongcoolingin the breakingregionand
Figure 1. Wind structurevariation in Exp II. Solid a heatingright belowit. The partition of the heating
time stepsis shownin Figure 3.
line' mean flow velocity due to gravity wave accelera- rate at corresponding
The peak heating rate at 15000 secondat about 81-82
tion; dash line' tidal wind in the zonal direction.
-100
-50
0
50
Horizontal Velocity (nu sec-')
-100
-50
0
50
Horizontal Velocity (m see-')
LIU AND HAGAN'
Time=
Time=
12000.0sec
1•_o
1•-0
11o
110
1oo
100
GRAVITY
WAVE AND TIDAL
15000.Oeec
• 9o
8o
•
80
70
70
60
6o
50
50
-0.030
-0.015
0.000
0,01õ
-0.030
0.030
Time=
-0.015
0.000
0.01õ
0.030
Heating rate (K sec-')
Heating rate (K see-')
Time=
18000.0see
1•-0
120
110
110
100
100
21000.0see
.
90
80
80
ß
70
70
60
60
descentrate of the gravity wave breaking level. As a
result, temperature structuresbearing the phasesignature of the diurnal tide are evident as in Figure 4. Each
heating level descendswith the correspondingbreaking
level with a faster downwardphasespeedat early stage
of wave breaking.
The followingsimplepicture illustratesthe governing
mechanismin this process.Figure 5 is a schematicplot
of a gravity wave in a tidal wind field. The wind profile
is shownon the left side. When approachingZ2, the vertical velocity perturbation of the gravity wave becomes
smaller and would tend to 0 if a linear critical
50
50
2943
pendent on the phase speed of the tidal wave and the
_.2
....... •_L'•'
90
COUPLING
level is
present. Therefore, the compositevelocity field from
Heating rate (K sec-')
Heating rate (K sec-')
gravity wave wind(thin arrow) and tidal wind (thick
Figure 3. Heating rate correspondingto Figure 1. solid arrow) can be constructedand appearsas a cell
Solid line: total heating rate; dash line' heating rate with its top at Z2, as shownby the thick dash arrow in
due to vertical advection; dot-dash line: heating rate the plot. (Noticethat the plot is for demonstrationpurdue to horizontal advection; dot line: heating rate due
posesonly, it doesnot representall the physicaldetails.
to molecular and eddy heat diffusionø
For example, the decreaseof the vertical wavelength at
km is O.004Ksec
-• or 14Khr-X• and the peak cooling Z2 is not shown.) This circular motion will causedyrate at 85 km is O.005Ksec-1 or 16Khr -•. The heat- namical coolingwith the maximum at Z2. Below Z2 the
ing ratesin Figure 3 clearlyshowthe tidal modulation gravity wave may becomeunstable and break, which
with the distancebetweenpeak of about 28-30 km. The in turn accelerates the mean flow at this level. The
coolingis mostly due to the dominanceof the horizon- mean flow acceleration will increasethe positive shear
tal advection over the vertical advection and turbulence
below Z2 and extend the unstable region downward.
diffusionplays a secondaryrole. The heating, on the Associatedwith the unstable region, eddy diffusiondue
other hand, comesfrom both the net effectof advection to turbulence mixing increasesand thus enhancesthe
and turbulence. The turbulence heating is especially downward heat flux and causesheating. Heating due
important right belowthe maximumcoolingand corre- to advectionalso contributesto the total heating, espespondsto the large positivewind shear due to gravity cially at the initial stage of wave breaking. As a result,
wave acceleration.
the heating occursbelow the maximum tidal wind and
The amplitudeof suchmodificationis larger at higher near the maximum positivewind shear(maximumand
altitudes and smaller at lower altitude due to the atmopositive with respect to the gravity wave propagating
sphericdensity change. As these breaking levelsde- direction). The relativelocationof the heating/cooling
scendwith time, so do the levels associatedwith the region with respect to the tidal temperature perturbaacceleration/heating/cooling.
The descentrate is de- tion depends on the phase relation of the tidal wind
perturbation and tidal temperature perturbation.
Temperature
variatio•0(K
)
-100
-50
0
•00
If the amplitude of the gravity wave is large enough,
120
then its instability may be independentof the existence
-0.030-0.015
0.000
0.015
-0.030-0.015
0.030
•øIItI I !/ / l••
0.000
0.015
0.030
I ofthe
linear
critical
layer.
However,
its
instabilit
is
still modified by the tidal wind. In the positive wind
100I
I I I /J//•/rr.
Jf•/////••/••• I region,
the
vertical
wavelength
becomes
smaller
due
to
•'
Z2
60
- -- ---b•-n•ni•a
/
I
,••
/
f
Heating
50
0000.00 12000.0 1f1000.024000.0 30000.0
Time (see)
Figure 4. Vertical profilesof temperature variation at
Backgroundand
Gravitywavepropation
tidal
wind
20 time stepsbetween6000seconds
and 30000seconds Figure 5. Schematic
plot of a propagating
gravitywave
(interval:1200seconds)
in Exp II. Eachprofileis offset interactionwith background
and tidal wind. Thin arby +10K. The two thick linesindicatethe profilesat row: gravitywavewind;thicksolidarrow:background
12000seconds
and 18000seconds.
and tidal wind;thick dasharrow:compositewind.
2944
LIU AND HAGAN: GRAVITY
WAVE AND TIDAL
The
Doppler shifting. This increasesthe local wind shear
and decreasesthe minimum potential temperature gra- script.
dient. Such changewill reducethe Richardsonnumber
Editor
COUPLING
would like to thank
the reviewer
of this manu-
and lead to instability. The heatingScooling
structure References
after wave breaking is similar to that discussedabove,
Dao, P. D., R. Farley, Xin Tao, and C. S. Gardner, Lidar
but the phaserelationbetweenthe heatingScooling
and
observations of the temperature profile between 25 and
the tidal temperature perturbation is more ambiguous
103 kin: Evidence of strong tidal perturbation, Geophys.
in this case. Details of the numerical analysis of the
Res. Lett., 22, 2825-2828, 1995.
stability featuresaround breaking level were presented Groves, G. V., Final scientific report, AFOSR report 8•-
in [Liu, 1996]and [Liu et al., 1998].
0045, 1987.
Groves,G. V., A global referenceatmospherefrom 18 to 80
In Experiment III, a linear critical level is not present
kin, AFGL report TR-85-0129, 1985.
for the westwardpropagatinggravity wave with phase Hagan, M. E., Comparativeeffectsof migratingsolarsources
on tidal signaturesin the middle and upper atmosphere,
speed33m•s. However,the gravity wavebecomesunJ. Geophys. Res., 101, 21213-21222, 1996.
stable in the westward shear regionsdue to tidal wind
Hagan,
M. E., J. M. Forbes,and F. Vial, A numericalinvesand the resultingacceleration/heating/cooling
structigation of the propagation of the quasi 2-day wave into
ture is similar to those in Experiment II.
the lower thermosphere,J. Geophys.Res., 23,193-23,205,
1993.
4. Conclusion
Hagan, M. E., J. M. Forbes,and F. Vial, On modelingmiBy comparingthe resultsfrom the three numerical grating solar tides, Geophys.Res. Lett.,, 22, 893-896,
experimentsdiscussed
above,it is foundthat the tidal
1995.
wind strongly modifies the gravity wave momentum
flux, heat flux and the stability structure. As a result, the dissipatinggravity wavechangesthe localwind
and temperature. The couplingof the gravity wave and
the diurnal tide affects the temperature structure differently for wavespropagatinginto differentdirections,
and can locally enhancethe tidal temperature amplitude. In our simulation, the amplitude can be more
Hagan, M. E., J. L. Chang, and S. K. Avery, Global-scale
wavemodelestimatesof nonmigratingsolartides, J. Geo-
inant for the heatingø The heating region corresponds
closelywith the strong shear due to mean flow accel-
of the meridional in the mesopause-lowerthermosphere,
phys. Res., 102, 16439-16452, 1997.
Hauchecorne,A., M.L. Chanin, and R. Wilson, Mesospheric
temperature inversion and gravity wave breaking, Geophys. Res. Lett., 1J, 933-936, 1987.
Hedin, A. E., Extension of the MSIS thermospheremodel
into the middle and lower atmosphere, J. Geophys. Res.,
96, 1159-1172, 1991.
Liu, H.-L., A numerical study of two dimensionalgravity
than 20K. ThesetemperatureheatingScooling
regions wave breaking, Ph.D. thesis, 158 pp., Univ. of Michigan,
Ann Arbor, September, 1996.
descendwith the breaking level, which is in turn dependent on the tidal wave.. This processcan produce Liu, H.-L., P. B. Hays, and R. G. Roble, A numerical study
of gravity wave breaking and impacts on turbulence and
an inversionlayer (or inversionlayers)in the heatingremean state, Submittedto J. Atmos. Sci., 1998.
gion(s) accompanied
by coolingaboveand below,and Mellor, G. L., and T. Yamada, Development of a turbubear the vertical characteristicsof the tidal wave. Such
lence closure model for geophysicalfluid problems,Rev.
Geophys.SpacePhys., 20, 851-875,1982
temperature variations are similar to those seen in recentlidar observations[Meriwetheret al., 1998;Dao et Meriwether, J.W., X. Gao, K. Beissner, S. Collins, V.B.
Wickwar, T.Wilkerson, and M.E. Hagan, Observedcoual., 1995;She,private communication].
In sucha develpling of the mesosphereinversionlayer to the thermal tidal
opment, the dynamical processis the controllingmechstructure, Geophys. Res. Lett., in press, 1998.
anism for the coolingwhile turbulencemixing is dom- Portnyagin, ¾u.I., and T.V. Solov'eva,An empirical model
Part 1., A mean monthly empirical model, Russian J.
Met. and Hydr., 10, 28-35, 1992a.
eration (positiveshearfor eastwardSnorthward
gravity
Portnyagin, ¾u.I., and T.V. Solov'eva,An empirical model
waveandnegativeshearfor westward/southward
wave).
of the meridionalwind in the mesopause/lower
thermo-
The simulation results suggestthat the gravity wavetidal interactions might play a key role in the formation of mesosphereinversionlayers and tidal wind and
temperature variations. This study considersthe gravity wave interaction with the diurnal tidal wind, but
ignoresthe tidal temperature perturbation. Further-
more, the impactsof the local heatingScooling
on the
tidal temperature may vary with latitude due to the
different phase relation between tidal wind and temperature. These issueswill be addressedin our future
studies.
Acknowledgments.
The authorswishto thank Dr. R.
A. Vincent for his very helpful suggestions.
The National Center for Atmospheric Research is sponsoredby NSF. The authors' effortswere supportedin part
by NASA grant S-97239-Eto NCAR. M. E. Hagan alsoacknowledgesthe NSF CEDAR program.
sphere, Part 2., Height-latitude features of basic components of meridional wind seasonal variations, Russian J.
Met. and Hydr., 11, 29-36, 1992b.
Tao, Xin, and C. S. Gardner, Heat flux observationsin the
mesopauseregion above Haleakala, Geophys.Res. Lett.,
22, 2829-2832, 1995.
She, C. Y., Colorado State Na Lidar temperature measurements in the mesopauseregion, private communication,
1998.
Yamada,T., Simulations
ofnocturnaldrainage
flowsbya q21
turbulence closuremodel, J. Atmos. Sci., •0, 91-106,1983
H.-L. Liu and M. E. Hagan, NCAR High Altitude
Observatory,PO Box 3000, Boulder, CO 80307-3000. (email: [email protected];[email protected])
(ReceivedMay 4, 1998; revisedJune 15, 1998;
acceptedJune 17, 1998.)