Atmospheric Buoyancy Driven Flows

Sylvie Malardel

Contents

1 Introduction 21.1 The Atmosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.1.1 What is driving the weather and the climate? . . . . . . . . . . . . 21.2 Buoyancy in a perfect gaz . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.2.1 Dry case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.2.2 Buoyancy in moist air . . . . . . . . . . . . . . . . . . . . . . . . . 81.2.3 Buoyancy in saturated air . . . . . . . . . . . . . . . . . . . . . . . 8

2 Circulations 92.1 Are atmospheric fronts buoyancy driven flows? . . . . . . . . . . . . . . . . 9

2.1.1 The baroclinic zone . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.1.2 Baroclinic development . . . . . . . . . . . . . . . . . . . . . . . . . 102.1.3 Fontogenesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.2 Feed-back of the baroclinic waves on the mean circulation . . . . . . . . . . 132.3 Atmospheric Convection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.3.1 CIN/CAPE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.3.2 Downdrafts, DCAPE . . . . . . . . . . . . . . . . . . . . . . . . . . 152.3.3 Organisation of convection . . . . . . . . . . . . . . . . . . . . . . . 15

2.4 Direct cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.4.1 Land/Sea breeze . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.4.2 Montain breeze . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.4.3 Katabatic winds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3 Simulations 193.1 Overview of Atmospheric Simulations . . . . . . . . . . . . . . . . . . . . . 193.2 Modelisation of Buoyancy Driven Flows . . . . . . . . . . . . . . . . . . . . 20

1

1 Introduction

1.1 The Atmosphere

The atmosphere, like the ocean, is a stratified fluid highly influenced by the rotation of theEarth. But, unlike the ocean, the atmosphere is mainly composed of a mixture of gases,the air.

The composition of the gas layer around the Earth has evolved very slowly since thetime of its formation. Thanks to the apparition of life about 3.5 billions years ago, themain constituents of the air are now the Nitrogen (N2, about 78%) and the Oxygen (O2,about 21%). Other minor constituents are Argon (1%), Ozone, Carbon Dioxyd and watervapour.

The air near the surface is about 1000 times lighter than the water in the ocean. Itis also much more compressible. The mean state of the atmosphere is stably stratifiedand in hydrostatic equilibrium (figure 1). The first 10-15 km of the atmosphere knownas the troposphere contain nearly 90 percents of the atmospheric mass. This layer is thelayer of the weather. The bottom of the troposphere, the Boundary Layer, is directlyinfluenced by the surface (land or ocean). Its mean depth is about 1 km, but it can bereduced to a few 10th of meters in a cold winter day and reachs several kilometers in awarm turbulent summer day. The layer above the troposphere called the stratosphere isvery stably stratified. The stratosphere is the layer where the ozone chemistry protects theair and the surface below from the incoming UV . The tropopause in between behave as alid for the troposphere because the vertical motions are quickly deaden in the very stablestratosphere above.

Atmospheric motion are generally faster than Oceanic currents. Atmospheric timescales are also globally shorter than in the ocean.

1.1.1 What is driving the weather and the climate?

The main source of energy of the climatic system is the sun (figure 2). The atmosphereabsorbes less than 20% of the incoming radiation. 30% are reflected back and then morethan 50% are absorbed by the Surface (70% ocean, 30% land). The atmosphere absorbesmost of the IR radiation emitted by the surface. The atmospheric fluid is then mainlyheated by the bottom. And, as in a saucepan of boiling water, this strongly influencebuoyancy driven flows like atmospheric convection.

Larger scale circulations are mainly driven by the differential heating in latitudes (fig-ure 3) but also in the vertical (figure 4). The meridional mixing is done both by the oceansand by the atmosphere (figure 5), the ocean being the main actor in the tropics and theatmosphere making most of the mixing in the midlatitudes and in the polar regions. Inthe vertical, the radiative cooling is balanced by the convective motions. The water phasetransitions play a very important role in the vertical redistribution of energy, especially inthe tropics.

In the tropics, most of the mixing is done by the zonal mean flow. The low level branches

2

Température (°C)

Troposphère

Tropopause

Stratosphère

Stratopause

Mésosphère

Mésopause

Thermosphère

0

20

40

60

80

100

-20-40-60-80 20

Alt

itu

de

(km

)

0

Température

NuagesVapeur d’eau

Aérosols

Méla

nge u

niform

ede N

, O

, A

r2

2

-610

-510

-410

-3

-2

-1

10

10

10

0,001

0,01

0,1

1

10

100

1000

Pre

ssio

n a

tm

osp

héri

qu

e (

hP

a)

Masse v

olu

miq

ue d

e l’a

ir (

Kg

m)

-3M

asse v

olu

miq

ue d

e l’a

ir (

kg

m)

-3

Figure 1:

3

Figure 2:

ÉQ

UA

TEU

R

Hémisphère Nord

0

0

250

500

W m

-2

30°30° 60°60° 90°90°

Hémisphère Sud

Figure 3:

4

Couches

excédentaires

Flux réfléchi et

absorbé par

l’atmosphère

Flux IR

net

Flux solaire

net

Z

Couches déficitaires

-S S

Rayonnement

Figure 4:

Latitude (N)

Tra

nsp

ort

d’é

nerg

ie (

x1

0 W

)1

5

-2

0

2

4

6

0° 10° 20° 30° 40° 50° 70°90°

Figure 5:

5

of the Hadleys cells concentrate sensible and latent heat near the equator. Atmosphericconvection transports and transform energy upwards and finally the upper branches ofthe Hadley cells export potential energy toward the midlatitudes. The final budget is anequator-pole transport of energy but the Hadley cells are very inefficient heat engines.

In the midlatitudes, the meridional mixing is mainly due to the steady and transienteddies which also transport momentum from the tropics toward the poles.

The spectra of atmospheric circulations involved in the climatic balance is very large.The buoyancy is an important controlling factor in most of them even if, for the largescales, the work of the gravity toward a minimal potential energy state is made difficultbecause of the rotation of the Earth.

As in the ocean, the Rossby radius of deformation Rd gives an order of magnitudeof the scale separation between the processes mainly driven by the buoyancy and theprocesses mainly driven by the rotation. In the atmosphere, Rd is of the order of 1000 km.Circulations larger than Rd are in quasi-geostrophic balance. The corresponding stateof the atmosphere still contain available potential energy which can not be extracted bydirect overturning cells. More complex structures like Rossby waves or baroclinic wavesare important for the mixing where the rotation is dominant.

1.2 Buoyancy in a perfect gaz

1.2.1 Dry case

The air can be considered with a good approximation as a perfect gas. The state equationis then the perfect gas law often written as :

p = ρRdT

where p is the pressure of the gas, T the temperature, ρ the density and Rd = R∗/Md thegas constant for dry air (R∗ is the universal gas constant and Md the molar mass of dryair).

The first principle of the thermodynamics applied to a perfect gas can be written as anequation for the enthalpy of the gas :

DcpT

Dt= −1

ρ

Dp

Dt+ Q (1)

where cp is the specific heat at constant pressure and Q is the heating rate. In an adiabaticprocess ( Q = 0), the evolution of the temperature is associated with a reversible processbetween the enthalpy of the gas and the pressure work associated with the volume changes.In the atmosphere, an adiabatic cooling is mainly a consequence of a vertical ascent.

It is possible to define a thermodynamics variable with is conservative with respect tothe work of the pressure force in an adiabatic evolution. A combination of the LHS andthe first term on the RHS of equation 1 (for Q = 0) gives :

D(ln( T

pR/cp))

Dt= 0

6

The potential temperature is defined as

θ = T (p0p

)R/cp

where po = 1000 hPa.θ is conserved in an adiabatic (dry) atmospheric evolution. This parameter is directly

related to the entropy of the system. Like the entropy, it evolves because of the heatexchange with the environment. θ is also the temperature that an air parcel would havewhen adiabatically moved to a pressure level of 1000 hPa.

The potential temperature is a very practical parameter for the analysis of buoyancystability in the atmosphere because it is more simply related to the stratification than thetemperature. We’ll see below that a neutrally stratified flow is a flow with no verticalgradient of θ (this corresponds to a temperature lapse rate of g/cp=-9.1 K/km). The meanstate of the atmosphere is stably stratified (figure 6) as θ increase with the vertical (unlikeT which decreases in the troposphere with a mean lapse rate of about -6.5 K/km).

80ON 60ON 40ON 20ON 0O 20OS 40OS 60OS 80OS1 000

900800700600

500

400

300

200

100

280

280

290

290

300

300

300

300

310

310

310

310320

320

320

320330

330330

330340

340 340

340350

350 350360360 360370

370 370 370

380

380

380

380390

390

400

400

410

420

Figure 6:

A classical simplified approach to study the vertical motion of an air parcel driven bythe buoyancy force is to consider that this air parcel is ”isolated” from its environment likea bubble or a buoy. An equation for the vertical acceleration of the parcel is given by thevertical component of the momentum equation :

DwpDt

= −g − 1

ρp

∂pp∂z

A usual hypothesis is to consider that the pressure of the parcel instantaneously adjuststo the pressure of the hydrostatic environment when the parcel is moving vertically. Theair parcel is also supposed to follow an adiabatic evolution.

In this context, the vertical acceleration of the parcel is directly related to the buoyancywhich can be written as a difference of density, temperature or potential temperaturebetween the parcel and the environment :

DwpDt

= −gρp − ρeρp

= −gTe − TpTe

= −gθe − θpθe

= B (2)

7

A first order development of equation (2) for a small vertical displacement around theequilibrium level of the parcel shows that

• the environment is stable with respect to a small vertical displacement if ∂θe∂z

> 0

• the environment is unstable if ∂θe∂z

< 0

• the environment is neutral ∂θe∂z

= 0

If the air is stable, parcels will oscillate around their equilibrium level with the Brunt-Vaısala frequency Ne = g/θe∂θe/∂z .

If the air is unstable, parcel will be accelerated upward or downward until they reacha level of neutral buoyancy (or the surface).

1.2.2 Buoyancy in moist air

The molar mass of the water vapour (18 g) is lighter than the molar mass of the air (about29 g). One of the important consequence of this difference is that the moister the air themore buoyant it is.

In order to compare a moist air parcel with a (differently) moist environment, meteo-rologists use the virtual temperature Tv which is the temperature that would have a parcelof dry air with the same pressure and density as the moist parcel :

p = ρhRhT = ρhRaTv

As Ra = R∗/Ma < Rh = R∗/Mh , Tv > T . Tv is a practical way to express the gain inbuoyancy due to the presence of water vapour. The difference between T and Tv may be ofthe order of a few degrees (air at 20oC with a moisture content of 12 g/kg, Tv − T = 2oC).

The vertical momentum equation for a parcel of moist air is written as :

]Ddtwp = B = gθve − θvpθve

1.2.3 Buoyancy in saturated air

If a parcel of moist air reachs a level where the temperature is low enough for the conden-sation to start, the parcel is warmed by the latent heat release (figure 7). If the ascendingmotion of the parcel continue, the vertical rate of decrease of the parcel is smaller (about4 K/km instead of 9.8 K/km) and the chance for the parcel to be more buoyant than itsenvironment are much larger. Most of atmospheric convection is actually possible thanksto the condensation of water vapor.

The positive effect of the condensation on the buoyancy has generally to be attenuatedby the effect of the loading of the air parcels by the rain and ice precipitation. In bigthunderstorm cloud this effect can affect significatively the strength of the ascents.

8

vertical

ascent without

condensation

condensation level

condensation

ascent with

Temperature

verticaltemperature profileof the bubble

level offree convection

condensation level

forced ascent

convective ascent(positive buoyancy)

temperature profile

of the surrounding air

Temperature

Figure 7:

2 Circulations

In this section, we will discuss a selection of three atmospheric circulations. The first one,the atmospheric front is still often presented as a gravity current. We will try to show thatthe dynamics of cold and warm fronts results from a different mechanism which is ratherdriven by the geostrophic balance than by the buoyancy.

We will then expose the basic principles of atmospheric deep convection. We will inparticular introduce the role of the wind shear and the downdrafts in the organisation oflonger life cycle convective systems.

In the last part of this section, we will list the different types of direct cell circulationswhich have their upward or downward branch directly driven by the buoyancy force.

2.1 Are atmospheric fronts buoyancy driven flows?

Extratropical cyclones and atmospheric cold and warm fronts are often presented as anundulation of a pre-existing limit between two air masses of different temperatures anddensities. In the ”Norwegian theory”, this pre-existing limit called the Polar front (Bjerknesand Solberg, 1922) is seen as one of the result of the general circulation. The vertical motionand the clouds along the cold and warm fronts are explained as a consequence of the ”fight”between the cold and the warm air, the warm air being lifted above the cold mass as in agravity current.

This description of the midlatitude frontal systems was exceptionally realistic comparedto the very limited observation system available in 1920. However, we know now thatthere is no evidence of the existence of the Polar front. On the other hand, no theory canscientifically explain the formation of extratropical cyclones and anticyclones of synopticscale along a limit between two air masses.

The theory commonly accepted to explain the development of extratropical cyclone isbased on baroclinic instability. The fronts are a secondary product of the baroclinic wave.

9

The temperature gradients are amplified by frontogenesis in a positive feed-back processcontrolled by the quasi- (semi-) geostrophic balance.

2.1.1 The baroclinic zone

The conservation of the angular momentum of the air parcels in the upper branch of theHadley cells results in the formation of a strong westerly jet around 30o of latitude. Thisjet (or the vertical wind shear associated with the jet) is in thermal wind balance withthe meridional gradient of temperature between the pole and the tropics. As the scaleof the jet is large compared with the Rossby Radius of deformation, the mean state ofthe atmosphere in the midlatitudes is characterised by a large reservoir of mean AvailablePotential Energy which can not be released by mean direct circulations because of theEarth rotation.

The zonal structure of the jet is not axisymetric. It is in particular modified by the plan-etary (barotropic) Rossby waves. Jet streaks are regions where the jet and the associatedbarocliny is reinforced.

2.1.2 Baroclinic development

An analysis of the structure of developing extratropical cyclones and anticyclones showsthan the main amplitude of the perturbation of the mean baroclinic zone is stronger nearthe surface and at the level of the tropopause. Such a structure is in agreement with thecirculations obtained by the inversion of the quasi-geostrophic potential vorticity in a layer(the troposphere) of quasi-uniform QGPV but with thermal waves at its upper and lowerboundaries (the surface and the tropopause).

The inversion of uniform QGPV shows that a positive anomaly of temperature is as-sociated with anticyclonic vorticity at the tropopause but with cyclonic vorticity at thesurface. Such perturbation will then propagate with a mechanism similar to the one of aRossby waves, but westward at the tropopause and eastward near the surface (figure 8).

The interaction between a cyclonic anomaly and the baroclinic zone generates verticalvelocity (this is not true if the cyclonic anomaly are in a barotropic environment), withascending motion upstream and subsiding motion downstream of the jet (figure 9).

When a cyclonic tropopause anomaly (which looks like an anomaly of low geopotentialof the tropopause) is situated upstream with respect to a cyclonic low level anomaly, thevertical velocity generated by each anomaly acts to amplify the vorticity of the otheranomaly by vortex stretching (figure ??). The tropopause and the surface waves are thenin a phase of baroclinic development. The two waves may remain locked for a few dayswith a westward global propagation of the system (figure 10).

But slowly the upper anomaly overtakes the surface anomaly and a baroclinic decay(vorticity shrinking) starts.

This approach summarises the main principles of the development of the baroclinicwaves in the midlatitudes. However, a lot of other factors can influence the real develop-ment of these synoptic extratropical systems : large scale weather regime, interaction with

10

FROID

CHAUD

ZONE BAROCLINENON PERTURBÉE

(a)

(b) (c)

Au niveau du sol Au niveau de la Tropopause

>0 <0

Da Aa

>0<0

Da

AaC C

<0 >0

Da

Aa

Propagation vers l’Estau niveau du sol

Propagation vers l’Ouestà la Tropopause

ONDES DE ROSSBY SUR UNE ZONE BAROCLINEA TOURBILLON POTENTIEL UNIFORME

y

x

Figure 8:

Sol

(a)

Z

X Sol

(b)

Z

X

Tropopause

Sol

(c)

Z

X

Tropopause

U

Tropopause

+ =

Figure 9:

11

Z Sol

Z

X

Tropopause

Usol

Utropo

C sol

C tropo

UtropoC tropo

Usol C sol

C perturb

Figure 10:

entrance/exit of jet streak, upstream/downstream developments, surface fluxes, large scalecloud formation, convection etc.

2.1.3 Fontogenesis

During the life cycle of the baroclinic waves, the cyclonic anomalies amplify the deformationof the baroclinic zone. The amplitude of the thermal gradient does not evolve uniformlyin the system. The deformation associated with the cyclonic wind of the vortex mainlyamplify the temperature gradient in the south-west and in the north-east of the cyclone(figure refdeformation).

Figure 11:

In a quasi-geostrophic system, the ageostrophic motion and the vertical velocity areforced by the geostrophic motion in order to restore the thermal wind balance which isconstantly eroded by the geostrophic circulation itself (ω-equation). In both zones offrontogenetic deformation, a convergent ageostrophic circulations appears near the surfaceand at the tropopause (figure 12).

12

Figure 12:

But the convergence of the ageostrophic wind also increases the thermal gradient :

D| ~grad(θ)|2

Dt= | ~grad(θ)|2 (−div( ~vag) + dg cos(2β))

In parallel, the stretching associated with the upward vertical velocity increases thevorticity.

In these zones, a reinforcement of the ageostrophic circulation is needed to restore thethermal wind balance. Then, more ageostrophic convergence will increase the gradient,more ageostrophic wind will be needed, more convergence, more gradient ect....

Thanks to the positive feed-back between the ageostrophic motion and the thermalgradient, regions with very high temperature gradients form near the surface and at thetropopause. They are the cold and warm fronts associated with the extratropical cyclones.

Even if they look like an interface between two air masses of different temperatures,these type of fronts are not gravity currents. They may be considered as buoyancy drivenbecause the origin of the circulation is a thermal gradient, but the circulation and thestructure of the frontal systems are driven by the quasi- or semi- geostrophic dynamics(quasi-horizontal phenomena for which the ageostrophic and vertical motions are drivenby the geostrophic circulation). The main wind and displacement of the air parcels arealong the front and not in the cross front direction. Parcels are slowly ascending from thetropical warm and moist region to the higher latitudes or slowly subsiding from the highlatitudes to the tropics in the ”cold” part of the wave. Stratiform clouds are formed duringthis slow ascending motion which is globally parallel to the fronts (and not above the coldair). Secondary smaller scale convective updraft may be embedded in the stratiform clouds.The formation of these convective updraft is made possible thanks to the synoptic verticalvelocity which balance the Convective Inhibition of the synoptic environment (section 2.3).But they are not the main feature of the frontal circulations.

2.2 Feed-back of the baroclinic waves on the mean circulation

Baroclinic waves contribute to the global meridional mixing by a transport of sensible heatfrom the tropics to the higher latitudes. They also transport zonal momentum from thetropics to the high latitudes, curving their own storm tracks toward the poles as they moveeastward.

13

2.3 Atmospheric Convection

Dry and adiabatic convective plumes are present mainly during sunny day in the BoundaryLayer. Their time scale is of the order of minutes.

These plumes are very turbulent and most of the transport associated with these convec-tive ascents can be described by isotropic turbulent mixing. More organised dry thermals(gliding) also exists but their vertical extension is usually limited to the top of the BL.Deeper convection always involves condensation.

2.3.1 CIN/CAPE

Most convective plumes are starting from the lower levels of the atmosphere. Quite often,the lowest levels are stable with respect to dry adiabatic motions, but if the ConvectiveInhibition (figure 13) is compensated by a source of ascending motion like turbulence, drythermals, orographic forcing, large scale ascent, the parcel are accelerated by the buoyancy.

LFC

LNB

C

Figure 13:

If the level of free Convection is reached, the convection converts the Convective Avail-able Potential Energy into vertical motion, until the Level of Neutral Buoyancy. Air parcelsovershoot this level thanks to inertia but the tropopause is an efficient lid, and most or theair is spread in the anvil at the tropopause.

The CAPE is the vertical integral of the buoyancy between the level of free convectionand the level of neutral buoyancy :

CAPE =∫ LNB

LFCBdz

14

We obtain an estimation of the maximal velocity of the air parcel if we suppose that allthe CAPE is converted into kinetic energy :

wmax =

√2∫ LNB

LFCBdz

But wmax overestimates the real vertical velocities in the updraft which are reduced by thepressure brake, the entrainment of non-buoyant air, the precipitation and the turbulence.

In the no wind, or no wind shear cases, the convective ascents are quickly killed by thedowndraft generated by the evaporation of the precipitations under the cloud (figure 14).The characteristic time scale of a single precipitating cumulus is about 15 minutes.

SolSol

15

12

9

6

3

0

km

10 15 20 25 30 Temps (min)

Figure 14:

2.3.2 Downdrafts, DCAPE

The maximal energy which can be converted into the vertical velocity of the downdraftcan be estimated with the DCAPE (figure 15). The DCAPE usually overestimates thestrength of the downdraft because the air is supposed to be saturated by the evaporationof the precipitation in all the sub-cloud layer.

The horizontal velocity of the gravity current under the cloud (gust front) may beestimated by :

1

2U2CD =

(ρCD − ρe)ρe

gh

2.3.3 Organisation of convection

The CAPE is a necessary ingredient for the formation of deep convective clouds. But otherparameters such as the wind shear (rotational or not) of the environment, the role of themicrophysics (in particular the ice phase) and the interaction with the surface (buoyancyfluxes) also influence the real development of convection in the atmosphere.

The wind shear is a key factor in the organisation of longer life convective systems.Unidirectional low level wind shear is necessary for the development of multicells systems(figure 16). With deeper rotational shear, the dynamics of the vorticity interacts with the

15

Figure 15:

Cellule

n-3

Cellule

n-2

Cellule

n-1

Cellule

n

Cellule

n+1

SolSol

S

Figure 16:

16

15

12

9

6

3

0

km

L

Overshoot

Enclume

Alimentationde surface

TornadeFortepluie

Pluie faibleà modérée

Grêle

10 km

Figure 17:

buoyancy effects and very active systems called supercells may develop (figure 17). Thesupercells are often associated with the formation of hail and sometimes tornadoes.

Ordinary cells, multicells and supercells may be elementary bricks of much bigger con-vective systems of more than 100 km in one of their horizontal directions. The mesoscalecirculation characteristic of this Mesoscale Convective System are hydrostatic. They areusually influenced by the Coriolis force but their time and space scales are not large enoughfor the circulation to be driven by the quasi-geostrophic balance.

One of the most studied Mesoscale Convective System is the squall line. Squall linesoften start like a multicell system with new cells developing in the upstream side of thewind shear. Older cells are slowly integrated into the anvil cloud and a large stratiformsystem form behind the active convective cells. In the mature system, a mesoscale circu-lation enters the system from the back of the squall line and slowly descends toward thedensity currents in the front of the system (figure 18). An ascending flow is forced by thegravity current at the front of the squall line. This ascending flow is associated with activeconvective cells and continues with a smoother slope in the stratiform part of the systemwhere it entrains ice particles collected in the convective cells. The sublimation of theseprecipitating ice particles amplify the negative buoyancy of the circulation which feed thesystem from the back.

2.4 Direct cells

Direct overturning circulations can be large scale circulations in the tropical regions, wherethe Coriolis force is not too strong (Hadley Cells, Monsoon). In the midlatitudes, directcells are mesoscale circulations driven by strong but short time scale thermal contrasts

17

15

12

9

6

3

km

H H

-grad (p)

n+2

n+1

n

n-1

SolSol

L

Figure 18:

near the surfaceusually associated with the daily cycle.

2.4.1 Land/Sea breeze

During a sunny day, the solar radiation is absorbed by a thin layer of land along the coastbut by a much deeper layer of water. The coastal land becomes then much warmer than thesea besides. The air above the land is heated from the bottom and a convergent/divergentcirculation is triggered as the thickness of the layer above the surface increases. A directcell organises with convective ascending motions and cumulus formation over the land anda compensating subsiding branch over the sea. During the day, a refreaching breeze isblowing near the surface from the sea to the land. If the breeze remains for several hours,the breeze is affected by the Earth rotation and the wind acquires a component parallel tothe coast.

TerreMer

Isob

are

s

Divergence

TMer TTerre<

grad(p)

Fp

(a)

TerreMer

Isob

are

s

Divergence

Fp

(b)

Fp Convergence

HL

Figure 19:

2.4.2 Montain breeze

The differential heating between the surface along a slope and the air at the same levelcreates direct circulations perpendicular to the slopes. We usually make a difference be-

18

tween the Valley Breeze which blows in the main direction of a valley and the Slope Breezegenerated on the steeper slopes on each side of the valley. These type of breezes is char-acterised by katabatic winds (subsiding gravity currents) along the slope during the nightand anabatic winds (ascending buoyant currents) along the slope during the day. Duringthe day valley breeze and slope breeze may interact and interesting helicoidal circulationsmay be observed in the valley.

(a) (b)

Brise de vallée

Bris

e de p

ente

Brise de vallée

Bris

e de p

ente

Figure 20:

2.4.3 Katabatic winds

3 Simulations

3.1 Overview of Atmospheric Simulations

The summary of the different types of Atmospheric Simulations is given in figure ?? (figureequivalent to the first slide of the third lecture). Global operational models and climatemodels still have resolutions which are resolving processes in the hydrostatic range. NH”convection permitted” models are just starting to be used as operational NWP tools overlimited areas with resolutions of 3-1 km. Higher resolution models with resolution rangingfrom less than a 1 km (Cloud Resolving Model) to ten meters (LES models) are used forprocess studies and for the development and the validation of the physical parametrizationsof the larger scale models.

When the hydrostatic approximation is released and the vertical velocity becomes aprognostic equation in the model, the acoustic modes become a solution of the system ofequations. These waves may be filtered by the anelastic approximation (ref...) or treatedwith some degree of implicitness in the time scheme.

Most large scale hydrostatic models are written with an hybrid coordinate (σ coordinatenear the surface and pressure coordinate above). Semi-Lagrangian schemes associatedwith a semi-implicit treatment of the gravity waves allow the longest time steps. Higherresolution models are often using a z-type coordinate and explicit flux schemes on C-gridin order to resolve smaller scale processes for which the local conservative properties of thescheme become more important. Global hydrostatic models are use for the longer range

19

forecasts but also as lateral boundary conditions for the higher resolution limited areamodels.

The predictability of the atmospheric flows decreases with the scale of the processes.An ensemble approach usually replaces the deterministic forecast for the medium rangesof NWP (4 to 10 days) and for the seasonal forecasts.

The assimilation of observations is a very important step of the NWP. Observationsfrom the synoptic surface network, radio-soundings, satellite and radar observations areused to create the initial conditions of the forecast. Usually, an assimilation is performedevery 6 hours in the assimilation cycle (figure). The analysis of the atmospheric stateprovided by some (or all) of the assimilation windows may be used as the initial conditionof the forecast. Operational and technical constraints as the cut-off time (time range duringwhich the system waits for the observations to be processed and sent to the internationalnetwork) and the CPU time are important factors which have to be taken into account forthe design of an operational suite (the forecast has to be finished as soon as possible to beused by the forecasters or as boundary conditions by limited area models.

3.2 Modelisation of Buoyancy Driven Flows

Mesoscale buoyancy driven flows like Land/Sea breezes and hydrostatic orographic wavesare simulated by hydrostatic model with resolution between 15 and 7 km. The shallowor deep convection which is often associated with these processes is then parametrized.The simulation of convective cells is possible with NH models which have a prognosticparametrization of the cloud microphysics with a correct parametrization of the ice phases(ice crystal, snow, graupel and hail) and a resolution of at least 3 km. (some figures...)

For large scale models with a resolution lower than 15 km, these mesoscale processesare filtered or have to be parametrized. The grid scale mixing resulting from the smallerscale convective vorticies is given by the parametrisation of the turbulence. For resolutionlower than about 1 km, the vertical transport by the turbulent processes is dominantand a parametriszation of the vertical diffusion of momentum, sensible and latent heat issufficient. For higher resolution, a 3D turbulent scheme is necessary. 1 order closure or 1.5order closure (turbulent kinetic energy scheme) are generally used by operational models.Higher order closure exists in research models. A parametriszation of the convection isused in all hydrostatic models. In the range between 7 to 2 km, the problem of theparametrisation of the atmospheric convection is not very well posed because the separationbetween the scale of the convective processes and the size of the grid is not possible anymorebut the resolution is not high enough to really resolve the convective processes. This ”grey”zone is currently avoided by most atmospheric model.

The interaction between the atmosphere and the surface below are treated by the surfacescheme. The surface scheme is often a group of several parametrisation or simple model fordifferent type of surface : ocean (from very simple parametrizations to full ocean model,but also 1D surface layer...), lake, nature (vegetation), town. The surface of each columnof the model corresponds either to one single type of surface or to several tiles of differenttypes (for ex. a ”coastal grid box with 30% of sea and 70% of soil/vegetation, but then you

20

can also have different tiles with different types of soil/vegetation). The atmosphere sendsto the surface the state of the atmosphere at the first model level, radiation fluxes (fromthe radiation scheme) and precipitations (from the microphysics). The surface sends backto the atmosphere momentum, heat and moisture fluxes (Bottom Boundary Condition forthe Vertical Diffusion Scheme), a ”Surface Temperature” and an Albedo (for the radiationscheme). If a grid box is covered by several tiles, the fluxes for each type of surfaceare aggregated before being sent to the atmospheric model. The turbulent scheme andsometimes the convection scheme are using the fluxes computed by a surface scheme asbottom boundary condition.

For large scale models, stratiform clouds and precipitation are parametrized by verysimple scheme. In most model, the cloud (non precipitating) condensates are prognostic(known from one time step to the next and advected by the advection scheme), but theprecipitating condensates are still often reaching the ground in one time step (or evapo-rated during their fall). In higher resolution models a more sophisticated microphysics ofthe cloud and precipitations is needed. The more simple ones have 3 or 4 reservoirs ofhydrometeors (cloud droplets, rain, snow, sometime graupel)which are described only bytheir mean mass content relative to the total mass in the grid box. More sophisticatedscheme may have more classes of hydrometeors and take into account prognostically ordiagnostically the number of drops or crystals in the grid box. For high resolution models,the feed-back between the cloud microphysics and the dynamics (in particular the verticaladvection linked with the buoyancy) is the driving process of the ”resolved” convectionand of the cold gravity current below the convective clouds.

21