Adiabatic assumption. Part III: Meteorology. Adiabatic assumption. Don t forget the pressure! The Temperature Profile

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Adiabatic aumption Pat III: Meteoology The key to undetanding it i undetanding the two timecale involved in convection, whee wam ai ie and cold ai fall.

1 Adiabatic aumption Pat III: Meteoology The key to undetanding it i undetanding the two timecale involved in convection, whee wam ai ie and cold ai fall. When a pacel of wam ai ie, it find itelf in a egion with a diffeent (highe o lowe) tempeatue and diffeent (uually lowe) peue. The pacel epond to the peue diffeence almot intantly (expanding lightly) but take longe to come to the ame tempeatue a the ai aound it: it take while to mix. Thi i actually at the oot of the adiabatic aumption, the aumption that ai doen t tanfe heat to it uounding vey apidly o that enegy tanpot in the atmophee i pimaily by convection and not conduction o adiation Convection v adiative enegy tanpot Conide a mall blob of ga. Raie it, without emoving heat. Let it expand, o that peue i equalized. If the eult i lighte (hotte) than the ambient ai, then the blob i buoyant and convection will occu. Convection caue eddie o convective cell. Enegy i tanpoted a a eult of fluid motion. If convection occu, it uually dominate ove othe type of enegy tanpot. Adiabatic aumption Of coue, the wame ai will eventually mix with the ai aound, but doen t do o immediately. A a eult, it may continue to ie a long a it till wame than the ai aound it. But if the ai above it i all coole, houldn t it jut ie to the top? Then it will mix with the ai thee, and the top of the atmophee will eventually get to be quite hot? The Tempeatue Pofile We ve etimated the peue a a function of height uing hydotatic equilibium, and ued thi to etimate cale height uing the aumption that the tempeatue i contant. When the atmophee i convective, the hydotatic aumption till hold (on aveage) though ai i moving Convective motion ae vey efficient at tanfeing heat, o if convection occu the tempeatue pofile i et by convection When a pacel of ga move vetically and no heat i exchanged with it uounding, thi i called an adiabatic poce. 65 Don t foget the peue! The key detail hee i that the pacel epond quickly to peue change on it way up. So a pacel of wam ai expand a it move to highe and highe altitude, becaue it move into egion of lowe peue. A it expand, the peue diffeence ΔP between it and it uounding caue it to exet a foce ΔP ove the ditance Δx it expand. Foce time ditance = Wok. Thu the ga doe wok on it uounding. Thi mean it ha to loe enegy! In thi cae, heat enegy i whee it come fom. 68 1

2 Don t foget the peue! Thu the expanding pacel of ga cool due to expanion, even though it doen t loe heat diectly to it uounding by conduction. Though wam ai ie, it i apidly obbed of it heat by the need to expand. Thi eult in the final T tuctue being coole at highe altitude. 69 The adiabatic tempeatue gadient dt γ 1 gm = dz γ k Thi vetical tempeatue gadient i alo known a the dy adiabatic lape ate. Dy becaue it aume none of the gae will get cold enough to condene out, and o i not tictly tue fo Eath (whoe atmophee contain wate vapou) Note: γ can be 5/3,7/5, 4/3 fo monatomic, diatomic and polyatomic gae. Fom thi and the value of the othe tem we ee that dt/dz i uually < 0. Can you ee why thi i the cae depite the fact that wam ai ie? (Note: dt/dz >0 can occu if additional heating i peent) 7 Fit Law of Themodynamic dq = du + PdV dq heat abobed by the ytem du change in intenal enegy PdV wok done on the envionment by the ytem Definition of pecific heat dq dq CP CP CV γ dt P dt V CV By diffeentiating the ideal ga law, it i poible to how that (ee text 3..), when dq = 0, γ P whee γ i the adiabatic index. 70 Fomation of Cloud When the tempeatue dop below the condenation tempeatue of a ga, it feeze o condene out of the ai, foming cloud. Eath pimaily ha wate cloud Giant planet have cloud of NH 3, H O, CH 4 Ma ha CO cloud Venu ha H SO 4 cloud 73 The adiabatic tempeatue gadient Uing the ideal ga law: which ha many fom (ee e.g. dep&l p63). Hee P=peue, k = Boltzmann contant, T = tempeatue and n = numbe denity Note ideal gae mut alo have an intenal enegy which i only a function of T, and o mut obey the adiabatic aumption: and hydotatic equilibium We can deive the vetical tempeatue gadient (ee Aignment 1) P= nkt U U = = 0 V T P T dq = 0 dp = gdz dt γ 1 gm = dz γ k 71 Satuation Vapou Peue The atuation patial vapou peue at tempeatue T i given by the Clauiu-Clapeyon equation: L / RgaT Le P = C Rga i the ga contant: t J/K mole C i a contant L L i the latent heat The height whee cloud fom can be ued to etimate the patial peue o abundance of paticula molecule. 74

How do cloud modify the adiative enegy balance? The wet adiabatic lape ate Cloud can be highly eflective in the viible eg Venu high albedo.

A cloud condene, enegy i eleaed and thi affect the lape ate (tempeatue gadient).

we ecove the dy adiabatic lape ate. The dy lape ate i lage than the wet one.

3 How do cloud modify the adiative enegy balance? The wet adiabatic lape ate Cloud can be highly eflective in the viible eg Venu high albedo. Cloud block outgoing IR adiation, adding to the geenhoue effect. The latent heat of condenation change the themal tuctue of updaft. A cloud condene, enegy i eleaed and thi affect the lape ate (tempeatue gadient). 75 dp cpdt = Ldw L Latent heat, cp Specific heat dw amount of vapou condening pe unit ma dp = cpdt + Ldw dp = gdz c dt = gdz L dw P dt g = dz c + L dw / dz P Wet adiabatic lape ate In the limit L 0, we ecove the dy adiabatic lape ate. The dy lape ate i lage than the wet one. 78 Cloud tend to fom at a paticula height The cloud fom when the vapou peue of the cloud i equal to the atuation vapou peue. Lape ate Condenation of wate doplet o ice eleae enegy, and thu the tempeatue of the ga doe not deceae a teeply a it would if it wee dy. Gaphed like dz/dt athe than the othe way aound. Thi height depend on T, P, and the volume filling facto (patial peue) of the molecule. If you have a fomula fo the atuation vapou peue (Clauiu- Clapeyon equation), you can pedict the height at which cloud fom The wet adiabatic lape ate When cloud fom, enegy i gained fom the latent heat of condenation. Thi affect the themal tempeatue gadient. If you aume that the humidity emain at 100% of it capacity at any given tempeatue (vapou condene out a the height inceae), you can pedict the wet adiabatic lape ate. The Galileo Pobe detected cloud with NFR (Net Flux Radiomete), which obeved ocillation in ky bightne a the pobe otated, and with NEP (Nephelomete), which ued catteed lae light between the pobe and an am 0.1 mete long. NFR detected a (believed) ammonia ice cloud at 0.6 ba. NEP found a tenuou cloud with a bae aound 1.6 ba, and faint tace elewhee. No othe cloud een, including the NFR cloud: poibly becaue it i patchy and the pobe went though a clea patch. Cloud on Jupite

Pecipitation Doplet and ice cytal fall unde the influence of gavity Vicoity eit fee fall The teminal velocity detemine whethe a dop i likely to continue to fall 1 1 Dag foce FDag = CD A aivtem =

F Gav tem v tem gr 9ν Speculation that Titan ha ea of hydocabon baed on obeved cloud 81 dop ai dop ai When the planet otation axi i pependicula to the ecliptic, the equato eceive moe unlight than the

Hadley ciculation 84 Fomation of dop and cytal Hadley cell ciculation on Eath Diect condenation a molecule collide Seed dut paticle o chaged paticle can be impotant ite fo condenation, paticulaly fo

8 When the planet i otating, the oveall equato to pola flow beak up.

4 Pecipitation Doplet and ice cytal fall unde the influence of gavity Vicoity eit fee fall The teminal velocity detemine whethe a dop i likely to continue to fall 1 1 Dag foce FDag = CD A aivtem = CDπRdopaivtem 4π 3 Equal gavitational foce F Gav = m dop g = dop R dop g 3 In the low Reynold numbe limit, the dag coefficient C ~ R ν ai ~ R v whee ν ai i the kinematic vicoity 1 D Equating dop FDag F Gav tem v tem gr 9ν Speculation that Titan ha ea of hydocabon baed on obeved cloud 81 dop ai dop ai When the planet otation axi i pependicula to the ecliptic, the equato eceive moe unlight than the pole. Hot ai ie and flow towad egion with lowe peue. Thi ai then cool, dop and flow back to the equato at low altitude. Venu, fo example, ha one Hadley cell pe hemiphee. Hadley ciculation 84 Fomation of dop and cytal Hadley cell ciculation on Eath Diect condenation a molecule collide Seed dut paticle o chaged paticle can be impotant ite fo condenation, paticulaly fo cytal fomation. Poible ole of comic ay Afte a eed i fomed, the gowth ate i detemined though colliion with othe molecule and paticle. 8 When the planet i otating, the oveall equato to pola flow beak up. 85 Wind: ola heating Themal tide Diffeential ola heating caue peue diffeential, which caue motion in the atmophee Hadley ciculation Themal tidal wind Condenation flow The Coioli foce beak up lage cale patten cauing tade/zonal wind. If thee i a lage day/night tempeatue diffeence, then ai can flow fom the hot day ide to the night ide: Themal tidal wind. Thee i a etun flow at low atlitude. The tempeatue diffeential detemine whethe uch a flow occu. It need to be lage. The tempeatue change depend on the total ma of the atmophee. The factional change i mall fo planet with thick atmophee like Jupite and Venu. Ma, howeve, ha a elatively tenuou atmophee and o a tong themal tide. The Eath and Venu have themal tide only in the themophee (high up)

Condenation flow Seaonal and obital change can caue ice to ublime and condene. Ma CO umme pola cap ublime, inceaing the CO content of the atmophee. The exce ga condene onto the oppoite pole.

5 Condenation flow Seaonal and obital change can caue ice to ublime and condene. Ma CO umme pola cap ublime, inceaing the CO content of the atmophee. The exce ga condene onto the oppoite pole. On Titon and Pluto, nitogen and methane ublime and condene with day/night and ditance fom the un. Conevation of momentum Dv = P + g i equivalent to F = ma Without vicoity o gavity: Eule equation With vicoity: Navie Stoke equation. Dv 1 = P + ν v D take into account change in the fluid and change caued by motion of the mateial with epect to the obeve. Note: conitent with hydotatic equilibium Fluid equation To decibe the motion of a fluid, we need to keep tack of the velocity and denity eveywhee. Ma flux: v The ate ma leave a paticula egion in the x diection: ( v ) If thi i zeo, thee i the ame amount x coming in one ide a leaving the othe, o the denity emain contant. If ( v ) 0 thee i a change in the amount of local ma. x Fo a one-dimenional ytem: Rotating fame and Coioli foce Becaue the Eath i otating, a paticle on an appaently taight path i actually on a cuved one, and o feel an acceleation. Thi additional acceleation i the um of the Coioli foce and the centifugal foce. Eule equation become: Dv 1 = ω ot ( z v ) P + g + ωot d = ( v) dt x 88 Coioli foce Centifugal tem Peue tem 91 Conevation of ma Geotophic balance d = dt x ( v ) ( v ) ( v ) x y y z The ma denity in a blob depend on the ma flux moving in the x, y, z diection d + ( v) = 0 dt When the fluid i incompeible, i contant v = 0 z Dv 1 = ω ot ( z v) P + g + ωot Dv = 0 Aume teady tate, ; aume ωot i mall. Take -dimenional i limit it (hallow appoximation): 1 ωot ( z v) = P Coioli foce i exactly balanced by peue gadient. P i pependicula to ioba. z v i pependicula to v v flow along ioba

Geotophic flow Example of Geotophic flow: Tade wind on Eath

( z v) P + g + ωot When the peue i balanced by centifugal foce

of cyclotophic balance: Titan and Venu global patten Equatoial

cell and a pola cyclotophic flow patten.

UCAR, UV Maine 10 image of Venu 94 97 Jupite The cloud conit

white) Ammonium Hydoulfide (middle, ed/bown) Wet ai ie, dy ai

The Red Spot Diffeential otation caue votice o eddie.

6 Geotophic flow Example of Geotophic flow: Tade wind on Eath Eath tatopheic jet team Zonal wind on Giant planet Dv 1 = ω ot ( z v) P + g + ωot When the peue i balanced by centifugal foce athe than Coioli foce, we peak of cyclotophic balance Example of cyclotophic balance: Titan and Venu global patten Equatoial flow Cloud on Venu Venu i a low otato: it ha one Hadley cell and a pola cyclotophic flow patten. The cloud how tuctue in UV image. UCAR, UV Maine 10 image of Venu Jupite The cloud conit of: Ammonia (top deck, bight white) Wate (bottom deck, dull white) Ammonium Hydoulfide (middle, ed/bown) Wet ai ie, dy ai ink. The diffeent colou in Jupite epeent diffeent humidity ga. The Red Spot Diffeential otation caue votice o eddie. The meging of two eddie poduce a lowe enegy tate. So eddie can inceae in ize. Lage eddie can be long lating. Non-linea D tubulence poblem

Featue on Neptune Simulation of the mege of two anticyclone 99 Voyage alo aw a malle

Recent HST obevation ugget the dak pot ha dimmed o diappeaed.

The ight image ue fale colou and contat enhancement to bing out ubtle detail in the

Uanu eveal a dak pola hood uounded by a eie of pogeively light concentic band.

into band by zonal motion of the uppe atmophee.

7 Featue on Neptune Simulation of the mege of two anticyclone 99 Voyage alo aw a malle dak pot in the outhen hemiphee and a mall iegula white cloud ( The Scoote ) that zip aound Neptune evey 16 hou. It may be a plume iing fom lowe in the atmophee, but it tue natue emain a mytey. Recent HST obevation ugget the dak pot ha dimmed o diappeaed. 10 Uanu i nealy featuele. The ight image ue fale colou and contat enhancement to bing out ubtle detail in the pola egion. Blue UV; geen violet; ed oange. Uanu eveal a dak pola hood uounded by a eie of pogeively light concentic band. One poible explanation i that a bownih haze o mog, concentated ove the pole, i aanged into band by zonal motion of the uppe atmophee The dak pot on Neptune Neptune blue colou i lagely the eult of aboption of ed light by methane (plu an unidentified pecie). At the time of the Voyage encounte, Neptune mot pominent featue wa the Geat Dak Spot, about half the ize of Jupite Red Spot. Neptune wind blew the Geat Dak Spot wetwad at 300 m/

Convection vs radiative energy transport

Convection vs radiative energy transport Pat III: Meteoology 63 Convection vs adiative enegy tanspot Conside a small blob of gas. Raise it, without emoving heat. Let it expand, so that pessue is equalized. If the esult is lighte (hotte) than