Moist static energy: definition, reference constants, a conservation law, and effects on buoyancy

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Yano, J.-I. and Ambaum, M. H. P. (2017) Moist static energy: definition, reference constants, a conservation law, and effects on buoyancy. Quarterly Journal of the Royal Meteorological Society, 143 (708). pp. 2727-2734. ISSN 1477-870X doi: https://doi.org/10.1002/qj.3121 Available at http://centaur.reading.ac.uk/71775/

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Reading’s research outputs online om Hu n ¨le 97 oaa19,Mrut19,21,21,Eaul19,Mrh n op20;MrutadGeleyn and Marquet 2005; Toop and Murphy 1994, Emanuel 2015, 2011, 1993, Marquet 1990, Ooyama H¨oller 1987, and (Hauf forms 03.Hwvr aaaayi n oeln tde nteltrtr aeyueteeeatdfiiin.Temtvto fti td is study this of motivation The definitions. exact these use rarely literature the in studies modelling and analysis data However, 2013). exact in variables these of definitions the presenting exist Studies forms. approximate in presented often are variables Thermodynamic Introduction 1. osrainlwascae ihtemitsai nry(e.3.Sm ute suscnenn hs osat r lodsusdin discussed also are constants these concerning laboratory issues further by Some 3). determined (Sec. be energy static only moist can the as with which Second, associated law 2). constants, conservation (Sec. reference approximation contains standard definition the its to derivation, energy rigorous static a moist under the out, of definition turns exact it the relate we first, issues: following relations approximate whether or consequences, sufficient. important be have variables may thermodynamic of definitions exact the whether examine to esrmnso ulqatmmcaia acltos novosqeto oaki h oeo hs osat nodrt anana maintain to order in constants these of role the is ask to question obvious An calculations. quantum–mechanical full or measurements etk h os ttceeg ( energy static moist the take We ∗ Accepted Article [email protected]. E-mail: France. Cedex, Toulouse 31057 Coriolis, M´et´eo-France, av CNRM, 42 to: Correspondence

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Please cite this b ahmtclepesosi antx ssml spossible as simple as text main in expressions mathematical where water, liquid the opnns,tegnrlzdetap eue owa sno call and is terminology, what to reduces com enthalpy gaseous generalized any the for components), law gas ideal the (namely approximations motn,tequantity the gravita important, found in enthalpy changes where of processes, definition laboratory–scale with standard a to corresponds which Here, terms), pressure. in change a through enthalpy rnfrain.Hdottcblneesrsta n cha any that ensures balance s Hydrostatic the transformations. that expected intuitively also is It energy. potential otn”,tescn emi oeta otiuint th to contribution potential a is term second the content”), g water, liquid of vapourization o liue eo bu 0m n t fetwl therefor will effect its and 50km, about below altitudes for where sp its approximation, standard the Under convection. moist proc adiabatic moist under conserved is energy static Moist Definition 2. ag iceac ewe h xc ento n h stand the and definition exact the between discrepancy dis large analogous an by inspired partially being A, Appendix the h hneo h ausi AE(ovcieaalbepoten available (convective CAPE in values the of change the conse the invoking by disc definitions this two these is on serious based buoyancy how But values. tropical typical for K 15 0 Z aigteielgsapoiain h pcfi nhlyis enthalpy specific the approximation, gas ideal the Taking ndrvn neatepeso,w a iieteaoeexpr above the divide may we expression, exact an deriving In h hsclmaigo hsdfiiino os ttcenerg static moist of definition this of meaning physical The with q c h ˜ l Accepted Articlepd n h rvttoa oeta nry Thus, energy. potential gravitational the and , steseiclqi ae,and water, liquid specific the is g 0 steha aaiyo h r i tcntn pressure, constant at air dry the of capacity heat the is eeec au o h ceeaino rvt and gravity of acceleration the for value reference a h l Thus, . h ˜ h h nhly and enthalpy, the eoe h osre aibe mam(00 e.54 cal 5.4) Sec. (2010, Ambaum variable. conserved the becomes This article isprotected bycopyright. Allrightsreserved. g ceeaino h gravity, the of acceleration h q t h os ttcenergy. static moist the = q v + h ˜ q (1 = l otiuino c scniee eaaeyi Appendix in separately considered is ice of contribution A . h mo hs he em ol ecnevdudraibtcan adiabatic under conserved be would terms three these of um rttr u oltn etn,adtels emi h spec the is term last the and heating, latent to due term first e = einrdhere. ignored be e h ˜ − se n ne yrsai aac,tu ti sflquan useful a is it thus balance, hydrostatic under and esses cfi au vleprttlarms)i endby defined is mass) air total per (value value ecific g ngaiainlptnileeg scmestdfrby for compensated is energy potential gravitational in nge inlptnilcnb elce.We hne npotentia in changes When neglected. be can potential tional . c r prxmt ento fmitsai nryi on,r found, is energy static moist of definition approximate ard ≃ uso netoyb Pauluis by entropy on cussion z q h eac?I re oase hsqeto,w vlaeteli the evaluate we question, this answer to order In repancy? pd ileeg)a result. a as energy) tial mlycle h os ttceeg.Hr,w ilaotth adopt will we Here, energy. static moist the called rmally vto fmitsai nryudrti rcs Sc ) W 4). (Sec. process this under energy static moist of rvation t ie yasmo otiuin rmdyair, dry from contributions of sum a by given h liue h eptnilcontribution, geopotential The altitude. the ) c = T srltvl nutv:tefis emi h r–i entha dry–air the is term first the intuitive: relatively is y h pd Z sinit h w otiuin:te“rpr nhly(t enthalpy “proper” the contributions: two the into ession d oet n nopesblt supin o h oi an solid the for assumptions incompressibility and ponents h ˜ + T h eptnilhih.Tepeetapoiaini very is approximation present The height. geopotential the + ntxboso hroyais hc r otyconcerned mostly are which thermodynamics, on textbooks in + T q + q v gz. v h temperature, the L q h v + L, v gz, + q l h l , q ls v h h pcfi aorvalue, vapour specific the tal. et h eeaie nhly ne standard Under enthalpy. generalized the 21) hr,prassrrsnl,a surprisingly, perhaps Third, (2010). gz h sa prxmto of approximation an is , d ae vapour, water , o epn the keeping for B iyt understand to tity fi gravitational ific L ahn about eaching loaddress also e aetha of heat latent hydrostatic d p o “heat (or lpy nryare energy l hneof change a fting–parcel efis two first he sstandard is accurate liquid d h v and , (4) (3) (2) (1) etcpct seaie eaaeyi pedxC. Appendix in separately examined is capacity heat -20 to down ranges incompressibili pressure as well as capacity heat specific constant a temperat atmospheric fo for accurate simple very is This which component. assumption each for pressure e constant zero-point at (a heat constant reference a is term first the which in ihtesubscript the with q 7 a ecniee h nlepeso ogt spres as sought, expression final the considered be may (7) Eq. where ol erpae yta o h oa i icuigcontai (including air total the for that by replaced be would ( enthalpy “liquid–water” called Removing E interest. of take range we temperature reason, a around this expression For (2005). Koop and Murphy by reviewed large the considering especially difficult is computations ( transitions phase excluding temperature, ne hssrc xrsin h eeec value, reference the expression, strict this Under titysekn,ec xrsini q 5 utb writte be must (5) Eq. in expression each speaking, Strictly ahseicetap au sdfie by defined is value enthalpy specific Each qain()i,hwvr adt nepe na nutv m intuitive an in interpret to hard however, is, (7) Equation Accepted relat are water liquid and vapour for enthalpies specific The Article h v yE.()i q 4,adsbtttn h eann express remaining the substituting and (4), Eq. in (6) Eq. by j ugsigacmoetwt h etcapacity, heat the with component a suggesting ◦ ( C e.g. This article isprotected by copyright. All rights reserved. cf. h mne 94,otie yremoving by obtained 1994), Emanuel , i.6o upyadKo 05.Teefc ftetemperatur the of effect The 2005). Koop and Murphy of 6 Fig. , d = h cf. 0 d itladKomr18,C.6.Hwvr h s fti str this of use the However, 6). Ch. 1980, Kroemer and Kittel , + h ˜ c ˜ = pd h c 0 p ,h T, c j p a la hsclmaiga netap au extrapola value enthalpy an as meaning physical clear a has , h (1 = T j c ˜ p = + (1 = − netite ndt oad h ii fteaslt zero absolute the of limit the towards data in uncertainties h q e odne ae) hc seulto equal is which water), condensed ned y gi,teeasmtosaeacrt o topei t atmospheric for accurate are assumptions these Again, ty. r n rsuerne.Tesml omfrtelqi compo liquid the for form simple The ranges. pressure and ure v 0 L eg) n h eodtr sarltv au proportional value relative a is term second the and nergy), v q ne in ented j L nteform the in n t dt h aetha fvapourization, of heat latent the to ed = = ) + − mfrtegsoscmoet sue htte r da gas ideal are they that assumes components gaseous the for rm ne:w xetta h etcapacity, heat the that expect we anner: c (1 + pd h Z q h t 0 0 v ) v + T c .() hti osdrdago prxmto o hsrigo this for approximation good a considered is that (5), q. − − + pd e.g. c q c pj h v q pj c + l t pv c ( . aqe 19,21) mne 19) natraieform alternative An (1994). Emanuel 2015), (1993, Marquet , ) tcntn rsuedfie safnto ftemperature. of function a as defined pressure constant at , pv T osfo q 5,w obtain we (5), Eq. from ions h q ,h T, t 0 ′ h ) + d c dT l l + . nta,i icse eaaeyi pedxA. Appendix in separately discussed is instead, q l ′ q c t l . h l 0 = l , h 0 l + c l T, L eednei h liquid–water the in dependence e by , c pd c xrsinfrpractical for expression ict o h r i nE.(3) Eq. in air dry the for , e ozr absolute zero to ted meaueand emperature eprtr,as temperature, otespecific the to etassumes nent s an es, rous (5) (8) (7) (9) (6) 68 67 66 65 64 63 h r etcapacity, heat dry the 4. Sec. in addressed be au fltn heat, latent of value notedyaradtewtrdpnecso h eeec c reference the on dependences water the and dry–air the into si(95,YuadAsi 17) uldeadHbs(1983 Hobbs and Rutledge (1979), Austin and Yau conde (1965), of Asai effect the consider example For case. the generally au fterfrnecntn a eansmwa counter somewhat remain may constant reference the of value thus h of instead However, rma prxmto 3 yreplacing by (3) approximation the an against from interpret to easier much is (12) expression This atmos typical for evaporation of heat latent the that Recall he latent the fin of we extrapolation temperatures, atmospheric linear typical from the extrapolated as seen be can which Sec. 2010, (Ambaum, gases ideal for equation Kirchhoff’s of and 0 l tmyb epigt ocueta o civn physically achieving for that conclude to tempting be may It usiuino q 1)it q 7 nlylasto: leads finally (7) Eq. into (10) Eq. of Substitution not we when alleviated be may outcome counterintuitive This o iudwtretap ntels em tmgthv be have might It term. last the in enthalpy liquid–water for , q t

Accepted Article = q v fcus hscutrnutv ucm stersl fst of result the is outcome counterintuitive this course Of . L c p c feaoain hswl aeasbtnilefc ntec the on effect substantial a have will This evaporation. of , pd eget we , ytefl aclha capacity, heat parcel full the by , c ˜ p endb q 8.I sas o biu h h oa ae is water total the why obvious not also is It (8). Eq. by defined This article isprotected by copyright. All rights reserved. c pd by h ˜ c = p c and p T L L L + L 0 by = hrctmeaue sapproximately is temperatures pheric 3 = q ≃ − c L d v p tnadapoiaeepeso 3:a xc xrsin( expression exact an (3): expression approximate standard L L 0 L sto ntetmeaueo acl tnadprocedure standard A parcel. a of temperature the on nsation 2 L n h aetheat, latent the and , ntns oeas that also Note onstants. ∆ 3.6): . . 0 0 = 0 14 5 ossetepesosivligetap,alw edt d to need we all enthalpy, involving expressions consistent nmr nutv oexpect, to intuitive more en nutv,i snwcerta t au sdtrie yspl by determined is value its that clear now is it intuitive, utemr,arfrnecntn au utb de.Alt added. be must value constant reference a Furthermore, . − q ,Gaosi18,18) noe h relation: the invokes 1989), Grabowski(1988, ), + × c htsbttto fE.()it q 6 ed oa integ an to leads (6) Eq. into (5) Eq. of substitution that ice h v × to vprto ozr bouetmeaue o ae va water For temperature. absolute zero to evaporation of at ( 0 h 10 = c v 10 0 l d − 6 c − 6 nadagbacmnplto.Hwvr t omi o uni not is form its However, manipulation. algebraic andard p kg J + h ∆ c kg J pv 0 q T, l t , − ) ( − T, 1 h . 1 0 . l − luae auso os ttceeg,a sgigto going is as energy, static moist of values alculated L h yisetaoae value extrapolated its by , 0 d L ) 0 . sabout is h 0 v seilywe h i sunsaturated, is air the when especially , 25% egtdb h eeec constant reference the by weighted agrta h yia expected typical the than larger L 0 oee,ti snot is this However, . 2 sobtained is 12) st replace to is o sfudin found as , tigi out it itting a version ral og the hough pour (13) (11) (12) (10) que. ftecntnstesle,whilst themselves, constants the of fagvnsbtnewihol eed ntecag nrefer in change the on depends only which substance given a of hseuto rvdstertoaefrE 1) n h sub constants the and (13), E. for rationale the provides equation This rearra some after and (15), Eq. into (16) Eq. substituting By anymo constant not is pressure constant at capacity heat The osdrn suoaibtcacn) enweaiehwt how examine now We ascent). pseudo-adiabatic considering cons reference first The constants. reference the involving hieo h au for value water, the total of choice specific the to proportional is term constant Thus, h nlrsl,E.(2 bv,i arycoet h standa the to close fairly is above, (12) Eq. result, final The Law Conservation a and Constants Reference 3. i is water total of conservation and (10), the Eq. when by (13), given as Eq. heat to equivalent be to out turns equation This h etcpct.S h prpit qainfrteconde the for equation appropriate the So capacity. heat the eso q1,te tdoes it then proce 12, condensation Eq version the under conserved is enthalpy that and “h the of increase the with balances side) hand (left heating where tcntn rsuei prxmtdb hto h r i,t air, dry the of that by approximated is pressure constant at o hsproe etk h oa eiaieo h os st moist the of derivative total the take we purpose, this For h bv formula above The h −

Accepted0 Article ∆ d h q a aeayabtayvle n emyset may we and value, arbitrary any take can 0 v l steaon fcnesto,and condensation, of amount the is − h 0 d hsi ifrn rmtedpnec nrfrneconstan reference on dependence the from different is This . appears h 0 l − not h 0 ob ae nteasmto htteetap sdfie by defined is enthalpy the that assumption the on based be to olwthat follow d This article isprotected bycopyright. Allrightsreserved. ol fettewoebde o h os ttceeg whe energy static moist the for budget whole the affect would h 0 l − d − h h ˜ 0 L d = 0 ∆ is dc c d ∆ p q h ˜ p o ietymeasurable directly not v T dT = ( = = − stersligices ftmeaueb aetheating. latent by temperature of increase resulting the is c + L c p c p 0 l dT dc T h ∆ ∆ q − 0 atterm, tant h ˜ t eun icsin oeta h au of value the that Note discussion. sequent sto is nsation a otn”o h i rgthn side). hand (right air the of content” eat T, d q gmnsb ealn q 1) eobtain we (10), Eq. recalling by ngements hs h au fti emcagswith changes term this of value the Thus, . e but re, c + vkds that so nvoked hus v = dapoiaeepeso,E.() xetfrtetoaddit two the for except (3), Eq. expression, approximate rd pd p evleof value he 0 = tceeg endb q (12): Eq. by defined energy atic s(mam21,Sc .) fw elc hseuto ythe by equation this replace we If 5.4). Sec. 2010, (Ambaum ss eas h hnigcmoiinfloigcnesto a condensation following composition changing the because = dq L + ulha aaiyi used, is capacity heat full c ) p necntnsars h hs rniin o nteabsol the on not transition, phase the across constants ence c dq c L T p ihu oso eeaiy nteohrhn,tescn ref second the hand, other the On generality. of loss without p 0 v t ∆ ≃ + dq − h ( + T q c 0 v ( pd v d + c h sjs osat n tde o hneb n processes. any by change not does it and constant, a just is , L, ( + h l ee hseuto ipysae htteaon flatent of amount the that states simply equation this Here, . l T 0 − − ncascleprmnsadi o rpryo given a of property a not is and experiments classical in ∆ l ∆ h − c q h 0 c pv l l d p h − = ) , sof ts ) 0 dq dq d h − fet h ugtmr precisely. more budget the affects t 0 v ∆ . d . L ) q dq v = . t L h . v steuultmeauedpnetlatent dependent temperature usual the is − anflsoto h acl( parcel the of out falls rain n h l h atri esrbeproperty measurable a is latter the ; h l − q h t n tloslk htthe that like looks it and , d eed ntereference the on depends fe,teha capacity heat the Often, s changes lso oa terms ional e.g. t value ute when , erence exact (17) (16) (15) (14) u etga st xmn h xetta n aaaayi r analysis data any that extent the examine to is goal next Our Analysis Data 4. discus further a with separately A Appendix wi the issue in equivalent discussed An enthalpy. the for values different to nta ftesadr prxmt ento 3.Frthis For (3). definition approximate standard the of instead o constant reference of change apparent an as up show not does eeec osat o h opnnscnb used. be can components the for constants entha reference specific zero-point the for values different have will be must bv 0 P,ad1 P bv 0hPa. 60 above hPa 10 resolut and vertical hPa, a 100 with above level hPa 30 to hPa) (1015 surface the Jorda by assembled season) hurricane the (for July–October it because small case any in is but (17), Eq. of term second amount the an by increased has mixture parcel remov the is in enthalpy its and liquid the process, precipitation ( process precipitation The manner. eaaeyt h rcptbewtr(naon of amount (an water precipitable the to noth separately step, first the In parcel. the from precipitat liquid the precipitating of parcel the within separation the 1) steps: entha the of consistency Thus, The parcel. the of parts solid) p a (and when enthalpy, specific the keeping book for only needed is suggests, argument above the as However, transported. also water, total of amount an As specified. be r components. enthal dry specific the in property artificial an is It substance. i)We h oa ae sntcnevd and conserved, not is water total the When (ii) safia odo ann adufruaeadtoa confus additional unfortunate (and warning of word final a As ne hs osdrtos ecnset can we considerations, these Under h esnfor reason The nodrt ls h nhlybde,teetap transpor enthalpy the budget, enthalpy the close to order In npcino q 1)last w conclusions: two to leads (17) Eq. of Inspection i hntettlwtri osre,and conserved, is water total the When (i) h soitdwt rcptto.Tu,teetap transpo enthalpy the Thus, precipitation. with associated sls ypeiiain h constant, the precipitation, by lost is 0

Accepted( Article l h − l − h 0 h d d a eseie na rirr manner. arbitrary an in specified be can ) dq h 0 t l ee hr sn hroyai rnfraininvolved, transformation thermodynamic no is there Here, . − h 0 d o lyn n ati h hroyaiso h aclmyf may parcel the of thermodynamics the in part any playing not i.e. , This article isprotected bycopyright. Allrightsreserved. dq h t 0 dq = l − h t dq dq stasotdfo n oiint nte,a muto en of amount an another, to position one from transported is , 0 h l t l 0 − d 0 = < dq − − h 0 = t h dq 0 0 h constant, the , eaae u h rcptbewtrfo h eto h pa the of rest the from water precipitable the out separates ) d l 0 6= t ensterate, the defines , dq n rtodrefc fcagn asfato ftevapou the of fraction mass changing of effect order first Any . ntefloigaayi,s httecag fcomposition of change the that so analysis, following the in ybde eutn nyfo hnigtems ai betwee ratio mass the changing from only resulting budget py n apn otettlpre,btteetap nteparce the in enthalpy the but parcel, total the to happens ing n iudadters ftemxuei h acl n )the 2) and parcel, the in mixture the of rest the and liquid ing t h constant, the , dfo h aclmxue u nti tptems fraction mass the step this in but mixture, parcel the from ed p aus hnr-acltn h nhlyo h e mixt new the of enthalpy the re-calculating When values. lpy e ntttlms)adt h eto h itr.I h seco the In mixture. the of rest the to and mass) total unit per ups,w s w aast.Tefis sama aiba sou Caribbean mean a is first The sets. data two use we purpose, 15) n sgvnb i al .Ti onigpoie v provides sounding This 5. Table his by given as and (1958), n hetoyi xesvl icse yPauluis by discussed extensively is entropy th t culvlepasn te ati h hroyaisof thermodynamics the in part other no plays value actual its ino h infiac ftoecntn values. constant those of significance the on sion aems eseie.Frti ups,tevleof value the purpose, this For specified. be must rate t o f5 P rm10 P o20ha 5haaoe20ha 0hP 20 hPa, 200 above hPa 25 hPa, 200 to hPa 1000 from hPa 50 of ion p ugti anandrgrls ftevleasge to assigned value the of regardless maintained is budget lpy re opsto hne hog rvttoa separati gravitational through changes composition arcel trt ypeiiaindpnso hieo h au of value the of choice a on depends precipitation by rate rt slsaemdfidb sn h xc ento 1)frtee the for (12) definition exact the using by modified are esults h mixture. the f spootoa to proportional is o) oee,dfeetcocsfrteecntn values constant these for choices different however, ion), h 0 l − h 0 ( h l h 0 − l d − osntafc h budget. the affect not does , h 0 h d utarcgiinta ifrn opsto mixtures composition different that recognition a just d utb pcfid seily hntettlwater total the when Especially, specified. be must , ) dq dq t h e hnei pcfi nhly therefore, enthalpy, specific in change net The . t htteetap sls oal ytransport by locally lost is enthalpy the that , rhrb nesodi h following the in understood be urther tal. et thalpy, clb aigtetwo the taking by rcel 21) h aeis same The (2010). h u oprecipitation to due 0 ( a eallocated be can l l h − 0 h iudand liquid the n scpue in captured is r no h liquid the of on l eoa fthe of removal dse fthe of step nd h r,tesame the ure, − ftedyair dry the of h acl It parcel. the h 0 nedlead indeed d h 0 le from alues h l 0 utalso must dn for nding 0 d − l nthalpy ) − dq h 0 h t d is , 0 . d a . yFg fYn 20) ic h netite associated uncertainties the Since (2003). Yano of 2 lift Fig. simple by a of that from reduced substantially is buoyancy (12 Yano definition in exact the adopting by values CAPE of change the s buoya Jordan reversible the the for and 2 (12), definition Fig. exact in the shown adopting are energy static moist the for obtain is buoyancy, “pseudo-adiabatic” called definition, th to leads computation this on based buoyancy resulting New The a by calculated is level given a at temperature parcel the water, total the that assume also and F nFg ()ad()aogwt h rcptto aei ( in rate precipitation the with along (b) and 3(a) Fig. in IFA wher altitudes find we case reversible the absolu for the and in large, change very the as dramatic as not is buoyancy parcel saturatio the Above manner. straightforward a in evaluated the level, saturation the Below layer. boundary well–mixed ifrnefudi i.3apasls significant. less appears 3 Fig. in found difference a ie au 0Jk agrta h prxmtdexpressio approximated the than larger J/kg 50 value a pe gives vertical TOGA-COARE 12: whole (Eq. expression the exact the for and axis) CAPE horizontal of types two of plots scatter cnetv vial oeta nry.TeetoCP ti CAPE two These energy). potential available (convective li is parcel The parcel. lifting the for variable conserved a ( environment the and S hPa. 25 of resolution vertical a with level hPa 25 to hPa 1000 ca topeeRsos xeiet nesv Observin Intensive Experiment) Response Atmosphere Ocean aasti rcse tteSaeUiest fClrd and (http://tornado.atmos.colostate.edu/togadata/ifa Colorado of University State the at processed is set data o h os ttceeg.Rcl httepre buoyancy parcel the that Recall energy. static moist the for th near coincide geoid the above height geometric the and for height offset constant arbitrary an introduces also energy constant, the as reason same the t for that budget, note also we However, (3). expression (12) approximate expression the exact the adopting By sounding. mean Jordan h bandpre uynyudrteetodfiiin for definitions two these under buoyancy parcel obtained The oee,we sn AEi uniaiefsin h adop the fashion, quantitative a in CAPE using when However, h etclitga ftepstv aclboac under buoyancy parcel positive the of integral vertical The h eoddt e soe h nesv lxAry(F)dur (IFA) Array Flux Intensive the over is set data second The Accepted Article c the examine to turn now we impacts, physical more seeking In c energy static moist the of profiles vertical the shows 1 Fig. tal. et 21) AEi sflmil saqaiaiemaueo con of measure qualitative a as mainly useful is CAPE (2013), cf. ofadYn 02.Hr,i optn h lifting–parcel the computing in Here, 2002). Yano and Roff , This article isprotected bycopyright. Allrightsreserved. q t scnevd sarsl,teseiclqi ae is water liquid specific the result, a As conserved. is , h 0 l aahm:Ciesielski data.html: − h 0 d a eabtaycoe sdsusdi h atscin (N section. last the in discussed as chosen arbitrary be can , db setting by ed xs.I sse htteeatepeso ftereversible the of expression exact the that seen is It axis). ee,w e h pcfi aort h auae au,thu value, saturated the to vapour specific the set we level, n oeta nry hc stpclycoe ob eos tha so zero be to chosen typically is which energy, potential esre r lte o h rt3 aso h OACAEIO TOGA–COARE the of days 30 first the for plotted are series me n–aclboac ya nrimn rcs ssuggested as process entrainment an by buoyancy ing–parcel tdfo h 5 P ee,a napoiaehih o h t the for height approximate an as level, hPa 950 the from fted pcfi aorvalue, vapour specific eo 5 /g() bv hsvle h prxmtdexpr approximated the value, this Above (a). J/kg 250 below n h ino h uynycagsbtentetodefinitions two the between changes buoyancy the of sign the e o–aho ehdasmn h osraino h os s moist the of conservation the assuming method ton–Raphson c erae yasmlrbtlse xet tfc au th value face At extent. lesser but similar a by decreases ncy eesbeboac,a owtrflsotfo h parcel. the from out falls water no as buoyancy, reversible e ihtecnetv nrimn ( entrainment convective the with vial rmteweb the from available surface.) e sdfie yadfeec ftevrultmeauebetween temperature virtual the of difference a by defined is ) hs iesre,aan ofimtecnlso rmFig from conclusion the confirm again, series, time These c). elclaslt au fmitsai nryde o lya play not does energy static moist of value absolute local he eid(O oebr 92truht 8Fbur,1993) February, 28 to through 1992 November, 1 — (IOP Period g evleo h os ttceeg.Hwvr h eaiech relative the However, energy. static moist the of value te h os ttceeg nrae y1 ttesraecomp surface the at K 15 by increases energy static moist the , udnsaegvneey1 hours. 12 every given are oundings hs w entoslast eesbeadpseudo–adiaba and reversible to leads definitions two these h uyny(eesbeadped–daai)adtetwo the and pseudo–adiabatic) and (reversible buoyancy the sceryntngiil,i sntdaai.A discussed As dramatic. not is it negligible, not clearly is ) n h OACAE(rpclOenGoa topeeCoupl Atmosphere Global Ocean (Tropical TOGA–COARE the ing mue ytetodfiiin 1)ad()o h nhlyfor enthalpy the of (3) and (12) definitions two the by omputed ag ftelfigpre uynyb dpigteeatd exact the adopting by buoyancy lifting–parcel the of hange udn.Teped–daai uynydcessb whe K 1 by decreases buoyancy pseudo–adiabatic The ounding. ino h xc ento 1)sesiprtv.Fgr s 4 Figure imperative. seems (12) definition exact the of tion tal. et q l idcluae ewe h prxmt xrsin(q 3: (Eq. expression approximate the between calculated riod 0 = 03.Tedt ossso ufc aus n ausfrom values and values, surface of consists data The 2003). ntefia result. final the in etv ntblt.Epcal,tevleo convective of value the Especially, instability. vective q v sas osre,tu h acltmeaueis temperature parcel the thus conserved, also is , uyny h os ttceeg sue as used is energy static moist the buoyancy, q l cf. = eRooy de , q t − q v ∗ ( T tal. et ) ne hs constraints, these Under . 03 ss ag that large so is 2013) t htmitstatic moist that ote AEconsistently CAPE h alternative The s geopotential t q sintends ession o example for energy. tatic o example for necnbe can ange hnein change e v :though 2: . . definitions oei the in role h parcel the i CAPE tic po the of op = efinition rdto ared q over P v ∗ hows The . ( T the ed ) n , ee h subscript the Here, gi,ta h constants, the that again, removing by obtained is entr of definitions different Pauluis under hand, coordinates other isentropic the On 3. Sec. in made is point Constants Reference and Enthalpy Liquid–Water A: Appendix upr fCR ISa ela h nvriyo edn a e has Reading of University the as well as PICS CNRS of Support Acknowledgement J/kg. 200 re the overestimating typically equations approximate the a into taking of importance crucial the is re–writing this of aaee svsl neti ( uncertain vastly is parameter constants. enthalpy the of values absolute the conservation the that applications, shown explicitly practical have We importance. in However, specified. be also must de the of re–writing a that shown have we Here, (3). definition ya nrimn ae hntecag fboac yentrai by buoyancy of change the when rate, entrainment an by sets ( pa data parameterization the tropical of properties from qualitative only CAPE when minor as relatively well as value buoyancy parcel ae hspprhseaie hsqeto ytkn h moi the taking by question this examined has paper This have? approximati standard Instead, used. rarely are definitions variab thermodynamic atmospheric the for definitions Exact Conclusions and Discussions 5. T value. exact the to Fo compared % rare. 15 are by value cases the such overestimates though underestimation, an to lead to nti epc,teetap osdrdi h antx cor text main the in considered enthalpy the respect, this In h rsn ae mhszsta h hieo nendcon undefined of choice the that emphasizes paper present The sepaie yMrut(05,we bouevle fthe of values absolute when (2015), Marquet by emphasized As rcia osqecso sn h xc ento rtes the or definition exact the using of consequences Practical Accepted Article en static moist the for (7) definition exact the sight, first At cf. w Yano , This article isprotected bycopyright. Allrightsreserved. saddt mhsz h lqi ae”dfiiin nargum An definition. water” “liquid the emphasize to added is h h l d rmE.()b q 6 nta of instead (6) Eq. by (4) Eq. from 0 tal. et and cf. eRooy de , 03.Freape h culvleo AEfrara parcel real a for CAPE of value actual the example, For 2013). h v 0 a ecoe rirr ymitiigtecnitnywit consistency the maintaining by arbitrary chosen be can , tal. et h ˜ w 03.Nvrhls,tetodfiiin iequantitative give definitions two the Nevertheless, 2013). = c tal. et p T p:mitadliquid–water. and moist opy: n r dpe.Te htkn fcneune ol uhap such would consequences of kind what Then adopted. are ons − 21)pitotadfeec ftema eiinlcircula meridional mean the of difference a out point (2010) esbeCP yaot5 /g n h suoaibtcCAP pseudo–adiabatic the and J/kg, 50 about by CAPE versible cuttetmeauedpnec nteltn heat. latent the in dependence temperature the ccount clboac rCP r ocre,epcal ncneto context in especially concerned, are CAPE or buoyancy rcel q a o h os ttceeg a ossetyb endwi defined be consistently can energy static moist the for law l e r nw nteltrtr.Hwvr npatcldt a data practical in However, literature. the in known are les L epnst h mit ento.Atraiedfiiin( definition Alternative definition. “moist” the to responds h nyterltv ausars hs rniin ltn h (latent transitions phase across values relative the only nto 1)mksi oepyial nutv.A importa An intuitive. physically more it makes (12) finition tsai nrya nexample. an as energy static st 0 h suoaibtcCP b,teapoiain()cons (3) approximation the (b), CAPE pseudo–adiabatic the r v emxmmdfeec ece 0 /gfrlreCP values CAPE large for J/kg 200 reaches difference maximum he adr prxmtosaeeaie ycmuigbt h l the both computing by examined are approximations tandard ryapasnta hsclyitiiea h tnadapp standard the as intuitive physically as not appears ergy mn sas ae noacut( account into taken also is nment + tnsi hroyaisfrua a opatclconsequ practical no has formulas thermodynamics in stants ofida lentv omo h xrsinfrseicenth specific for expression the of form alternative an find to aldti collaboration. this nabled mdnmcvralsaecnend h eeec constan reference the concerned, are variables rmodynamic h d ae nbt fte.W hwta h oictosare modifications the that show We them. of both on based 0 + q t ( h v 0 − h n aallt h n aei h antx says, text main the in made one the to parallel ent d 0 ) . ol ieyb oesrnl affected strongly more be likely would h osrainlwof law conservation the h cf. i.2 ao20) h latter The 2003). Yano 2, Fig. , yvr ifrn aus with values, different very ly in endin defined tions lqi water”) “liquid hu defining thout ayi,these nalysis, proximations convection f as r of are eats) tcorollary nt h ˜ yu to up by E ne this ence: w roximate alpy: values t . istently ifting– . ( A. 1) ealta h osraino nhlyi aifidol un only satisfied is enthalpy of conservation the that Recall law. conservation thermodynamic the that fact the contradict not does this However, entropy. numeric different two to lead definitions two these Clearly, h nhlyi otb rate, a by lost is enthalpy the difference, above the conserved, is water total oa ae otn.We hsi o h ae h ainei variance the case, the not is this When content. water sta total moist or entropy of conservation underlying some assume entropy. of definition the of choice the on depending results Pauluis entropy, to analysis same definitions the two the result, a as and constant, remains longer pedxB otiuino c oteMitSai Energy Static Moist the to Ice of Contribution B: Appendix 3. Sec. arbitrarily–rela the defining of effects subsequent the and water, of definition the with where find we ne h tnadapproximation. standard the under oeuiaeti on,w a aetedfeec ftetwo the of difference the take can we point, this elucidate To hs ysetting by Thus, oee,we h odne ae sls rma i parcel, air an from lost is water condensed the when However, h otiuino c sotie yadn h c enthalp ice the adding by obtained is ice of contribution The q L t

Acceptedi Article ee h rirr osat r e eofrcaiy Thi clarity. for zero set are constants arbitrary the Here, . steltn etb c uin sarsl,i lc fE.(7 Eq. of place in result, a As fusion. ice by heat latent the is h d c ˜ 0 p = eann h aebttecnrbto fteseicice, specific the of contribution the but same the remaining h l 0 This article isprotected by copyright. All rights reserved. 0 = h l − nE.(2,and (12), Eq. in h d tal. et and 21)so htteietoi–oriaebsdma circ mean based isentropic–coordinate the that show (2010) h v q − t L h 0 d h nycnrbtsafie constant. fixed a contributes only , epciey ne h w entos rmta on,t point, that From definitions. two the under respectively, , d 0 h ˜ h ˜ = = ˜ = h ˜ e eopiteege ftedyaradwtrcomponents, water and air dry the of energies zero-point ted h nhlyudrbt entoscnb sdt ananteco the maintain to used be can definitions both under enthalpy w c h ˜ h ˜ lvle o nhly sepaie yPauluis by emphasized as enthalpy, for values al v c oee,t nepe uhcruain naLgaga sen Lagrangian a in circulations such interpret to However, pd e osraino oa ae,a ugse yE.(7.S (17). Eq. by suggested as water, total of conservation a der fetap ilso ifrn ptotmoa distribut spatio–temporal different show will enthalpy of h p 0 − = = nrp rmitsai nrywl edet h ayn com varying the to due be will energy static moist or entropy n i i nry sidctdaoe hsrqie arninco Lagrangian requires this above, indicated As energy. tic T 0 = y, T = h ˜ c c definitions: + p p w h + xrsinfrhrrdcsto reduces further expression s h a,det h rcptto,teisebcmsmr involv more becomes issue the precipitation, the to due say, i T T nE.(.) eoti w ifrn xrsin o h ent the for expressions different two obtain we (A.1), Eq. in q = otefrua rsne ntemi et ee iia to similar Here, text. main the in presented formulas the to , l q v v − + − L q L ,w obtain we ), t q q L − L l v − i L , 0 L q q . 0 i 0 i . L , L i i , , q i nlddt ntedfiiino h oa specific total the of definition the in to included , lto nlsslast different to leads analysis ulation tal. et edifference, he 21)i h aeof case the in (2010) os yapplying By ions. ew implicitly we se sepandin explained as ssec with nsistency srainof nservation oga the as long o d Now, ed. q position halpy: t q (6), Eq. L (A.2b) (A.2a) ( ( ( 0 B. B. B. no , 2) 1) 3) where subscript the (C.1) Eq. In to from J/K/kg of unit the into converted be easily can it but (2005), h osdrddt ag.Teui stknt eJKmli o in J/K/mol be to taken is unit The range. data considered the Water Liquid the of Dependence Temperature C: Appendix (B. Eq. under heating ice–fusion constant t a that of Note assumption solid). an B.5: (Eq. formula exact the and dash) long yacresoni i.6() ee ute eraeo h h the of decrease further a Here, (a). 6 Fig. in shown curve a by by shown as important, becomes dependence temperature its water–v (1998). Grabowski specific saturated the interpolate linearly condensate also total the We among ice of fraction the that assume we e.g. homogene increased is CAPE level, freezing the above frozen buoyanc parcel reversible the of change the investigate can q B2 ed otefia expression: final the to leads (B.2) Eq. -20 effect. of definition the Here, with h eprtr–eedn etcapacity, heat temperature–dependent The c heat the for considered is dependence temperature the When srmre ntemi et h etcpct ftelqi w liquid the of capacity heat the text, main the in remarked As profil buoyancy reversible the of modifications obtained The o hsproe eielz h pia uv hw nFig. in shown curve optimal the idealize we purpose, this For (B. and (B.3) Eqs. definitions, modified these introducing By eas oe iia oE.(10), Eq. to similar note, also We ◦ ofadYn 20) nraiy usata rcinof fraction substantial a reality, In (2002). Yano and Roff , sarfrnetmeauei pligE.(.)i computa in (B.4) Eq. applying in temperature reference a as C L ∆ 0

Accepted Article i c 3 = l stecag ftelqi–ae etcpct yconsideri by capacity heat liquid–water the of change the is . 0 × 10 This article isprotected bycopyright. Allrightsreserved. 6 /g ee ycnieigarltvl togtemperature strong relatively a considering by Here, K/kg. c p ean h aea ntemi et u h pcfi ice, specific the but text, main the in as same the remains 0 saddi enn fteha aaiyi re oexplicitl to order in capacity heat the of defining in added is c l nE.(.)myb eaae notetoparts: two the into separated be may (C.2) Eq. in , h ˜ L = h i l c = yadn h c uinefc.I swl nw htwe al when that known well is It effect. fusion ice the adding by y p c pu from apour = l water, the of mass molar the by it dividing by L T 3). edfeec ftetocre setal oe rmteer the from comes essentially curves two the of difference he = h h ul y10 /gapoiaeyi rpcldt nlssa analysis data tropical in approximately J/kg 1000 by ously 0 ieryicessfo eot nt from unity to zero from increases linearly e.g. ae ean uecoe iudwtrblwtefezn p freezing the below water liquid supercooled remains water rmFg r hw nFg ohwt h prxmto (E approximation the with both 5 Fig. in shown are 2 Fig. from e + 0 drt aiiaeadrc oprsnwt i.6o upya Murphy of 6 Fig. with comparison direct a facilitate to rder l i tri arycntn ont -20 to down constant fairly is ater ) fteetap notedfiiin()o h os static moist the of (2) definition the into enthalpy the of 5), fMrh n op(05 o h etcpct fteliquid the of capacity heat the for (2005) Koop and Murphy of 6 l c − = l q pct,tedfiiino h iudwtretap utbe must enthalpy liquid–water the of definition the apacity, a aaiyblw20Ki o osdrd eas hti be is that because considered, not is K 210 below capacity eat + 0 i.6o upyadKo 20) hsapni xmnsthi examines appendix This (2005). Koop and Murphy of 6 Fig. , v ( in eo ( below tions c ∆ + Z c L l 0 i 0 0 T gistmeauedependence,. temperature its ng − T − T c c c w l l q , pv dT i to L ) T 0 T i i . i.e. rmtelqi au oteievleb following by value ice the to value liquid the from q eedneo h c etcapacity, heat ice the of dependence , i nlddt h oa water, total the to included , c i niaeta h etcpct sconstant. is capacity heat the that indicate y 2106 = /gK.Sbttto fE.(.)into (B.4) Eq. of Substitution J/kg/K). ◦ .Blwti eprtr,however, temperature, this Below C. T 18 w . = 015 − 5 q × ◦ t . to C 10 − 3 T h ae is water the l c kg/mol. i i hw by shown s osdeto due rors eadopt we , nry we energy, it Here, oint. = dKoop nd changed − .B.3: q. 20 ( ( ( ( ( water yond B. B. C. C. C. ◦ C. 1) 3) 2) 5) 4) s feti ieyt engetdi oto h rcia appl practical the of most in neglected be to likely is effect -30 h below 250 is above temperature only the seen and minor, fairly is capacity heat water ogdse uv gis h eal au ihu hsef this without value default the against curve long–dashed account into taking buoyancy the of change the that expect we eprtr ag,tefatoa change, fractional the importantly, range, temperature More values. higher presents itself capacity ii ( limit sa fetv hneo h etcpct ycnieigth considering by value, capacity reference heat the of change effective an is where by given is h eutn hneo h eesbeboac ytkn th taking by buoyancy reversible the of change resulting The oeta ahruitiiey h iudwtreffective water liquid the unintuitively, rather that Note n we that noting and (C.2), Eq. into (C.3) Eq. substituting By i.e.

This articleisprotected bycopyright.Allrights reserved. Accepted Article , T ∞ → c l 0 o ossec,telqi–ae nhlytkn noac into taking enthalpy liquid–water the consistency, for ) yfato of fraction by , ◦ ,adms ftesproldwtri xetdt reeabo freeze to expected is water supercooled the of most and C, ∆ c l ∗ /c l 0 ∆ hsfcinlrdcini hw nFg 6(b). Fig. in shown is reduction factional This . c l ∗ /c l 0 fteefcieyha aaiyfl ytelqi ae is water liquid the by felt capacity heat effectively the of , ∆ h c ctoso h itn–aclboac calculations. buoyancy lifting–parcel the of ications l l ∗ et(oi uv) h feto h eprtr dependenc temperature the of effect The curve). (solid fect yfesls etcpct ntelwtmeauelmtalth limit temperature low the in capacity heat less feels ly lhuhteha aaiyisl nrae oeta 0%ov % 60 than more increases itself capacity heat the although ( = = eprtr eedne the dependence: temperature e fti feti lopootoal small. proportionally also is effect this of a hr h uynyi led eaie oeta bv t above that Note negative. already is buoyancy the where Pa, T c 1 sefc noacuti hw o h odnsudn nFig in sounding Jordan the for shown is account into effect is l 0 e orcvrteoiia ento C1 ntehg tempe high the in (C.1) definition original the recover to eed Z − T ∞ ∆ ∆ c l ∗ c ) l T dT on ftetmeauedpnec fteha capacity heat the of dependence temperature the of count effective eti eprtr nraiy hs this Thus, reality. in temperature this ve etcpct eue rmthe from reduces capacity heat esta 0% Thus, %. 10 than less fteliquid– the of e uhteheat the ough i level, his ralow a er ya by 7 . rature ( C. 4) 2]Yu .K,adP .Asi,17:Amdlfrhydrometer for model A 1979: Austin, M. P. and K., M. Yau, [23] 1]Rf,G .adJ-.Yn,20:Cnetv variabilit Convective 2002: Yano, J.-I. and L. G. Roff, [19] 2]Yn,J-. .Bse,Z uh,L ead .Phillips V. Gerard, L. Fuchs, Z. Bister, M. J.-I., Yano, [22] probl parameterization cumulus The 2003: J.-I., Yano, [21] and mesoscale The 1983: Hobbs, V. P. and A., S. Rutledge, [20] 1]Puus . .Caa n .Kry 00 h lblatm global The 2010: Korty, R. and Czaja, A. O., Pauluis, mod for [18] foundation thermodynamic A 1990: V., K. Ooyama, [17] definiti general a On 2013: Geleyn, F. J. and P., Marquet, [16] 1]Kte,C,adHKomr 1980: Kroemer, H and ar C., Indies Kittel, West the for [11] sounding Mean 1958: L., C. Jordan, [10] 1]Mrut . 05 ntecmuaino os–i spec moist–air of computation the On 2015: P., Marquet, potenti entropy [15] moist a of Definition 2011: P., Marquet, an [14] Definition meteorology: in Exergy 1993: P., Marquet, [13] 1]Mrh,D . n .Ko,20:Rve ftevpu pre vapour the of Review 2005: Koop, T. and M., D. Marphy, [12] * 9 af . n .Holr 97 nrp n oeta tem potential and Entropy H¨oller, 1987: H. and T., Hauf, [9] modelli resolving cloud Towards 1998: W., W. Grabowski, [8] 7 rbwk,W . 99 nteiflec fsalsaeto small–scale of influence the On 1989: W., W. Grabowski, [7] s of parameterization bulk the On 1988: W., W. Grabowski, [6] 1994: A., K. Emanuel, [5] Hohenegger, K., Fr¨ohlich, P., Bechtold, C., W. Rooy, de [4] 3 isesi .E,R .Jhsn .T are n .Wang J. and Haertel T. P. Johnson, H. R. E., P. Ciesielski, [3] 2 si . 95 ueia td ftearms transfo air–mass the of study numerical A 1965: T., Asai, [2] 2010: P., H. M. Ambaum, [1] References hs Chem. Phys. 115–127. 2003, November rainbands. warm–frontal in process ’seeder–feeder’ Sci. temperature. 79–92. overview, an convection: cumulus in detrainment pool. warm the over climate and convection 131 This articleisprotected bycopyright.Allrights reserved. , Accepted Article 1539–1565. , 55 3283–3298. , , ur.J o.Mto.Soc. Meteor. Roy. J. Quart. 13 4111–4131. , topei Convection Atmospheric hra hsc fteAtmosphere the of Physics Thermal hra Physics Thermal , 139 .Clim. J. 85–100. , xodUiest rs,580pp. Press, University Oxford , ur.J o.Mto.Soc. Meteor. Roy. J. Quart. .HFemn&Cmay e ok 473pp. York, New Company, & Freeman H W. , .Ams Sci. Atmos. J. , .Briia n .M iiu 03 hnmnlg fconv of Phenomenology 2013: Piriou, M. J. and Barkidija, S. , 16 nteCP hs space. phase CAPE the in y ltmeaue plcto oFR– aaflights. data FIRE–I to Application temperature: al 2370–2384. , rpriso os vial enthalpy. available moist of properties d perature. fi hra enthalpy. thermal ific mi h otx fMOsimulations, MJO of context the in em mto vrteJpnSai winter. in Sea Japan the over rmation shrccruaini os snrpccoordinates. isentropic moist in circulation ospheric Brunt–V¨ais¨al¨a wi squared associated the frequency of on ea. go ag–cl rpclcruain:Asml lu mic cloud simple A circulations: tropical large–scale of ng . okr . ioo,D,Seem,A . exia . Y J., Teixeira, P., A. Siebesma, D., Mironov, H., Jonker, C., 03 orce OACAEsudn uiiydt:Impact data: humidity sounding COARE TOGA Corrected 2003: : irsaesrcueo lusadpeiiaini midlat in precipitation and clouds of structure microscale orpyo precipitation. on pography ln h os atmosphere. moist the eling o n t plcto oteqatttv tde fpreci of studies quantitative the to application its and now srso c n uecoe ae o topei applica atmospheric for water supercooled and ice of ssures rwhadeouino anrpsz pcr ncmlscel cumulus in spectra size raindrop of evolution and growth jm ie–akel hcetr 239pp. Chichester, Wiley–Backwell, , , , 15 .Ams Sci. Atmos. J. 40 91–97. , 1185–1206. , , 139 ur.J o.Mto.Soc. Meteor. Roy. J. Quart. , 44 –9 O:10.1002/qj.1959. DOI: 1–19, , ur.J o.Mto.Soc. Meteor. Roy. J. Quart. 2887–2901. , ur.J o.Mto.Soc. Meteor. Roy. J. Quart. .Ams Sci. Atmos. J. .Mt o.Japan Soc. Met. J. ur.J o.Mto.Soc. Meteor. Roy. J. Quart. rceig o h J workshop MJO the for Proceedings , 47 , 2580–2593. , ur.J o.Mto.Soc. Meteor. Roy. J. Quart. 141 2,2317–2333. 128, .Climate J. 67–84. , , cinprmtrzto closure. ection-parameterization , 43 115 hteseicmitetoypotential entropy moist specific the th ohsc parameterization. rophysics td ylns II oe o the for model A VIII: cyclones. itude 1.–15. , 633–650. , iaingrowth. pitation n,J-. 03 nrimn and Entrainment 2013: J.-I., ano, tions. , 23 ls. , 3077–3093. , .Ams Sci. Atmos. J. 119 ur.J o.Mto.Soc. Meteor. Roy. J. Quart. ndansdpoete of properties diagnosed on 567–590. , , 137 PAGEOPH CW,2–5 ECMWF, , , 768–791. , 36 655–668. , .Atmos. J. Atmos. , 127 , , prxmto E.3 ogds)frteenthalpy. the for dash) long 3: (Eq. approximation iue1. Figure This articleisprotected bycopyright.Allrights reserved.

Accepted t under obtained energy static moist the of profiles Vertical Article eJra onig h eutbsdo h xc oml (Eq formula exact the on based result the sounding: Jordan he 2 oi)adwt h standard the with and solid) 12: . uvsaeudrtesadr prxmto (3). approximation standard case the under pseudo–adiabatic are the curves side) (right chain–dash and dash 2. Figure This articleisprotected bycopyright.Allrights reserved.

Accepted J the under buoyancy lifting–parcel the of profiles Vertical Article h oi n hr–ahcre r ae nteeatformu exact the on based are curves short–dash and solid The . ra onig h oi n ogds uvs(etsd)s side) (left curves long–dash and solid the sounding: ordan a(2,weesteln–ahadchain–dash and long–dash the whereas (12), la o h eesbecs,weesteshort– the whereas case, reversible the how nteeatfrua(2,tesotds uvsaewt the occasion with is are it thus curves budget, short–dash water-vapour the the from (12), estimated formula exact the on 3. Figure This articleisprotected bycopyright.Allrights reserved.

iesre o h rt3 aso h OACAEpro:(a) period: TOGA–COARE the of days 30 first the for series Time Accepted Article lyngtv u obt h bevto n igoi erro diagnosis and observation the both to due negative ally tnadapoiain() c rcptto ae(mm/da rate precipitation (c) (3); approximation standard eesbead()ped-daai AE(/g,i hc t which in (J/kg), CAPE pseudo-adiabatic (b) and reversible rs. ) oeta h rcptto aei indirectly is rate precipitation the that Note y). esldcre hwtoebased those show curves solid he OACAEpro:()rvril,()ped-daai ( pseudo-adiabatic (b) reversible, (a) period: TOGA–COARE iue4. Figure This articleisprotected bycopyright.Allrights reserved.

cte lt ewe h xc vria xs n h appr the and axis) (vertical exact the between plots Scatter Accepted Article J/kg). xmt siae hrzna xs fCP ae nEs (1 Eqs. on based CAPE of axis) (horizontal estimates oximate )ad() epciey o h whole the for respectively, (3), and 2) prxmto E.B3 ogdash). long B.3: (Eq. approximation iue5. Figure This articleisprotected bycopyright.Allrights reserved.

Accepted 2 Fig. in as buoyancy, reversible the of profiles vertical The Article u ihteiefso fettknit con:frteex the for account: into taken effect fusion ice the with but , c oml E.B5 oi) n the and solid), B.5: (Eq. formula act This articleisprotected bycopyright.Allrights reserved. Accepted Article ∆ iue6. Figure c l ∗ /c l 0 This articleisprotected bycopyright.Allrights reserved. fteefcielqi–ae etcpct,we t temp its when capacity, heat liquid–water effective the of ,

Accepted liquid–wat the of temperature–dependence idealized An (a) Article rtr eednei osdrda n(a). in as considered is dependence erature rha aaiycniee yfloigFg fMrh and Murphy of 6 Fig. following by considered capacity heat er op(05.()Arltv change, relative A (b) (2005). Koop iue7. Figure ln ah,t ecmae gis h eal aewithout case default the against compared be to dash), (long This articleisprotected bycopyright.Allrights reserved.

Accepted taki by sounding Jordan the for profile Reversible–buoyancy Article sldcurve). (solid git con ftetmeauedpnec fteliquid– the of dependence temperature the of account into ng ae etcpct hw nFg 6 Fig. in shown capacity heat water