Pressure as a Factor in the Prediction of Fog Formation Citation Hubbard, Jack M. (1941) Pressure as a Factor in the Prediction of Fog Formation. Master's thesis, California Institute of Technology. doi:10.7907/dasg-d125. https://resolver.caltech.edu/CaltechTHESIS:01312025-171246433 Abstract No abstract. Item Type: Thesis (Master's thesis) Subject Keywords: (Meteorology) Degree Grantor: California Institute of Technology Division: Engineering and Applied Science Major Option: Meteorology Thesis Availability: Public (worldwide access) Research Advisor(s): Krick, Irving Parkhurst Thesis Committee: Unknown, Unknown Defense Date: 1 January 1941 Record Number: CaltechTHESIS:01312025-171246433 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:01312025-171246433 DOI: 10.7907/dasg-d125 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 16978 Collection: CaltechTHESIS Deposited By: Benjamin Perez Deposited On: 04 Feb 2025 22:48 Last Modified: 04 Feb 2025 23:08 Thesis Files PDF - Final Version See Usage Policy. 10MB Repository Staff Only: item control page

PRESSURE AS A FACTOR IN T.Hlt PUDIO'J.fIOtl Olt FOG FO.WMTION la.ck M. Hubbard In Partial Fulfilment or the Requiremen~s tor the Degree or Master ot Science 1n Meteorology Oalitornia Institute ot Technology Pasadena, California 1941 TABLE OF CONTENTS I INTRODUCTION 1. History or Fog, 1 2. Fog Dissipation. 2 3, Conditions Favorable for Fog Formation. 4 4. Present Methods of Predicting Fog ]'orrnation . 6 II III :page 7 THEORY 1. Van der Waals• Equation. 10 2 . The Pressure Saturation 'l'ernperature Curve. 12 3. Dependence on Specific Humidity 16 4. Variatj_on of Specific Hum l.dit~r j_n the .Atmosphere. 16 5. Modification of the Fog Zone Within an Air Mass. 19 IV MJi.:'i.'HOD 22 V DATA AND HESULTS 27 1. 'rhe Fog Zone for the Polar Canadian Aj_r Ma s s. 34 2. Application to the Synopt ic S ituation 35 3. Prefrontal Fog 39 VI C8liCLU0 lON 40 VII ACKNOWLEDGEMENT 42 VIII BIBLIOGRAPHY 43 l I IlffRODUCTION 1. History of Fog In the da.ya of railroad and ship travel, fog did not present as great a problem to operations as it does today. As a oonsequenoe, the pl:lysioal basis of conden ... sation was limited to theoretical considerations and a. few controlled laboratory eA--periments. With the ,:idvent of the age of air travel, a more thorough investigation of the problem of fog formation has become necessary; but as yet the problem has not been solved completely. A silnple method of predicting the time of tog formation and the length of its duration would be a vital step in increasing the operating efficiency of air transportation. It was first thought that condensation occurred in the atmosphere when the temperature reaohed the dew point. No consideration was given to impurities in the air, It was left to laboratory experiment to show that pure air was condusive to supersaturation with tog formation vir• tually impossible, As a result, assumptions were ma.de as to the nature of some type of condensation nuclei upon 2 but by Dr, Irving P. Kriok of the Ga.1.ifo:1~:i.a .Institui;e or ~T.'echnology. The met hod t'J.eveloped by hi..m determines tha time of b.roalting of a fog or t:.1 t ratus system 1 tm.t a.oes of a fog or ot1·atu.s requires heating ot the syst,em m1.til 3 This heating may be done by the advection of the fog . or st r atus into e-. reg ion of higher temperature, or by surface heating and turbulence produced by insolation. The convective activity produced by insolation causes an upwa:ra. t ransport o'f heat in the lower layers of the at mOBl )here. If insolation continues long enough, the c onv ecti on and turbulence 1,,1\Jill transport ehough heat a l.oft to evB:porate the fog or stratus. 'rhe convective activity is y)roc1uced in the following manner. '1.1he portion of the solar radiation vtnich is not ref'lected b y the fo g or cloud top passes through. to the ground nna. i s effe ctive in raising the temperature of' the surf ac e. 8 uperadiabatic lapse rates are produced near t he ground, and an overturning of the lower layers of t he atmosphere results. The overturning reduces the specific humidity near the su.r1.. ace and increases the temperature. This dissipates the lower layers of the cloud o:r. stratus and the process may continue until the entire s ystem has evaporated. The problem then reduces to a determination of the surface temperature which vdll p:r.oduce an upvm.rd transport of heat sufficient to eva porate the fog or stratus, The adiabatic che.rt is useful 1.n det ermin:i.ng the critical temperature of dis rd pation. An upper air sounding is made and the temperature and specific humidity curves are plotted on the adiabatic chart. As the fog or oloud dissipates from the lower layer upward, a constant value ot specific humidity is assumed to exist at the base during the process. The constant speci:t1e humidity line whioh is located -at the base of the system is followed upward W1til it intersects the original temperature curve. point is the point is dissipation. This The point is then traced downward along a dry adiabat to the level ot station pressure. The temperature ot dissipation ot the cloud system corresponds to the temperature of the final position upon the adiabatic chart, and is the temperature which must be reached at the station in order to dissipate the fog or stratus. The f'inal step is to determine the time of day the critieal temperature will be reached at the ground level. This can be done with a knowledge of the diurnal variation ot temperature under the conditions present. 3 • Conditions i'avorable JPor Fog E'ormation. The fundamental conditions for fog forroation are that for a particular value ot pressure and specific hwuidity, the temperature must approach the temperature of saturation. A consideration ot fog formation as a 5 tunotion of pressure, specific hillnidity, and temperature, is fundamental. It saturation pressure is :plot.tad against saturation tempera.tu.re a very definite zone of tog is found to exist tor any particular value ot speoifio hwnidity. If two of, the variables are known, the third may be determined i'rom the functional relation, The tog zone appears as a singular $elution of the equations involved. The position of any point in a field of temperature and pressure, or one ot pressure and volume, will determine whether or not a fog will form. Pressure changes on the Earth are determined by the movement of pressure centers. The volume changes are a tunotion of pressure, temperature,and the amount of water vapor in the atmosphere. Temperature changes are due to inaolation, raiiation escaping to space., adveotion and turbqlence, and adiabatic expansion or compression. Large variations of specific humidity change the volume occupied by a unit mass of air only slightly; but this variation of specific humidity changes the position and form of' the fog zone in the pressure volume field. 'l'he va.riati on ot the fog zone will be discussed more fully. Theoretically, no fog will develop in a dead cci.lm as there can be no cooling to any altit;ude,. The conduc- tion of heat is very small in air, and under these conditionB a heavy dew is all that will develop W1.1en t he temperature reaches the dew point at the surface., 4, Present Method.s ot Predicting Fog Formation, The adiabatie chart may be used 1n the problem ot fog to:nt!.ation. '!"he teinperatu.re and epeoitio humidity 01u-vea are plotted from an upper air aoundinth It the diurnal variation of temperature hi great enough to decrease the te:mpe:rnture until 1t !nters-e cts the specific hum.idi ty eurve at any point. condena,1t1on will oeou.r, It the intersection occurs at a high level stratus will ttevelop. • It no 1nter::eation 1.s ;possible ror a part1oular diurnal range ot temperature, no con4.e naat1on will ooeur. It is impossible to determine from the adiabatic chart whether precipitation will develop trom e. cloud or :tog. It also does not take into account the ettect of a oritieal pressure of saturation , as it includes only t emperature and spec1:t1c humic:U.ty. 7 II HYPOTilli13 IS From e. descriptive point of view., the conception that a fog is a cloud on the ground v.rhich limits visi- bility to one mile or less is quite ada.quate but of' little value to t he forecaster,. A less qualitative concept would be to describe tog as an equilibrium condition between ·water vapor and liquid water. 'i1he restriction ot vis ibility may yet be retained. From. th.is point of vievr , a fog; together with t he air in which it has formed, may be considered as a vapor which does not obey t he equation of stHt -e of a perfect gas. It ia necessary to apply corrections to t he equation of 1 state; and this was first done by Van der Waal a.'1.d later by Clausius and D. Berthelot. The Van der Waal eque.tion can be derived from lcinetic theory and is not strictly em:piriea.1 in its cortception, used in this investigation. For this reason it vdll be Planck 2has shown that an equation such as that or Van der Ya.al applies near the saturation for mixtures of gases, and is t herefore valid in a consideration of the atmosphere. 'l'he cubic form of Van der Waals' equation indicates the form of an equilibrium or fog zone in a :field of :pressure, volume, and 8 temperature, An evaluation ot the constants involved fixes the pos ition of the equil ibrium zone. The purpose of this investigation is to show from a consideration o:t' the Yan der Waal equation t hat fog can form only between narrow limits of pressure and saturation temp(-;rature for any ·•, a rtic ul a r distribution of specific humidity. The zone of f og in e. pressure Yolun e field, alBo in a pressure devv point f:i.e ld, has been determined. i'or t he atmos:phel"ic cond itions appearing over the United States and Canada. !1he solution of t he above problem. together with a 1 lmowledg e of the s1)eoific humid:i.ty diDtribution i n the upper atn.osphere will enable the forec as t er to deter1:1ine, from an. examination ot t he pressure and dew point at a particular station, whether or not there is a possibility of fog for.ming . 'l'he method described vvill a pply to relatively stable s it u.at :i.ons and. v.rill eliminate fog forecasts under unfavorable pres.sure dev.r point combinations. 9 u.re 1 . '-i- ,.,.. 6 p ... I ,' ,, , - I I I I I ' I ""'0 , •-I ... (J -- --- - -- - --, \ \ \ \ \Zl. V .. 10 III THEORY 1. The Van der \/aal Equation. 1 Van der wvaals• equation is not accurate over a large range of temperature; but it has the advantage of applying to both the gaseous and liquid phases of mixtures such as air. li S the equation applies in the neigr1borhood of the f'og zone, the result will be sufficiently accurate for this consideration. Van der Waals* equation (p 3 t- ~ ) (-v- b .J ~ P-'T' Expanding in powers of V y 3 -(b +- ~ ) v 2 - + R y - o . . b : : o p p where nan and."b" are constants. p 'T he term a/v2 is added to the pressure to compensate for the diminution in the pressure of a real gas due to the attractions of the molecules tor one another• and the constant "b'' is subtracted from the volume to take account ot the space actually tilled by the molecules. Pis the pressure term. 'Vis the volume occupied by the gas ,. gas in absolute units. T is the temperature of the R is the universal gas constant. It is seen that the eqwtion is a cubic in v. The critical 11 p oi nt i s t hn t po i n t. v1t:ere pre :rnu:re and temperature a re such as to rn.s k e the t hre e root s equal . Above t he critical po i nt th.e equ a.tion h:'l. S only one r·e a.1 r oot; below, it has t hree . i~xpandin.e the binomial rel a tion betvJeen Vol ume and .·, er)· l.• -<" . V. o 1 ume o f• t 1.1e cri• t. • , vm h ave "t' 1.1e ::)p i J..C ,ic r-1 .l poin-c ( V - Ve. 13 -=- V 3 - 3 Ve. V ,_ -t 3 -"¼..1. V - 3 Ve...,_ -= o v,r..'l c h , ·when co:m.p a r erl with t he expanded form. of the Van der Waa l equat i on enables an eva luation of the constants . - Ve.. 3 'l'his flxe s the constants in tE::.r-:ms of qur:mt it ie s whi ch may be clet~rnined experi mentally . Tri gnre 1. represents Van der V!aal s ' equa tion g r nphionlly lJ'1ith the fog or equilibrium zone de:t':tned t or a particular value of specific hmnidity. 'l'he isotherms h ave been sketched in near the reg ion of the critica l point n c'1 • For pure water va:por, " c" occurs a t a temper- a ture of 33 .8 degrees Centigrad.e , and a pres s ure of 4 14. 0 a tmospheres. Fo:r,_a mixture of a ir and wate r vapor th e cr i tic a l poi nt i s different . The liquid line i s repre s ented by "be" and the s aturated vapor line by 1tae", Onl y inside the c urve '' a.b e" may the liquid and vapor e:-::t ern1 :l.ng should be borne in mind . It apr e ars tha t th e Jr es cnce rm e x_pres sion vvhlch :ls ind ependent of t110 c:har.'.'l eteristics of' t ho rn. rti cu .. the SAtura t i on 7 one :fe r th o free r:1 t mo:3ph ere will be made. 2. 'I'he Presrmre Sa.turation 'l'emperci.ture Curve . It iYill be note ri. in figure J... t het th e. i)Oint \Vhere an i sot hE;rr:-1 cr·os',e ';; th e satur·~1tio:n yr,;por line c orr r-s:ponds to e p8 rticul nr pr e ~' :rn.re and vollL'11.e . 'I'he tempe r ature of t h i s r.1 .<:1. tnra tion point is anH. logous to the dew point. It 1.s evident tha t a Jy1rtic u1 ar dew J)Ol:nt , or sat ur: :, tion teu1peraturc, cor:r.•e ,,J)On d :::; to u parti cul a r· ~,nturc.tion press• u r e; and t hnt su tur2tion will not t ake pl a ce for this t emperature nt :rres::iu.res other than the ~-3atu1~ation pressure. 13 'i ,ure <:> ------- ------ ------- -----Ts 14 In figure 2. pressure is plotted against saturation temperature. The fi gure is constructed from t he Van der Waal diagram, and shows the saturation or fog z,one to be a very narrow line when plotted in these coordinates. Figure 2. shows an increase in saturation temperature with an increase in pres aure. This condition holds for any adiabatic process. Figure 2. shows also that the temperature of' the atmosphere can become a saturation temperature only for a particular value of pressure. Variations in the position of the saturation curve have been •included i mplicitly in figures 1. and 2 •• It is necessary to investigate the relation between volume and specific hu..c~ idity in order to determine the shape and position of the curves. It is readily seen why temperature an~. dew point may approach each other at times without restricting the visibility; and at other times causing fog or drizzle. In the first case; any point to the right or the sat- . uI·ation line in figure 1. will not have a visibility restriction as no condensation can occur. If the pres ... sure doE~ s not correspond to the pressure of saturation, the temperature may approach the saturation temperature isotherm outside the tog zone and no fog will form. 15 or on t irn c u:eve i n figure ?. ., i\. point so loca ted will be i'ound to proo.u.o e :fog 1mc1.e-r n o:<'.'!nn.1 a t r1osphc ric condit i ons# Cas e nmnber t hree c orr·<';:Gl)Ondn to a J)O nition lo cated uell vith in the saturntion dome , or even i~ the li quid :r:egion of figure 1. In :f.'igure 2 . such a poj_J1t v,auld be located to the J.ef t of t l1e curve nn.d a drizzle vJould re s ~11t. No compl ete conclusion can be dravm i mme( iat e ly f rom this anal ysis as ot her e.t mospheric factors enter v.rh ieh ten<l to ch,smr;e the i d.e a li?: ed satura tion dome a nd t he curve which has been derived from it,. The following generalizati on can be made~ 1. A fo g zone mdsts in a pressure, velum.et and tempe r ature field, 2. Points on either sicl.e of the fo g 7,one perm.it the temperature end dew point t o beco:me coincid ent ·without t h e formation. of fo g . Having reduced the fog zone to a linea r function in a f ield of pr e~rnure an.d sa turation tempe r ature, it is ne:x.i i necessary to det er mine whether or not the zone 16 is conservative in the atmosphere. 5. Dependence on Specific Humidity. The volume occupied by a mixture of water vapor and air, in addition to being a fu..'l'lction of pressure and temperature, depends on the specific humidity .. This is shown clearly by the following equation which 5 is taken from Brunt. V-=- JlT-(1 p KVJ) The variation of volume with s pecific hum.idity is reflected in figure l* by a shift in position of the equilibrium dome. A.n increaae in specific huraidity shifts the saturation dome to the right; where-as a decrease shifts it to the left. This in turn displaces the saturation curve in figure 2. In this case, an increase in speci:t'ic hwnidi t.y decreases the pressure of saturation for a fixed temperature. the ou:rve. This lowers A decrease in specific hwnidity raises the curve in figure 2. 4. The Variation of Specific Humidity in the Atmosphere. If there were no variation of specific huio.idity with altitude or geographical position in the Earth's atmosphere, the problem. of fog formation would sirnplifyJ 17 It would be necessary only to l'"Jiow the value of the specific humidiJGY to tleterm.ine the location of the fog zone in t h e pressure volume field,. The rorraation of fog would then be determined b y whether or not any point in t he field lay within the equilibrium zone. In t h e atmosphere it is found ·t hat a variati on o:t' spec ific humidity with altitude as well as position on t h e Earth's s ;1rface occurs. b v produ cing a dif'ferent 'l his coruplicates the problem location of the equilibriwn zon e f'or e a c h value of s pecif' ic hu.midity. Each specific humidity introduces a nevr set of cons tants in Van der Waals• equat ion. The distribution of s pe cific hwn..idity in the atmos- phere is a problem which has not been solved completely. The complete s olution of the fog problem may have to wa it until such an investigation can be carried out fully unless a method can be fow1d which will eliminat,e the exac t distribution function. A distribution of specif'ic humidity within an air mass may be determined empirically from upper air soundings. If s uch s oundings are made during fog conditions, the dintribution of specific humidity most favorable for fo g f orniation may be deter-.m.ined. The optimum conditions are likely to be reproduced i n air ma sses which have 18 ~~igure 3 . p ----------- --- -- ---------- ----- ------- 19 recurring trajectories. r.rhe periodic outbreak of the polar Canadian air mass is a good example. If the optimum. conditions of fog formation can once be recognized, it is possible to reco~~ize them aga in. under similar circumstances and make a t)rediction which is accurate. 5.. Modification of the Fog Zone 'li'lithin an Air Mass. Any s ystem in which the s pecific htuuidi ty var i es may be described by a pressure saturation temperature diagram. It was seen in section 3 that a variation of s pecific humidity shifted the position of the satu- In such a system. of ration cuJ'.."'Ve within the field. varying specific humidity; a family of curves exists as indicated in figure 3. For a particular pres sure, each curve of the family is intersected by a different saturation temperature• The points of' internection of the curves are determined by the solution of the following equations. p -:: J- ( l( / Lj I 1. ) -=- w -: s- (__ "X, C D IL ) t- l-j J 'f. ) The solution of t he above simultaneous equations form a cuJ'.."'Ve which is continuous. For pressure va riation within an air mass, it i s necessary to indic ate t he intersection points formed by the following curves. 20 The curves intersect and t ;-ieir sol ub i on i s a continuous curve in the press i-1.re satarect.ion te;:1:perature field. p - f (_ ,Ci y ) 1:. ) w - J- l x: 1 y; 1-) 'l'h e curve resulting :i.rom t h e i n tersect ion 01' the above c arves is t r1e true fog zone. 11' the functiona l rel ntionship between th e var:iables could be determined for a part i cular a ir rn.ass, t h e problem of condensa t i on wit hin t he air mass would be complet ely solved. Con- d ensa tion can oc cur onlY a t t he points or' intersEh; tion of the t wo curves. .l1l1e temperature of condensation ca n 1 be read directly f'rom t he absci s sa of f i gure~ •• Having lo cated the mos t probable points of condensation within t he air mass , t he problem t h en j_s t c determine .whether o r not the temperature will reach t l1e sa"turatior,1 temperatur e a t these points. This can be done from a knowledge of t he diurnal va ria tion of ten1pe r at ure wi t 11in t he a ir mans. The vertj_c al dist r ibution of specific humidit y wi t:.hin the air mas s is ve r y impor-tant • Due to the motions of the air 1vith:ln t he mass, st:rati1':L cat ion oc r:ur s wh ich leads to irregul arity in t h e c on dem;;ution patt ern. It is expected t hat -~he pos i t ion of the s a t ·1rat ion curve will be differ en t for di:tfer ent a ir 21 masses. It is also pos s ible to have dif:f'- erent satur ... ation curves in the same air mass. If one pa:rt of the air mass has had a different trajectory than the rest of the mass this is true. If the tra,iectory of the er..tire air mass has been over a uniform. surface, the di :~tribution of specific hu.1D.iditJr within the mass will be a continuous functj_on. The saturation or fo g zone will be a continuous function also and may be det,e rmined from upper air soundings and surface data. The dependence o:f' ground fog upon :pres~mre and the form ot the saturation curve fo 1md from a cons i deration of Van der Waals•, shows that pressure i n the zones of fog must lie within very narrow lin its. Optimum pressure conditions may be reached j_n air mas s es as they move ab:Jnt. These critical values o:f' :pres s ure will be determined by the specific humidity dis tribution vli th in the air mass. 22 IV METHOD As an ex:perb1en.tal check on t he foregoing considerations , t he daily synoptic weather charts were consult ed i n an affort. t o determj_ne the limiting values of pressure and d.ev,r po int for fo g forniat:J.on. fog occ urred were exan~ined. Stations at '\AThioh All stations at which temper• at nre and dmi, point were coincident ·Nere tabulated along v-rith the weat he r conditions prevailing at the time of observat ion. Fogs existing in relatively high pressure areas we:r e inifestigated a s the y inc l ude the most uniform and t ...,e widest variation or specific humidlty and temperature. As nearly all sta tions are at different altitudes, it ·was necess ary ~,o convert the red uced pressures to t he actual pressure at each s tation. Reduced press ures v,ere plotted a gainst saturation temperature in an e:ffo r·t to obtain. a result ·which is usable. Table I. includes sta tion pressure, reduced pressure, and ' saturation temper- at ure occurring at stations within the polar Canadian air mass. 'fhe station pressure was found by the use of the adiabat ic cha rt although conver:1ion t a bles are ensier to use, ., t . • • . ... ]'igure 4. 4 TAB..w!i, 1. ; TA.ble 1 . iricludes t e 'ct al )re.rnure e"""LJtin~ at t11.e stations a.·.ring for cot1_d.:.t::.ons . 25 Figure 4. is plotted from the data in table l. a nd shmvs the fog zone in term.s of pressure and saturation temperature. 'l'he zone of red s11a.ding is the fog zone in 't.errns of sta tion pressure. '£he region of green shading is th e fog zone in terms of :reduced pres sure,. Both re g ions a.re continuous and i dernical exceut for a shift along t he pressure axis. The curves tend to converge in t he positive reg ion of t emperature . Th is is due to , the fact that the stations in this r e g ion ·were at low elevations. It is significant -c.;ha·t a plot of t he red uced pressure does not dest roy t he f og zone b •rt merely s h i f ts it i n t he pressure field. This i ndic ates t hat reduced pressur es may be used in a dt: terminati on of t he fog z one in the pressure acturat ion t effiperature field. Reduced pressures were used in this investiga tion i n an etfort t;o obtnin a re s u1t whieh wo uld make use of t he pressures found on the weather chart. This faeili- tates forecasting as it c:trcur1vents t he calculation of s tat i on pressure !"'rom re(i uc ect pre ssure and se.ves time i n making the forecast. fi1is ·procedure no doubt lead.s 1 to discrepancies, but t he r esults are quite con uist,ent a nd wa rrant t he neg lect ot rigor fo:r more practical methods. 'l'empc r n"ture n j: • V Vi Di bilit y. 11 Ce iling aa Bar (.1me tric tenden c y dur ing t he 1,ast :i hours. pp Amount of b a rorc.etrie ch ange i n t he r:-a: ,t 3 hours. w ; peclif ic lrn.!n.idit:r. 27 V DATA AJTD HESUL'I'S • " • . • Ii'ir,ure 5 . < 0 fl lJ, .-- t t I t '2 Vt- I 4 I Table ,., . incl des dntn. air a~s i~ sprin~ . ad ~ip re 5 . shm~ a tn'rn'1 fro t e olar a r dia e fog re ;i ,--1 is rat er ex-+:.e si VE i1ite fog 70ne . • •• IPigure 6 . 3. Bl, ' • J -, ( I 1 ... of V 0 ~ able orth ~ r d . eric' . ried gre t 1_ Of, for i'1r>l1des d, b t ' tinn. 1 .J. ,.. -:;a:f'l :'ro ,c va~io s re-;io 1s e ca .d-; tio s ,_ d r • 'licl 1'op :·or ed fin- re { . S 10 f' E1 rat er : ini te zo e • . 31 • 0 ri Figure 7 . 0 ,..0 0 - - () 0 '11 4. ....,.I!, /1) f-,-) pp IIJ ,, "' t I T , !J ..., ). .l ' I 7j / I 'i I,._, e, ., , i. I j \.. , IIC> .,,. f ;L J ,r 7.., Jl. ~J- ' .., V I e e C V () a ' )t r .., ·r _ t c ren ed i1t) tre re 7 . s' '"')'i. s (D V t.l.' t·tcc r~.' 11, r .,. ' i. , f i .: " .,. 1 'a .I. ... ,. ~ ). .. , f" J ,I.. ,. ss . ·v IQ fr,. I ' ~ i ,,,,.-f ' ·' .. ? ' Ta..,le 4. also i , t ., c, I -'fJ.. ., ', J fr 71- f /1 C' L -<. 7 ;i. , 'O '. J'--. J > I V )... .pin it e 'C' zone . ,e. _, dian. . 33 . • . . . . . ., :F'igure 8 . 34 1. The Gt•apbJ.c c:~l :Form of t h e Fog Zone i n t h e l 'olar Canadian llir Mass. ]'igure 8 .. in a com.postt e o:t' the a.aJGa included in t a bles 2, 3, and 4. This figure was constructed from dat a foun d en dif f erent days mid at different pl aces within t.he pola r Canadian ai r mass. I i. furthe.r check of t h e v a lue s cf pres s ~re 8nd dew point favorable t o fo g forrr.ation wa s r.iade f'or a g rea t man y ca.:-,es. It was f ound that the fog zon e s haded i n green in fig -re 8. vms valid in nearly every ease. If the po i nt i n question lies to ai ther s ide of t he fog zone, .i.10 fog will f orm at the station. If the pressure and dew point lie above t h e fog z one, t he re ·will b s no fog al t11o;i. g ) t t he te:i:a1_:;er a ture and de·w point a pproach each other. Th e points lJ1oG-~ ed in green in figure a. show this condition. Clear skies s hould be fo r ec2st f'or suoi1 a condition. I? t h e pressure a nd. tempe :r-ature ;~oiTt. l i e :J belmv the fog zone in figure a.• fog will not. forrn.; t ut precipi t,at ion may be expect ed. is shown by t he poin'c ;._-; plot ·ted in red in fig ure 8. r1•nis If the point lies within the z one of fo g in figure B., a pred iction o f fGg vdll very l :Ure l J verify. 35 :? • ;i._pplica:t;ion ·to the Synopti c ,Situat ion . Un 1'Aarcll !5 , lJ 4l nn d ,1j) r i l 9 , 1 J 4l , a. foreca st of :fog -.,~,as mad e f or -thci great :plai ns ar·ea of ·t:ne ,.; nited Stat es. This fo recas t was based upon the expected pr essures and dew pcinLs bein g loeaten within t h e i'og ~one of figure a. 'I'he day the f ore (:.e st. vva.s made no f' og e x:isted in the 1'olar Canadian air mass . 'I'l1e 1'ollov1i:1.:~ day, the fog a rea was general and v,ri •: e sp:cead . The preBsu1·es and. dew points of t he sta tions having vi s ibtlity r estrictions were within t he cri ti cal v-al uea indicat ed in figure a. Another case of s uccessful forecasting by t ne use of f'igure 8 . is t t1at of· 0eattle, V✓ ash i ng~on on Lfarell 23 , 1941. A h igh pressure cell wm; movitlf', toward :i eat tle West• I'1.·o ri1 t he A forecast of clear was n ade v1ith t n e e7,:p ec t at.ion t hat t lle p ressu 1'e would be g reater th,w 10 28 nd.llibo.rs at ma g t i n.e . 'l' lie pre~:sure :.:-eac hed 1029 . 1 mj.ll i ba::-s a nci no fog appea r ed at 3eattle. As the high passed over ~eattle, fog was foreca s t s, J. ~en t h e pre s :::;ure bee ai'.le les::, t h an 1028 millibars. On l -1 arch 2ti , tile .f:ires s ure at .:.,eattle ·, H:l.S 102'7 ,8 millibars and t he dew point 3? degrees F . Fog verified . n o fog was _p ..:-edi cted for ?.iarch 26, and the press~tre dropped to 1012 .. 5 :millibars wi t 11 u d ov1 yo int c f' 47 degreer,. I t is signii'icant that flgur·e 8 ., whi eh was devel oped from f og condi.tio :,s :Ln t he polar Canad ian air mass, should e.JJply to condi t ionr:1 of :f og fo r mat ion at Se a·t tle. 37 .. Figure 9 . C 5. ,_, I,,, • r [~I f ., I r I ., ,- 'I tO 11/ £/ ,., '1 ' I ... •/ I I I J ~ t ,. ... " I . Table 5 . include3 da a taken from ro exit. g vitti u c3clone . conditions 39 3. Frefront al Fog . :rre:fr ont a1 :fog 'N°hich is found c:.t low values of :pre ss ure in cyclorH';S is ins truot i ve. In most ca~:::es it i.s neee~1sary for the tempers.tu.re t o rE;ach the dew : oint at the ground in o:cdcr t :i. a t a f' og ::n.a-y form . 'I1he fog zone as outLl ncd in figu re 8. is ,3till c ontinuous, nnd .;"" ..L •J _··1ocr, ... .,, . 't°'-'"dt. J. J "..:-1 ·1.1ri·-r,·}· ·11 a• • '-1 1 -· era ture range . '"e'"t ·•·J·,,·ted ..£.. ..J -1. • '-" --c.•,~·11··e 1·•·)re , .,:) ~ \. · a- "'nd t·e·,.,. l~l. -,,.) .!. Unstable conditions ex:h1ting within the cyclone may c auBe the speci1'ic llwnidit.y to vary grea tly • '.Phis ·will cause the zone in figu. .ce 8 . to becon e quite thick and poorly defined . In the cyclone, t;empere.t u:;:•c drops due t o noctur:u.11 c oolin~ are restricted b v e~tansive cl oud decks ru1d the cliurne.l va riE:1tion of tcmpert1 t «re is 8,W-.ill. Fogs t1ave been knovm to form ben eath such -cl oud decks and are a ccompan ied by substantial drops in l)ressur e . 1111y pre2.::n1re drop is a<:conrpanieo. b y an udiabatic ex_parwion a n d. cooling . Th.is temperature change is small, being of t he order of on e degree~ . for every 10 millibars cnange of pres s ure. The combined. e ffe ct of r ad.iativ-e c c1oling _ may b e suff'icient to bring the temperature to the s a tur• ati on point a t the gr ound.. :Prefrontal rain is anot.her f a ctor which tendB t o prodne:e fog. r11h e ei'tect. of t h e r 2 i n is to produce greate r -val u es of specif:i.c :num:l.cl i ty near the ground. 40 VI CONC LU;::; ION ··n~re ••t-i <)f V ,;1 ....., gr, . c~ t.;or, .J... .,.. . The ~ +l·Jc. '..J.J..,\..,1 made from the :£'1..rn.do;;i_entn l tion of' st ate. "{)'T'()ble·"'o r-·J ..,.,,rr!l t1· on Li.L ,..,~ J. C.~ .': --- _ .. • lJ.l.. .J_._ } 0 U. iden of a cor: ·ected. eou.a:J. Vnr:. a.er Waals' equation was as:c-m..rn.ed to apply to a m:txture of vrater VHp0r and atmospheric gases. As the pressure and sn turc:; t:ton ternpe1·0ture were conservative vdthin the C(;Uilibr:tu.r11. dome of the Van CJ.or Waal dio.gram, it ,:vat::l thought th r:J.t th:1.s dorae could. be reduced to ·a line by chen{;ing the coordinates from pres tmre an.d voltun.e to pressu::e and saturat1.on temperature. I t was fou...11.d t lv:i.t e. defin:L te 7,one •1..vi t~1in. a :pre:T:.;ure s o.turat.ion tem1i eI':=i_ tiure field \'!HS n.cces ·:ary to produce fog, and the location of this narrow zone was attempted for atmospheric eondition3. The defini-:e zone of pre ~1aure and dew point exists and was fou,.'1.d to he condusive to fog f'orrn.ation in high prei=rnure cells. The limj_ting values of pressure and saturation have be en determined :in fi gure 8. It was also found t hat prefrontnl fog could be for:me d from a drop in in•e~Bure and the accompanying adia• batic expansion ano. eooling throughout the atmosphere. 41 The fog zone found in fi eure 8 . a };J)lies t o ·prefront a l fog, but the inst:CJ.bil:ity nondi tions within t.he cyclone causer.; a wide vax·iation of spec ific h1.rn1idi ty. rnds variation of s pecifie hum:icli ty cat;,::.,01:-1 ·t he fog zone to become po orly def ined.. fo~ the production of a radiative fog, press ure und devr point m.ust be vr:i.t.h in certain critica l lin its.. limits a re cleterminea. in fi gure 8 . cUs trib 11t ion must be conti~rnous. '1'l1ese 'rhe specific hu.nidity The s;..i.rface wino. must be belovr 10 miles per hour to pr e vent t urbulence and t he de s truction o:e t :1.e tenq::,e ratu:re i nversion a1:d a lov;erinv of the s pe cific hi.F•1idity near the ground , F u r-th.er Problems Wh ich May Be Developed. Theoreti cally, the fog zrn1e in a pres8~re saturat ion ·t e··n~'e"'"1"· 1·"e ·"':i.· ! . ,y ..,.. J. . eJ • . c1.. 1 c : ln ;.; J s'-1l)''l' u1 > c. L .!. be ·~ 1i·r1e ct • rJ.'ilA fi" 1··1i· +:e w_·i dth v • ~ - prr:ipe:tt ieG of the nuclei neeessa.:r·y for fog fonr.atj_on. A raon sure of the width of' t he fog zon e may be used as a me asure of. t he hygrosco· J:tc !)I'Ol)ert :i.eiJ of t;hese nuclei. 42 VII ACKNOWLEDGEMENT The author wishes to express his appreciation t o Dr. Irving P . Krick~ whose encouragement and gu j_c1ance wa s a great factor in ma.king this inves tigation pcss lble. VIII BIBLIOGRAPHY l. Page,, L.: "Introduction to 'l1heoretioal Physics." second Edition, p, 310, D • Van Nostrand Co~pany, New York• 1936 Planck , M. t "Tr-efl,tise on Thermodynamics." Third Editioh translated from the seventh . German Edition, p,. 15 ff., Longmans., Green and Company, London, 1927 3• Ibid, Page . 4, Schae:t"er , c.; 1 Ein:Nlhrung· in die theoretische Physik"· Zweiter Band; p, 119• Walter De Gruyter and Company, Berlin, ., 1929 5. Brunt, D.: "Physical and Dynamical Meteorology. " Second Edition. P• 53, Cambridge University Press• 1939