Some Criteria for Distinguishing Large Scale Weather Processes Citation Montgomery, John Osmer (1947) Some Criteria for Distinguishing Large Scale Weather Processes. Master's thesis, California Institute of Technology. doi:10.7907/yzj1-fk03. https://resolver.caltech.edu/CaltechTHESIS:08132025-183358936 Abstract The concept of a large scale weather process covering a hemisphere or perhaps the whole earth and lasting for periods of twenty to thirty days presents some possible value as an aid in extending weather forecast periods beyond those now used with any degree of confidence, In defining and studying such processes various factors must be considered such as tl1e general atmospheric circulation trends and flow patterns, centers of high pressure and low pressure action, and zones of convergence of airflow; and the movement of these zones. Comprehensive charts, flow pattern charts, or any other chart giving a broadscale weather picture over an extended period of time are of much use in making a subjective study. Statistical studies by computation of correlation coefficients or better yet by use of contingency tables furnish a more objective view of the problem. It is the purpose of this study to make preliminary investigations of these factors using some of these techniques. From a study of these processes it is hoped a procedure will be developed for forecasting the general atmospheric flow pattern and from this a reasonable weather forecast for several weeks. 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): Unknown, Unknown Thesis Committee: Unknown, Unknown Defense Date: 2 January 1947 Record Number: CaltechTHESIS:08132025-183358936 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:08132025-183358936 DOI: 10.7907/yzj1-fk03 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 17620 Collection: CaltechTHESIS Deposited By: Benjamin Perez Deposited On: 14 Aug 2025 17:45 Last Modified: 14 Aug 2025 18:10 Thesis Files PDF - Final Version See Usage Policy. 119MB Repository Staff Only: item control page

SOL-IE CRI'F.-,:__'RIA FOit DISTINGUISHING LJ..,_"qQE SCALE \iF...nTHEi1 PhOCESSES A Thesis by John o. Montgomer1 In Partial Fulf1llment of the Requirements for the Degree of It:eteorologist California Institute of Technology Pas&dena, California 1947 ( SGI,S CHITElUh. FO:t DISTU~GUISUING The concept of a l&rge sc&le weather process covering a hemisphere or perho.ps the whole earth and l&s ting for periods of twenty to thirty days presents some possible value as an aid in extending weatl·i er forecast periods beyond those now used with any degree of confidence, In defining and studying such processes vt.rious ft::.ctors must be consiciered such as tl1e genE:r&l atmospheric circulc.-.tion . trends and flow patterns, centers of high pressure and low pressure action, and zones of convergence of airflov; and t."1--ie movement of these zones. Comprehensive charts, f'low pa.ttEorn dwrts, or 6.ny othE:.r ch&rt giving a broadscale weather picture over 6.n extendec period of time are of much use in making a subjective study. Sta ti ~,ti cal studies by computation of correlation coefficients or better yet by use of contingency tLbles furnish a more objective view of' tLe problem. It is the purpose o·f this study to mo.k.e preliminary investigations of these f&ctors tisin~ some of_ these _ techni(lues. From a study of these processes it is hoped Q proceedure will be developed for forecasting the gener~l a tmospheric flow pattern and from this a. re&sonbble weather forecast for several weeks. TAB~ OF CONTENTS CH.APTER I. PAGE TI-'.E PHOBLSlvi AND I'l'S B~CKGROl.i:ND The problem • O ♦ • 0 e O O . . .. . . . . • • • O O • O 1 1 • Statement of the problem . . . . . . . Import&nce of the problem • . . . . . . . . l -~ 2 Definitions of terms used • • 0 • • • • • • 2 Natur~l synoptic period . . . .... . . 2 ~lemento.ry synoptic process Large scale weather process Comprehensive chart .... Flow Pattern Chart o Background . . • • o 0 • • • 3 0 • • • 3 3 e 3 • ... . . . . ... Sir Gilbert 1'; alker Unite6 States Weather Bureau. German inv~s tigati c•Ls ·4 4 • • • 5 • • • • • • • • • 0 6 Rhythms and oscillations. 7 Hussian school of extended forecasting . . 8 Broadscale processes observed by Elliott. 11 Centers of action, flow patterns, and zones of cor...verge nce in the northern hemisphere . . . Sourc.e of data . . . . . . . . . . 12 . . . . . . . . 16 Crg&nization of rem&inder of thesis 17 iii CEAPT:SR II. c or,;prmEEl~SIVE CE n.HTS As sump ti ons . Plotting . 18 •••o•eo•o4>o•• . .. Analysis. . • • • •o .. . 19 q o • 9 Results of investigation III. • D 20 . . . . 20 • • • PRESSL1RE TIW UGES • . 26 Collection of data . . . • . 26 Statistical study . . . . . . . . . . . . . 27 Computation ·• . . . . . . . . . . . . . . 27 . . . .. . . . . . 33 Conclusions Analysis of a pressure curve . .. .. . .. .. 33 . . . . . . • . . 37 • e 38 . . . . . . . . . . 39 Comprehensive charts . . . . . . . . . . . 39 Trough passages 48 Thirteen month rhythm ~ 1 wenty five day rhythms 1 Conclusions IV. e t e O O e ♦ • V O e O • EXlulfJ.PLES OF' LAHGE SC1i.L~ WE.t1.T1ilih P:-:JCESS:SS Selecting the pro-~ esses . . . . . . . . . . . . • Analysis of processes . . . . . . . . . . . 50 Flow pattern charts . . . . . . . . . . . 50 Comparison of processes Conclusions V. 33 POLAR OU TBRS~J<:S 0 . . . . . . . . . • ♦ Q II O 0 • • • • • 0 Collection of data. O 52 72 ... O O O O O ♦ 0 0 • 74 74 iv CEh.P'l'ER P, ..GE Statistical studies 0 • • • • • • • • • • • .. . .... Means and variances 76 76 Correlation study by use of contingency ta.bles ..... Summary VI. SUI&.ii,.RY • ... .. ..... 0 .. ♦ ♦ ♦ ♦ e • b ♦ 3d 85 89 Criteria for defining the transition period. Distinguishing one process from a11other Conclusions • • • • • • 90 92 0 BIBLIOGHi.PEY • 1-.PFSNDIX THOlX}F POSITIOl•~ D.1.T.n ...... 1..PPENDIX B: Di2 .. FOH TEE STUDY OF POL • ..i.1 Ot;TBlili.t..r.S OUTBRE.lJ<. STUDI:SS . • .... 97 129 146 LIS T OF' FIGu:r.:. :-~ s FIGUl{S 1. Axes of Paths of Ei ghs Over SurS)pe in Winter 8 2. Axes of Paths of Eighs Over :=urop·e in. SwriD.er 8 3. Centers of Action, T.: inter Flow Pattern &nd ..... Comprehensive Chart, Zanuary 25-31, 1929 • . . Winter Zones of Convergent Airflow 5. Comprehensive Chc.,r t , April 11-15, 1929 14 21 • • • • 22 Comprehensive Chc::irt, August 13-18, 1829 • .• . 23 7. Comprehensive Ch ert, October 10-16 , 1929 • • • 24 8. Gr aph of Ls.g Correla t i on Coefficient .Against Lag Time Period 9. ~ . . . • • • 0 0 9 32 e 3raph of the Da:i,.ly VCJ,lues of the Lowest Isobar Crossing 135° W. Between 35° N. and 55° N. , January 1, 1925 to April 30, 1930 10. . .• . • 34 Graph of the Daily VE,lues of t.l1 e L0WE:St Isobc.r .Crossing 135 ° ti . Between 35° N. anc 5b0 N •' JariUary 1, 1930 to April 30, 1986 • • 35 11. . ComprE:hensive Chart, January 1-5, 1933 . . • • 41 12. Comprehensive Cha.rt, Jo.nU b.I'Y 5-9, 1933 • • • • . 42 13. ComprE:hensive Chart, January 10-14, 19 33 • .• 43 14. Comprehensive Cha.rt, J aLt:.liry 13-16, 1932 • .. 15. Comprehensive Chart, January 16-20, 19 33 .• • 4.G 16. Comprehensive Chart, Januc.ry 20-23, 1933 • • • 46 17. Compreh ensive Chart, Janu ~ry 23-26 , 1933 • .• 47 .. . vi . r,r. ?. ,.\.i.e.. FIGURE 18. ..., Trough Passages at 135° r:.,. ' 135° if • ' 4ti 0 VJ•' and 1 :. ; 45° E. During Three Selected Large Scale Processes • • 19. 20. ..• ..........• • • - December 6, 1931 • Flow Pattern, December 6-12, 1931 . . . . . . . ·Flow Pattern, November 30 .• • 22. Flow Pat tern, December 18-24, 1931 • . . . . • 23. Flow Pattern, January 1-5, 1933 . . • • . • . • 24. Flow Pattern, Janua.ry 5-9, 1933 • . • . . • . . 21. •· 49 Flow Pattern, December 12-18, 1931 0 53 54 55 • • ' 56 57 58 25. Flow Pattern, J·blluary 10-14, 1933 • • . • • .. • 59 26. Flow Pattern, January 13-16 , 1933 • • ...• • 60 27. Flow Pattern, Janu::..ry 16-20, 1933 28. ..,...,u Flow Pattern, January 20-23, 1 0':l') 29. r-,~ 2---o, 1833 Flow Pattern, January c:;.j• • • • • • • 30. Flow Pattern, January 26-31, 1933 • ...• • • • • • • • . . . 31. .• • .• • Flow Pattern, January 31 - February 6, 1933 . . 32. Flow Pat tern, February 6-11, 1933 • • • • 0 • • .• • 34. Flow Pattern, February 14-18, 1933 • • . . . • 35. Flow Pattern, February 18-22, 19~3 • • . . • • Outbreak Stud~y • . . . 36. Varic..bles Used in Pol 33. Flow Pattern, FebrucJ.'y 11-14, 1933 • • • cir 37. Cumulative Probability Curves-Poisson Exponential 61 62 63 64 65 66 67 68 69 75a 86 LIST OF T.i-..7:..uLS T;J3LE I. Computc..tion of Lag Correlc.tion Coefficients . II. Means and Vari1;;.nces of Data in Polar Outbreak Study III. . . . . . . . . . . . . .· . 77 Significance of Varic.nces in Polar autbrei:..k Study . . IV. 29 .. .... 79 . ... 84 Significant Correlc:.tions from the Two Variable Contingency TL.bles CHAPI'ER I THE PROBLEM 1J\°"D ITS Er.Cl<.GnOUND The forecast of weuther for perioos of more thc.n two or three do.ys ahead has been subject to much investigc. tion __ .. / and numerous attempts have been made to set up rules for forec&sting days, weeks, and sometimes even months or yeurs ahead. The concept of a large scale weather process,covering a hemisphere or perhaps tl1e whole earth and L..stin5 for periods of twenty to thirty duys, presents some possible vc:..lue as an aid in extending wec;i.ther forecc.st periods beyond those now used with any degree of confio.ence. I . I'EE PhObLEk~ Statement of the problem. It wa.s the purpose of this study to make preliminary investigations of criteria. for distinguishing large scale weather processes by the cor:i.siueration of such factors as the general circulation trends and flow patterns, the centers of high pressure anCi low pressure action, and the principal zories of convergence of airflow by the use of such technil1 t:es as comprehensive charts, airflow pattern ehc.rts, iLvestig2..tion of some rhytluns ooth by visuc...l study of graphs and by time lag correlations, and a statistical study of temperatures ano flo-v~ patterns arounci the northern hemisphere. 2 Importance of the problem. •,,i th the v.:...st incre&se in the number of weather observc.ti on .st6.tions all over the world, with the standardization of we&ther records all over the world, and with tbe corripilation of the fourty year no1·thern hemisphere daily surface historicEil wca-c,r.er map files, it has now become possible to make hi tberto impossii::ile studies of weather occuring in wide ar•eo.s OVH' the ec:.rth's surface. Much evidence has been presentea th.at la.rge scale weather processes do exist. Many techni~ues 1or invcsi.i.gation have been suggest.ea and it is intended th~t this pap€r summarize and expand upon fu ese. II. D:SFINITIOI'{S OF 11Z~-{./;S uSED Before discussingmethoas of approi.ch which have been suggested, some definitions of terr,is useu througho~ t this paper are needed. Natural synoptic period. The naturc.,.l syrtoptic perioci is the period d~ring which the curreLts in the troposphere move in a certain direction causing the dynamic centers to occupy a given position in space which chbnges with transition to a new periodJ. 1 s. T. Pagava, editor, Th~ .B~sic Principles of the Synoptic Method of Long Range Web.ther Forecasting (Leningr·ao Moscow: u.s.s.R. Hydrometeorologic1:..l Office, 1940:), p. 119. 3 :Slemer.. t&ry synoptic process. ~:i.n elewent~y synoptic process is one "during which the sign of tJ1e b&rowt:: tric are& and the ma.in currents of warm and cold air rt::.main constant throughout the synoptic region. 112 Large .§Cale weather process. The large/ scale weather . process is a long process consisting of severa.l natural synoptic periods in a relatively uniform succession. During the process, lasting from twenty to thirty days, certain features may remain permanent. Comprehensive chart. A comprehensive chart is a chart upon which are plotted all th~ positions of the centers' of tile high and low pressure areas for the period of the chart. On the chart may or may not be trajectories of higis and lows, lines separating the highs from the lows, or lines drawn around higis or lows of various intensities. Flow pa.ttern chart. J... flow po.ttern cha.rt is c:. chart upon which is located for be period of tJie chc:.rt tl:.E; principal centers of action, paths of airflow, &no zones of convergence of airflow. 2 Ibid . , p . 115 . 4 Most inveE tigations into extend ea wee:. ther forec.:.s tir1c; fall into one of two categories. One is based upon studies of what has happened before and upon stua.i es of variations and rhythms in weather records. The other at tempts to relate some phenomena occuring now or in the p~st to some phenomena occuring at some time in the future. Sir Gilbert Walker. Sir Gilbert Walker3 during the late nineteenth end early twentieth centuries attemptea to correlate the Indian monsoon witll various factors such as the snowfall in the Himalyas, tl1e April-May rain at Zwizibc:aand Seychelles, the South American atmospheric pressure, the Indian Ocean atmospheric pressure, the May monsoon in Ethiopia, and ship reports in the Indian Ocean. This data was fit into regression equations or forecast formulae. It is interesting to note that forecast formulc:1.e made for one period of years did not verify 'Nell ir. c.11oth er group of years. Walker also noticed a group of oscillb.tions in pressure patterns over me earth's 'surface.4 The so\..i.thern 3 R. B. Montg>mtry, et c.l., RepQrts on Criticb.l St~dies of Methods of Long Range Weo.t.her Foreco.sting, Monthly Weather Hevie,~, SUpplellient No. 39, May 3, 1939. pp. 16-19. 4 Ibid., pp. 3-12. 5 oscillation is a v~riation from high pressure over South America, low pressure over the Indian Ocean with a stror16 monsoon to low pressure over south America, hi[;h p.1•essurE: over the Indian Ocean with a weak monsoon. The north Pacif'ic oscillation varies from a weak Pacific high, weak Aleutian low to a strong Pacific high, deep Aleutian low or from weak circulation patterns to strong circulation patterns respectively. The north Atlantic oscillation is a similcir rel~tion- .... ship involving the Azores high and the Icelandic low. Empirical formulae were devised for·interpreting the intensity and vari&tion in these oscill~tions. United States t·,·ea tl1er Burec:..u. In addition tc :walker's work on correlating datc:t from v~ious sti;..tions all ove1· ih e world, Weightman of tile Uni tea States Wec..t.her Bure"'u hc.s investigited the correl&tion of pressures from sixty fot..r stations all over the world with selected statiuns in the United States. 5 The zonal index has been devised by the Uni tee Ste. tes Weather Bureau Five Day Forecast Group us a measure of the westerly flow between 35o and 55° N. A high index inc.ii cc.. tes zonal- flow and a low index, weak or no zonul flow. In add• i tion to _the zonal index, indices of subtropical eastt2rlies 5 Rich....rd H. Weightman, Preliminary Studies in Seasonal Weather Foreca.sting. Monthly \Vell.ther Heview, Supplement 45, Sept. 1939. 99pp. 6 and polar easterlies have been defined. 'I'he forecasts of this group are based largely upon forecc..sts of these indices and the interpretation of the forecast vc:..lues of these indices. It is interesting to note thut the zonal index has irregular rhythms of from five to ten weeks in-'length. There is also a good correlation of the North iill1E:rican index with the northern hemisphere index ar..d & good lo.g correlation of the Pacific Ocean index with the Atlantic Ocean index. German .investigs.tions. E&ur attempted to cor..relate the circulation with various rneteorologic&l phenomena so as to devise forecas Ling rules for weat.he1· in GE:cmc..ny. Ee divided the study of weather into three ports; we&thu· ..occuring from day to day, ''Bro&d WeaU1er 1' -- a similo.r circulation occurin6 throue;.t1ou t u per ioc averagir.6 five aLCi a hal:f days in length, and "Grossvetter'' -- a lc;.rge weati1t::r process lasting from fifteen do.,> s t::, o. wor;th. 0 Le ooserveci the followir..g in invest.igat.iri~ tne 6.Lli10spheric circulation over the 1'.:6rth Atl&ntic frorr. month to month:7 (1) u.n &bove normal pressure g--raoieEt between Pontu Delgacia ,mo Icelano with neg& tive pressure dep2.r 1..,UI'E:S in t11E: circw,1polar ar..a -+ 6 F. baur, Official .Yiec.th.s:..£ Forecc..stin,; for 10-g~ Periods _in Germany, Bulletin Arnericc.n Eeteorolo 6 icc.l Societ,y Vol. 17 9 1936. pp. 148-153, 252-254. 7 Iv:ontcom_ery, .2£• ci,:t., pp. 60-62. 7 subpolc...r regions will be rnc1intE..ined the f'ollowines month; (2) an irregul&r pressure departure ·aistriL,ution is not choract.erizec by the contiLu&nce of &n abnorn1c.-ily high Nort.h 11.tlb.ntic circulc..tion; (3) with a positive pressure a.epw·ture in the circumpolar an6 subpolar regions plus c.. wed pressur.e gra6i~nt from Por:..tc.. Delgada to IcelW1d the ~ruoieLt remai~s abnormally low; ( 4) an ir.regul&r dis tri bLl tion of pressi..:.re depc.r "Lure in the polar regions c:.t tendea by a ·weak presst.r·e graaient no longer maintains- thE persistencG of the weak pressure graci~nt . .hhythms aLcl Oscillations. .;-..rnong the many inves tig- f;.tions into rhythms and oscilla.tions in we&t.he1•· phenor:ienu. the following are of interest. DeFant8 founa r'"irifc..ll perioas in Europe and Jup~n of 5.7, 8.7, 12.7, c..no 2~.6 days with a possible error of plus or minus ten per cf::nt. Durlinef in an investigution of the e'-'stun lobe of the p;;.e;ific high pres s ure cell discovered waves of 24; 29, 95, and 381 d&ys in duration. German inves-Ugc..tions &t Leipzig1 0 sbowed U-.. ;;.t the winters in :Surope &re predomir;&ted by press1..tre oscillc:.tions lasting twent:/ to twent:,,four days. 8 rl. DeFGi.nt, Die yer!!no.eruri.g in der ,l-~llgemeinen Zirchulation der A'UliOSill}_Lre i!:! OE;r Geni£ssi 5 ten Berieten derErder,Sitz. J.kc.d. Wiss., Wien, Vol. 20 I1io. 121, 1912. p. 379 9 Don.:...ld A Darling, "Report on the Accomplishmer..ts of the Statisticc..l Project, June to Sei-=- tember, 1942'', (unpublished report to the Iv:eteorology Dep.:.rtrnent, Culi:t'ornia Institute of Technology, Pasadena, 1942) pp. 6,12. 10 Pogava, .2£0 cit.,p. 7. 8 Rus.si<ill school of extencea forecc..s ting;. The Hussio.ns have approached the problem of extended forecc.stir,g through a study of the general circulc:. tion of tt~e a tr.uosphere with a special emphc:.sis upon c.ixes of polar outbrec...ks, rn:..tur&.l seasons, and naturo.l synoptic periods. The ax~,s llb.VE been cla.ssified in two categori.es; the norm&.l outbreak moves from northwest to southec1.st and the ul tra-polc.r outbreaks come :from the north, northeast, or ee1st. In Figures 1 an<i 2 below the various types of c..:xes m&y be seen. FIGUIB FIGUHE 1 Ji.XSS OF Pri.I'ES OF HIGHS O~h EUWPE IN ~VH JTER . ll POL.ia .nXES lJUI'.t~ri.-POLhR . . ...x:::;s 2 OF' P n.TllS OF HIGhS ,.. ELHOi•:; IN SUii..i,:Eii. l 2 > - - - ,➔ 11 and 12 Pagava, ..QQ• cit., Fi 6 . 9. 9 The five hus.siu.n see,;,sons &re sprin2;, sunrner, f;;..ll, _ pre-winter, c.n6 winter. The lengtLs of tLe seasons vo.ry from tv,enty seven to thirty sb; d&ys in the wc..rm months and from thirty to sixt;y four days in the cold montl~s. Eb.ch seuson is typified by cert&in influences; each influence in tl..rn is typified by some group of anti-cyclonic tracks. - The influences h&ve been divided into five grcups- depending upon the oirec ticn from which the hi,g s move. The natur&l synoptic period has alreac.y bE:en defined. l:sually in the two days of trW1si ticn c..t the beginning of a natur&l period lines of demarc& Li on between high and low pres.sure centers are formed holoini:_; the rernc.inoer of the period. The natur&l synoptic lasts from ttu>E:e to six days ano compares roughly with the v,e&.tller type pattE:rns developed at the Co:li:t'or1iic. Institute of Teclmolo 67 • Both are derived from the idea th&t tl1e interuction of differ1:;nt air bodies along zones of separc.tion are c.i.rl effect rc.Uier than a c&use of the ger.eral c:ttn1osphE:ric circulo.t.icn po.tttrn. The Hus.siw-1s in invE:stig;;;.ting the forec&st of various extremes in W( & tLer phenomena ho.ve r.o ti ceci that the cases of an extreme are usually precE::e6ed by a similar cho.in of weother events over c:... wide area l"'stin6 a monU-1 or more be- for·e the event to be forecc.st .. The chuin of events ff..11s into a group of two nu tur6.l synoptic periods and a. trei.nsi t- ion or intermeciate period between them. These groups are 10 called by the Russians lurge scale weather processes.13 Several groups may fall togetiier so that there are three or more natur&l synoptic periods tied together by two or more intermediate· naturul synoptic periods. This is known as a "Macro-process". Jui' example of a large scale process describing action exerted along the Scandinavian (ultra-polar) axis ana the Hungarian (ultra-polar) axis usin6 the Icelandic (normbl) axis as a connecting link is given as follows; . . . an area of high pressure gracually develops in the middle latitudes in western Europe extt::nding eastward approxim4tely as far as a_;__line connecting Stalingrad and Gorky. Cyclones moving in an easterly 6irection develope in the regions of the centra.l Volga, Vyatka, and Kama Rivers . . . . The process is very lo~ ano occupies a period of as much as ~ne month . . . at le~st three natural synoptic periods. 1 By combining this process with a similw-- process for succ;e ssi ve action along the Norwegian (normal), Scanainavian (ultra-polar), · and Icelandic (normc.1.l) axes a "Macro-process" is obtained. A fifth axis of action must be included to complete the process which is summarizeci as follovrn: 13 Pc:..gava, .QQ• 14 Loe. Cit. cit., p. 73. 11 J-i.XIS NorwegiE.11 ( normal) to Scandin~vian (ultru-polar) to Icelandic (normal) to Hungarian ( ul trc.-polar) to Kar& Sea (normal) CE.N'I'i:iJ:tS 0.F' 11.CTION DE.nish Tairuyr AmericcJl high low l1i 6h high high high low high high low low high The development of thE: AmE:rican center is very intensive. The ·activity is causeci by the activity of the American center of action plus the interrelate6 state 01· thE: Danish and Taimyr centers of action. 'fhe existence of the process depends upon the state 01· thE: primary centers 01· action in the subtropicE.l zone,such- as tl1e Azores and the Pacific high cells, and upon the intensity of the polar centers of action. In ti e absenc.e of necessary conoi u.ons, yarious links in the process may drop out of tt1e common chc:.in and the process itself will eitl1er proceed more rapioly as a result of inadequate development of tL.Eo diffei·ent parts, or develop in a,.different direction on rei:.ctir.16 o. certain stage . lo Eroadscale processe,s observed £l. Slliott. Elliott has observed several broadscale processes. The Connect.ion Process occurs off tile west co~st of contineLts.16 In the 15 Pagava, 212· cit., p. 75. 16 Robert D. Elliott, Extended Weatht::r ForE:castir\,.; ~ Weathe:r ~ Methods, (Washingto, D.C.: United States Weather Bureau, February, 1944), pp. 10-15. 12 first ph&se & low deepens ro.pidly out in the mioale of the ocean building up c. dynamic ridge oheao of the low by the second phase. This warm dynamic ridge then drifts e&stward with a cold stratospheric ridge above it on phase . three pulling cold air sou th ahead of it as it moves over tile continent. In the last phase the cold air is pulled down over the continent causing lower pressure in tile continer.. t and also causing tie ridge to remoir:. stutionc::.ry aloft. In the Building-back Pro cess 17 a lc..rge dynblllic pressure cell, usually over a continent wi t.h a cold shield at its base, exists in the initial phase. 1-.. series of troughs pL.sses alon6 the northern edge with ec;1ch trough bringing more fresh &ir in behind it and cc.usin6 ti1e cell to b~ild back wi ti;. each trough passage. In the Blocking Action Process a blocking high over Surope is followed in one week by a blocking high ever North America. Added evidence for ih is is the gooo lag correlb.Lion of the P~cific zon~l index with the htlc:.ntic zonal inoex. Centers of action, flow patterns, ano zones of conyer,_;enc.§. in ih e northern hemisphere. In conclu0ine a dis- cussion of what ho.s been done in studyi% lorge scale weather processes it is w8ll to review the . prine:ipal cer..ters of 17 Elliott, ££· cii.., p. 11. 13 ~ction and the most importan t flow pat t erns c.i:io zon E; s of convE.:rgence in the northern hemisphere. In .F'i 5ur·e 3 ~r e se e n the mean centers of acti c,n for the five Hussian nc:..tural seasons; 1 8 the g eneral winter flow pc...ttern inaicated by large arrows labeled acc ording to i n fluen ce; "P 11 for polar, ., "SP" for sub-polar, and "T" for tropico.l; anci the principal zones of convergence of airflow in winter inch Cc.. ted by the black lines, the width of the line indicating the ir".t tensi ty of o.ctivity in such &reas. The principal source of cold air in the vvinter is the Taimyr Eigh which extends over most of Siberia with a wecige freqently exten6 ing towards Alaska. This center of acti on provides the strongest outbreaks of colci air in the northern hemisphere. The Pacific hi 6 h cells provide ih e long est winter trajectory of air over a wc:.rn, water surf.::.ce in the northern hemisphere and therefore the tropic&.l air coruing up from the soutl1 off the east coast is the most humid in the northern hemisphere. The r~gion off the eas t coast of Asia is proba bly the most intense zone of convergencE: in the northern hemisphere. Kr ick has sug 6 Eostectl 9 th o.t rhythmic impulses set up by the gener&tion of cyclor;es in this zone 18 P &gava, Q.12· Qit., Fig. 8. 19 Irving P. Krick,~ ~nornical Theory~~~ A:tfilQ.spheric Circul~tion &nd Its Us e in Weather Forecbst.1ng, ( Pasaaen~, Califonnia: Californic. Ins ti tl.i. te of Technology, Februciry, 1942) p p . 9-10. 0 I I d, o, ~I ,.,, ;,,.- I "Q.. ,, ' •• ....s u (V 0... \ I o; I -,.._ ' ,/ ~. / I / I / / / 15 may start the eastward moving three day waves obberved frequently over the rest of the hemisphere. In tb.e winter a similar zone exists of the et-.. st coast of North America and extending back occasionally alor.g the gulf coast. Also in the winter minor zones of c,onvergence exist when proper conditions are set up. One is in the middle of the Pacific Ocean between r,:idway Islan6 anG the Hawaiian Islands occuring when the Pacific high cell is in two parts or when the western lobe contains fresh air from Asia which is being moaified and the eastern lobe is the stagnant remains of the old cell. When ti1e circula. tion is such that cold air tends to flow w t over the Gulf of Alaska from Alaska and British Columbia, a zone of convergence forms up the northwest coast of North America with storms traveling oown into the great ba.sin area .of the United States from the northwest. A region of ro nvergence exists from the Cape VerdeAzores Island region thro~gh the Mediterranean are• when fresh masses of cold air come down from the northwest, north or northea.st and are trapped in s. pcsi tion fa.rt.her south than usual. This can happen ·e i tl1ei-· with a.n intense Iceland low and a deep trough bringing cold air far sot.th, or ·.vith a high moving a.cross the Atl&ntic Oceo:n until its east8rn lobe extends through Europe pulling some cold l.ir out of eustern Europe, or with an ultra-polar outbreak from Russia. 16 In the summer the Taimyr high is completely missing a.s a center of action. The oceanic high centErs of action are greatly intensified ana therru~l low pressw-e areas occupy large portions of the continents. There is no real source of cold air; however some zones of conv~rgence do exist. 'I'hese are usually boundaries between tropicc:.l and sub-polar airmasses. IV. so:r~CE OF D.aTi>. The primary source of d&ta for tb.is thesis was the . file of Historical Northern Her:iisphcre \veather Maps. The maps from January, 1925 thro Licsh Mey, 1936 were used since the duta for this period were the most complete w1c. consistent for any continuous period. In using this data several dangers must be re&lizea.· First, only a comparatively small perioo of time was used. It is quite possi ble that in c..nother period m~ different features mey be found. Th&t is why this thesis &t t.ellipts only a study of the gener&l techni(iues _for investig~tine; lc.r~e scale weather processes. It is felt that a mt;,ch longer period of d&t& must be examined before. ari::1 deiini te results as to types of processes may be obtaineo. Another danger is in using the an&lyses &s they are drawn on the m~s. Very often inciivicual tenciencies of the analysts ha.ve crept in an6 frey_uent,ly the dO.tc;;. is such that 17 no really definite analysis can be □ ~de. In inves tigc.ting and usin6 the actu &l ciatc.. on the maps great cc:.re mu.st be used in selE:cting Oi....tc;. for tl1e same I time period throughout thE. study or , if this is impcssiole, correc tin~ the dL.tc.:. for ciif'ferences in time. ot·ten it is necessary, if a few cio.;y s are missing from a rE:cord, to rnake A further oiscussion of the p1·obleLiS of colJ.ec ci.rA-6 data. will bE: included in the inai vidL.Ll chap ttrs when such matters are conc E:rned. The rem&ina er of the ti:',esis 1.s civicEoc intc oiscussions of the v.:.rious investig&ti.ons mc:..cie. ThEc first sti... aies weather processes by the use of compreb.ensi ve chc..rt.s wi t.n trough passages Lt v2.rious rner·idiar:.s dis t.,ine;i... ishin6 tht: length of the precesses. Kext arr.ore cetaile<.:. investigution into troue:,11 passage s is rnuie, first frorn b. statisticc:.l view point and second by amily sis of graphs. From these st.L..aies thrEc.e large scale weather processes were selectec &no studied. Lastly a statistical investigc.t.ion wc:..s ma6.e in a study of polar outbreaks ov er. the northern hemisphEre. In ti.e finc.i.l chapter L swnma;.,...y of these investigations aui recommend- ations for furthsr study are made. A comprehensive chb.rt is c.. cllc...1·t up on which c.rE: loc E,ted c~ll the centers of low <.inci high prc:s b1...r1:;; a:rec:.::o for / the period of tLe ch1...rt. This cLc.p tET is i .ntendE:Ci to 6 i v8 sor.Je of the uses to v,hich tLis type of chl:.r L h,i::..°J' bt:o put to in using such c... chCTt. Assumptions. In first invest:i.gc;. tin6 t.he c:xis1-ence of large sec.le wc2,.tJrnr processes by Lise of corr.prehensive chi:.i.rts it was assumed that (1) the shorter processes or elelll1:;ntary synoptic periods would consist of one pat tern of circul&t- ion lasting threE. to six days over &n area, (2) sevt.::rc.l of these shorter processes woul6 ma~e up lon~er processes lasting two to four weeks, &nd (3) grot..ps of these loI1e;er processes woulc. m1:1l<.e up a season o.r.1a gi Vf; .it its chc-..ro.cter. It w&.s &lso assun,eo tha.t trm1 6 h pc:,.ssa.6 e s or p21ssb.o'e.s cf frontbl zcnes of convergence at fixed loc~lities w~~e good incicc...tors of a change of process; UihL ti1f; st..ccE:ss.ion o.i a certain kind of trot.: gh passa6 e or certaj_n kinos o::t successions of trough pasEag es might indic&te a longer process; and th~t between the langer processes anc between the seQsons there might be seve.::-a.l tr&..nsi tiori.:;.l tro1..c:)1 passt..ges. 19 From <.i study of trcLl.6 h po..ssC46es for the wir~t€:r of 1928-29 it Wc..6 noted that at al.most re 5ulur intE:rvals of time troughs were located simulto.neously within 15° longitude of 135° 3., 135° w., 45o w., and 45° E. It · was oecioed to use tl1ese inter vals a s tl1e periods of the c omprehensive charts. Plotting. On the comprehensive chhl'ts v~ere plottea all the positions of highs ana lows, weoges, w~ves, and marked troughs occuring in ih e period of the clu,.r-c. using the symbols illustrated below. High Presst..re Center o Hidge J:f \✓edge o Disintegratir.ig Center -{>- The pressure of the highest iso bhl' was placec. above the symbol and the date below. The weage symbol points toward the area of highest pressure and. the rict 6 ·e symbol is oriented along tHe axis of tie ridge. Low Pressure Closed Center • Open Wave .....- Trough ~ DisintegrQting Center -+- The pressure of the lowest isobar w~s placee o.bove the symbol and the date below. The wave symbol is oriented 20 c...lon6 .tLe warn~ sector isobc:~rs b.nc.:i thE trrn.• gh syrnuol points toword the area of lowest pressure. Analysis. In an&lyzing thE: comprehensive charts, first, a line separating all higi symto ls from low symuols was dravm. Then lines surrounoing all highs above 1030, 1040, 1050, and 1060 millibars respectiveiy ~nd lines sur- rounding all lows below 1010, 980, and 970 millibc:.rs respec t.L vely were drawn. On some chc..rts reci lines were drawn in the troughs o.ppe c:.r ing f'r om the above a.nc..ly sis b.nd blue lines along the wedges. Very little difference coulo be seen in these comprehensive trough &r:..o Wtdge lir.es frorn the actual trajectories of highs ar.Ci lows ano so on most, of the charts the trajectories of highs anu. lows are drawn in blue ano red respectively. Chctrts were plotted f01• the perio.d from December 11, 1928 to December 31, 1929. In Fi 6ures 4-7 are seen exwnples of chi...rts frpm e2,,ch s1;:;asun. Results Qf investiga.tion. 'I'his first ir;.v1::;s.tig;;...tion showed. th a. t the cornprehensi ve chc.rts 1;1erE: r.elpful in th c:..t, in such an analysis an appro:>_irnt.. ti on to a □ ean flo\v chert and a dynamic cho.rt wt:re combined in one. In loo.King c..t (.;A, series of char ts the i::,Taau;_,l change in processes can be readily seen, appearing frequently like sEries of syr.optic charts. I O O 0 I 0 --1._ 0 0 !' f '1-.--_j_l-------,-\--~J-----r__.~~ l \ ~ 0 ... , ti-- 10,, I ,! ,;, . o " ••ar l~-1 2' 2'> ,, ... ,, ,,o . .,o / I , 0 /• I Cl \ 110 't-- - - - - - 10-- ... - po __,.- 'f,fl"°""'\,j ,.,; C;...-"(."y~ \ • ,· \ \ . . - ' I <j> ~, ., , 0 \ • \ (, . ' y, ~ , ' (i -<V ~ .o _ ___-<_,.,./ ,~~ ,~_\ I I ~ 0 + ____. \ 25 This study wr::.s not suc c t:s s 1\:.. l i r. t L . . t fvrtr.cr i n ~ vEs tigc. tion shoheci thb. t tJ:, e troughs did not act o.ccord in2_; to the trends first noticed; tha t, tl.is observec troL s'h passag e pheLomena v✓ o.s mere l y & ch,;u'f.:..cteri s ti c of t lt& t pc:.rt- i cular winter. In p a.rti cul,:.r, U.c-: t r oufi.b.s &..lrr1 0s t Gi s.s.ppe&red I entirely ir, some zor;es during the c h arts \vE:re ·o fte n SlimwerG ·rh2 cornpr ehe n si ve h&rd t o a11alyze since severc.l p ro ce s:ae s [:.pp e c..red to l:e going or:. in one rt.: 6 ion ·v✓Li le one or part oi· one Wc.,.S occurir;g in b no t h er o.nd s ince t he proce s s e s . all over the nort.li.ern hemisphere oi6 no t app e a.r to st op and s thl't 2,.t the s~e time . From the previous study of comprE:hensi ve chi..rts it was seen UHit a more thorough investig c.<tion of prcssl..i.re trm~ghs or zones of convergence wc:.s needed. If such troughs are to be of aid in distinguishing WE:c.. ther processes, a study of the re ;::;ulc.ri ty or irrei{UL,. ri ty of tro\.<gh passages at specifieo localities sho"Glc prove beneficial. -rhis stuay wqs attempted, first, sto.tistico.lly secono, when stat- &La'j istical methods proved too cumbersome <-1.DG uncertain, a graphical s tLdy was ma.de. The raw d(:.tE. t~or tl1is study were obte1.ined from the files of' tbe r;orU1ern ~'.E:rnisphere "i:'..i storicc.cl We~ther I✓iaps a.nCl are reccrded in 1.ppendix A. Date. were collcctea for t.he period fr cm ~ c;;,rn..: EL.ry 1, 19 25 to Apri 1 30, lS135. ?res sure data -:;.F.o •N . , 1 ..,~ ,, ~o •· ,V • , Llv and 4' o- o tr ougl1 position dut£.. for troughs near ea(;b of theoe meridians w-~re collected. The pre s s1.~ re db.ta, listed under ''P" in i~ppendix A, ccnsists of' the vttlue of the lowest isobar (l&st two numbers of the vall.;.e; ie., 20 for 1020 mb.) between 15° N. and 0 35° N., 35° l~. and 55° N., and ob N. and 80°N. along each of 27 the meridians listed above. Pressures or tropical storma, typhoons, ano. hurricanes are succeeded by a ''t" , ie., (OOt). If no isobo..r crosseci the rnf;rician wj_·t:t.in t,he limits of c.. zone, the value oi' tJ-1c next hi 6 hes t isoli&r w2.s recorded. The posi ticn of e1.;.ch trough in de 6irees of lon0 i tude from the selected meridians anG within fifteen cegrecs of these meridians is recorocd unoer "T" in the appendix. The position Wc;is recorded as plus if the trout;h was located to to the right of b e meridian and minus if to the le:ft of the meridian. If groups of positions a.re corn.ected by a bra.cket. thus ~ , the trough is stc.c.tionary at that position for the period included in the brackets. II 6 SLdISTIC1~ STUDY T:sing data fron; the winter of 1920-26 at longi tuae 135° W. between latitudes 35° N. &no 55° N. correlations of lowest isobar values for time l&.g periods up to eighty two days were computed. Computation. A strip of 162 days from November 15, 1925 to april 24, 1926 was prepc:.red and labeleci the "Y'' strip. i ;. strip of 80 dE..ys from November 15, 1925 to February ·2 , 1926 was prepared a.nd labeled the 11 x 11 strip. The "x" strip Wo.s moved along the ''Y'' strip ht..vi.ng a oi1i;;;rent position for each day's lug. 28 The lag correlations Wt:.re computed using the ex2..ct where mx and my are the means and Gx and Gy are the stw1da.rd dev.iations of the 11 x 11 and The variance of x 11 y 11 strip duta respective.Ly. , 6-i. ' is the sune in all lag correl)( ation coefficient corrrnutations but the variw1ce of y b-i. ·~ ' y' changes with each computation. Snedecor's ''F" Distribution1 was used to find the vall.;e of 1. '°y above which it vvus sig- nificantly different f.com G~ • Values of ~~ with which t.rie probability that the difference in variances due to chance is less than one per cent are called significantly different .from 1. ,x: • Values of •• 1. Gy for which the proba bility lies be- tween one per cent &nd five per cent c.re barely significantly different from • ~.,1. • . Probab+e errors for the more Sitsnificant correlo.tion coefficients WE.re 9ompute.6 t;.sing the formula 1 P.3. = .674 The computations an6 resLllts are given in Taole I and Figure 8. l ~John F. Kenneyj Mathemo.tics of Stutistics, Part Two (Few York: D. Van 1{ost:c&n6 Co., Inc._1 1938), pp. 14b-46. 29 TABLE J-s.. I ST~.TISTICS FOh "x" SThlP "' =4355 run X=Ix. I l. - n 6x?. = ~x 2.I - _1-,.Jf._x;)1.. M ~ 1 1 =245925-22.70'74 =<3661 l3. L'S\SLS OF SIGlGFIC,J,JCE FO.i\ 6; Snede cor's ''F'' distribution for this stLGj was taken ')\ 61. as F= ~ where x and y have the srune number of valu e s and ')\ ~'L 1. '" >'°x X 'L ,,-2- • Then, usinc--; the Vcilue for ~"'x-, obta ineci in pc..rt, A, o above, a formula for~~; is c1eve lopE:d. • With 78 deg re e s of freedom for both x &rn.., y, 1. fer a l 7o level of signific&nce, .F'=l . 69 and mGy -=149c0 fo:r- a 5·; ; level of significance, F ""1.45 ond I" ~~ and G'"r = l '.:::o~) ,. , 0 ~ In pw:-t C values of ""c.; which are bi..rely signi fic ;;-.ntly oi:fferer.t from "',; ar e succE:eGeG ·by "ES'' W-Ki thos e ·w hich o.re si;;nifi.cc:,ntly d.iffer ent ure succeeded by "S" . 30 CO!•.'J .>LTi,Tirn; OF L.ti.G C0i{.:U.£L.ai'IUN C0E.b'FlCIEl\TS • ( CGitrihl_;-;:;D) c. s ·:1,.·I11srr1cs FOh "y 11 sr:(;:.2s ...1:v C(\ ~~-IEL... L'IOE CO~i<'FICE.I:Ts 'l- "'m,'( Day T a,g 1 .-, ,::_ 3 4 r- 0 6 7 8 0 ;:; 10 11 12 13 14 15 16 17 18 19 20 21 22 23 2½. 25 ,, 20 27 28 29 30 31 32 33 34 35 36 37 38 39 40 th I ("" '1. f - D rxy -"i 0 ~fxJr; LYt-i(rYJ lX; Y;-~Iyf-c,, ~.,, ;,: ~:r;) Yt ~Yi 24 1350 4:330 2344t:,1 243800 235718 fx;Y1 6.,, ---,, 9 309 -+-0032 ~.618 t- 8720 +.905 242800 4300 231150 241700 204080 10550 235250 4300 2311.SO 241700 2:..,-4030 l0bb0 +1170 +.121 233775 4290 2300b l 240700 223b3o 10649 t 20~ +.025 231250 4270 227911 233700 202448 10769 -llSS -.123 280026 42-s.5 225250 235575 201)87 10320 - 10c;2 -.111 230925 14210 221551 232260 229 182 il0699 ,t l743 +.180 1,229800 !4205 22102[) 23162[; 228810 110600 + 880 +.082 1!227425 i 4 185 218975 230525 228365 10 050 - .097 -... 940 L.] , •. 1229225 14210 221551 232100 229132 •10549 ;t,.) .... 004 230650 4215 222078 202675 2c:9484 10697 +-1166 ... 121 229 160 4205 221025 2~~147~) 228910 10450 240 +.025 -,. 940 +.097 229850 4205 ?.21C)2S 231475 228910 10450 229075 4210 221551 232000 229 182 10449 10'1 -.011 - 340 228025 4195 21S97t 23027:::, 22836.5 10300 - 1~8 -.035 1 228500 4 200 220500 230750 228638 10250 .014 - 4 37 -+.046 229075 s200 220500 2307b0 228638 102b0 + 228825 4200 220500 230750 2286::-,8 10250 i- 16? -+.018 22G825\4180 218405 229150 227c49 10745 - 724 -0074 ,--,,-.~· ,41·7··0 21'7883 228625 2272'1'? 10742 c:. c:o 1-~Q ,-llb2 -.113 225350 416[, 216 E40 22'/525 226732 10685 -1382 -.142 1225200 4170 217361 228150 227002 10788 -1808 -.185 22572b 4106 216840 2275?5 226732 1Cl7~5 -1007 - .103 22G775 4 135 213928 229575 22?80t; 10647 -100~~ -.106 -1'?£"~]~ - .1B5 22b02~ 418L 218928 229575 227820 lO E/27 226700 L.l220 222b05 2332!::;0 22~73t: 1064b -302c -. 312 226500 4240 224720 235450 230816 107;30 - 431.S -.445 -501.:.; -.567 225800 42-tlO 224720 225450 220815 10730 -386b - • :."JL.xO 226950 42401224720 235450 230615 10730 -3129 -.313 228775 4260 22cb45 2380,jJ 2::: 18 04 1120b -260£:i - .260 230600 428~-j ~29585 24092[, 23062D 11340 -2S0l -.2b0 232075 4310 232201 2<..4050 234620 11849 -2981 -.288 233550 L~3LJS 235988 2s.S07b 236531 12087 -2817 - .274 235075 4370 238711 250700 237892 11989 -1830 -.178 236600 4380 :239805 251800 238436 11985 -1166 - .112 237825 439 0 240901 202900 238981 11988 238875 4400 242000 255300 239525 13300 BS - 6b0 - .060 01S· -.047 239550 44.10 243101 256500 240069 1338~J :JS -1130 2414()0 12360 4435 245865 25822b - .106 1240300 1240875 4440 246420 208800 2414~0 l23b0 828 .079 I . - 31 c rn:::Pl:T..·:rm\; OF L.-..G Cvhi,:.:::L, .. T:.: J 1; CO:S.Fl• 'ICILN'l'S ( CONT DH.JED ) l. h\ IYl1.y Day T .<=< Cf' 41 42 43 44 45 ' 4t 47 48 49 50 51 vr:rc 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 7b 76 77 78 79 80 81 82 ~ 0 M6y ""' [y'). Yxr __jL_ "' "" i:yi-4 'l. I Q,::,v)'l. fX-Y· ,¼});LY1 ~ 1; f:li-~r 1\-\ <c,,v I I ~\ ,k_,(fy} I 2405~5 4445 246975 2594 25 2419?5 12450 ., -14j0 -.137 242200 4460 248645 261000 242792 1235b 59 2 -.067 242625 4470 249761 262100 24333c 1~:339 7 11 -.068 ;:-;ll -.049 242825 4470 249761 262100 243336 12339 -4, 761 ~.076 243300 4455 248088 2,50375 2425.19 12237 .,. 475 +.046 242500 4440 246420 258650 24202;;, 12230 242750 4425 244758 257075 240888 12317 +1802 -1- .1?8 243425 4430 2<:t5311 2b7650 241158 12308 +226? 4- .217 244650 ~460 248645 261550 242?92 1290b BS .J.lo6d +.174 2454b0 4480 250880 264150 2438d0 13270 BS +1570 • .145 246000 4495 252663 200175 244687 13612 ES +1~03 .... 118 246175 4bl0 254251 268050 245513 13799 :ss + 662 +.060 246100 4bl0 2bL~ 251 268050 245013 13789 BS ,J. St/I +.053 24480 0 4505 253688 267325 24b241 13637 BS 4"'.:.:l - .040 244975 4505 253688 267325 245241 13c:<: '7 BS 206 -.024 245975 4b00 2.53125 266600 244969 13475 BS +1006 +.08 1 244925 4<.95 252563 26587 5 244697 13312 BS + 226 +.020 245500 4495 252563 265875 244697 13312 3 S + 803 +.073 246925 4 495 252563 265 875 2~4697 13312 .oS -4-22 28 •. 203 245925 4490 252001 26b300 244424 13299 BS +1501 +.137 246575 44 85 251440 264825 244 152 13385 BS -1-2423 +.222 247500 4485 251440 264825 24.:.-" 152 13385 BS ~3048 -+... 308 248700 4500 2b3125 266100 24 4909 12975 BS +3731 •. 047 24S600 449 5 252562 2c;S6?5 244697 13112 BS 44803 ;- .4 54 247350 4475 250320 263476 24060 8 13155 BS +374 2 +.346 245800 4470 249761 262850 2403~6 130&9 BS +24 <.l4 +. 228 244450 4455 2480 88 261125 242519 10007 BS +1931 +.179 , 242525 4450 257531 260600 242244 12969 BS + 281 +.026 28:S -.026 242800 4465 249202 262225 2-S.0033 1S023 ES 861 -.080 242475 4470 2497611262850 243336 13089 BS 40 -.003 242750 4460 2..:l86L15 261550 242792 12905 BS 133 - .. 012 242950 4465 249202 2G217b 243063 129'/3 :.as 111 -.001 243125 4470 249761 262700 12L.3336 12939 .3S 244500 4480 2508 80 263500 24:3830 12020 +- 620 +.Ob8 372 -.036 2t;432.j 4495 262563 264Tlb 2L,.;_"1o9'/ 12212 3o9 -.035 244600 4500 2531 2b 266200 244969 1207b +.0 31 1246350 4510 2[:;A 251 266 300 24.5513 120-s;::. + 8~6 + l c:~r· (· ) 0,·- +.123 247050 4515 25481b 266825 245785 12010 +-1482 +.. 138 248850 4545 258213 270125 247418 11912 +1202 +.121 251100 4590 2633bl 274850 249868 1149S +1552 -,..158 253325 4625 267383 278175 251770 10792 +1182 t-.128 255950 4680 2737 80 283400 254768 9620 "' - - - ----- ConcJ:u si.cns . 'i 'he rncs ·i., si i;l1J.f.icc.nt. values of cor- rel 2.ticn coeff'icif;nts ob tc..inec': v,Gre these of .618 - .047 for & one dc.:.y lag, . 0()5 -. 014 for L t wo dt..y l&g 7 -. 567 -.052 ?he rc. l& tl.vely hit), coef:ficients for thE one c...r..C:i tv.c ci&;y· indic Lte,p eI'Lc:1.ps, the exi::::ter,cc c;J.· &.. s i:s. c;y four dc..y rL.;tiJn. I t mus t be ren;en:bE::.::·ed that tlLt: d.L.. t .;... l.seci wE;r·e fer only one r c 6 ion i n orie se&, E-G 11 of 0 1 ,8 yew·. Con;:;iacru'"'le more work mu st be do ne be :"'crc c.,r.y rec.l l ,y v a lid c oncll... sions cc...n i...JDOUnt o:f compu t& t ion nece s :ar;y i l W~-c nc t pr&c t.i. c.: ... l to continue en thi ::; s tudy . o:f. 1-r . betwsen Vi &s plc ttEd ag6.i :ns t tirne on a grE.ph fo r the 12t; month perioo oe 6 innin6 .,;c..m,u·:,-· 1, 1925 a.mi ending Apr i l 30j 1s:::,s~ 'I'hi.s 6 ri...;:•h :is pr E:s er.t.ec in Fie!l)res 9 anc'. i 10 . I t c&n b l:'., e.Ecn u p cr1 exw1iining th i E grEip h t Lc:..t cE:r ta ir, sec-:.i01,s cf t he curve s eun t o :fc...11 i nto v,:o.rious rhythr.-1s. SOEd:: oc cu.rer,ces of i nterf.: s ,__. w-e to be Thirteen rnontl1 rhytrJD. LotE: oo This rhytlim may lu.•ve so.me FIGURE 9 OF Th!!. l...O'iiSST rsoa~Ji CE-{OS;:;ING 135° W. BET',iEEN 35° N. i,.ND 55° N. Januury 1, 1925 to April 30, 1930. Periods w-e bo 1...n6eo by vbrtica.l <~ ·- : __ A-~·•i : ~ ~ : J~; ~---: __ , __ , : I .L•• ; • . • .L . - -~ , --~ ~ - + - ~ ~ ~ -'- +-!~ ~ ),_ _ - , , • ' · ' j. -1 : !_~ r__~ _.:. • __ 1_ :- - "V ' i , ; ' -- -, ·~ - ' _ , 1 ...... _L_~l_Y : __=-:--+__: ~ ,:_~il' l ·, i -------' -.i - : '. . ,' -·: -- -ii - -; - " l ! i ' : '. t ! .- J ___; ' i i i -t · : black lines ano sub-perioas by vE:rti cal dashed lines. ! ; , The trough passages inuico.ting a thirteE:n mon-+-..h rhythm ore murkeo by 11 A' 1 • DG.1-slH,c vertical lines thus mc:J'kec are us ed wt.er, sevtrc:J.l pcssil.,ili t-ies exist. 36 indirect connection with the t;ype of lhl'ge scale wec.tJ:1er processes occuring at various times of tne yew:-. In the cb.se studied the rhythm v&ried from t',,elve to tl.i.irt.eE:n wi.d a half months. Perhaps the twelve month 01:,cillc.tion wc.s merely the annual oscillation to be expected. It w&s first noted th£it the dEepest trough of tl1e winter occured within one day of tl1e swne aay in the yei;;Xs 1925 , '26, and'27 in the month of Fe iJru&ry. There :is ;:.; lso a c er tain s irni lar:i. t y in pre SSl,.re trends durinl.':> tl.. e first two . morl t h s of these Jet..rs. In tl1e next two yec..r•s the thi r teen month rhythm w&s apparent with deepest trou6 h p2.ssc.6 es occuring in !;~arch 19 28 and April 192t, . Lowevn· the sh&dcw of t r; e annual rhyt:b. m . rem&ined, wi tiJ. aet:p trol.-6 hs occurin6 1928 c:.no 1829 vri thin a few d &ys of' t.he first. or.,serv8c d e ep e st trough d s.te .snd in 1929 a lllW't'..ed oeepenir;g occurea :i. L FE.rch within tbr ee dc:.ys of the date of the 1 9 28 deepest trc ugh .. For the next fe\v years it is hc...rG to ae.tect tL.c r hythm since it pas ses thro1.. . c;:;l1 tl1e sprinb ana surumE:r months. l lov, ever some unusual dEeper,in6 s did occur i:..ria it is possible to weakly •trace the csci 112. tion. L:&r.kt:::d trouc)L pc;.SSc...6 es oce:ure6 on Eay 28, 1~) 30 a.no June 9, 1830 deepening to 990 mb. In 18 31 & tr cL:.gh pc.s sa6 e July 12 of 1005 mb. wo.s ooscr·ved and in 1932 on Sep t er.Jbcr 3 deepening to lOOOmb occurec.. On September 28, 1933 t he rhytLm agfain E!LO\NS itself strone_;ly 37 with the deepest trough of tll~t se&son occuring on this date. Next year the deepes't low of the 1934-35 season occurs on October 8, 1934. Other similar analyses can be made but much care must be taken in considering season~l variations, general acceleration or retardation of weather pc.tterns, arm the chances that trougps sometimes may travel off' to the nor·tll before they reach 135° w. '.J'Went:y five day rhythms. At times a rhyti.llll of tvwenty :five days plus or minus ten days was noted. The principal variation is from year to year; once a rhytllm of a certain period is set up during a season it continues,with few exceptions, within a few days of that period for the remainder of the season. A summary of the periods bet11,een major trough pa.ssages follows; November 10, 1925 to February 21, 1926; six periods varying from fourteen to twenty one days. October 24, 1926 to April 6, 1827; five periods varying from thirty to thirty three da.y s with tiie first and fourth periods split into two equal parts each. (For the same season the correlation coefficient study showe6 a sixty four day rhythm.) February 3, 1928 to April lb, 1928; three periods varying from thirt;y six- to thirty eight d&.ys. December 7, 1930 to April 12, 1931; five p~riods, four ·of which vary from twenty five to thirty d&ys and t11e period of Janu&ry 4-22 bein6 only eighteen d&.ys iB length. 38 December 1, 1931 to April 12, 1932; six periods, five of which vc:ry from t we nty to twenty five dc.ys anci and the seventeen day period of February 9-26 occuring thirteen months after the eighteen day period in 1931. October 14, H?32 to Mc:.y 24, 1933; tEm periods of a marked but irregular nc.(ture running 20, 24, 24, 10, 25j 27, 22, 13, 16, 17, and 25 days respectively. Conclusions. This method of analyzing pressure data is very subjective. The analysis of the norti1E:rL hemisphere cho.rts from which the data wE:re taken is subject to the ide o..s and idiosynchroses of the ant:tlyst. lJ);1.ny cases arise in interpreting just wh&t data to record, especially if the pressure field is very flat. Once a graph such as illustri.;. ted is drawn up, it is ec.(sy to start reading into it relationships for which no positive proof exists . .... As yet no certain treatment. can be applied to such irreb,ular rhythms as these. Statistical appro&ches req_uire the employment of large computing sections, too lurge perhaps for practic&l consicer&.tions. Earrnonic am.. lysis also requires extensive co.lcul&tion. Othu· metLcds of testing da1,a for periods have been consictered but none 01· them take into accot..nt the testing of data for periods of a va.riable duration. Usi:r:g tile in: orr;1 .,_ti.oL obtc;.ir;Ec in tl'1c previoL.s in- isolated. In no W,;;,.'j Whs it exp€:ctcd that thcse' proces:.o~s would be typical of all ic.r 6 e sc&le processes or of lr.:-1-I'ge scale processes in benero.l. There is wuch aou.ot thc.t 1;;.ny two u-e ever alike. I'he first step wc..s t o look &t tLs- large grs.ph ( Figure 10) of the lowest isobar value alon6 135° W. be tween 35o N. ano 55° N. an6 selE:ct sections with ths sruoothest curve in oscillations of approxir.J&tely tvvent,; f'ive dL., ys and &lso with the most markeG trough conoi tions. Us.irJ.6 these criter ia. the pEricds fror.:1 t.:"anu(~.ry 1, 1933 to J&rn_;_&r:,· 2C, 19 :_:<.:: and frorn rr,or.tl1s before tlie f irst of tlwsE: two p(;rious Wc..s selscted. plotted on one comprehensive chart but this proveo much too • complex for q l'~~- kinci of anc.l,';sis. I'he procf::::os ,·,&s then divided into tvvo p:"rts, tlu. . t cl1&racte.ri;,:,ed b;y a gsnscal rise 40 in pressure s.long the 135° W. meridiW1, o.r:.ci tlic...t char&cterized by genEr&l f&ll. Eere ago.in the si tuL tion vw<b.s too complex for any complete analysis. Hovv ever it was noted that the storm tracks off the east .AsiE;. coo.st ter:.ded to move to the sou the&st in ti1e period of general prE=ssurt- rise in the eastern r...,Etcific Ocean and back ctgain to the northwest with generul pr essure fc.,ll•. This muy indicate soLiE: sort of eastwest oscillbtion in the Pacific high cell. CompreLer:,_sive charts were then plotten for each natural s:i·noptic period of the t wo la:r·ge sc~le procEsses from January 1, 1930 to February 22, 1933. The first was dividea into two sections, one of tl1ree tmu thE: other of four natural synoptic periods. These art presenteo in Figures 11 through 17. The second process We.ts divided into two sections of three n&turlil synoptic perioos each. · It wc.1s fccnc that sEveral of the processes overlapped &.nd iJ1 lit occ,.-.s ion&lly the periods stw:-ted b.t different times in various regionso For these reasons ·some: of the cqmprehensive charts overl&p. The d;.hl'ts wE:re plotted anci analyzed as in Cha.pter· II with tl1e trajectories oi hijLS .s.nu lows in blue and red respectively ano with lines beir;6 drawn urouna groups of h i~hs and lows of various intensities. For the pE,.rio6 from l~overnber 30, 1931 to Dece1nber 24, 1931 a series of comprehensive chc..rts 9 each approximately one natural synoptic period in length, were &v&il&ble f r om the 0 0 I 0 o'\ \ • \ OI \ ..... •••~•,O ----------- 0 0 I 01 Q.. / I o' ,r / I I I I I I I I ---- t- I t - ; I ~,. ·"·•.,,, I I r <lt.. 1 • .,, ,, &f I I r ~ / I / I ,.. / / I ~ Y' I t 0 if---- /0 ~ --0 0 0 ! ¥ 0 o 0 <> 0 0 0 0 0 f , 0 0 I I° f ---- . •' i· 0 . ~ 0 ... l 0 0 0 O 0 .... - $ j ., 0 ' O .... u- 0 0 \ \ ~ 0 \ . ----- /~\ : " '...,...... f'4"' f I \ ----j_t I t --J.___:__ ! .. / l ! 0 o 01 0 I __ .. - - - ~t ..... - z.o -·~ .~ • .v< e"'-f"'_.,.,,, I I o/ I ,"'- I >< ~/ ..... -~ '"<•' ,,,✓- / ' / ~ . ' )<'~ ..• ··"'-.,p \ ,.~ '"'/' \/~ ~ - - t-- - - + - 20--- - ,10 t --· - \ I I I I -~ 0~ J I ''9 ' :·'_.- ~/ ., "Q.. ... .., tj' I I '- I I .,_ Or I I~ I I- / ' ' >- ft 0. ' X 0 I I ,J. I -+- o, 0 ----- ........ ; I I • ~ s~. / I l I / I I / ' / I I I / I" ' ~, ' )'"-.... ✓ / / \ ♦ oo 0 0 ....o I o, \ ' I / ·,:_:· l 0 '1 0, - "•-o ....t , ---,. \ ' - \ , ' . ,,. ., I ~l -....... -! I :-, c; ./ . \ \ --\;,,.,,< \ -.....,;. I . . . > to • '! ' _..,.I.--'---- .i..--- -r..,--+-__-1--- - --\- ·--\ ' -· -. -~ _,---- I ,.,., / I I \ ;.,. ;' I / I . , ., // ,,. /o 0 0 / / -. ,•o .. / "~ / O o \ \ o'l \ \ I \ OI o, \ ' ., \ - ,... -\' \_ \ ' \ 48 files of the Meteorology Department at the Calif'or·nit. Institute of Technology. 'I'he pE:rioci covE:red by these four charts agreed within a day of the period indicated by the graph. There is little resemblance in this por·tion of the pressure graph curve to that of January 1933 thirteen months later except that both processes begin and end with notable deep trough passages and that the second deepening is more intense. Also in each case the last natural synoptic period of the process begins with a deepening as deep or almost as deep as that of the -final trough passage. Trough passages. After the comprehensive chfil'ts were plotted and an&lyzed graphs, Figure 18, were prepa.red :t:or each of the processes showint; the daily trena of the lowest , 0 isobar vulues at longitudes 135° E., 135° w. 'j 4 v \v. ' and ,_,. On the graphs values for lowest isobars between 45° 1:' latitudes 35° '!IT ... 1 • and 5 5° N. are connected by solid. lines and values betwe en 55° I-J. ~mci 80° N. are connectea by dc;..shed lines. The vertical solid lines mark the lirHi ts of the large scale processes; the vertical d~shed lines, the division of the 1933 processes into two sub-processes each; a.no the vertico.l dotted lines mark ti:rn limits of the nc.tural synoptic periods. Favorc..ble indico. tions of some sort of correl&tion betwee n marked d cEpening in these zones and the limits of ;~:-~--- -_±0: ~/ • -.: . ' . , I I -:·,1·••L· ' I . . :. j. .. ·• - ~-~~ ~' • I ,' j · , ' .,.- '" .' - .• .. • • "" ·- '" 1 • I I ~-- --i- - I _.---.-.- __ 1 1 1 ·• · ··:. ::.1;.J~•.·-'./ I ' • . • • • / : · '. - --1---• l :-1· ' ·· t1f~ -¥ f ------, -·--- ! ' i--- ~1---- i- A - t. , ~~~-- . I er J ·.,r. . r: , Q :... £ J/ I -~ - ~ -r lirn: 1 .: ~>rnou&u PASSAGES AT: 135° 1 -[£~~ •. . • ! ~-L-l)URilKLTBREiE 1 E $ £ , . 3t:P: ~v : 4 . " [ 'iNJ! 4150, •. i \ : ·smLECtrED~~d&hl~¢dE~~s;n;::i:·rf: J::t:r. j I 50 the large scale processes can be sed.1. in thc:..t a major trough p&ssage occured at all meridians wi U1in Q. day of the start of the January 1933 processand that at three out of four meridic.11s major trough passages occureo within a d&y of the beginning of each of the other two processes. The major trough was delayed four, days in eastern Europe with the beginning of the December 1931 process and accelerated five days in the Atlantic with the beginning of U1e February 1933 process. l'nfL.vorable f&ctors to oe consi6ereu in investigating such a relationship are the apparant randomness of th1:: curves and the high degree of subjectivity that must be employed in interpretin6 the curveso II. ANnLYSIS OF' PrtOCESSES Flow pc.ttern charts. I'he comprcher:i.sivE:: chart is often very complex and cont;__,.ins of necessity many f'inely plot tea points. To bring out the general flow pattern, the principal centers of' action, and the m&in zones of convergent air flow or frontogenetical and cyclogeneticw. activity it was decided to dr&w up a composite chart. From the comprehensive cho.r"ts it was noticeq. that some hi 6hs an<i lows during each nc.. tur&l syr.optic period remain fairly st&.tionary. These comprise Uie princip&l centers of action for that period and on U1e composite 51 flow pattern charts a line is drawn encirclin5 these positions with the lowes ~ or hi g hest isobar va.lue of the lo~i or high cerlter of actior1 re spec ti vely pl&ced insice this line. ThE: cases of movj_r16 hi 6 bs c.nd lows were more diff:: cult to analyze. Cst,;.-.llJ tte lows develop &s cyclonic wave formations alOii,s the polu· or arctic fronts·. Or, tLe flow pat t.erL cLarts E. l ine is drawn alon6 thE:. genu·al c:,· clone pt1th during the period £.nd represe:r..ting the mehll. zone of convergence for the perioci as well as a mean :frontal positicn. A widening of this line an the chc:,r ts indicates a zone where marked deepeni ng of storms or mc.rked frontogenesis occL.rs. Dashed lines indic&.te a wecJ<.. or uncertain zone of convergence with no intensive &cti vi ty. ·rb.e :wovin5 higLs, beir,g re&lly large mo.sses of lJJOVine; air, were trec:.ted as part of the general flow pattern. To represent the fl0v...- pat tern arrows are drawn inctic&ting the general flow around the centers of action, the UJovelllents of high pressure areas, and the outbreaks of cold air. The type of flow was consicered as 'to influence; on the cho.rts "P" for polar, "SP" for sub-polar, and 11 T 1' for tropicc..l. Polar air was defined as any air coming from arctic or continental polar air source regions auch as Canada, .Alaska~ Siberia, Greenland, and the Arctic Sea. Sub-pol&r air was defined as rnari time polar air ro ming from the Pc:.ci f ie and 52 Atlb.ntic sub-polar highs. Tropical ~ir Weis defined as air coming up from the sou th around the sub-polar high cells or as warm air pulled up from the sou th by deepenir.1.c, low pressure areas. In some c&.ses where polar air flowea out for some time over water it was called sub-polar. Likewise tropical air pulled far northward was classified as sub-polcu". In cases where a cold high .moved out of a continent p :, •• 1ing up tropical air behin6 it with the whole ruass being mixed, the mixture of the two air mb.sses was cc.llea sub-polar. The length of the arrow in most cases represE:n ts the distance traveled by the air du,r-in,e;; th t perioa of u~e chart anci the width of the clI'rm. in most CL·.ses the intens i t;y of flow. In both the estillJution of the lerlc;th ana wieith of the arrows ~ lar 6 e ar.;ount of subj ecti vi tj' Wb.S used. Flow pat tern charts for ec.ch natur~l synoptic pE:ri oci of each of the three large scale we~tht:::r processes st1;ctied are presented in Figures 19 through 35. Comparison of Processes. In coIJJparing large · scale processes thirteen months a.part; tho.t of January 193~ with U-12.t of December 1931, the follovJing sin.ilari ties anci differ- ences are found. The December p::..~ocess ho.s only f our no. tural synoptic period whereas th e January process of equal length has seven periods. This may indic&te th~t either the first 0 0 0 21 + . 0 0 '/ ,,;. 0 0 ·.\ I{ _.,. I 0 \I 0\ I ♦ 0 + I : -_;__{ ,~ l 0 + . l 01 0 < / I . _____.., -;-----.-- + I / 0 c> O . I o, I - '"'"• / I -~ / ✓--.,,,,✓• ,·t />\ .I I" ;' I / / / I ~( " /. , ✓ / 0 l..__ 'c. I I /' / 0 I"..,~ , ~~ I I-( o,.,~ I ' ', '/', ,.•" / ;"o ' I ,/ I /. "> / ~4 I 0 .,.• o ,.,;, ,., 0 I .... 0 :, 'f o /$ l '··1- '--., 0 ---- I ~---',"' ,_ O' --- 0 - --. v------- I o, .,.. I ✓ ,I I .,. o.- /' ' I / ., / f'~/ / ~ ~ ' / / ' o, !¼,/ / 0 0 ., g / X / + " 1 i o, / ~, 0- ~ 0 0 I I 0 0- 0 -+- 0 0 / ·"' . 0 0 \ I 0 + ,'3 , ''.t. 0 0 0 ... ~ , 0 ~ .t I ', / ~ '-- . -~ r d ''--_:-.. 0 0 0 f f ~ I -,.0 , /'~ 0 0 0 0 0 ', / 0 I D OI -or I o, I -f-., . ✓ • ~ ... 'J -< _,o •. ·• \,•,.'0 ·, ✓, {- •ttJw .. I f I I I o, • I ·°l . . I 'I' , ,, / 0~ < \ ~ I °ts / ~ , ~r "" .p ,, / " I 'v ' o; . 0 .,,.. o / ,, / / /' - 1• ('/ ' (', / 0 -0 /• ' ., 1 o ! 'o ·" It0 ~ .~ . .., ' '/ ·"' ',;, / ;<< /' ✓ / I, ' ,, ,, I ,+ \ / / ·o, / ' ...., ~,; O') "- ~ .,,:s t: ~:}' ~ ' 0 o / 0 ',o ✓'x:; + I .,..., 0 '' '4 I ·' ~ ', / . ~.,., 0 I / / ,, 1-__ I ! - QI - I • - I I ' ~ --.,..__ • •lo 1111 0 : \ ' \ '. ' I o, \.,; .. ~ -- ,. .,•o , .. J . .,f '! ,...- .. ,"'lili;l;_i~Z.'J.~!.~-- . ~?.J ~·....:x , • .r .. -0:. t,- ,!, • ~11.· • - J"ff ,,~ / . ~ / -1- .. '. ) \ t ~ t, l / . ' +-- Ji/ "' _.,·~ - ~ 0 .. c... ' ' I" -; 1 , , .>~ .~ ✓ __,.. .I - -- \ . .... 0 - • \ .y- i·" ' ~ ,'1-,..•< lot',_•.~ - I f1 ·, I •• .,.._. _ , . . _ / I : I. o- ---- ~ _rT , I 1 I --, • ./ 3 •~ • ~I - - • ---/- • /... / 'Co ,' ' °" .., , / X ~,. .... , / " ' . , ,"> o, / / ,:. ~ ',./ - / / / • / ·o, • ✓ ,/ l( / / ; ;~,u r· -i ~ i I / :\?, rr I o • / .) I 0 l ~ ' ,/17 0 0 ; --, \ ~. 0 / 0 >~ ', <> 0 0 0 0 C 0 o/ '\ /. I + I I ~ / ~-. '1 ~,\ / / / . + " , _...., I ,/ lJ 0 co o"t \ I QI o, 1 I ~"-~- 1, I l ;. I - I I :~ I I . o! 0 I fJ . 1 0 I 9"' ' '( ~ ... / • x~~ 0 / ,. ./ ' --0 ....--.;. .. .• / o; / $;> I I ' / ".· ~!- /, 0~ . 0 ' • ' , // ,1 .p X - #~ •t - ' .~· "/ " / / ·o, / A ,~ I O 0- 0 0 0 j. /.~' I I --~--✓ - 0 O 0 0 ~·- - t' >--:•~o , ,! j 0 t i\ IO 0,, - 0 ! 0 0 I O o J ; ----1____ O 0 i r \ 0 ~ j --; I g i 0 oil 0 ,.s;, 0 I I----1-_ Cl \ \ 0 0 01 0 p o o -'Lu I 0 o . I . o, • 'o f - ''"'."' "' . o.,.>.., , ~- t - -1- 4 ., . . '6"'°"'~.,,-1 ""0·l "o .._ ' ( .. lr) ti) ~ 0 , o,. ,i-0 >< - -j / / -------- n, 'I, 'x' / x_ .". , ,)" ~ ' 0 .... 1 / X / / ~. . • • /: / 0 <> ,' 0 'I- 0 0 0 0 [ o· 'o / o / '' / '\\.. / /,,/ ""x / 0 0 \ 0 ,~ -~ '~ ; 0 £> i 0 / 0 I 0 o q I ,? :--i I F 0 0 0 0 ' O 0. 0 0 10 0 ~'\, 0 .. ~ 9--•.• ,, ..,,. ~~~~- .,,•• • o , 4~ ·, . o o -~: ~ ~ - '"ti" ,. ' ♦- OI .,..... I -l -Ol - 0 zo--·.,.._ o, I .I o, / / o/ I ✓ 1 / ~ / . ,. .' ;( ~ ,, / / / X ., , / .~ &-/ ' \ "!)~ ~ 0 ' ' 0 / )\ X. 0 ' 'o. ,.,_ Y/.,,.. , / ' ' / "'- 0 0 01 0 ,, , ~ ., r0 lJ) 0 ~ Ot ,,< ,,,. ,,. ., ~~ o,. ,,< I / / X 0 I I I / ✓ 0 ., 0 0 0 1 , I 0 ,,..... .. i I I I 0 0 < ? .. • , .. / ..... ,_.. eb".-a ' ~ '• ..... I \ - n - \ I I o•'•••1 \ I ,~o . -· - , \ \ -~- -- --- - 1 -- - - n ~ - I \ ' I ' / / / I I ' \ ~ t 0 0 oo 0 ~ + ... C', 0 ,••• , IS 11 ' ... .~-L 0 j ··-1.L -~ M 0) ~: /']f: -~ .>.. 0~ _J LLl / 0 0 0 0 0- + 0 0 0 0 0 0 0 1 ,. ~ \ + I I I /-: -----j__ / I --+-I . --\- I I / o, LL 0 Ir 0 0 0 ~. .• ..... 0 0 di, 0 0 o..., ~ / .. 0 ~ 0 · " " 130 '' -- / -~J •.LO · / ,.>,o~. -I- -.., •o•o '"o,,4,, ''I:, ~ ;· "&- 0,. ,; .,._ ,.,. ,. > 0.: o,, / ,- / / ,, )< / ,A :/ / o, / f') ~ ._; ~ ;. ,, .D l,. $ ~ ~ i.- N _J, ~~ 70 .p rocess was made up of slower,more persistent periods or that some of the periods of the first process mi 6 ht have been split into two natnr~l sy~optic periods. Comparing the two processes by posi tior~s and intensities of the centers of action it is seen in the initial / period that the high centers of action occupied -approximately the same areas with the exception 0£ the Pb.cific center of action which is considerably larger in area and located between the Hawaiian Islc1nds anci Midway in .the December process, and smaller and area but with a higher pressure and located east of the Hawaiian Islands in the January process.The highest presst.;.re of the centers of action varied within five milliburs bet1i,een the two processes in each case excepting the Taimyr anci Al&skhl~ ce1-. ters of action which were ten to fifteen millibars higher in the January process. There were more diff'E:rences betw~en tl1e two processes in investig~ting the low centers of action thb.ll in invest, ig&ting the high centers. The Icela.nciic low was markedly deeper in the Jonuary process than in the December process when it is weaker and shifted toward Spitzbergen. The tendency for the low centers of action to be shifted in the January process to the west of the positions in the December may be seen to a certain extent all over the hemisphere. In comparing the tv.o processes it is well to point 71 ot:.t similar circulation feat~res. The gencr·o.l floi.-, pa.tttrn is very much alike in thE: tvvo proces s es for thE:: 1·ir ;~, t nc:.. tural synoptic period. The second perioc.i of the Jo.nuary pro<.:ess contc..ins mt.ny of the features of the initic:. .l December process. The thirci period of the Jo.LUc:.r;i' proc s s .s is much like the second period of the December process exc~pt tr.&t the pattern in !-Torth Am e:ric & has bf:en shif'te6 to the WE-st in the December process as comparea to the January procE::ss. I.-ne principal zones of convergence in the A. tlan tic are sl..ifted some twenty deg:r-ees eastwc.:.rd in December due to t:i:i.e 1·aster outflow of cold air from Canada which in turn was ruutiv,--. te d by an upper Hudson Ba..Y lo w center of action. The fourth naturai syr.optic pe1·ioei of tl'ie ~ t..rn..ia.ry procE:ss i s similar off t he east CO L.st of Asic.. ~no ov1:;r tJ1e Jitlantic Ocean anc :'.!;urope to the third perioc 01 the December process shifted f 'ift2en to twenty degrees ea.s t.vmrd . :::: lsev.-here it is difficult to see any similw· i t;y eJ1..c epting perhaps the minor conve r·gence zone ofr the 3ri ti.sli Columoic:.. coast and the polw' outbreak to the Great L&k.es region of In the next respective period.s of ec.:1.ch process a similo.ri ty in convergence zones is seE::n off the eas t COc:l.St of Asia, in the centr&l Atlantic Ocean, and ir! the lv:ieuiterranean Sea areas wi tl1 almost identicc.l polc.r cu toreaks 72 across CarJad h and tl1e r1ortheastern Cni teu Stc.tes t c tLe A tla.nti c Oc ean a.no a.lmo st identicc..1 h igl1 ceritt:I' s 0 1· o.c tion off the sou tl.teast co[..st of the Uni teo Ste.. t es . Flow po. t,t,E:rns over most of Europe anc Asi~ were shiftec from tl1ir 1,;y to forty degrees wE::s t in the Jb.nuc:.ry prccEs s fr or,. ti1ei r posi t ions in the December process. The Fet-ruary 19:?)3 proc 0ss h c. s some sirni.lc..r fELtures to the January 1933 ar.d December 19 31 processes wi tL tLese fe c tures i n general shifted to t Le scutl1 b.DO away frcr.:; the continents. For the most part h ow2v0r go ou uno.logi es b.re difficult to find and a compu-ison of U~e .Febru ci.ry pr ocess with either the January or December proces ses is 1:..o t. reaaily mad e. II I . COl\iC LUSI(jl,:s The ~Toup of flov,, patter·L c l1 L.rts is pr i:::scr..tec. as c.i.n idea of what is to be expected in the w&y of oLaly zir,,::, · large scale we&tl1er processes by mecms of mups. It is t ruE: t.h&t such a s tudy i e even more su bjecU.ve th wi Ll1e use of comp~ rehensive charts but i f' proper care is t c.J(ET1 flow p .:...ttern ch arts can preser.t a much clearer picture cf t he pro cess . In looking b.t the d;.a.rts it cun be SE.E n thc;.t in winter the cor. tinenta1 pqlar hit:J,s are evic.er, tly a. d on;inant featu re in tlie mechL-nisms cperc. ting t Le . lorge sca lE: wea tl1er processes. The large polar high c enters of ac U.on builo. up 73 and release their air in ih e form of polar ou tbreak.s. 'I 'hese outbreaks may occur simultaneously in various parts of the hemisphere or as one concerted push through one area. In the summer the maritime highs domin""' te bringing sub-polar- air to the west coasts of continents ana tropical · air to the ·east coasts. Here age.in there may be some evio.ence that the tropical air may come in surges in Vb.rious parts of the hemisphere or in one concerted push through one area. By the use of flow pattern charts ano comprehensive charts it is possible that the study of cold c.nci warm air surges may lec:.d tc a clearer picture of the large scale weather process .. POUJ.i OUTBnZ.n.KS In the pr~vious study it "Jvas seen that poler air masses and pol&r ot:. tbreak.s seemed to be u domina i:,ing influence in the developrner,t of lc..rge scc..le wec..thE:r processes in the winter. This pointe6 tc o. more thoroubh wid objective study of such phenomena. I. c o.i.,.L:.Ci'lON OF Di.i'.n. T1~E: do.t& w&s collected from the files of the n c,rthern her-ii sphere historic&l daily we&.ther mo.ps. In aocl.i tion to records of polar Ot.,;.tbre &k s actua.l ternper&.ture datb. wa s collecteci . Dc:..tc.. for eight va.rit.bles wcre col l ected as follows: A. The intensity of the strongest polc.r high in the northern hemfsphere. B. 'I'he meo.n teraperc.ture of five east AsiL..n stc..tions. C. Polc:.r outbreaks ir,to the Pc:.1.cific Oceun c l. t of' the Kcilllchc. tku region classified as to how fc:.r south they move. D. The mean temperature of five Aluskan stations. E. Polar outbreaks into the centrli.l North ArllE;rican region classified as to how fc.J> south they move. F. The mean ternper&ture of five northeastern American stations. G. Polar outbreaks into the Atlantic Ocean from Greenland clas s ified &s to how for south they go. 75 H. The me&:n temperature of fi vs. Euro pe&n s t&tions. I. Ultra-p olar ou tbreuks to how fc.,r • sou tl1 they go. intc- :.:. uropE: classifiE::o c:.S The soL thwc.J'd movement c,f the ou tbre"'Ks vms defineo by one of five Vc.;;.lues$ four of these i naicc..ting a p osi tion &nd the value z ero indicatint; no Oi... tbreak prcsenL The intensity of th e strongest polar high wt.s given five possible v&lues and the mean temperatures tEn p cssiul.e v ;_~lues. The mean temperE:..ture and polur hibh intensity values are continuous numerical variables but the polc...r outbrefJ( data are discontinuou s in that &n outbreak moves so1., th an6 either stagnates or moves off with the· westerlies follO\Jed some time lc:1.ter by &ne th er outbreak. A summc.:.ry_ of · the va.ric.. Lles for which data was collect- ed and of the values ass igned to each varictble is given in Figure 36 .. The recording of the ternp erc;;.ture Oi;...t& f or tl1e most pw,t w&s purely objective. Now a.no then missin6 repo rts required tl1e estimation of a temperature. In the followin 6 cases data for a station was off time fr orn tLe rest of tlie data for tr.at st&tion; .five month s of Shanghai o.nd one month of Moscow and Rostov were six hours early, and one rr.ontiJ. of Blogoveschensk, Nome, and Bethel w&s three hours lc...te. Estimating the intensity of tt.e st.corigest ;:::ol.hl' high was a little less objective tl1t.n collecting thE:: tempE:ro.ture data. The recording of tL.e sot...thward extent ot· tl1e poJ.ar \ ~'[) - . \ ·< </ ''-. // 0 ·,o, " '"'x _ // ,' " , I/ , '· / 0 0 0 0 0 0 • 0 ~ %,-~ / "'. /~ 0 . 0 ' \ \ I OI I .:.)''\y-~'~ 0 // ' '-' . '• oc-., ll·. ' - "- /""'• I / ,"', ' /' .... ,,.- ,< .,, ', / ,,;, • • '- / ',(, I y" o/ / . . . '-,.'• ·-,• ',' I ' , ..,,,/' ~~_,/ / 0 0 0 01 - 0 - + I I o, I o' ,~ ~r- ' I' / f'- ' / ')( ~/- / . / <> / .- 76 outbreaks was much more subjective 9 especL.. lJ.,y in the t~1:J1J- chatke.-Pa.cific and Greenland-i-i.tl&ntic zonE:s . .F'or these reasons little has been done with anything bL.t the telliper-- Do.ta were collected for the months of December, January, Februb.ry 9 and iJ!b.rch for tli.e vilinters of 1928-29, 1930-31, 1932-33, and 192,4-35. These b.re presenteo. in Appendix B. The selection of -U1ese i,vinters VfoS rn&c.ie on the basis of selecting the most complete an6 consistent date.. over the longest period of time. The intern,edi&te winters can be used to check any results :from this study. Eeans and variances. The means o.no vo.ri;;;.nc2;.;; 1;., E;:c.·e cornpute c1 by months, by seasons, and. for the. entire popuL. . t- ion of each variable o For a v0.riecble 9 x~ having va.lues x19 . . . , xn wher•e n is the number of oc.tc.:. in the sa.mple 1 • given • b y m=1 / n"'x ~ . a.no. th e variance ' ? is • th e mean, m, is s~) 7 1 ,,t given by s 2:::. 1 / fx?-m2. A summary of these computations is Di=l J. given in Table II. The means W( re then tested to see if the meu.ns :for each month and for euch season were significi-.ntlJ,' diffE::rent from the rne&n of the tott',l population. The probccbilit;y 1 P 1 of the differE.nce· in me~:...ns is expressec. by P=l-2Jf( t)dt 0 where :f( t) is the normal probabjli ty distribution funcU.cn 77 T..-i.BLS I I Dec J an I Feb 1928- 19 30- 1932- 1934- Total 19 29 18 31 19 33 1935 .w:.1.r I - I I A m? 4 . 4 0 4 .7 0 ,4. 35 3. 68 4. 35 4.37 4. 53 3. 89 4.29 .71 2 l. ◊05 1. 352 . 925 . 987 1.283 1 .529 1. 331 1.296 !; B m2 3.36 4 . 87 3 . 9 1 1.70 3 . 59 3. 71 3 . 81 2. 73 3. 46 1 .654 ] . .l3Q_ 3..__~99 1.1v_ 3...~ 0 3...8_ ~ .252 ::, . 856 2.018 :; .159 .14 .10 .21 .16 .10 .51 .04 . 57 C m2 . 08 .122 .235 .138 .160 . 175 . O-s.l .220 . 3'i' d' 0335 s D m 3 . 26 4. 40 4 .31 4 . 3,2 3 .43 i4- 20 4 .76 3 . 85 4.07 s 2 3 .759 . 8 24 4__._2 HL ~3_._4_8Q_ 5_. 9 841 .645 4 ~367 . 244 3 .2» ~c... tiu . 61 . ?'/ . 88 . 83 1.11 .76 1.05 E m2 . 6 1 _Q_ . 623 1 .24 5 . 9 11 . 748 .39 3 .727 . 721 . 961 .908 •-C e v;;;;; 4 .14 3 .71 Fm...., 3. 37 4 . 18 4.27 3 . 03 3. 66 3.41 Re 1. 377 3 .157 1. 4 28 1. 8 1 1 i2 .266 1.1~0 2. 20 3 2 . 9 S3 ~.149 . 32 . 36 · .41 . 36 .19 .16 . 32 .38 .31 G m 2 L. L~ •) .416 .508 . 375 . 5 17 .lT? . 265 .470 e44 0 s • :1.V U 2. 62 3 . 40 2 . 82 2. 50 2 .75 2. 26 H m 3. 70 J3.74 1. 32 s2 1.120 2 .189 8.012 1.741 4. 0 20 8.510 2. 651 6 . 3o3 ~ . 09 2 .so . 16 .25 .27 .30 . 36 . 44 . 37 . . 0 3 I m s2 .507 .758 . 622 .039 . 7 17 .247 . 508 . 489 . 503 i::, ~ I ~ ..., ..:> J n 124 124 112 ! 124 121 121 121 1 21 4 84 78 1 and m'.::: r&- tM 9 ..u.is the of the population, 6 is the vci.riance . 61.. I of the popul &tion, ano m is the mean of the sample. Probabilities of less than .01 were considereo. significhllt a.no those from .01 to .05 ·were considered barely significant. Vii t h probat ili ties of morE than . 05 thE: mew1s not consin0rcd 1dei'e significa.ntJ.y different. Kone of tl:e means in this study prove d anywhere new- beine sigr,.i.ficc-ntl;y- d:;_fftrent :fro.Li their population meo.n ; tLe lowest p1·obabili t;y, . 60 f'or the 1934 -2.:i season of varic:..0le A, wtts consic.ierc..bly above even t he .O b level of significhllce. The variance of each montb anc of' eo.d; sec..son ·,foS c ompared with the variance of "frie populc.. tion using SneciE:cor 's F distribution 1 , F;:; 6t where s 2~ is the l ar·ge.c of the twc . s,. 1 varic..nce estimates. The v&ric.nce estimate is give n b_y The oegrees of freedom employed in using this test ;:_;;re N ,,.n -l ano=N n -l. The v1:;ri.:.nce is consict:red signi f iccintly 2 2 1 1 diff1:::rent if the p rob&bilitJ of it not 6.ii·1·erineS i'I'c,Li the population varicir1ce is . less tban 0111:; percerlt, b,ic~ly sic-n- ific c...nt if tile probabi"li t y is between one o.nCi .f t vE; per cent, and not signific1:.ntly difi'erE:nt if t.ne probo.i..ili t.:, is more than five per cent. Tc-ble III contains the results of' tLis test. 1 John F. r.enney, Mathematics of Statisticsj Pa.r t Two, ( New York: Do Van Nostrand Co., Inc., 1939), pp. 14,o-46. 79 Ti.BiE III Under column s, .§ ind .i cc.te s ci si g nificant difi'erence. BS ir..ciicc..tes e1 bc.r-ely significant diffE:rence. NS indicates no sigrlific.:..nt difference . l l,r'l I N2 F A s Dec. Jan. 1. 80 483 123, s l ,,... I 1.41 123 483! ,:) ! Feb. Liar 1.05 11114S3 iNsl 1.38 483 1231BS I 1928 -29 1. 30 L122l120 BS 1930-31 1.00 4831120 NS 1932-33 l .18 120 14 83 !'TS 4 R0~ .NS .. l ~34-~§,.. L._04 1/I 20 ~-;· -- --~-;::.., ·, --:-:-- .... -Cl Dec. 1. 89 -:, ,3 le:,: .:;i , B rs I J·&n . 2.64 433 123 ! _, r , 11 Feb. 1.08 111 ±--'50 l'~s I Mar. 2 .08 ~83 123 Si 1928 ..:29 ·1~·02 1183 120 l{S ! 1930-31 1 . 36 483 1 20 BS 19 32-33 1,10 4 3;.:1 120 KS - lil.3fl_- ~.s 1.55 4 _;..; :1 120 ,..,, . s. Dec. 1. 67 l,.80 1 c:,.::, s C Jan. 1.44 123 ..,,..., 483 s F'eb. 1.46 4 cj -.; 111 s t:fil' . 1.32 483 l c:'.0 BS 1928-2f: 5.80 4 83 120 s 1930-31 1.06 483 120 1·NS 1932-32 1.62 120 483 , S 1°3~-3._5_ __l ._9_1 4 x :: 1 ?('- ' s_ .,, ,...,,.. J.J De c . 1.16 .1 c.0 483 NS Jan. 3.90 483 123 s Feb. 1. 31 111 4 83 5S Mar. 1.06 1 23 483 NS 1928- 29 ]_ c85 120 483 s C 1930 -31 1.96 4 ~•·; 120 ..., 1932-32 1.36 120 4 Ou BS 1 031-35 7JY/ :llr~ l ;,;() s r._, Dec. 1.4.2 4 8 2 1 23 BS .-~ e, ._,'an. .. 1 23 483 BS l v, I Feb. 1.01 111 4 83 fTS I Mar . 1.20 483 123 NS I il 928-2S 2.28 483 120 s 1930-31 1.24 L.l:t.0,0r-- 1 20 rrs 1932-03 1. 2<. 4 -3 2 120 NS 1934-35 1.07 120 4.33 NS -o '1 I < r,<' •..__J\..._,; 0 -• e 1 ,- ·1 I ') I ' iF I s ·, ,· 1. 5 b 483 1 .--,, c:,._;, s 1.48 123 4.c33 · s 1.49 483 111 s ...p l -•·-l i:) II ' Dec. Jw1. Feb . I Nl N2 1.17 483 1 23 , ~ NS 1928-29 ; 1.07 1 20 4 CV NS 1930-31 1.8? 4d3 120 s I i 19~32-33 : 1.04 483 l i::'r- ,.•I...•'r-'\ NS i h--- 19;3L~_35 .. - : J . 41 , ~a 4_{<.. ~· s_ IG 1 . .:,6 483 120 s I i Dec. J ,..n. 1.14 123 463 NS 1.07 111 483 NS .Feb . 1.10 123 483 NS Lir.u- o IC23-29 1.22 120 483 NS 1800-31 ! 1. 10 4 33 120 NS " r , 193~~-32 '' 1.26 1 20 4 cs~ NS ,. .. 42:~ l 90 s 1.9..;,;;,s. - 3 5 2 Dec. ~o60 480 123 s IH I 1. 86 460 120 s J fill i 1.98,111 433 s Feb. i I,Iar. 2.3~ 483 12;~ s 192:8-2~! 1.01 40~~ 1 20 NS 1930-31 1. 62 482 120 s 1932-33 1.63 433 120 s 19.'."~4- ')5 J ._fil l ~O 48:~ s Dec. I 1.6 2 123 483 NS Jan. 1. 62 12;; 46.3 s Feb. lo25 111 4 63 NS l'.,iar. 7.94 4 83 123 s 1923-28 l .-s4 120 4C:2 s H)~0-21 2.01 483 120 s 1832-33 1.02 4 o•' ...'<, 120 NS 1934-0b .1.02 120 4 o~_ Ll& ~-Llc:.r. l ~ l 0 -< 60 From tliis study it appeared tht.,t the vc.rib.nce was not stc-~ble enough from month to month or from Seo.son to season to warra1lt any furtl1er study oi' t h 2. . t st& tis tic. Correl<.. tion .§tt;.ci.:[ .QY. use_ of c ontiLt:;E:r.cy t i:-. bles., i,. contingency table is a tc..lJle of tLe fre ,Nencies 01 1uc...tch es of the va.rious values of the variables for which the s tt...(iy is being made. It is felt that this metho~_ of attci.ck yields a broader and more analytic picture of the correl ,~ tion of variables than that obtained by the computc.ticn of correlation coefficients. This study wo.s made with the ternp~r;;. ture ds.tfa only. In set ti~ up a sys tern for recoraine; th6 rn.1miJE:r of matches all the 6.&tc:;. were first recora.ec on one largE: sl!eet. Then strips of paper with holes cut in them at tLe appropiate places for tile relb. ti en ship to be s tudie6 11;E:re rnoved down the lc-.rge strip and the rno.tchES were thus sor-c,8u. out and recorded in the contingency tO:ble. In ma tchirit; t',1✓0 vari::...bles this cont: :.- ins but two dirner. s ions ctnci re~uires but one sheet to record all U1e fre 4 uencies of mc.tch. Ill a t hree variable study three dimensions are necessary c.Lc. thE: tabulation of matches req_uires as m&.ny sheets a.s the number of values the third variable assumes. For each table, both two vc.ric:.blc ar1d three var·i&ble, t t .e su..rns of each row c:.r:6 of each column w--e computed and 81 recorded alonr; the r:Jcr 6 ins of thE:. t2.ble; tL.ese w--e cc..l.wd the margirn::,l totc.,. ls. For a three w1::,.:y matc.;h tliese rnhl' 6 :inL-l totals may be combin12d into u mc.r~ina.l tot&l tc..Lle. Thrt;e of these m&rg inc..l tot'-'-1 t.sl.JlEs W'E possible for ec...d1 tJ,.rce way contingency t&ble o.na e&cL of' tLese 1.uc...rc!;i.n,~l to t.s.J. taoles may be consiGerE.;6 b. two ·,1hy contir.i.scncy tc.blE:. To.bles of twc w&:y Elc... t.ches v~t.rs mi:..oe tl1e lc.g or' 01 tE:mpE::ratures in .t-~L. ska. aftE:r· those in. ec..st ;~siL. in l,Abs of three, six, nine, up to thirty days. Lii<.E,wi se taole s \--iEore mhoe for the le.cg of' ter1per __ ture in nor U-1 co.stern North A..TJ.1E:r1.cc:. aft(r those in Alo.sko and of t11ose in :2:urope o.i ter northe&stErn I'Jortb dlJEric&. Two threE wo:y ce;ntingency tc..bles were prep~red, one of ti1e l~g of t~lliper&tLres in ~1~sA~ '-'fter tLose in €cost ,.sic. ano nortl"1t=;a.stern 1;0I'th ....rneric8. and the other of the lc.g of ternperc.-.tures in ncr tlH:ic..S U;:,l'Il :iortl1 ;i.1nsric'-' &:ftt:r thos s in i~lc..skc. anc :Surcpe. Ey e:0llc.psir'6 these tr.. ble.s tv10 wc.y rn-::,tches \·iEr<:o: atures iri :::::urcpe w j_ tJ:i. 0 Gt2..ir,E::C thcce in 1-'.lc.Sl'..c;_ &n0 for wit: U.02,E: 1-vi th tl1O', e in n nr1,,L e& GtE:.rL rorth iilli SX'ic:;.;. &nci tl;e te1uper- in ec.,tt ;~Sic.. l"-6 in temperatures in r.'.01·U,e1.:,~ tE;rL J'-: o:cth AIGerica c.ftt.:r tltooe in ~i:urope &..nc: t h ose irt Alo.ska [cf' tEI' these in ncrtl.1.E:~ ~: tu·n 1•Z orth AL~sk~. ::. ·-tcr th c Ge i n ec,st Asi& anc in rorth AfIJE::ricL e-1.'ttc.r thos E: i r r.l :,.sksQ All of the &bove rr1t=:r,tionec contin5 eLci tu.tles c,re shovm i E ;,.ppEnciix C. 82 To look :f'or a signi::.' ic "'nt relc..tior.ship grot..ps of matche s must be tested for signific~nt 6iffu•E:.T1.ces from those expected by clu..n ce. 'I'"ne groups of m~. tche s a..i..O~ eo.cl1 of tile di&gonc:.ls of each of the two way tables were testE::d to see if there W!:, S ar:iy direct linec..r correL.. tion betweE:cn the V<....ric..bles m&tched. The method used in testing for E. significant di1'f'er- ence of means is employee here to test for c.. si 6 nificc.;.n1, difference of the obst:rved m.uni.)H' of m1;.tches, M, from the expected number,)-<-. The prob&bili ty, P, th&.t the observed number of me: tches is not differ·ent from the e:>.1)ected number o( of mLtches is given by P::.l-25f(t)dt where normc.l devi&te, 0 M-AA «:: ~ • If a contingency t&ble hus the murJinc.l totctls t.. 1 , A , . . . , 1½:- and Bl' B2 , . . . , B8 with ~ totb.l 2 r .s number of n matches in tl1e table~ tl1en {'½_=i-Bj=n. Foi• a. group of cells in the table, G, the observea number of matches is merely the sum of all the rnc:. tches in ti1e t,---roup; .M;Im,.J·· The expecteci number of rnc.tches is given by 11 .:: 1 /. r1i..B. e:, r • 2 and the variwice 1 6, i.s given by 61.= n<z J. J 1 t:T + 2'-:-~~- t ~ ) [AiB.;(A;tB). ·L th For these tests, since a large numoer of~ possioi li ties may be realized 7 the significi:...nce levels must be strengthened. This was done by considering ncrmo.l devic.tes of :3.00 or more b.S significant and of from 2.80 to 2.00 as b.s.rely significant. The prob&.bili ty of 6. norm&l oevi&te of 3.00 is .0026 and thc.t of b. ncrm c..l devic:.tE: of 2.80 is .0062 . 83 In the tests the diagon&ls of a positive correlation are lc:.beled I and those ot· a neg& ti ve correl . . . tion c.1.re lc.1.beled II. In some c&ses a relation proved signific&nt with one dia.gon&l whereas ~ diag onc.:.l of the SEJJ.Je sign a.no with the S@De do.ta but shifted several cells over showed no si~nificc.nt rela.tion. In tc:ible IV is listed a sunm1c.•ry of tLe compu tc;.. tions anc. results of the tests of the two wc;;y- tc..b l es i 'or signi:f'icunt correlc.tions for only those tests giving L>- normc:..l devibte of 2.80 or more. In studying tile three Vfari1:.b le contingency tc..bles thE: freq_uency of m& tch in ec:..ch cell is so smb.ll and tl1e margin&l tot&ls cil'e so smb.ll compc..red to tlrn total number of' rn"'tches that the problem must be approached by u study of re.re occurences. In computing the ·pro baLili ty tJ-i;;..,t the oosE:rved number of matches is net significc.ntly difft;.r-ent frQm the expected number of matches t:l:.1.e normal distribution must be replEiced by the Poisson distribution. This simplifies mutters sornewh c t in tho.t with such o. distribution only the expected value need be known. In u three vari &l>le ta.bl E.: this is computed fer eb.ch cell by the equc:.tion /A= A-~~ where A~ B, and C are the marg inal totE..ls for the cell and n is U1e totc.l number of mc..tches. For a group 01· cells )A.-= ~ A-B·C <ir ~').. J ~ A grapb of the cu1ult.ti ve p.robc..cili ty curves h;;.s been ,,,,_J derived from the Poisson exponential, P.a:-1-[1+ /11..+~-t··•+A:-Jifl . 2.! , (,,...-1)! ) 84 TABLE IV SI GlaFIC,J,; r COh.."iiEL.i-SlOKS n is the totc..l number of mc;;.tches. mis the observed number of matches. fa i's the expected number of mutches. 6~is the va.ri~nce. G is the stund~rd devi~tion. S is the sign of the correlo.tion. oe is the norm'--1 devi.s.te. Cases where tests using two aifftrent sets of ci.~tc:.. were made a.re given even though one set of da.tc sliowea no signific&nt correl&tion. l ificance 6 lfortneas Alaska w Si 6 1d. f i c: &nt Si ·:niiicunt 5.83 + 3.92 5.39 t 3.14 ~==-=--=---------====================================---------, Alaska_ after t A.s_.' a. (..B_l~ ..:,· _DJ .. _ --- -·r----.,---- - -- 9 days 304 71 53 .184 40 .143 9 da s 364 55.286 -- -------- ----···- - 2 .80 I Bo.rely significant 1 Not significant_ 21 days 304 42.226 31.696 .97 . ·c.i.rely sit:;r1ificQnt 21 da s 364 70 52 9 43.,..BQ2 6_,..Q.2 .5'"' N.Q_t__si~:rdfic&TLt__ 'iorthe,. . st Nort J\nlE:r:i.ca after Alaskc;(, _ D l&g__EL._~•----------l 3 daYS 20li68 50 • 421 39 .174 6 • 26 - 2. 81 1Barely significant ' _ 3 day:s 3§4 63 57 .958 .. . __ ____ . Not si ·· nificant 6 days 304 72 57.861 40.703 6.39 - 2.99 Barely significc.nt __Q_~'.Q. 364 9..l 53.211 Not signii'ico.nt r.~urcne &. ·t~T ~ler __ America,___(J'-la.g Jl.1. -- I 2 Las 3C4 74 52(1782 39.513 6.30 30;37 i Si nif'icc.L.Dt 9 dai_~ 301 _73 54 .4~j 40. 798 6. 38 2. 91 ' ~ci.reJ.Y-__ 9jggj,_f:i,_C~D.t 15 da s 3Q4 65. 4~.Q.8. ~~2..0..k 5..J_8_5 .~_O _S.ig_n.i.fi.c...~t..=== c-AlasK~ _a~e-~ _NOJ"theast_ North America, . (F lag D) .____________ _ ____ _ l = = = =--=--: -- c,.,-,,.,c~9.-.-c·8 j;_gnj._ ft~an..t c.QCT..e.l~•.ti.o_ns. __fo_und..__ Northeast__.H..Qrth .Ameri_ca after Euro e, __(II lgg__ _EJ_.__ _ _ _ __ 6 da s 361 8-8_ J:.7.,.3_3_5, 50_q_979 7 .14 _ z_~_S.;,3 Be.rel si nif'i~c:J;i.:t_, 30 da s 364 62 42.302 32.281 5 .68 - 3.47 Si ni1'icant Note: For dia.gonELls used in u~ese tests se:e Appenoix C. 35 by Thorndike 2 . For purpcses of this an6 sirnilw• stt:.dies it is nece2sc..ry to extend tr.ese curves uown to expE:ctE: u values of one tltousandtho SincEc the d..;i.tu WE.re not <iVo.ilc...ble the curves coulo only bE: extE:r.cied 6own to expecteci v"'luE: s of oLe hundredth; .F'i 6-ure 37. By examination of t h e cor..ting ency tables it c::..n be seen th&t groups of cells must be to.ken in ordt.-r to get marginal totals large enou~h tc give expected values large enough to be used on ti1e [:,Taph. Eecuuse of' tb.is tl1e tt2st is perhaps too crude to use when the variables are 6 iven .so m~ny values. 1-:o successful tests vvcre made in view o_f' this needed change i:n the orgar.izli. ti en of the contin6 er;CJ tables. III. SlJlvl}.f.,JW The study of pol&r OL...tbreaks by tl1e m8thocs just described and illustr&teo is by no means complete; or:ly o. preliminary ·ex&rninc:, ti on was intende6. To make a morf; coniplete study all o f the t&bles for time lal S day by day up to at le&st thirty day s shoula be reccrciee. TE..olc:s of zt::ro la. 6 shoulci be mu.de for each group of tiivo j three, au'-1 2:.ll t·our contingency tables shoulo be prepc.rea lai 6 in0 • the temper- 2 Fr c.nces Thornclike, .App lice. tions ot· Poisson's ir:.Q.Qabili.ty Sun1mc.. t ion, Bell S;ystE::rn I'E:dmic<:,.l Journb.l, Vol. V9 pp. 604-624. FIG. 37: CD1vIULc.TIVE PiWR .EILI TY Clli{'/ES-P OISSON EXP Ol\J~l\'" '1-'I.ii.L. 86 n 11 10 9 8 / /1 / I 7 6 'lI Ii y / V 11 /1 1v / I ~ VJ I 1 ; I/ I I I I JI I I I I I I V ,V I V V J V I I I V J V I I V I I 11 / / I 1 4 / I I I I J J / I 1. 00 0 . 90 0 .so 0 i / 'I I ,--- >--· J I I". V I .- , I I . I I I - .20 I .10 I 0 ~09 I .08 0 . O'I I I I 0 . Ob ,_ I 0 ' I I 0 I 0 .02 I ,/ 1/ I 0 . 30 I I I I I /i '. . I I J ' I/ I I I < I I I II I I !/ I/ I I I I / J / I :/ J I I /j / I I I 1 J V V / I I 2 / I I/ y V I V' 3 I I I I I I 5 0 .02 I '' 0 .01 10 - 5 10- 4 10- 3 10 - 2 )"'.) ( '1P . ,~ 1'"\ ,-y~, 1) , ." h "i"":' ~\ •• ·1 I~ ,- ,,-., - - :,/ / ' ~.,.;~·-, .:; ,,, c~ 87 ature in the European zone afte:r those in the: two adjoining zones and the temper a tu:ces in the Asic.tic zone after those in its two adjoining zones. Tnis work should be c.r1eckcd with fresh data frc r:, the intervening winters. It cc:.n be seen !"rom the results obt b.ined th& t a signi1·1.cunt rel a tior, 1·or one period mc..y not holo 1:·or another. In this study the following important features were observed .. There is evidently a good positive correlation of' the temperatures at opposite sides of the hemi spher e which may incii cate that polar o.utbreaks or surges of cola air occur on opposite sides of the hemiphere &t the same time. J'hi s is born out partially in the observation that similar weatl1er processes often occur in the Pacific and Atlru1tic oce ans sin,ultaneously. 'I'her t.:• is a series of lag relc:. t i onships between the temperc:..tures in northeastern North 1.rnE.ricc.. ana Lurope which appear to have so me impor tance . The t es t s showec significc;illt • three anc fifteen day lags of a positive no.ture of the :Sur opean temper a tures ufter tllose in nortliE:& c~ tc.rn 1;orth America ino ic&ting, perhaps, that three &nd fifteen du;ys af'ter a polar outbreak occurs over North i\rDErica polur outbreaks occur· ove r :Surope. A thir t y day neg& ti ve lag of the temperatures in nortl1easter n I~orth 1-un Eorica after those in Europe was s h own to be significant indicating trrn.t a polc:.J' outbreak may occur over Korth Amer.ica thirty do.ys g,fter a w2..rming 88 period or surge of w,:;;rrn air in Europe. Because of tbe incompleteness and the unte 9 tec vE..l.idity of the significance of these tests it is irLpossible to incorporc:...te these results into a l<:<rg8 scE-.a.le weatLEr process scheme until much more work hQs been ci.one. It is e:r.ti rely' possible tlfr.t the use of date.. fro11 c:.. oifi'e.i:·E:nt period of years will give very different resi...lts. ·Like most sto.tistical studies o:f 'Neuther phenomen~ the preserd:, arr.01...nt of data, voluminous though it may seem to those used to treating with such mE:thods, is all too little to m&ke ar;;; rigoroLs conclusions. TLe problen; oi' ti s ti :-igui shing l,-r 6 s sc~lE ·i.-sb.tilt:r processes can b e dividet into twc p ~rts; firs t , to 6efine the transi ti or: per j_oc be t v,een proc,;.";s ::,es .:.Lu~ seccna, to sh ow how one process differ s f r 0m c:.ncth er CLiid ho v; p c:;,:::·ts of processes m.:...y ho.vs simiL..r fEc.,. ture s~ Criteria for defininr£ t.he trL..nsi. ti9n R ~rioo.. uni:.: criterion of th e bet; inning ano end oi' lc..r 6 s sc1:.le Vitc- ther •processes is the occurence 01'"' t r o1. ,.§;}., pci SSc;;.gE s vc.riows 5.t fix ed positions aroi;nd tr..e h er;1i sphere . EcwE ver, tJ.i s ~l s o may be used to sep&r1:tte the n aturc. l synoptic periods a nd the problem is to t e l1 which tro q)1 p ,;.f,SfagE:s mb.rk the tr a nsition period. "'ui te often, usually onc e c.. mo r.t."'1 at l et.st, i n tE:! ise Ln deepening will occur siml, Itaneously or wi tl1in 1;;. natL,r Gll s~Tloptic period at two or more zones ninety degrees c..p&rt around the hemisphere. This cc..r1 be 1..; s2d a. S a tr hnsi t ion since it usually ind icates the star-t of b c or... s iur:r ht; _Ls flow of cold air south and WW'I!i air north . Polar outbreaks anG sur ~es of tropicf:,l. t.l.ir used t o ma.rk the transiti on fro1 ;, c n e pro c ess t o CC~l b (:. U,O thE:r • Several consecutive n &tur2.l synopt:J_c p erioc s may hc:..vG similo.r surges of air. In selecU.n,:; a.L ini tia1 rn_,tu.ral ~) 0 s ynoptic pertod of a proc s ss with s0.ch a se½_uence of' perioas it would be bettEr to se lect ei u~er tho.t perioc as s oci a te d with the most mc:.rked tro1.;gh dev elopments or tr.le first of such a group of · nfatur:::.l sy noptic p1::rio os. The wet..ther pc:.T.,terns occctsionally ft.11 into b. group of natur&J. synoptic peri od s of zont.l flow ano c.1.r.o ther grot.p of meridionctl flow. In such cLscs t Lc s8lec tier. of lt. .rge scale processes is f ::,irly str&.ightforwhrd. The position of th e principu.l zones of convE:r 6 ent airflow and the vari c:-..tion in this position c2..n be used to interpret the ·beg inning and the eno of the processes. These zone s eith er tend to move in one directior. for sevi:=ral nt~tur a l synoptic pE:riods or to re□ &i n sta t..i.o n ury ti1L.s defining the cho.r ucter of t h eir uctivit/ durin6 the process. Distinguishing 2.ne :groces.s from another. In observ- ing the similarities and differences of lc.1• 6 e scale wec.thtor processes one first notices the lenc.;-th of the process anc.. the number of natur&l synoptic periocs into which it mc..y be divided. Many .processes are sirnilE;.I' but for the omission of a p eriod or the substitution of one perioo by some oti:i.8r type of period in the seq_~ence of periods. Some processes may be fast versions 01· t.. slower process. Toe loc&tion c.nd intensities of the centers o:f atmospheric action is ar.1.otl1er factor to be exoo,ined ir. 91 compc.rine processes~ A most striking ·compc..rison of similar and asimilar features is obto.ined using this me:tl106.. It is often necessary to shift the whole pattern of the centers of a.ction over the her.::iisphere or just in one zone in one direction or another to compare processes. The timing ~no intensity of polw- outbreciks mey be used to differentiate the lw'ge scale wec..tl1er proce s ~,t:s o A certain sequence of' outbreaks in vc:.rious pb.r1,s ot the hemisphere may charucterize ~ certain process. Studies in correlation of temper~tures in various pb.rts of the hemisphere mc.y be valuable in determir~ir..g hovv· long after an Ol,;. tbreak occurs in one region an outbrea.k or perhu.ps a surgE: of warm o.ir may be expected in ar:.otber region. This timin_s may vary from year to year or from gro1..;.ps of ye<.:.I's to groups of years as well as from season to sec.SOL. Flo;; pc.tterns b.re an 2...cidi tional aid in this type oi· analysis. Zones cf cor.vergent airflow are 1:1ls o vo.luaule in d E.:ter rn ining sirn i le.ri ties c:.fa.i di1'ferences ir.. '1-iec.. tl .i::.r processes. The intensity of cyclonic developments c:1lon6 these zofo=.: s may lead to the inclusion of an extra m.. turo.l synoptic period or thB st~gnation and prolong ation of a natural synoptic period sc th -::.t two processes starting out with sillii lc...r features may not appear similc...r in their. l&ter sta~es. From the study of pressure curves it was seen thc.t there is frequently some chE-r a cteristic rhy thm each season in the intensity of trough 92 passages. Perhaps this could be used to indico.te a ch'-'-nge in the structure of the process. Conclusions. 'l 'here are mcmy difficulties in using all these cri terio. for oistin§;-uishing lor 6 e sc1:;..le vvec..ther processes. Over most of the materic..l avo.ilable. only a subj ec ti ve investigc.,tior, can be mc.cie. When cill objective study ie me.de a tremendous mass of computc...tion must be 1;.ccoL1plished bef·ore any results of significc..nce are to be found. In statisticc..l ir.vestig2..tions ther-e c.re many pitf't.11s lea6.ing to erroneous conclusions as to the significE:.Ilce of relcJ.tionships so discovered. From these studies further work is inciic&teo in the study of trough pas~ages at meridians equally spaceci around t h e hemisphere; in the studies of polc..r outbreaks, tropical air inflow, and temper &ture fluctuation; in the compiL. . tion of, an extensive file of comprehensive charts o.nci flow p(;.j,ttern charts, and in the a.pplicution of thesE: stuaies to both h en.isphereso It is felt that tiiese large scale processt:s mo.y be depenaent upon WE::ather phenomena occuring all over the ew>th' s surfb.ce as well as just ovc:I' t11c north ern hernisphere o The large scale proces s as yet hb.s no soliu position as a forecast tool. It is much too nebulous a conception to be adopted for rigid foreca ~ting rules. It is thou6 ht that 93 eventually a dynamic t.11eory will be evolv€a which \'Jill tc.ke into account such mechw1isms in the atmosphere. At present data are f&r too scarce to mo.Ke b.ri.y defini t,e co1 ;clu si ons . From these studies and further work of a more thorou 6 h aria objective nature it is hoped thc,t a proceedur·e vvi.11 be developed for forec& sting the general &.tmospheric flow pattern and from th&t, a reasonc.ble wec:.ther forec t:..st for period of several we eks. 2. BIBLIOGnl.Ph'Y 9b Allen~ R. A., and others., Report .QD an :2:xperiment if! },i ve Day Weather Forecasting, Pap ers in Physical OcEc.Dog-r aphy and M:e teorology. Cambridge and Wooos Eo le, lLass.: IV:&ssachusetts Institute of TecLnolo 5 y ano Woods Ocear,ographic Ins ti tu tion, 1940. 94pp. Bhur, F., Official Jt_(;a th ~r Foregos.ting for .lQ=da;y: f__ert_oc.is in Q_g;rm.QD.Y. :i3ulletin of the ArriericaI1 L:eteorologicc...l Society, . Vol. 17, 19 36 . pp. 148 -153, 252-2b4. DeFant, A., .D.ie VerM.nder1mg in !1£.r: 1,ngerneinen Zircb11Jotian der Atmosph~e in der .G.filli~imD Eereiten ~~£ Srcer. '.Vien: Sit. Ber. Ak.w:L wiss. Vol. 20, No. 121, 1912. p. 379. Darling, Donald A., Report .£!l _}he Accomplishments 01· tne Statistic &l Project, June to September, 194g. Unpublished report to the Meteorolo 6ry Depc...rtment, Californib. Institute of Technology, Pas&dena, Californio, 1942. 25 PP• -;11iott, Robert D., Extended WeathE.r· Forec1-_.stin,s !?x V.J eather ~ L:ethods, u . s . Navy DepLrtment, N.s.vy Long :.tarig2 Forecasting l.ini t. Washington: U.S. We&thE:r Bureauj 1944. 55 pp. ____ , Studies of Persistent Regularities .in 11~ti1er Phenomena. Pasadena, Calif.; Californi & Ins ti tu.te of Technology, 1942. 16 pp. Kenney, J ohn F'., hfa t i1em G. ti cs .Q! ~ta tis ti cs 9 Part 'i'wo. New York ; D. Van !,1 ostrand Co., Inc., 1939 . 202 pp. Krick 9 Irving P., h Dync.1nj_cc...J Theory .Qf the Atrnosph sri c Circulation ~nd Its Cse 1:n Wec:.ther Forecasting . Pt.sao.ena, Calif.: Cali:fornic.. Institute of Tec:hnolo&, 1942. 42 pp. L:ontgornery, n. Be, and others, l~eports on Criticc.l St udies of Methods of Long-Ra ~ Weather Forecb.sting,, Iv1onthly Weatl1er Hevi ew 9 Supp. 39. Washington D.C.: U.S .. Government Printing Office. 130 pp. Northern Eemi sphere Daily Eistoricc.:.l Weather Map Series, c.s. Weather Bureau, Washington D .. C .. , 1945. Forty yei:::.X's of weather m&ps. P&gava, s. T., editor, .Ihg Be.sic .I:,rincit2,uls Qf ~ ~noptic I::ethod .Qf 1&.Dg Range Weather Forec<:..s ting. Leningr ad, t'Ioscow: U .. s .s .R .. Hydrometeorologi cal .Office, 1940. 'T horndike, Frances, [Wplic c.. tion~ Qf ,Eoisson' s Proba. Gili ty ~ o n ~ Bell System Technic&l J ournL-1, Vol. V, 19 26 . pp. 604-624. Weightman, Richw-d H., Preliminary ~tudies in .§ea.sonc;1.l Weather Forec c.. sting, IJionthly WeathE:'r Review, Supp. 46. ': Vashington D.C.: U.S. GovernLient Pr intir.t.s Oft'ice, 1939. 99 PP• TROUGE POSI'l'I01{ Did.ii. 98 . . _!o_ .Ir •J---"'!-+4-X-'-"'---"''--"--=--l""""-+=-,,,:'-+'"--!'-c'L~4L-='-- :- ;"¥--f'.L.£.~ -.14---""'-<l'-l--~' - - - ·~-1.t a . . ' • i...;.¥f,,~~~~~~~'±-'~""'-'~¥-1'4-fL." '~..c;==-;---r=+=:::9--"':::!.:..:'- - -~ ~ ~..JG.., ·• 2.0 .IS"' . ;2.c. • i:20 l ' iI li ' !' ·1 . ·· + · •T ..,' ! 1rl I I l I I l J__ T~ i -j t- - I .. ) '' ~-- ••.. I -•-•-'T""" .. -1 - t- --+ ---1 - -· J __ _ : ---- . -· 1--1 • ' ~ • j~ : I 'i : j· i, ··-·f · •. L ___L__ ,_ ______t_ ~ _ _J __ - I : f·· · ! 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'r 'p p ·p _9. . ~ - , . .+s-: r p . / _D ·· - - ,M o i . ✓r . ."'° ~ .(o - e> _l'o _ /~~ - _Z-C /o . oF /,:, l'o _o_r _ j -I 1- I ! l I f I I I j_ I i ,. I ----il 1i.P.?ENDlX :a. DATA FO:i:{ TE:; S'l,UDY OF POL.iili OUTllitl.1,.i:\.S Stc::..tions 1. Shanghai, China. 2. Tokyo, Japan. 3. Zyosin, Korea. 4. Mukden, Manchuria. 5. Bl&goveschensk, Siberia. 6. Dutch Hu-bor, Alask~. 7. Saint Paul Island. 8. Bethel, Alaska. 9. Nome, Alaska. 10. Kodiak, Alaska. 11. Moose Factor;)', Cane.Ca. 12. Pittsburgh, U.S.A. 13. Boston, U.S.A. 14. Sable Island. 15. Cape R&ce, Newfoundli::i.Dd. 16. Stockholm, Sweden. 17 . Muni c h , Germany . 1 8 . Bucharest, :::lum&ni&.. 19. Moscow, U.s.s.H. 20. Rostov, U.S.S. n . Estimated d&ta is placed in a circle unles s otherwise indicb.ted. December 1928 lP 7 C3 9 Jo .. t . -· · - ·j · .• -·- ---· --i··· : -·· r··· - · ·· -- ,-··- . ·-i-· • •• - - - -- - - .. . I -- Z,_j . • 1!·. ·1 .22. 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L ...L. i i ! ·-·· ··- - ---j- __, _ - i - - +- - : - \--- L --1--- - L -- - ?.5" 1'1 i- -~ I L ._;' +I 1IiSLl' Ch 19 33 t,,7<;{1£0T ll !(. IL 17 ( g I'? :,. T -----t - r · - 1: ! ' : -i -+- - :-· -·-·-·t- ·-- , l--- - _i - L .. . --- i--.... - · j __ ·r ( i I - -·- - ' '--~ -. - . - - -· - - - -- - r- ! r + -+ 0 0 0 ·O "l I I L t J __ L _ ---~1·-:~_:1 -' '------ - ---- -- - - -___ ··· ··. - i . -- - -- 142 December, 19 34 II I2 i .. . 13·t j_ ' I -- ·· 1' t-- +---+- .·t I i ' '----lI !I ' , ' I : 1-- 1- - -i I---+--+-- - + -+---+- - ---- · - - l!'i • I- _L_-i - -+- 1 I I ·t-·· : -! . i ~- .J · ~-~ . ·'T • i 19 35 (to 17 19 20 /'l :l I I I I i . i -+--- -i--·--· •. - - - + ---+- ·---1- i - ' -+----- - + - - - - + - - - + - - - -- - + I -- t -- - -- ~ - - + - _ , _ _ . _ -+-----+---+--+--+--+---11 ---r-~-i----;---1---1- -i----;--- -t--t-----t--t------,......---1- -¼--t------,......---1~ --+-·---- -l--t • ----'-:=--t-=::=P.'~___,...,_~+-'>'--+-- -+;;.....+-l-+--+---+--- t · . 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I 2- I'? r-_ __ .~- __ _ __ -~ - ·-- __ • __ -·· __ ,l ~ - -1--.l---+----J--+-----1f---+--+--+----+---+--' +-·- +----+--+---o 7~ ~ ,,,. -i, ~ -, J_ - --- - f - -- -- - ,,,,, u ,, ___ ,_ 1 - - tf - -.....- .+- +-----l---+-i--+--+---+---r-+----r- 1 l ll t-L--+-'--+---+ l3 ..... ~'--+''=-+-""-""· - -·-- 0 - --· --· ··1 ---- - - -- - - - --·-- --·- la. ·-- -+-----l--t----r--t--+- +-+- - - - - ·· ·-+--e--+---r+ -- + - J '-ll f--+--+-+--4--+- - ,, 30 ' ' - - 1 - -- -- '' -- - +-----+--+---+- - t---t--+---.-, - +---t i 1----+---+-+-----+----+-t---+---+--- r-- - - - 1-----+--+----lf---+- -+-- - -·' -- ,, '·- -· ---+-+--+----lf--+---+------1- - 1---+---+-+---~---+- t----+----+- ·- - : ' - -- -+--+--+--+----1----lf- -- - ·---t-t_,-,1, .-.. -- • -- I---- ---f · 1• 1- - + - - - + - + -·--- "3 I :SI '' ;~ - -- - - - --- - -~--- -+ -+--- -i -+f---;- __- ,: _ - -_-_,._ ·-_ --· ·-·- -•• - - -· ·• •· · -- i - - - - - .--- - , -r -- - ·- - --- - - - - - - - -- ---+--+---!-·+--+-+ - - t--- + -1 -·. - - .. -··•· - ·-- - - - i--- - 1---'--+-- -t---+--tf-- ----·--- -- - ~ - - -~ i - - - --- f---- - - i--- - - - -1--+-----<r---t---t -- +-----lt--+-+ - ·· ----- - -- -- - - +--+--+-1, --+--l- +---+------ 1- - -r--+---t- f---+--t---+ -·-·· - - -- --- -- - - -- - -- -1 - - - 1 - - 1 - - - - t -..-- - -· - - - -+-- +---+~ + - -+--t---t,--+-- -f-- - -+---+- ·~-+---+---· ---•~ t---+---+-+---+---t-1--·-1-------- - - - - -- +--+--+--+-+--+--+ - +--_.__,.___ _,_____,I_ _ - + ---+- - + - - - +- + - - + - - - + -+ --a p--- - -- - - • - --- - --- 145 Mar ch., 19 35 I / I " 7 g, "L p- R C O f=' F ,_ /-1 er to /1. 13 ll l't ff i {{,:, /7 {~ (9 l o I (oL 1. 3 1 Lt3 t---.L-t-~+---,-'--f--L-~~--"'----jf----+· r-- ··-+--7 ~ I -- ~3 3 _ir _ 2_ _ ___ t - __ i "' , ~ - + - --+--+-~o---+-----+--· -- - -·- +----,~-+--+--+--+---+---->---4--4-r--- + -- __ ! ____ ~ 7 +--+-- + -+---t--+--f-----+-,,--+--+-+----+-----+--+--+---+'--- j i +--n--;---}---i - - - ~--- ------- ---t-~- -_a~,-!~,_-_. . . .II 1 _,_-_-+-1-- -_ : ·-___ 5 _j_ ___ -~ [:l. e. w .l / .J 4- ___ :2. I ~ '.l. ;z_ L . 'f "L _ _ 1=-_ 3 1 11 I i ::;l.. • "T 14 3 ,s ) ;JI 14 I l , i :Z... j I II _[ o ~ ~l , - - ,...~I _ - 1 ·- I 1 11 /i _j . - -----<-->-----+ - -+----+----4- - + ------ - ------- + - - + - - + - -----II i . . . --- --- , -- +--+--+-+---+- +--~-+-'-----,f----~ 13 • --L-- - --- ---!-- -~-t--t---+--+---+---+----+----+--+--+------+------+ - -+--- .L"i - -+---+-t---+--+---+-- -- r - -- - --- --- - - - -1----_.___ · --+-- 1----i 1 1 1 15 1 I '3 / , . I COFI'INGENCY T.u.3.LES FOR TES POLlJ.~ OUTBhEAK STuDIE.S All the dic.gonal groups tested are inaic~tea in the tc::.bles with values of the normal devi"-te gi vE:n along the dL.:.gonal line only in cast:s of significW1ce. TVvO VARI.i..BLE TABLE D af'ter B 147 8q i D., .I - ---+----. - -1 -- ---. -- o, - -. • 3 _ ...__._ _1.__f_ ~ -2 __ __~ . l i ---~ - - --i' ---- 9__2,__ + .5_ _ __ fo _ .. (p ~ • I __ _J - - 8q I_D _ 4 _,__ f - -- : ?,__J I - : I l' ' S-7 ' ~ • -io D ~ I : 'l- _ _i_ ___ .. _>_ ·- I -1 . - SI ~ _ 4'2. - -- ~ - : J _ (g I ,n 48 2, i ii. 1 3 304 ~ __ . ____ _ 3 2.s'" _.>t '1= _ J_ .92 , - ~-+--- ~ __ _5-_ _i L _ _!,__ 4-z.._ - -f- ·- • I I b J 1--=c.---+-- '2. I 0- 1 - - L - - ---"'- 4 f- - - ! _Q+l---+-------"'lloc- £ ._ 17 /t. 11 -r--- -+---"-+ 'i . (. __)_k_ ; --;. 1, . L I ! I I __ ; .l - 27 OI _ '2.. . - - - __3_ __ 4- ~-4-____,___...Q,_.!._ 1----4--="""-~ - + - - - - - 1- - _i .L_3__ ___1__ __ .l i __-__le_ -f 4. > IL .__~i2._ _ 4 _ _ .. -- 7 I I '6 'l • !' ( . I I . - -! --- l --,--- -- ~ . + - i ___J 1,.. ) - --- . 4- ., ) (i, 7 'o q ~ n : 4 <.. r" 4/ • 4o : J t • I - TWO VAlU.n.BLE TJ-.BLE F after D 148 I 0r 7 0, I .. 1-. - >_ . 4 0 ½, __J _ _±_ __ . '2..1.. .. ~ -- l, 'r i 3 ! /() > '2.1. , -~_.... - - -- Jo Cf _3 . -- 0} _ ~ • ~L S- I / 4+ & I ~7 '2. ) 2..'1.. 1> g ! .I. , . .. 9 lt I C,4 _GJ: _(o( - - {cf {oz ] :.s- . ~ 2. 4-':l _'7.':r '2..7 '?.... 7 I , _7_ _ '3q t... '2.1 :, ~, TWO VARL .BLE TABLE H after F 149 9 - -~-+--- 4 3o:f.. - · ·-· --•- 1 ~ -·· l. • - ! 1. : :;-- ' -- - -__~-- i t7 1-7=c - --- '1- . ~_er__ ... 3. G . - _4-_ ) 30 d - + - =--+--'~:--'----t---J--+-.....:::1...~ · • _,~·_ :_ _ _ ___ ll___01 , - <]:J,. _ - L -----'--~ ·"""""'--'--_.;.._ ~3. •~9 0g - ~ ~ -~ I i ~-l _"t- _- - 1 i -- ----- . - -q 2.. 0 --+---<--+---=-,,.r-_;::;'-t-'~~-+--'8'."-- t-t _ _ '.3 ; I - s• c+:s I I ---~-'-=---"'----,~-...:........+--'---'---+-=-----'---"c.,_' - - - - ~ - - ' - - - ' - - + - - " - --.,__.,....--'. . . _ 30 /'2.. 4 3 0 4- THREE VARIABLE TABLE, D a:fter Band F. D~l . -~ o 1: 2. I 1 - 4- i ~ c. i 7· r"I ~ ~ o , 1 > 1. 3 davs 18 days 6 dav s 21 days -~L -_I : f-++-+ I : _! J_' i 3 ! • : I -4- _,__ __ - --, 7- --. •--'----+--- · -·- - I 7 t :4 9 days --+ r- • 1 · 2. 7 ! Ss 'r i z: . . • - - -- It q- - i)\ t: l I 4- · '1-, _ 24 davs I ~ j_ I g - ·--~- 1----f--- -r _- ~ :_ ____---- --. - I /3 s. r I . - ~, -- -- - - i- - +- - -- J.. _ __ . . . __ __ I I I - I - - - --·- --3- -- ----- I" '3 , > , 4 150 17 / 'L 'l, \4 '2.. / 'J ' • THREE VARIABLE TABLE, D after B and F. 151 Ir-2 3 davs 1 I ~ ~ 18 da rs 1 ,1 , I / ; t I~ ; I & ! 2.. b'/ 6 davs / 9 ,, 21 davs 1 I I> i '1 2-, -°f_L'- _L4:1 lit11f :J-,- --',i?_ -◊4( i i; !f {- -=~ T .,, , ~ ;;;, __£"_ -~-~--'r __ I _ : 4 'l ·r-'2 . _J_,_J. _+ J ·:_: : 'L. ----~- 7 -- ~." •- I -/-- - - _! ~- : /_O_ i -- - 1 ; ¥ t.. _ 1 / , : n i z. 3 13 I 9 '1- i ', > -j !-- ~ ! '2... ' I S-- _} -_' -~ _ (c, -~- ____ , ___ _ __ 1--~-.+-'!- l> --~ - ___]_J _~-~ -~- r--- i·- - ·r- ! r -- - 1 i c;- 7 IG -23 ---_c;- 1 7 -- - - --- - ---~ '{ ~ '2-- t:, ,, ,z:: / 1 1- 9 9 davs 1 t; i 1-i.. 1 , 5,- , s- , 2. 1 ro 24 days 18 days _¼J_ ___ 27 davs ~ ____2,_ . _ _) .± ~- I ~ -- - - - ·· ·· 7 · · - 1---- t, 9 1 Fl davs 30 da.vs i -::-r tt ~E1-~ ;; -I--~±fk~-~{1-~r~- fr _(.),_ _,_ _ j / I Cf ' 'L , 3 - {L_ _(, l ' ! - I l - - - · - - l. '4L:?-:-_L ___ L/ ( l --L !- I /2 2_: I ' s-J I : s- b~ 1 ~ ~ J '"l-- 4 , ':J- 'L ! I 7 ~ '1 Z: ~ 7 2. I 1.. i ! s- I ' 1 I !9 /~ J f0 / : 4 : '1-. I I __ 7 i_ I fu'i ,::: I t __ It i lCf ~ I iS f 'l./ /4 ; 5 I 1-- K l"'I THREE VARIABLE TABLE., D a:fter B _and F. D~ ~ c 1 ' 2. I 3 -t '> 1 (, i 7 ~ ~ ~ ~ u, I 2 '> 3 davs 18 dav s 6 days 21 davs 9. navs 27 davs 9,J ... _) ,. ~ . ! ____ 3 t'f • I 'l.. , I /'! · ••> 'l.. • ~ I I ! / I/' Co '> '2. 9I 7 8.'7 4 5 fG 7 · ,'>~1 ct· ' i !· 'r ___ 6, I ! ·-· L . r- '2 [ -- 1.____L _____ __'Ll -:,_•- -~---·! -- -~ .'? ,-. ~--c--L L _ L.:1:....;._J___l_2::-j__ ___j___ ~ : ~ ~ ~ -,~; ; ~<~ ~. ·-··! ~ 0 152 _7 <is',q, l ~ - I I 1-. I j- i_l_~-rf-~-, 3 4 ! 'L ~ ; - /J /2 I , !J 1 -~ 1-_ __ _~~ I THREE' VARIABLE TABLE, D a:fter Band F. D-:4 . ,=;;--..z o 1 2. i > 153 4 1 ~ crJ ~ ? i 7 :Z: ~ 3 days ~ 1 ~ Rq 2. -2_ • 4· r 1)t'if 8' 3 I Ct, i 7 g9 z... ; / t:.ro 18 davs 2D i 17 1 1'9-! fo 3 , (,b ~ 12 dava 7 o1 1 'd 11 27 dclYS 'L I : L 4 , 7 / ·--~-q "t /8 /4 / 2 1..- I THP..EE VJJUABLE TABLE, D a:fter B and F. n~ s---.E o 1 '2 i > 4 i ~ ' (, 1 7 r, 9 ~ 13'--t 0 ·1 I i. 3 days · 18 davs 6 days 21 davs l i "I '1( /4 -> ' + i 3 L 4 l~ s;-~ \ G i ·-7 1 4 17 11 I '1 F.'cr z:- • n.? THREE VARIABLE Tii.BLE, D after B and F. 155 D"°6 ~ · ~ ciavA 18 davs 6 days 21 days 1£ davs 27 days { 1 /3 i /'J 1 g j S <f7 ~ 15 days c: n I (1 5 i /o ! '> ;... 4 /1 10l/2. C. I '9--7 30 days 47 i. b l2. 8 I rz. 6 <1.:1 THREE VARIABLE TABLE, Dafter Band F. 156 D==? 3 da.vs 18 da.vs 6 days 21 da.vs T.dREE VJ:..RI.iffiLE TABLE, D after B and F. D=8,9 157 3 · de.vs 18 day..s - . __ - - --- - - -- - l - -- I I 1 2 .-7 :, ~-'___l_ ____ ... I i i . . - !. , ___ _ I I --- 4 ~i4 I s- 'l-- 4-, 1 21 da.vs 6 davs C> i .) f • --- f -- - 2-____ -- :__l_ __ _ --1_J : 3 • 3 1 • -- - - ~ --- --·- · --- -· t '2 'L : · - - ' . - '= _._ ---· - _ ·' • 'l.. : l : - - · - ·· · - - - · - t - ! - ·· - I -• 7 C I 9 days 24 da..vs ,_ 0,..1 ~ , • 9 rls:ivs . !;' 7 ! '1.... i I {(:;, <z. 3 ''G < a.vs / 4 i TiffiEE VARIABLE TkBLE, D a:fter Band F, Marginal totals for B. Dafter F. TW6 VARIABLE TABLE. - - - il --- 6~ _ >-'.. ~ .. . J cr 2- . '2. , r -~ i -.~ ~(, }>--:. :'1 't7 &J-.1 __ s:_. l - __J.& 4 i 1... , : , ()), '/(J ; GJ 44 1 {( ,._...._ ___,__..cc.___:.-.; 7 1 /J 9' S.9 (ofr:, s.~-- . 47 ,i . 61 -+-----.--- -~fi"_'l_. I 6 =11111,~+ - · -r··· ··+ 1., g : . ,., lb ' I '.3 I I -~3 . . ······1 · _· r (,. 7 .i f £.. s--:G 4-1 THREE VARIABLE TABLE, Dafter Band F, Margina~ totals for D. TWO VARI ABLE TABLE.. B- with F 159 ~ o1 -i_ I > c'.\ 1 1,~ /,, : 7 If er 7 ~ 6 1 'L '3 4- ~ I & 1 7 •gr :;; THREE VARIABLE ThBLE, D af'ter B an::1 F, Margino.l tota.ls for F. TWO VARIABLE TABLE. Dafter B. 49 0,1 I '2. ..:et_ __ 1___ .. ft;, <fJ g3· Lf- __ t. 7 _ L _S(, _I / .. . I L L J.. ~ _ '. 1 ! ; , o, : I '.3 A ' !. -· • --·- - _1-_'t -..?_ _;_J ___ --- 1.. I 2- . 0 4 4_) _,><q , ,,/L' I(,, _q_ J Z. - ? 2... ].L0 . 7_ __ 1: .u I . Iu 'ts ! --. j_ - -~ I I ___:,... (2 Qr I 'L. ]J > . -~z. t l n . 4 ill - • '3 y ~3- ·- -~ - 'T}>= ''f --: ·- - ~ 7,.'2- . ' . J -· · '. 2. /I) fo . . - ·• ~ -- 7 _9__:!_ i--1-j 7 . 7 : .. _j'__. I _q .s- "-8. __5 __ 4S: __ _k _. . -- ~ - . <f - Gi I THREE VARIABLE ThBLE, F after D and H. F~O,l ~ o, 1 161 '1-- l3 I4 3 ' 3 days • C)) J . . .... ~ - 1 I _(:)} I I i. 'L ____'t __ ,_ , . -· I I -- - - _1::_ ---> q3 ~' ~- .. --1?.. rL ,- ,t· 0,I / I 6 days I 1.. • ~ - --·-- -1 -------- ·-· ___:±_ __ _'1:_ .. - J. - .. j - ! i T -- +I' --- -- - -----r ; I l,, J .. ~ - ! . J 'L ; · ' '3 1 I 6,f 3 1. i .I 2. I c;- i I ! I q I 21 da.vs ~_Q,L ___ y_- .. . I II > / - - + - - · ·1·- - - •---· 1. 4 18 days I I - -- . __L __ J_·__ 3_ 4) I .. ~- .. 1 7 .7 .. __ --·--- xq Jq q '2.. II .....<\I _ - 1. > I -L · - - · - --------r- i 'i >- 4 . r i 'L , I ! 'L 27 days 12 days I l.. I I . 'L I 4- 1.. 15 days 'L 30 davs - -·· .L _ '2.. '2... l. q THREE VJiliLJ3LE TABLE, F a:fter D and H. F:.2 162 3 days 18 da,ys 6 davs 21 davs ~L I 'l.. 'L I ·15 ) JS- l, ! ~- t . - 0g9__ --, 7 / t i (,, S • C/-f: 2- I 'L 11.. i 5' ' 1.... • I 'tr< f 12 days i.. I ~-- (0 9 days £. l I - J _ -~ ) _ ____ j-_ - - !i '> 'L -~ '1 z. I ') i I /1... t 4d ! -, ' 7 I ! 4- '. IC,- I x' i "1- i 1- i 24 davs '1 'S /4-- If i L 4 17 1 I ~ q.g 4R 27 davs 1:,- : Cfk •~ IL <i I to > 1-fJ THREE VARLillLE ThBIE , F after D and H. F-=-3 z:__ -,:;--..t!.. 0,( I 7... J 3 days 18 dav; qq z.. 6 davs 163 I 4 7 1 / 8 '\(" I /C, S-- \ 0 I 7 S/? £ g I I/ l"/ I _'L I'.} 21 da.vs I 'l. -- 5j __j__ - - --·· _ . 11 -Z.J _/_l __ I fJ (f q <; 9 davs i. 13 l1-2.S- : /'f 15 davs i ('t 'l.L I ,z._C, ! (J I 7 i 1.... 1- cr9 lb \ ;, 9'9 ~4 dav s /1 , 1 I I 9°! i 9 1 2../,z.(f- ! 2.l. 1/t.. 30 davs 1- THREE VARIABLE TABLE, F after D and H. 164 F-=4 ~ n , 1.. I J 3 days 4 r G. i 7, g_ 9' '.2: ~ /'L : /4 3o 1... I 3 4 l s-1 ~ : 7 & er 18 days 6 da.vs '£ o. , 21 davs 'L1 3 ; ) j ~ 93 z.. /4 u,., 1 1.1 /1 i '1 7 ') ~ THREE VARI1illLE T.h BLE, F after D and H. F=5 ~ 1.65 '2. 0 I i 'l l 4 ; S- (., 7 i,r, 3 days OJ 1. ---~- _ ---3::.,__ _ ! ] _I J..z_ : _ 4 I ,I u __ 1 J 1 ; , 7 I I g,'f ~ ; ~ . L ~--·--· . ·3 i s- ?_ [ '2 I . [. / _ / ___ _ 4 . 5 3f '1.. ! / z .-2T '. _· .. .. / ,_ 2 1. . . ' ) I s:; /CJ day.s 1 I 7 , / ' I c , <rJ z... ! 1 c-2- l n O I I 5"" _ __ __ __ I o--t1 9 l ! t I '2.. i "J I 4 j ~ i e, ' 7 ~? E 18 days S _.o,_1 I / I ! _ ! .. ' _ I 2 /~~-- --2-- - ... I L 1 ·S - 1 s 'Z . - - · - - ,__J__3 lL ___j__ - J_ .l_J._ ___q ___l__ 4. J .:t ~-:i. - __!7__ / '.L _____4 ___ . ..; _ q . 3 _ 1. i i I II ~ s- _c. 7 ;?, 9 z. 6 1 .. ;~ 1 I , I , t 4 ' ' I ; r i 1 ~ I I I 1 . ·--- , ! ... _ l : .G. 'iJ 'Y I I , 2- ' 12 n ' 1c; Is : 7 21 days Z. I , Giz. C, __j}> _ If II - .t_ I l..f· 9 c'!A.v s 24 dav s 12 days 27 davs 1-- I O l'6 14" 7 , 7 : -Z 1. (.. 2 2 (o IC:· : I 'f l / S- I S- / 0 2.. 3 THREE Vi-JUABLE TABLE, F af'ter D and H, F ==6 166 1- 7 3 days 181.davs - O, I II 7 , ! '2- : '3 I I - - - I - -- - + - "i '],, - - Il ---r . I 1 _j_ L L 1 _L_-: _2:_-t -- - ,--- -- - .. - __ _? _ 11 4 J ' s .l. 1 -2 7 ff '1 2. 5 O,/ /J I --- t ----··· ·' 'l-__ _J : i _ --- -- z - c- - ~ - I ./ 1.. . I / + '-- I · ·- ' ··- I -· ·- I -1. ··- --- - -- ; L. · - --· · 2.. ) /_ 'L i 'L I _5_ : _ ' I i j ~ -- ~- l- , - I !I •l I i '2- ! ' i 1- j : I 3 • 7 /1- I( 21 days I 2- ,1- ! iI! '- s -• 4 ·- ·- >'L I 3 ; I II 1 47- 9 1- 4 /2 '6 _) - _<] _ l 7 j i > (, - > ->-· I 't i 2. I 24 days 0,1 1 1-_. "i 9 days >- I 9 '8' 9 s ! __ 6 days I I : I i I . !____; _ 3 r .J 2 . 1 '2 _ 1_-__ 2 J· 2 ' s- __ . __ q ! ' 4 }I (._ 7 s- I " ! 7 - - . - - -r· ·· •• - ---- t ?.. 4 10 3 'L --~-l l 't I lo / __> _ I 4 -· - 3· - --- 1.. . -- ·- - .. ___ -- : {' 4~ 4- / 5", 12 days 4 {,., ' 3 > ! '2 . ~ •··· - 'i t L 7 I fs, q I lo. /7._ -- ~ 1. 'L i 3 41. I 27 da.vs I I I .3 t 'L '1 I . --- I. 3 -·- I 1- er 15 davs Iu 10 - 1 1 1... s-- 4 7 ~ , 1 , o i ; e:, 30 davs n 1 2- i 4'l. TJ..BLE, F after D and H. THREE VARIABLE F=7 167 3 days 18 days l I I '> '2. 21 davs 6 da.vs II __L __ '' 2. l l 2 . ttl3 9 days /f i i £ ; -1 24 dav s - - •-- · > 3 'L . __j_-·----I i,·. '["' - 1. - --····- ' - --· 1- - - --- - ·- 3 It '2 ··--·-+-- -·· .. ! i . Z: 1. "> 1 4: "1... , fl i... 1. 12 davs 'Z/ da.vs 15 davs 30 da..vs : i 3 if 1.... ' ,---- f ----; ! l 1.. 2.. ! I ,. I - -- ~ I 1 -- - - - --+------1 'L iI I I 0 : I (( 7-- l I i (p { I // THREE VARIABLE TABLE, F after D and H, Marginal totals for D. ·o VARIABLE TJJ3LE F after H. 168 Of <t L ·ii_ q'( ' __3 __ ± '13 - ~ · -· -'-~- -· ' (, 4'L '' /J ·9 days .9,.1 i. ___9_ 1-8 , ,_ t , i? .. __J.... 9 3. . '+ G,1 ~ 4..~. ' .~ ,, 7 g Cf .. / ·-'1: i--- l_.,. --~ 'l '. 4-! ; 48 .i.. . ~ L i...~ i't. t '2 L'l.._ '11 l2. ;,' ...,,.....:::r. ......, 4-2. ({ ' 3b4 TEREE VARI JJ3LE TABLE, F after D and H, Marginal totals for F. TWO VNiIABLE TABLE, D with H. 169 o------t:!. c 1 1. i 1 I 4 i ) {~ i 7 t .9 2 ~ o, I "1. I > 4 ~- , ~ i 7 •g i ~ ~ 'I'IUIBE Vb.RI1J3LE TABLE, F after D and H, Marginal totals for H. TWO V1JUrJ3LE TkBLE .• F after Do 170 D't 1- i J \ ~ C:, 7 s, 11 ~ o I i '23 I j ~I ? i, '1 ~ 0 , I 3 davs 4 '. D F 4 6 ' 18 davs Ito _£1__ Gg 7> St. <f-L ' 3~ - t-- - · . (0 9 davs 24 days 12 days 27 days 15 days 30 davs