Upper Wind Components and Forecasting Citation Gringorten, Irving I. (1939) Upper Wind Components and Forecasting. Master's thesis, California Institute of Technology. doi:10.7907/4s8z-st73. https://resolver.caltech.edu/CaltechTHESIS:12172024-170211031 Abstract No abstract. Item Type: Thesis (Master's thesis) Subject Keywords: (Meteorology) Degree Grantor: California Institute of Technology Division: Engineering and Applied Science Major Option: Meteorology Thesis Availability: Public (worldwide access) Research Advisor(s): Unknown, Unknown Thesis Committee: Unknown, Unknown Defense Date: 1 January 1939 Record Number: CaltechTHESIS:12172024-170211031 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:12172024-170211031 DOI: 10.7907/4s8z-st73 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 16935 Collection: CaltechTHESIS Deposited By: Benjamin Perez Deposited On: 18 Dec 2024 19:33 Last Modified: 18 Dec 2024 19:43 Thesis Files PDF - Final Version See Usage Policy. 27MB Repository Staff Only: item control page

UPPER WIND COMPONENTS AND FORECASTING By I. Gringorten A thesis submitted in partial fulfilment of the requirement ror the degree of Master of Science in Meteorology. California Institute of Technology Pasadena, California 1939 1• WI NT:, COMPONENTS k 'D THE TR RELATT ON TO FORECASTING 1. Purpose of paper. ( A) Departure of Actua l Wi nds from Geoetrouhic Winds. • • ( B ) Use of this dep arture in f orecasting movements of hi ghs , lows, and fron t s . (C) Re lative Magnitude of wind components . 2. Theory . ( A ) Development of Eqn of Horizont a l motion. (B ) The approximati ons ( C) Relative magnitude of the wind components. 3 . The numericctl determingtion of e nch term i n the wind equa,tio n . Lj • Determination of the ve r tic al wind com~onent. 5 . Changes i n wi nd cause d by e a ch of these comry onents. 6 . How to make use of this the0ry. 7 ~ E~mmple. 8 . Rapid Qualitative rules. 2. Uppe r Wi nd Components ana Forecasting Purpose. It is ge nerally assumed t h at uppe r winds may be t aken as g eoetrouhic wi n~ s to a close a pppoximation. ( See REferences ¥ j 1,2). However all too0: fFequently upper winds at a hei g~t, s a y, of 5000 ft, show serious departures from grad ient winds, especially in direction. So g reat is this d eparture t ha t at once the suggestion arises to make use of it. Th e isalloba ric comp one nt of t he ~ind g ives the direction of rising or falling pressure, ~l s o the magnitude of t he g r ad ie nt of the nres sure tendency. By finjing t h e is a llobari c fi e l ds it i F nossi ble to determine the mo ve :nent of pre ssur e centres and [ ronts. Finding such fields a lo@t has it s advantages ove r using the isalloba ric fillds on t he s urf a ce of the earth. First, such fiel d s at th e surf a ce e.p ne a r very i rr egula..r. The t erra. in changes elevation, and such fields at t he surface do not g ive a true picture of the h orizantal is r llo baric gr adie nt. Further the surf ace press ure change s a r e affecte d b y d a ily variations du e to t h e su n 's h eati ng . They a rea a lso rad ic a lly 1adicalJ:77 a ffecte ~ by turbule nt condi ti on s sucb a s in thunderstorms. Again, uppe r front a l s~stems a re not easily found by ✓ surf a ce pre ssure te ndenc ies. Furth er, fr ont ~l sy ste ms and low pressure cent r e s freque ntly exist in the lower l a yers of the atmosph ere wh ile t h e upper layers are subject to prevalifug winds onl y and the r ef ore the daily weather cha rt will not be i n a ny wr: y useful for the for ec a sti ng 3. of· upper winds. Yet this latter type 4of fore ca sting is of utmost importance in aeronautical meteroro+ogy. iilfiflt~ilfittttiil~ti~~t~i¢/if/i~¢/1tiilii¢iiiiittl it~¢l/t~ttli~¢/i¢i¢tliw~tilii¢w¢~¢it/lttlttlitltrtlt~¢ Exampl e s of the usefulnass of this dep arture from gradient wind are given in Show.qlter's papert;(3), e~nd in Bjerk:aes and · Pr-lmen' s "Serial Ascents". ( 4). As for the relative magnitude of the wind components other than the geostro-phin component, it is partly the purpose of this paper to determine them numerically. Theory The Equations of Motion. The following follows clo~ely Sutcliffe(5). Begin with the equations of motion as developed in Brunt (6) for axes oriented in any direation: ~+ :i_ w(w-UI-:) c/cr.>(3 - v ~ /J) ~ -~ ?'¼ r ~- - - . {;) 1h- ~ t~P + u ~I) ,. -f ¾ r - -- . ~ J 1tr - w ~ ~ (uetPt3 - tr~~) ~ - :; --f ¼ r z - -. -(3,) f .2 { (,q' lf-l t- I .l where u, v, w, are actual velocities including vertical velocity. ~ =angle with east-west direction. !,Y,Z a.re exterior forces like surface friction. Although the gravitational force is a vertical force, a nd is given by?'in the 3rd equation, yet it may nroduce a horizontm.a. acceleration like its effect on a ball on a hill. Th i s force will also be included in the X,Y terms. 4. The vertical velocity, by comp a ~ison with the horizontm.a. •ve~mci ty is small. The terms :2.. CAJ c.,,,o/c.n13 u/ and :2 c.o C,(p t/ ~,{!J W" in the first two equations are to be neglected.. Later the order of magn itude so neglected will be determined. After this a.pproximmtion equations (1) and 02) These combine to give: !rt t ~ t'(;A) ~ c) ii ., _ - i f> v" F -t- - ~·---v' is the horizontal wind, a vector quant.i ty. - where - •-.·---....') r n ,, . ( , F i s the horizontal a cceleration caused by turbulence and g ravity. From(~) 1 #(~ f~e-·w~(J~ Assume that it(~D )and. F aresm:mll b y compar ison with the . t other two terms in the equation. )V (,,' 7{ ,, .2tiJ~cf • From (6) yI )7 :;) v Tf" t- v d) t- v-- 7i ; ii Put ..2 w ~ From (71) F. = V • Then • /.:\ C.7 '.ft f ,, , t- w- ':JT JJ(,-l I 'Je -t c' ..z'<J ~ Cf v';"' -t -v/-t- ;::::-. cl " j · if <t rf + (" ~ + v--}£) f- "" ¼ r- <'/i • -f '7f t- T F11r gradient wind I:, , "" ,J 1 or ~ ~ "k f • Tr or_oe · ~ 11 ' Vf (~~ 5. Therefore, l ·j- ,I)- II ~ l ,( .v_,_ --rp ~r - u 4i7 ' ' ( ~ f- u- dV) '1 - wJv TI f- F---' a Deal for the moment with the term u rt11 -r- u-) -;7 ~ {)"' v~~ · v- =- Take v~ (§. t):: 0 )LI Vt) I) Then these components become V ~ , ~ .' The first com-rJonent will be in the same airection a. s V , J../ the second perpenaicular to V. Put», the ndius of c urvature of the stream-line(•~!), ~ the distance along the stream-line. Then the components &.re 11 ~ ' *i.. ,,..--- \ ~ / ~ The wind equation may now be ~ritten c'w ~ '.1. ? 2 -:-_y r• I ! l I -·- · - ------ ---- ---- --- - _..] , if it be Now -j.1,/~i:/ be decided to neglect all com'."Jonents of the wihd except the geostrophic component, then there will be no change in the pressure fields, and the atmosphere will be in e quilibrium with no changes occurring. Here, then, , appears a limit to forec .s.stingfJ The relative 1r>1port-4nc.12 of all terms must be found. Offhand it ·wo uld be convenient if th e most important 6. term were the is a llobaric term, 2-rnfl t h at the other terms werB of smaller order of magnitude. Considerations ne a r the equator are 6 0i ng to be different. There the geostrophin term is n e g li g ible, and the :l s2,llobari c term mus t play a v e ry i rn:_)o rtant role. There must also be, by comparison, l 2rge verttcal ve locj_te:es. The aeterrninati0ns o f tl-1e r elat :l ve rncu:i: nituaes !Bf the 'T'er,.1 s. To work with t h e ori g inal eq uations (1) and (2) seams hope l e ss. It wj_ll be necessary to use the s im ·l ified equation ( 8 ). To find wh&t ovder of magnitude was neglected in the simnl if i cation, the terms 2 t,,.J #Ce,Jf CA(3 , :i. ".'-J(t)-C(f) r~# must be com~)ared with the otJer terrus of the equat ions(1) and (2). It will be sufficie '.-;t to compare them with th e t erms ::2.t() ,t;-~f a (10 -<-· u; u' ~ f Tak e the e,xes E-W, N-S, the ratios of t he ter.us to be compaJoeO are : uJ "'f C) V'-~ At latitude '+5 °, the first term is ~ . In any cc-~se -~-ff does not materia,lly cr:ca nge the o rder of ~1 r,1e,gni tua e o"f' 1{;..· ~~ . , so the ora er of rnc.::;ni tuc e of ~ w( a lone will be found. It will naturally be of the ~~me order of magnitud e ~ t he f,lo r,es of fronts or less. Hovv· shquld the v,:·r tic c- l co;n;)onent of t he \\•ind ve l ocity be determined? In making isentropic charts i t is c=,l.ssud ed tha t, a s long as t:c1e c: . ir :re ,nains unsa tura,ted, it move s up o r down isentropic surfe,ces, t hat is, sur:f1:-ces of .,,,efore , f:!!:: equa l n otential t~mperature. r:i1-e J_ 1 •. ,(r-" i·s. -'-'-l,l 1 e of the ise n tro p lc surfa ce in t he N-S di r2 ction. s lo pe a-" y whe :ce tanO( is the :Slope in a irecti on of the wind, / is the angle of w1n3/ wi th N- S c''llrection . I n sp aces lik e the s outh-Western U.S. t h e lap se-ra te in th s atmo sphere may b e adi abatic, o r ne arly s o, ~nd then the vertical motions may 'be appreciable. Yet the wine s will not have corrspondingly larg e horizon t al components. The lines of eqaal height may be <iXIKWNX far a.part, or ·Jii:iJt at le a st arawn so. Then the vertica l motion is i ndete11ni nate by isentropic ch art. Use of such a ch art shoul d , therefore, be restricted to the cases wh e re the l apse-rate is reasonably s t able. Working with ti-,e isentroD surf a.ces for 1. ic ~ •• for Hay 10 -18 (incl), stations OL. WKS. ZN, orKF, the following results were obtained: '.IDATE: ....... 8. .. ... ... .. .. .. . ... . .. %@53 . .. • • ,r . ... . • WKS OL DATE ::TANo<.: y ~ foo May. JlT: . . -:ioC) /0 l b . . . • . . ·. 'J ZN .. •?.t_pi....__;::Gu-' •• ..=~ F v=::: .. TANK: ;>' : : 60 ° II ! : ./).... .: "I2. /0 0 ·· :. : -z 2. C) ~. . •O>vo_.:;: : _£2_ {) wo /{.) /3 14 • l'r I(, 17 ... . ·.. ,. ... .·,. ::~ : : 940 ~ /g( .22 0 .~ 2 0 ..._J . .. .'.zO . .·:z..o . ' . ' .. ... . . 0 Average r a.: -Y,lrJ/rJfl'l'iil value of the ratio J:t=- is of the order /o -3 or· less, comparable with the slope of frontal surfaces. This, ·then, is the order of magni tuae that is being neg lected in obtaining e quation (8). The order··•:,, of magnitude of the terms for the horizonta. wind comporumt_s ( 1) Gratl.e.dt wind. (Vg ) :·_ Th is will always be comparable with the actual wind velocity, ,so metimes smaller, so·metimes l a rger. ( 2) . Term l t»- J ·-:7 ,. dll,. TT ---:C- TT mean the change in the horizontal v elocity p er unit increase in height above station. This cab conveniently be found , _I from ball ~on run ob.servationsx L'.'.J V, both in mag ni tua.e ana . ... direction . per 1000 ft, a t some fiirJt.~1. specified height. . 9. It may be argued that balloon-run observations are not sufficiently accura te -to give a reliable figure for This can only be decided by studj~ng the observations for aby one day and seeing if they show systematic changes both in direction and magnitude. Studying chang es in directi , n first, the following are the changes, every 1t:)~~ ft in the 11AM (EST) observations of Feb. 16, 1939: HR.: Betweeri 4 and 14 thsd ft directio6 changes gradually from 350 to 280. VC.: Direction constant¼~ after 50 00 ft, 270 . CV.: After 3000 ft: Directi on chc=mges t3er 1000 ft are -20 ~ o, -10, o, o, o, o, o, -10 ~ 0, KY.: Direction 310 to 320. WA .: Direction ch anges: 0, 0 ,-20, -20 , O , 0 ,-30, O. Ignoring changes in direction for the moment the changes in wind magnitude , with average per 1poo ft are given below: Only the ~k~lK!lr:&.tarn: winds above the height whe r e the directim becomes steady or stead ily inceeases are taken:;:: Feb. 16 PM Station ( Initial hei ht Incre a ses HR -8 200 vc • CG 6 EV 000 CV 3000 6 2 4 2 2 Ave 2 0 4 4 -1 41 0 4 4 0 4 6 4 - KY 6 4 WA _ _," co cc HX 4 2 . 6 0 10 o -2 -4 6 . 10. Station ht Initial PK 6000 7., 8 , 8 ? -7 , -2 NU 5000 - 1 - 1 , 5 ,7 , 1 ID 5000 6 l Increases per ~ 5 1 ") -? - ? • ? 5 7 ? o , -1 O 1 -3 1 7 , -2 , O J 5 3 ') ' "J TOO LI GTTT KW cs '\ Ave 1000 ft 4000 4 4 ., 9, 7 ,, 6 .., 5 "4 _ -1 ., 3 ' 2 ? 2 I LY NC a0 u RW GW -1 - 0 .,5 . - 1 1 , " _i:: 7,/ 2 7 4 -4 .)-15 __; ") . ? .: , U , 4 , '.:) ?-5 , 0 , I.) , -'.:) -4 ? 6 ) 6 -1 ,·, -4 19 6 0 • -2 . 3 . ) I -8 .., 8 ? 7 ~ 4 2 ' I .) n ) 3000 , ~ 8 -/ 10 ., -8 _,, ~2 ? ,-6 , 5 ; 6 :. 13 ,, O ., 4 ? 10 SU 8000 ' 6, 8 ., 8 ? 6 ? 5 -? 1 1 xw 9000 14 ") 10 , -3 -2 3 5 7 4 Another· observation to be made is that when the winds are easterly, the velocity decreases generally with height ( once past the turbulence layer). The result s arn:x~argm: above were taken from observations of westerly winds, in general. The one ca se of decrease of wind velocity is actually a case of eas-terly winds. Ther is a physic al explana tion for this. Air-masses moving e a stwa rd lose apparent weight, whi.le air-masses moving westward increases in apparent- weight. Therefore, a mass moving e E,stward will have its main ma ss move ment close to the su~face of the earth, this mass simply forcing the older airmass aloft. On the other hand, a mass moving eastwa rd will move moBtly aloft. 11. 1f·, The above results est ablish the e xistence of the term the incre e.se ( or decreas e ) of wind velocity with height. It is a very real term, which for west winds is of the order of 3 to 4 miles per hour. per 1~Pf;) ft incre~se in hei§ht. To _find. w, it will be ne_c e s sary to find the slope of the isentropic surface, <Jt,_ , • where 63 is the horizontal --;;s distanc~, taken in the diBection AV, for a rise /jk.in the surface. ,// IP--~ 0 '006:l.l c::;t... ( -:) 11 ·- d --:. • oS where vr is measured in m.p,h. ,ei/,__ is. measured in aekameters aS is measured in miles. ~ .: .2. ~ ~ rl =c O -~ ~ IA. !:f in miles per hour ,._ / ·4.Zcfx/o 1 .w-<J . oc..- The isentropic charts used were those for May10- 19, 1938. ~0~xxn~xx~~tx~axxx~x0~~t1x ,., ,.___ • rf~ ~TE S"TATIO:N 6.J' VEL -A ) urHA) av~~A -,~ ~ L..~ ~ - -;er=-../ ~ -~d({ ~ . -; o.r V e. May 10 FO 0 1S 0 0 ' . BI · -~½so / O¾?tJ x:t • SM s-t>/2/o cG r~'>=v, ¥(b?i) 0 0% 6 II ¥®«&i .0075 ~tJ" 0 .7~ 12% .0402 x*fl 1. 14 10% ?3 .023 ~ ' 1.96 9% f>':. , OH 0 ex /~ :.ZZ--0 0 -;;;;; " 0 0 14 .0394 8 x10 4.49 J% , SL 1roo 16 .0198 EO %ci 7 . 0 152 26 . 0115 »~o KF I \ .. 31 6x10 -¾- 4x10 1.69 - 11% 0,66 0% - - 12. rt; vr(~)~v{~~ !k{IY-) lli I 32 QO 3OO DATE STATICDNt(~) VH --r:- D·oot2iv May 11 9- -/i·o CY SL OA EO BI 2 0_0048 2XlO ~ ..2.../ /} 2 QO118 8x 1O -- -- -- -:r:Fo 12 o.o l 1 i 1Ox 1O / 0 I) 28 QOOS 4x1<Y _.:.---- .2,/ t) KF 12 -- 1.34 67% -- -- 1.57 13;l o.46 2f, --- -23% 32 QO11 6 0 .94 -::z.5o 40 0,1 0 8 3 4 .63 12% 0 4 0 2 0 0% OL ,,.o o 22 I ;,tio not t o b e u ~ec 0 BI - OH 0 I .5-() SL BU 19 0 13 .) 3 0 .882 0_02 0 6 I ! 9% 3, 16 35% -- -- -- -- -- -- 2 1. 07 .J.3 (J ~ JJQ ~- 09376 18 1O.P447 1 00 /f'O 0 7 QOO827 ~-= ,p._ 0 ~83 -:: 14 3-!--:::10 ,~ 5. 84 .,__ 4 I Q '.) 13~ 15 : 2 !' 0 ! 2 I ' ,;,. i : 0 ' 0.021 9 0,067 { i::; __, II 15.3 QO41 0 I I 24 .:? 7 I .sg/.? o ! 12 I ! 1,n; ! 28 ~ -.. q,O 177 45 340 I 40 4 2 V,, .lDJ- BI 0 12 ..:;J d 0 BI 0 000 18 5 /O D BI .. / V 9 .,:lr 0 WES , 01 0 1 ¾ ~ SL i r!.c e fi n ite I O-L~ i ndete r rni nat e ' 3% ! CA FO I ! ·10 /~O ex 7°/, 5 ,05 KF 10E O. 14 12 OA 16 24% 0.02 $) 6 5-0 BU 15 - :;3 7.69 --- -- D- WKS ex -3 -}(674) I -- .ex 14 . -3 I ' , ,:2.:3 0 13 _ 3 / :!, 0 .£' I) _ -3 18x1O __§J-: • F=- FO · ~ ~ -Z-1:c,. 3% 85% ' 3.52 21 % 18% I 13% i 2. 95 74% ! ....._ r,! O;v i ! ! i I 0 ' 6 25 ' l~ , 77 i::; olo. .,., I I ' 17% 13. DATE STA'l'ION May ~¥~ /)(,.v-f ~Ji1di d V (,;,,-__ -}L,j /Ar~ V) v' 7\ LR ( [L h~ ~·o -do,2 0-v - 2 -p 1/i ,....,.-, [/; 17 SL s3J~o 14 n NA s:%, , /40 18 SL OA ex 19 EO .. NA AVE:Fli,.GES The term :_,l.. A= <-v 1 1 o~ O _,,, I *(6 I 0.0289 . 5 2.06 26 0.0575 6 4.9 19% s ~'7 0 35 0.0402 2.86 8% J:1/ 5~ () 7 0.0145 0 .62 9% ~-x 5 -3 14% 9 · 0.0056 11 0.877 10% '% 26 j0.0620 // 0 0 0% 0 ~3 ! 0 0% ~OU - 1/.3 0 --- * I I I9.-0~0 18 I / 5 i I 0 I 6.7 I 2.43 ·1 ; I ! 16% I is generally of the o~rder of 3 to 4 m, p, h per 1000 ft increase ift ht, which makes the term;-~in the eqn for the horizontal wind an important one, as the percentage values on the last page show. 11 ~" is the r adlhus of curvature of the i:astantaneous stream line. It will have to be found by drawing the stream-line n icnure from the upper winds. The procedure should be to draw stream-line pictures for 5000ft, 10) 000 ft -~:, 14,000 flt and at the same time draw isobars at these levels a s a p OS$ible guide for the shape of the stre am-lines. However, the first case drawn, that for Jan.31, 1939, 8 AM, showed the stream-lines far from conforming with the isobars at 5 _~ 00 ft. But it is quite easy to draw a stream-line picture just from the 50 odd ba:)..loon onservations, Fememberi ng to crowa them together where the wind velocity is greater. (() - C\J 0 C\I I I / I JAN 31, 1939 5 AM WINOS AT 5000 FT. ~ T :1 If '-,' \ 0 ◊ I ./ ◊ 1 I I ' I I ◊! 0 I:/ l <'>- I I. I ----- -- - \ ◊ I:/ \ 0 ),"!, 0 ~ 0 ,o j I I . - I I y- f I o o I I -r ~ J"9AI 31> ~93Y 1 .,. . •/ ;{'. ~-A/1-1 t -W/N-!' S } .stJo o ' ~r P,: 1..., ---- ., _,.,,, JAN 31, 1939 4AM EST PRESSURE /4, fr ,I ) I I I I I I I \ 0- 0 °I'ti, ? QC I .~- -- ---◊ 0 \a I --- . I .~ ' 0 I - ·- ---- -· f I - I ,A' -- -. 0 0: o I' I I I' I i i "" •. I ¢'. I r I ·o·0 -(., 0 ,¢- o 0 0 0 0 0 (:) T" _.,, c.. ( J-7 \ It-is also obvious that many streamlines will have to be ori gi ngted in areas where the wina_ velocities show marked incre as e, in s uch caees where horizontal conve rgence will not account for the inc r e a sex, but rather convergence from layers above or below must be considered. Whe re the velocity decreases without horizontal divergence, t hen the streamline~ are brought to an end, indicating vertical motion out of the horizontal surface tha t h ad be en chosen. For the 5,000 ft surfaces: DATE -(~ ·I - - --~ ;,l."' )·'-· /2, ( ~ j -,,;:; ¥" =2·&jy___ ~ voo ?o. STATION v J.-A.) vz.( n-fa JAN. 28 I NA 33 CG 27 EO 2"3 TD 13 c. , i /1,; /I/ 1009 169 800~ 3,7 11% ~ 0 0 .,L) 0 0 340 1 8% ~ OA V I I I G I I 0 2630 900 8 16% 12 144t 330 1 8% 2, _.,t:J ID S1 GW SivI JAl\J 29 0 ,ID OA PQ. 24 576 FV 34 1150 0 ; 1150 1 4% 450 7 21% 9.5% ;,{ JAN 30 JAN 31 KY "37 1370 1050 3,5 ON 16 256 530 1..4 9% KX 43 1850 500 10 23% BH 40 1600 470 9 22% DV 1S 22'5 270 2."3 1i;~ CG 18 324 oD \ "'" EV vs '576 484 24 22 - - ·- -~ . -.,_. ot ... ! I 1 .~.-♦ I II l 400 520 171 4 2· 5 l 11 cfo --~-- ---- ----------J Vf" - -~ ,I ?, -- . I I I I 0 f' L. -- ~✓ -_ . - ... 2/ ; {\ ◊ 1= n( 0 / I L 1' h 0 ◊ 0 -·-' 0 ... 0 _-- - - I 1 ◊, ' I \ , .◊ 'I' ...,- ·-..., I /'I , J ~t /t: T 'I' ;;,- J..,...L ~ I /\ i i◊ ' ◊ I, 0 ' ! 0 I I oi \ I '?- I • \ '◊ • I \ 0 I ~--·-;·1-· ' ';J O ) •• -·~l \ N 0 0 \. \ --) , _yj,,, (' ' ~ ~, \ . \ I I p, , - !--.._._ I -. ,.t \ r _\ -\---\ I I ··--._o ,I i \ \ - \ ~-\_ \-\~~\ ~, ·-·-,- . - . --o/- I I 0 , I ◊ -~ s~_\ ' ~ ~ I I I I -... I ...... r -r ' \ ~ I I I / JAN 28, 1939 5 ~M EST WINDS AT 5000 .Fr J I J I I I , I ~ ~_,,,_.::;.._......,µ.,"'~-""" ---- -··-r-··--- 7 • ---- ❖---c 0 >0 ~ -- 0 I ✓ - /4 l ,,, } ,? i fl ~ ~ \ 0 >~ 0 ' ·----;I , . I' ' 0 ,, ~ ~-: .. j I : ,..,.. ,... j/ I ~: <> • 0 ! 0 ❖ oo • / o\ o o l~c- I ) \ __ .\_ I + J ,,, 111. ;u,,.. ":SJ I J"'Ary ~ l '., 7 W //I/ d;>_S ~ /1 T jrt)() 0 --- \ I \ • I 20. v=t. :r;:; is These calculations indicate that the wind compt • comp t -;r Ur Ji; generally not. as importan t a s t'ne if. 1]v1oreover, 1• t has 'the same direction as the v·ind its elf, and so Kia alters the magni tuce of the wind, on - a.n average 11%, but not the direction. :D ;)7Tvz.. -_ T v ?sJv "' l/2 t' - (4) Term It is : ~oing to be more a.iff icul t to determine this term, The reason is tl:at the ballon runs' indicate greatly varying wind""'.speeds from one statiot1 to t he next. Yet the s~reamlines do no·t necessc;1,rily converge and di verge to I the same extent~l As a typical e xam:·1le of this, note the winds at 10,000 ft for 2pm, PST, Feb.22, 1939. In th~K the Mississippi River area, or the middle West the wind velocities show a great dispersion. Yet the wind directions oo not v a ry g reatly, so the streamlines must be drawn parallel to each other. (see p.21) In s pite of the difficult-yin determi n ing this quantity it must at le bs t be considered qualitatively. It is a term which changes the direction of the wind, L,nd therein ~ ill lie its imp o rtance. whe re~ ) VJ ~ V are in mil e s p er hr .::::i ~ is in mil e s. An attempt will be made to dete nning the magnitude of~6V is alwa~s the increase or decrease in the dire ction of the stream-lineK , over a distance 65. ,.. \,/'\ /,. y -,,., .. _,, "'-- _ I I I . i . I I I <>- ◊ 0 I ◊ I I C C. :, • I . ? ! v ¢, {f I \ c \ 0 -¢, '\ \ p ___>vi, 0 , )✓ ...:::r. /0 --.' ) I , I I 1 0 ,., ' - \ \' i{ \ '\ ,, • -- .... .J. \ o;-. \ \ i L o ~ o o I -=----\....,._ "\, ? --: 0 r---.__ ---:...:...:.__~=.~ - -- \ I • iI \ i. - . I . • ( J ' t 1,,,7 . fr r I ~ T \_ -+- t - ¢- \t \t- \ I I \ I I · ' \ \ \ ~ I \ r £ ~ Z'?, A'~-9 \ t~ -_,ii0~ S s /-- _l _ ~ )L'V/?"'g~ 4"'r -t I. _.,..~t:Jdti j1, -r ----'--~ l ~ / I 0 f \ ◊ '\ ' I 0 0 / --- __ _ ... I f• ,., :.oo I ~ ' } I • I I I -- ·-· J i - I \ \ L r ~◊- ~I _.., -."'--'... I ~ ~! -r r +- I \ t I J--- I t-° \ \ I I ◊ I 0 ! I .-.. I o o'(> \ Q ' ~, o ,~ ¢- _ - " " " ~o~ ~ ,-... ·- ..__ "' ' ~ ~---""------ -- - .... -- ! ':' .::. -·- -~ ❖ I O ' '" -·--. ----.,... 0 . -.L ,, . ' ·P ~ I' o I !• . .. I ---------1 f I I I i : i ~0 ), 0 I -1. lc'/4 o 11 O O tt 0 0 0 0 0 0 0 " " ·, I ( \~ ' I I I- i 0 - I ~ ~ I I -,. --- ~ ~---t I -- 0 0'9 r .E ~ ..2 .21 .,,_ !).3 .9 . // p~ ,6"._s ~ 25. ' DATE 61 ( ~ i (> "' I J:r / I .::)j ~ STATIONS v ( ~ ~v(7) (t.tJ,_,;) J AN28 8AM '5000 I I 4 ( ?~ / CC - PT 35 15 350 2.0 6% vs 38 7 330 1. 1 3% UN- GW 55 28 300~ 7 13% PDR- FV 40 40 350 6 15% RK- MP 20 20 380 1.5 7% DO.- KY 27 16 270 2.2 9% FV- ZH 43 22 210 6 14% 58 ? _o,.. 4 10 5 Feb20 5pm 10,000 HU - Feb22 5nm ~000 Feb22 5pm 10000 PS- UN i ' Feb22 11nm csooo 9% ' I DO - KY 29 21 3 .3 270 ; ! KC- PS 53 17 : I 370 3 .3 ! 11 % I i 6% i The above ex a mn les we 1 e choseh for cases wh ere nei g hbouring observations indicated a , more or less, systematic inc rea se or decre a se in wind velocity, without much ch s nge in direc tion. Only such cases wh ere a sig nificant i n cre ase wa s indicated were chosen. Theref o re, t h e results g ive maximum v a lues of the terms .(Nowh ere was a veloc i ty g reater t hen 7 rn . -o . h . found, or percentage T a tio of actual wi nd g r e ater than 15% . Therfore, this term is essentially a small one, KNOCX If there be reas o n t o be li e ve t hat its value will exceed 10% of t he actual wind v a lue, then it can be computed by the for mul a . above 26, I ( 5) Te r m ~ er f ' An 2. ttenmt a t - VI - • t he· rna g ni tude of t h i s term can b e ma,de b y taking the pressure changes a :b e,l ti t ucles for 24 hour& peri ods. These will be abtai ned fro m the me teorograph obse r v a tions. As a n examnl e take th e st a tions SL , CX , BI, and fi nd vrf for these sta,tions . The distances SL- CX , SL - BI are both 370 miles . This simpl ifies t h e problem . Kn owing two components of t h e vector qua.nti ty Of, the vector itself can be fo u nd by 2n e a sy g eometric a l c ontruct io n. in inches o f Hg Der hr per mi le. where Jl is t h e vector resul t of tl1e is s. llo ba ric o i:"'f e re nces b e twee n the s tat i o n s . e . g , if (~JL and - ( fh)c x - ()·O JVl (itL - (~)L3 / ~ 0 tJt) f-es u lt for <;r::::O·OJ ::: :.n n c e J:,i s c;e ne :ca ll y of tl1e o rd e r () .1 t ii.is i s c:.. c~ico u r eg :i_ ng r-e, sul t . It w, s this term t hat ws,s to a cco u t, t moveme nt s . Hov: e\ e r )' i t rnu st be r c rne mb ered t .'cla t t he p re s s u:re ch a,nge s, espe ci r:-.:Lly t h o s e d ue to fro i1t a.l l'!ove rnent s and i s :;J_ lob a ric fi e l o s , v;ill be noted on l;y ovel' t he 2:1o r te 1' p e r io c') s , c,na no t ov er sucl1 long per iod s , s 24 110 LU' S . 27 . As an example of the magnitude th a t c an be reach ed b y t h e i s f l l oba ric term, t h e c a s e of De c . 25 , 1938 a t 10 , 0 00 ft wil l be t a ken where th e surf a ce b a ro:ue tric te nde n c i e s i nd i c a ted s t r ong i s all obar i c g r a die n t s. Page 29 shows t :;_ , e 11 is .s.ll ob &_.ric '1 wi nd s , unc orr e ct e d for They Bhow a. dist j_n ct converg ence :f.:0E and c i s nonti nuti. ty i n s id e th e shade d a re a . Ag e i n·, t o -" i nf t he a1agn i tud e of t i~e i sall obaric wi nd 1:1t th e surfac e v.: e c an t s.ke the i s 8.ll o1_., s ri c t,1 ·0,0 J.ent a t t h e s u. lPf a ce an d s e e - \vh I<' t the corresoondi n.e; wi nd component shoul d be . Th e r e l a tion i s I _~ / 1 I:) ) V I .c 3 / ? v.:here 6 .c, ..J f i s mea s ured in L!.- )' 4 (/ po i n ch es of Eg p e r 3 hrs . i s r'eB--sured i n 111 il e s . .ciS Tak ing , a r b itra r ily , t h e map s for t ee. 193 8J the ab ove f or mu l a can be anp l 1ed t o i sal lob ari c ~i e l d s as fo llo wsl DATE ... A,(. De c2 ,ec3 ,,- ,T D,e c4 STAT IONS 4/if'J Uo)~i.-/1, ;• ~(&) 3/? CH- YA '7 I 2 00 1 1 mph FR- PLA 16 4 30 12 OE- SD 11 35 0 10 DE- FO 9 200~ 14 PTZ- PBE 16 3 00@: 17 QT- VC 13 28 0 15 DJ'T D ec7 A' : Dec a3 ~.s P IT D,ec 13 t,. rJ {l ;ec 17 NORTH AV Dec2 3 AT\_1r .. 10 250 13 16 300 17 D A1<i'"' rr' A Lil...KE rYi\Fr ,un n I I I I I ' \ • tJO ~ \,rC . \ \ ◊ 0 ✓◊ "" c_:=- ,., A o / - ◊ 0 -0 ! 0 -. I -.;; V O Q' ---.:..:_~ I r 0 I I 0 ' ' 01 I ' ( 0 r ~ /t--141 ' f C' r I t i Gs r' P/f 1:,.-,t~ ,;~ I{ .Yo✓ I o o ,c 'T . - (;;{?J/0/$"1Jr \ A\; \ W-/A'"II/S t- --+ ~ / {;> 0 ~ ' 0 ◊ ◊ C ~ \;;. .. o 'S7 0 ~ Q- : o ;... I ...\I ~_,.a.tV---At. 0 I>· { o --1- l- \ 30. Areas _of large pressure tendencies we r e tak en in the above examples but t hey do N.iX:t illustrate ,vhat magnitude can be reaehed by the isalloba ric wind at the surf a ce of t h e e a rth. Aloft, the reverse procedure will be used. T' .&t is, finding the is a llobaric wind, after correcting for all other wind components, th e isallobar ic , gradient will be determined or else qualitatively determined. The rel a tion on ~age 27 will be more useful written in the form: where ,t::,.S is distance in miles between isallobari~s differing by 10 units. (6 ) Te rm -; r. Thi s wa s introduced in the equation, simply to complete the theory. Such wind coni:µionent is caused by friction, gravity, or possibly some other way, like heating by radiation. It cannot be measured and discussed as were the other terms, a nd for higher altitudes will be considered negligible. However, it will be considered as of importance in the case of sloping isentropic surfaces, and qualitatively used. Thus, an a irmass blowing up-hill will be retarded, blowing down-hill it will be accelerated. 31.- The changes in wind caused by each component Having de a lt with the @.is em:w~!i-~~ ;nagni tuae of the wind components, it is now necess a ry to see how the wind chang es with each of these components: v=- l1J --f:o q \ - ti ::::- f + 4 as ;)'??.(v\ _ £(71 ./ti/ ./Jv vJ ,,,!x I + Vt- .J. I ' In the cc se of the term-~~Ofthe wind co~ponent is directed into the isallobaric low, or away .. isallobaric high. \ (a) For w-')o) wind co~:rnonent(ti;) crosses oV -gt >O For w:!-- ~ V-... ( C) to left of changeei //- . 01, Wind component (Vt) crosses ,,,.o - . . ~ } ,,,. to ri ght of ch&,nge cd . ((J-,,o ¾<o J ( a ) For Cl.>-<.. 6 ~ind comuonent ,. (-) ~ crosses to ~ <,o~ left of change CJ V . .xxxaxx:fl1§:iilrn:.wx:xx Usually, the change .:j V , with height is a change in magnitude only. That is the directio n of the upper wind will not change apprecia~bly with height. Hence the above rules could be used Hl instead of the term term II t1 change oV t1ij, the f ti were used i nsteaa. t. ~ 1' Tenn - fi v ( Vv) ~- Vt. ' I Remebering how jphis term wc s obtained, the rule is a s follows: 32. (a) For c~clonie curvature of thestream-lines, this component is opposite to the actual wind V, being still in the s ame dieection. That is, it t~¢~t slows the wind up. (b) For anticyclonic curvature, the wind is assisted by this compt. (A) For__~n increase in velocity in the I dieection of the wind this component cresses to _the left of the wind. (b) For a decrease in velocity in the direction of t he wind this component crosses to the right of the wind. For rapid. calculation of each of these components: (1) Geostrophic: Draw 'isobaric chart, a,t 5000, 10000 or 14000 or at two of these A. t ~1 Use Haynes wind scale(Ref .1) or any other scale to find geostrophic wind, in direction of isobars. Y Draw isentropic chart, given ht ofisentropic surface. Find~~ graphically (between 5 and 6 thsd of 4 and 5 thsd) (between 10 and 11 thsd or 9 a nd 10 thsd) Find ..st-. from_;-i sentropic chart . ..c,.S ;z_f \ ~0 I I ~ '). I I I ◊ ◊ f c.) . \ ◊ .,.____________ / ~ -·-- ' . \ I ?- o .. ❖ ! ❖P ❖ -·---~---~----~--\- ____ o 0 /,1// / ,. ' o❖ o 0 ,ro,, ' - ·; I I J I p-. 0 C , 0 "tr o;-- - - 7 - -(" I 0 I ' I ; 0 ◊ ' I I I I .. 0 -.,.. - • I 0 0 •- - '\ ~ ~ ❖ ·i/:l/t~__-.._---"' C 0 ❖ .u -- -- q 4' 'I {j. "- 0 ~~ 33. With 6/... in dkms, L::,S in miles /Ar;: ()'OcJ/z v in miles per hr~ 10 I /1 ·)._S)(./o'> w::: . 4L_ C)s v. 4 V ai'- where ..r is a i stance between 011£:~!K contours with hei ght d ifference of 10 0 d km s . y _is vlHoci ty c,- v is incre a se p er 1000 ft .. F j_ n d ~ raphic a.l l y in miles: v in miles per hr ' .,_ ti.. =-< ·t f -57 t. lL Find · ..s in miles: <5t/in miles per hr = {' VClV ;;T ..2_}. Vin miles p er hr l (4) V3-- n oS v~ .=:- 1-.Jr v gJ( . 6.J' s must al ways be me a sured in direction of V . L .SC,tL E W//V.0 B"' I -+ ,i,- ,,-l (o 'OO(l ~~ V, 2- V _.,, .e:1 V >o W--<O c! V5 v.j' . c,v<:.0 1 ~) 0 To £.GFT V c ,eoss,ss ' lf l C.H / \ .J:- i / '\ Tc, V j C -fO_:.S6"S oj ~0 < <QV <fw- I/ ',. V1 r ( ~) - t \...) 0 J ~ + f .SENS~ ,.q.SI/ /;f/ .S-'fl'?li. TO OPf'o.s IT{ .S £.1vg tF //V A + ,2·{, 7 _i_ v,. y; vi * 0 f·8 , ) (fs) ( v) (6v) /C/- ,,2, LJlt')"O f 1 -o w- ')LJ w-> 0 + T , VY /,1//) VJ :::: V -+ (feltD/£.NT VJ =- V Vr = V + --/- ,_ _ I, (c; r (<) (i) j (2./ j /) ITT O 1).1 T 7 o I .,4 T /= (J /( • ·1 \ v' / ) .j- o tJ 0 (f-f/-JIPT f/V/,/Y .£) G If ll I> le:- /V T ;SA-l L08AIII( ( - 7'f v /'91 Oo 0 /D, 0 0 0 ~-Q O 0 S U I( F"'1 (! ,£. A T ?Olf' C # ,1 ,f T ( 4 ,) W ,,-,¥0 /s.cNT1?0P1 c C fl ,4 ,e T (.3) (g..) /.s 0 B '4 .R I C.. -+ + I - 7'i vf Sy,voPTIC / Vl~ FS l/ 7 6 /r I C:/1 T C..('o.!'!6: V '" v (II) C,fo!Jt;--_s 'FFT ..c.....S V ~V ?JV ' ~ (/) tfEG vl-.,1/~ .c V <:: <'.l - AV>o 1· 3 s~ G .2/ _c_ _) k t,.) 35. Example: The first example of the application of this meth!bd was a forecast for Mar.1, 1939, using morning chart and signals, and fore casting for periods 24 hrs, 36 hrs, and 48 hrs ahead .. First an ordinary weather chart was <flrawn, no more time being spent on it than necessary, the:!ll maiin fronts lacated, and. the rain areas located. It so happened that there wwre no ,rain--areas for the American f orecaste:r:_- to be concerned with. Secondly , the isentropic ·surface was drawn for & =- 295 F. Then the pressure field at 5000 ft and the wind chart at 5000 ft. r,,vPICA-//oN This latter chart gave goodAof an upper frontal system over New Mexico, Texas and Eastern southern States. Three stations were singled oyt for forecasting, MP, . PS, CX. Since Cheywnne is at high axt:t1iuxllf al ti tlilde, the pressure map a nd wind chart for 10,000 ft were also drawn. Beginning with Minneapolis (MP) at 5000 ft: MPI1 - 0 • 31 mph v, ~ 3 10 30 mph V "'.330 V, ::: 5 mph to right of v Vt..:::- 0 or pra ctically o. Therefore , no change in pressure field, ana_ so no change in airmass movement i .n dicated for MP. 36. F0: V ::: 310° 24--- ·/'· L HR: I/~ 290 17 ~ u," 300 32 v✓ =- {?·f'r')o V,==-~=O c,J!J J / ::o ( VL 2· 69) ( 24) = 3 V = ( 1.35)(24)5 = 180 1 o VL = O practically ~ "' ( 1 • 35) G17) 8 < 1 300 0 V I~- V: 290 15 BI: V = 260 14 v," 300 20 11, "' 290 22 V, -= small v ~ (8.8~)(14)4 = 2 miles V= ttt RZ: "' l.. 550 .), ,,, 310 25 vL ~o. practiaally 330 12 ' 2 0 Vt.. : 0 1/2 ~ 0 V 1 -=- 160 13 Summing th~se results they indicate that the wedge of high over the Dakotas is building up slightly. The air-mass that will be over MP should follow pretty closely the wind • trajectories as they are seen on the present map. Possibly by the 3rd. period MP will be affected by the low that is indicated as approaching BI. But not enough moisture to give precipitation. Hnece the forecast on page 37. Now to arrenge a forecast for Memphis(MX (PS) 37. 2. Developments expected during the forecast interval. II. s H Wthr. t 0 a t i u r 0 0 0 • n R s - FORECAST Spcl. Phenohena Ceiling Vsby. Pption. foggy smoky dusty hail thdrshwr. tornado sleet frost 1000 1000-5000 5000 < > <2 2-4 >2 none lgt. T-.10 mod . . 11-.50 hvy. .50 > Surface Winds < Calm 6 Same Lite 0-10 as 1~ /1 Mod. 12-22 Surf. 2 Str. 24-38 2~ 3 Gale 38 > 5A 0 / c::; 7 4 nr.nP. NR 1V/P 5P () 7 5 / none E 7 ~ 4 4 4 none none SE 5A . 5A ps 5P 0 5A 0 0 5P () 5A ex 0 5A • c::; 7 5 r ,"> ":> i::; ~ 5 ? 5 ) c::; 5 / / III. ~ ') 4 4 4 ) 4 / 4 '" '"'n o none non e nnne none 8000' Winds N\fi NE SE w w w s li g h t 2.10 s li ght 2?/J s s mod ~ 1 i trh t ..,,0 Temp. D.P. 0-5 5° or fraction thereof, one error Same as Temp. n .!) 24 24 24 /5 ~~ /.!J 8 39 .2{' G 39 3 / 12.to M... 1 i::; I :J 25 25 ./ ;J 1 i .o·ht. ~Sb 2,U) .ll g m:, light li ght ~ s light .'>..lo s - /,3 6-HOUR AIRLINE FORECAST (____ ) 1. Conditions over route _ _ __ _ _ _ _ _ _ _ _ __ _ _ _ _ _ _ _ __ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __ 2. Ceiling _ _ _ _ _ _ _~ ~ - - - - - ' - - -- -- ~ - - - - - - - - - - - - - - - - - - - - -- -- -- - 3. Visibility _ _ __ _ __ __ _ __ __ _ __ ~ - - - -- - - -- - - - -- - - -- - - - - - - - - 4. Winds at 'flying levels _ _ _ __ _ __ _ __ _,..__ _ _ __ _ _ _ _ _ _ __ _ __ _ _ _ __ _ _ _ __ 5. Special phenomena (icing, thundershowers, etc.) - - - - - - - -- - - -- - - - - - ~ - - - -- - - -- - - 6. Terminal conditions _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __ FORM AL6 5M 8·38 38. V ~ 300 12 PS: "9 . -: : 0 VS: V. =(!-~2).::-~ ;?<'l • 'IJ· /.... ,2_ 2- ~t:>O I o VL : Vi, (1,35)(12)(12) V,; = 350 ( 1 mile hr :: 0 v': 230 10 / V ::: 280 14 AG: //; 250 32 V, := 0 ~ : deflects Vto right,; 0 ~"' 0 Vt.. V I ~ 270 32 These results indicate that the centBe of activity must be closer to Georgia than to Memphis or Vicksburg. A low pressure centre must be active aloft and must .be moving to the north west from the pcean. (Compare this analysis with that which would be obt a ined from the synoptic map alone) The centre of the dis~urbance must be too far away to affect Memphis, but nevertheless it should a.ffect the wind making it Na nort herly wind and rnoderateJ., OL: V: Vr AP : 100 12 ==- 1h "' 80 15 o V; "' · ( 8. 85 )( 12 )~ -4) =200 "' ( 2 • 6 9 ) ( 144 ) II t. 150 24 !; := 130 = 2 mph 3 mph lt1 ::- ( 8. 85 ) ( 24) 4 ~ 300 Vz. = ( 2. 69) ( 24) v~ = (,1.35)(12)(12 _1_== 1 .1 150 2 mph i. 700 V:1 V 1 •~ .:. 3 ~ 170 18 =c 2 39. The isallobaric winds at MP, VS, OL, AB would indicate a high pressure build-up between these stations. This •will mean good weather for PS, and that no low pressure from Texas will invade this area at least for the next two days. Hence the forecast. Forec a st for Cheyenne: v: 280 22 for 10,000ft. 115 •. 280 25 V, :::- 0 v._ =- o I V ~ O good enough. The winds for Cheyenne should continue as before. And observing what th f, weather is back of Cheyenne, the forece.st is made a.ccordingly, in this case clear weather. The ournose of the above abalysis is to give c1. picture of what movements will take place when it is not obvious otherwise. Rauid Qualitative Rules In the above case chosen for analysis the components have g e nerally been too small to b e considered. Unless some snecial conditions exist, likelarg e wind velocities, ranid increase in wind velocities with height, o~ sharp curvatures of the stream-lines, these components may be neglected. In the previous part of the paper an a ttempt wa s made to sel ec t the e~treme cases. Page 34 is the all-important summary of rules, quantitative and qualitative. It sho u ld be kept 10 v I I f I I () \ . ' 6/ - ◊ \ o◊ ◊ - .... .._ ... ........ J'I '\ ◊ ' ~ 0 ¢- 0 0 ?- o I ~ 0 0 0 0 ~ \-<>--; 0 ,,<)-~ /o 0 0 0- C) I I _.,. --. r ( ...... ( r I I'" ~~/~/939, I --I- J .,;;z.A#· ,\ ~ :: :l , s" . t" I 41. ff 0 ◊ i, I ' 'I I. \ ~ • \ ~ -------~ \ I -"'\-- i .. • ◊ - 0 a 0 ., 0 / \' .-' " ◊ I 0 I • --- 0 4---..C.. t; - - C 0 1 2 / ,,,7 , ,7+-z /~ ) o I.I ◊ l ' i cl ! 0 0 f -1 0 IQ 4 2.. ') \. ' -l3 ~./\ ff' 0 ' I "9- ""' I I ◊ ' I I I I ' I ◊ ◊ ' I ' I ;.4 ◊ i -- I ◊ 0 .... ----- \ 0 \ I ..... ----.. ... ______ _ !◊ I I ,0 0 C ·- ·'-.. --r· 0 I' p o_l ◊ (\ C. L._ I ? --- -- () ') 0 ◊ Q 0 Oo 0~ Q ,o4o o. ~ ◊ ----- . Q ',J I A~ o 0 ~ ◊ 0 ~-------0 0 , ❖ 0 0 '? ◊ C 0 I r ◊ I \ t ----- ~ / ' ◊, ◊ >-., , ~·-"?.· ,,..,· ,'--" __,,1' ,. .....• "'" l f -.+ i - L,r- .I I , I I' \.,''\ •,'- .... ' I I i C ◊ ~-} 0 i i '-·-·- - --· I . I I JJ, · - ~· I - . ..0_ _ _ I 0 • t -8----.-1. ·-- -; a:- - -- 1 0 I I 0 I I I o o I o I ; ◊ 0 0 () 0 ! I I I' I 0 I ' ' Oi I iI I Z:o_\ 0 I ◊,' \ 0 ( ' ..,,~ f · ~ .. f 0 \ o \ o◊ ◊ ·-- ____ ) I ' ( \ 'I ' in a conspicuous ~~Hocxx~0Nx position during the forec a st. The tools for this forec a sting are a protra ctor, a convemient line a r scale,( a cm. scale appears b est) and wind scales for finding geostroph ic wine s. These may well be made se parattly, and desi gnated a s scales for 5000 ft, 10,000 ft, and 14,000 ft respectivel y . There will also he needed a scale for me a suring distances on the map. List of Referen c e s. (1) B,C. Haynes: Upper Wind Forecasting . Monthly Weather Review, January, 1938. (2) E. M. Vernon and -E.V.Ashburn: A Practic a l Viethod of Computing Wi nds Aloft From Pressure and Temperature Fi~lds. M.W.R. September 1938. • (3) A.K.Showalter: Front&& Movements Contrary To Indic 8 ted Gradient Flow Produced By Mi nor Waves. M. W.R. June 1938. (4) ~.Bjerkaes and E.Palmen: Investigations of Se lected European Cyclones by Means of Serial Ks cents. C.s. se -. ., 4, Feb. 15 to Feb. 17; 1935. . Geophysike Publikasjone::r, Vol. Xll, No,2. (5) R.C.Sutcliffe: ·on l!revelopni.ent in the Field of Barometric Pressur~. ' Quarter)y Journal of the Royal Meteorological Society, July, 1938 . Vol 64, mo 276. (6) Brunt: Physical and Dynamic Meteorology, P. 166.