Construction of a Model Monogram to Show the Variation of Insolation with Season and Latitude Citation Obenhaus, Gus F., Jr. (1943) Construction of a Model Monogram to Show the Variation of Insolation with Season and Latitude. Master's thesis, California Institute of Technology. doi:10.7907/ffbp-s465. https://resolver.caltech.edu/CaltechTHESIS:03102025-221810941 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 1943 Record Number: CaltechTHESIS:03102025-221810941 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:03102025-221810941 DOI: 10.7907/ffbp-s465 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 17051 Collection: CaltechTHESIS Deposited By: Benjamin Perez Deposited On: 11 Mar 2025 19:13 Last Modified: 11 Mar 2025 19:13 Thesis Files PDF - Final Version See Usage Policy. 2MB Repository Staff Only: item control page

CONSTRUCTION OF A MODEL NOMOGRAM TO SHOW THE VARIATION OF INSOLATION WITH SEASON AND LATITUDE By Gus F. Obenhaus, Jr. In Partial Fulfillment of the Requirements For the Degree of Master of Science in Meteorology California Institute of Technology Pasadena, California CONSTRUCTION OF A. MODEL N0MO8-RArt, TO SHOW THE V ARI.ATI0N OF INSOLATION WITH SEASON AND LATITUDE In constructing this Model Nomogram, the main objective was to give a graphical three, dimensional picture of relative amounts of insolation received over the earth's surface at all seasons. In this way , not only the amounts of change could be shown, but als o the different degrees of the rates of change, which play a · very important part in the location of the Arctic, Polar, and Sub-Polar fronts.3• rhe amount of Solar r acUa tion reaching a unit area of any pa rt of the earth's surface -in one day depends upon: a. b. c. d. The Solar constant The trs.nsp arency of the atmosphere The latitude The time of year Since this problem is mainly concerned with the variation of the sun's radiation with season and l a titude, certain &ssumptions must be made. In order to make the variation presentable, the earth's atmosphere 1s assumed tr be t r ansparent. Dy doinc this, a uni form n-on-v ariation of the sun's radiation field is obtai ned ove r the whole earth. It is of interest to note at this point that about 43 per cent of the t otal heat received at the outer layers of the atmosphere is lost, due to scattering and reflection of the rays.* Another term that must be considered is t hat of the solar intensity, or solar constant. The value of the solar constant is derived from a series of observations over a period from 1905 to 1926, taken over various parts .of the world. The value varied very little in the series of observations, and is therefora taken as a const a nt of lo94 grrun calories per cm 2 per minute, at the outer limit of the earth's atmosphere with the sun at the zenith, and reduced to its value at mean solar distance--which is the distance equal to one-half of the major axis of the earth's orbit. The actual variations in the amount of heat energy received from the sun thus con110niently becomes a function of latitude and season. The season is dependent on the position of the earth in its orbit . It will be noted that figure s for the Southern Hemisphere do not correspond with the figures for the Northern Hemisphere shifted through six months. This is due to variation * According to .Abbot, Fowle and Aldrich in Ann. Astrophys. Obs. Smithsonian Instituion, 4; 381, 1922. C.I.T. Meteorolo gy August, 1943 -2- in the distance from the earth to the sun across t r1.o ma j or axis of the earth's orbit. The totals for the whole earth s how a ruaxi rnmn in December for t ll e Southern Hemisphere, a:ad. a maxiraun in June for the Northern Hemisphere. The maz im1lm of De cember beins gr eater than the maximum of June, corresponds to 'the times of perihelion and aphelion, or the times ~ l en the earth is closest to and farthest from the sun respecti vel:,-. A"t aphGlion, the distance of the earth from the sun is about 1.034 that et perihelion, thus b y the law of inue~se squares the intensit y of heat energy r.:.ust be at perihelion, 1.069 that at aphelion,1° It m-. ;_ st be noted here, however, that in the course of a year~ each he::rrisphero roceives equal amounts of hoc.1t enerKf because although at perihelion the earth is closer to the sunj the path of the orbit is shorter than at aphelion. Thus wha t is las ~ or made up in dist once is also lost or r:i::i.de 'J.P in tir.:10) BS tbe case :nay be. In the consideration of the variation of the latitude, it is shown that a variation of the intensity of the sun's radiation on a sloping surface is a function of the angle ~;hat this sloping surface makes with a surface perpendicular to t h e sun's radiation. Or that the sun's radiation is directly proportional to the sine of the angle or solar altitudej or t o the cosine of the sun's zenith dist ance. These angles can be expres s ed in obsorvable quantities 3.s a functior.. of latitude, of the time of day, and solar declination, and ma:r be expressed b y t:--~0 followin formula: 1:; in which Q.= amount of solar enorg-J deli ver ,3d i n a c; i voI'< t i:oe, is the ~un's declination, q; is t he lati t ude of t he point in 0question, His the sun's hour ai.~gle, vJ is ans;ular velocity of earth's rotation, and I is t h e solar constan·t. In order to represent the decree of insolation received at various latitudes and seasons, the followin s unit is cialcula ~ad. On the day of the vernal e~uinox at a sta~ion located on the cellestial equator, it follows that ~ ~ O dnd t h e ho~r a nzle is T and the latitude 1s o 0 • Substitution in equation L y ields: Q.= 2 I vr 2 ')-r Where I is the solar constant and equal to 1.94, and w= ~ radians per minute, then: C {l ?~2 1 • , /, . _ . 2 _ Q.= 2 17 ::: 6' 8 '} C4.,,:ir, e1/ C">-Yi /~ The values applied to the nodel nomogram are expressed in terms C.I.T. Meteorolopv Au.gust , l 94~ .::,., -3- of the unit calculated above, namelJ, tho i:nsola tion re,Jeived at the equator on the day of the vernal equinox. The I1:odel nomogran is constructed in three dimensions with Latitude 1.:md Seasons (t,y months) on a hortzo:o:t.al 11lane at right angles to each other 1 end uni ts of insoL3tion on tl:e v0rtical scale. The horizontal base is made of pl:tvvood, 24 x 24 x 3/8 inches. The background is painted white with lines of latitude and months ruled in ·black ink. The m~nth lines are 2 inches apart, the latitude lines are li; incbes apart. The verti(),0:. l 01..:rves ar 1:) drawn on 8. ccll 11loid s11e et 10 t Deb es b igh bj-·· 23 inches long~ and re_:-Jresent the vari8tion of insclation with latitude f,:>r each individual month. There are thirteen such curvest witl: Deoe:::b er being the first •ind lust curv8 in consocuttve order~ The curves 2r<2 mounted 1Jpright on the plywood ':,ass. The nom.ogra..71 is made with a vertical scale eaual to 4 s ,.1.ch 1 units for ea.ch inch, hence for any latitude and/or season the degree of insolation may be rapidly scaled to a small dcGree of e:r.roro It is well to take each □ onthl7 curve as reDrese~tativo for the 15th day of that month; t~erafore, for the 15th iay of October at latitude 60°N there would be 9/30 times 809 calories Per 2 "lli '"'-' rece;TTeu·' d1•..,..1 r i r1::: 4--l7A+ a."a·,r .._ 'I! f..:_;. 1.,, l .._._ \.; ,.,; O .&-. 111.•ew1·~.,.. f'nr .._:,.. , i,.,.:- \..' ....., _, r.'.[1'-" ~ .., Q 1c::-1-:·,.., ~ .,; .L J. df:>Y" o·f·' ""· ..,' • A::>ril at 1a:;1tude 20°N there would '8e :30.?/~-0 tines 889 cal .)!'ies 1 p;r cm 2 received during that day. A curve· runnin~ parallel to the latitude can be extrapolated between the 15th day of conseoutiv9 months. It would, therefore, follow that the 1st day· would be midway between each monthly curve. Using this method it would have to be es2u.o.ed t",at e1.1.ch 1:1onth contained 30 da;;s 1 which is a satisfactory assumption. If it is further desired to reduoe the degree or insolation with respeot to time, reference is made to s. 'Thesis cry Ca.pt. J. Vern Hales, in which he has divided the da:y- into hourli variation of total insolation incident since sunrise for the Northern Hemisphere.1· C.I.T. Meteorolog:r August, 1943 •4- BIBLI WRAPHY , ..... 1:-f(Thff'HRZYS , Wo J. Inc., New York. Physics of the Air. McGraw-Hill Book Co., 1929. 2. BRlmT, DAVID. Physical and Dynamical Metoorology. The Macmillan Co., 1934. 3. KRICK, IRVING P. 4. HALES, CAPT. J ~. VERIL New York, "Elc.rn.on ts of '.7G a ther Predict ion''. California Institute of Technology, Fasadena, Ga lifornia. "Hourl~,r Variation of the Toto.l Insolation Incident Since Sunrise by i~nths for the Northern Hemisphere". California Insti tu te of Teahnoloc::y , Pasadena, California, 1941. C. I.T. Meteorolosy August, l9 t13