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May, 1928 Monthly Weather Review 179 Solar Radiation in Middle North*Germany According to Measurements at Potsdam

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May, 1928 Monthly Weather Review 179 Solar Radiation in Middle North*Germany According to Measurements at Potsdam MAY, 1928 MONTHLY WEATHER REVIEW 179 SOLAR RADIATION IN MIDDLE NORTH*GERMANY ACCORDING TO MEASUREMENTS AT POTSDAM IMdeoralopi6cAc Zeilschrift, January, lo?] By JOEANNSCHWPRT The intensity of solar radiation at the surface of the at the Potsdam Observatory during the period 1907 to earth is determined by the intensity at the outer limit of 1923 there has been determined the daily and yearly the atmosphere and by the loss sustained in the path march of solar radiation in middle North Germany, which through the air even when the sky is perfectly clear. forms a reliable basis for further investigation. The amount of heat which the unit surface receives in The question of the radiation on surfaces of diflerent the unit of time with normal incidence of the sun's rays slope and exposure can now be answered unequivocally. is called full radiation, intensity in the direction of the The values of full radiation with cloudless sky presented sun's rays, or total intensity. The radiation upon a sur- in this paper are taken from W. Marten's work, Das face whose normal forms an angle with the directjon of Strahlungsklima von Potsdam.8 Berlin, 1926. For the the rays, or the radiation component in the direction of declination of the sun (6) values are taken from the this normal, follows from projection. Nuutisches Jahrbuch for 1925; such values agree well Calculations of the solar radiation for different lati- with the average for the period of observation. The tudes and also for surfaces with different slo e and expo- latitude of Potsdam (Q) is 52' 23'; the hour angle (t) is sure (Himmebrichtung) are often underta f-en without counted from noon. The point of observation lies (since reference to the atmosphere and, at tunes, even without 1909) about 106 meters above sea level and about 25 regard to the changing distance of the sun under the sim- meters above the ground. ple assumption, which by no means corresponds to fact, We resolve the full radiation, or total intensity, J, into that the full radiation is constant at the bottom of the a vertical component Z (directed downward from the sea of air. Eser calculated for the latitude of Munich zenith) and a horizontal component or intensity H; the the duration and daily totals of radiation on planes of latter is resolved into a south component (intensity of different slope and exposure taking as a unit radiation radiation from south to north) X and a west component at normal incidence for the period of one hour. Others e Y. Denoting the sun's elevation by h and its azimuth have developed similar formulas or graphic methods. by A, we have Recently Gessler has renewed and extended such calcu- lations, and Hopfner has published as a supplement to H=J cos h. an older work a voluminous, orderly, and highIy com- X=J cos h cos A=J (-sin 6 cos p+cos 6 sin Q cos t), Y = J cos h sin A = J cos 6 sin t. mendable prize paper on solar radiation b in which the sun is assumed to be a point-like source of light with Z= J sin h= J (sin 6 sin cp+cos 6 cos (p cos t). constant energy and the earth is considered as havmg no These formulas give radiation for the following surfaces: atmosphere. X,south wall; Y,west wall, and 2, horizontal plane. In order to take account of the depletion of solar radia- The radiation on any plane whatever or the intensity tion in the earth's atmosphere it has been assumed, after in the direction of its normal can be constructed from the example of Lambert (1726), that in the passage these components, for example : through equal air masses the radiation is diminished to Southeast wall, (X-Y) cos 45'. the same fractional part, which holds, to be sure, only for South slope of 30°, X sin 30' + Z cos 30'. homogeneous radiation. Especially through the work at Southeast slope of 20°, (X- Y) cos 45' sin 2Oo+Z the American observatories, which are thoroughly cos 20°. equipped and favorably located (some at great elevation The values of full radiation with cloudless sky are above sea level) has it become possible to determine the calculated symmetrically with reference to true noon degree of transmissibility of the different wave lengths, by taking together each of the two hours equidistant to take account of the influence of water vapor and dust, from noon. A preliminary investigation to determine and to determine accurately, to within 1 per cent,.in the finer differences between forenoon and afternoon absolute quantity the mean intensity of the solar radia- was made by Marten (Das Strahlungsklima). Accord- tion outside the earth's atmosphere; that is, the solar ing to that the highest values shift to the forenoon in constant.' 3 summer and to the afternoon in autumn by an hour or By careful, extensive observations at a series of places less. the actual solar radiation at the earth's surface has been The values of solar radiation on cloudless days are determined for different elevations of the sun and different multiplied by the duration of sunshine to obtain the seasons. Through the exact measurements of W. Marten radiation values with mean cloudiness. In addition values for the middle point of time were calculated 1 Ewr, C. Fotschungen au6 dem Qebiete der Agrikulturphysik, hsrausgegeben von E. Wollny, 1881, Bd. 7, p. 100; Zeitsehrift der Ostarreichisahen Qesellachaft fiir Me& from the sums of the duration of sunshine for four ad- rologe. lS35, Bd. 20, p. 11. jacent hours m,,, m,, and m3 according to the for- 3 Bteiner, L. Meteorologische ZeitscMIt, 1888, p. 183 and1806, p. 294; Zollner, E. Mob- rn2, logische Zeitachrlft, 1808, p. 92. The intensity with normal radiation Is considered mula lo eonstant. 3 Oemler R. Abhsndlungen de8 Preussischen Meteorologischen Instituts, Bd. VIII, m&2+6(----. 2 2 Nr. 1, Berlh. 1925. One equetar-hour Is taken 88 the unlt of lull rndlation wnstantly recslved. 2 m'+m2 m0+m3) 4 Hopher, F. Metaorologische Zeitschrift, 1QC4,pp. 384 and 388. 8 Hopher. F. Gerhds Bdtriige zur Qeophdk 1926 Bd. 15, pp. 116 ff. 6 Hnnn Julius. Handbueh der Klimatohee Bd I 83 Hann, Julius and Slirhg, Values for early and late hours were determined approxi- R Lsh;buch der Meteordogie 4th edition pi. 24' sbl.'aOe: . i 8- papers on solar radlatloi (Sonnenst&hInngj fisted In the index volume (1W- mately; the recorded data on duratioy of sunshine were 1908) of the Meteorologlsche Zeitschrift also the fanowing papers in that puhllcation: c Hrurer J 1912, p. mi and 1916, 16: Delant, A.. 1913. p. 239; Fowle, F. E., 1814, I Abhsndlungen des Preussi*hen Meteorologlschen Inbtituts, Bd. VIII, Nr. 4; p. 270; HA, Julius, lQi6.p. 79; De&, A., 1916, p. 211; Kron, E., 1816, p. 228; Kimbsll. Ergebnisse (d. Preuss. Meteorol. Inst.) 1808. p. XXIII and 1912, p., XI. H E 1816, p. 377, and 1918, p. 1% Marten, y.,1920, p. 26T hgstrh A and Dorno. * Brbnow F. Lehrbuch der sphllrischen Astronorme, 4th edition, p. 81; Hammer, C' 19hhp. 3& Dorno, C., 11322 p Saq. Dietriua 1Bx1 161. AleoB&&-und Him- E. Lehrbuch der Trigonometrie Id edition p. 511. m'elstra' ung In the indexes to tbeMeteorologischbZeit&ft for 1924 If. 16 Echubert, J. Der jllhrllche Qaig der LuIt-bnd Bodentemperatur. p. 32. Berlin. le00. Unauthenticated | Downloaded 09/25/21 06:53 PM UTC 180 MONTHLY WEATHER REVIEW MAY,1928 supplemented by reference to measured values of radia- TABLE2.--Maximum values of solar radiation with clear sky for different exposures (gram-calories per minute per square centi- tion. meter). Potsdam The paper then presents in tabular form ll. the values of radiation, in gram-calories per minute per square centimeter, with clear sky and with mean cloudiness Radiation Exposure in gr.-cal: 1 Month Hour received at Potsdam at each hour of the day at the middle 1 miu. cm.r of each month of the year on ten differently esposed surfaces as follows: Plane normal to the direction of the Under normal incidence _______ ___________I 1.278 I May ______________I Noon. On horizontal plane ______________________ rays (total intensity), horizontal plane, walls facing On north wall________...___._ ~ ___._.___._ On east wall .____________________________ north, east, south, and west, and slopes of 30’ facing the On south mall 2 ____ ______________________ above directions. On west wall_____________________________ 911 June ______________ 5p. m. On north slam of 300-. ___________________I :654 I _____do____________ I Noon. From values for clear sky there has been constructed On east slope of 30°.-- - ~ _________________ _____do.- - - ________ 10 a. m. On south slope of 30° _____.___.___________May ______________ Noon. for presentation here Table 1 showing values of radiation On west slope of 30° ______________________ June ______________ 2 p. m. at 11 a. m., when the intensity of full radiation is only slightly below the maximum. 1 Also 7 p. m. 2 1.016, February, noon. The maximum values of solar radiation with clear sky under different exposures are given in Table 2. It TABLE3.--Solar radiation (gram-calories per square centimeter), is to be noted that these values like those preceding with average cloudiness, received daily at the middle of the month. relate to the middle of the month. Potsdam Table 3 (part of Table 5 in the original paper) gives solar radiation with average cloudiness, the actual radia- tion received, at Potsdam during one day at the middle of each month of the year. Assuming that the mid-month values are average values for the month, Schubert presents a table of mean Under normal incidence.
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