Radiosondes are to be launched at Cape Canaveral Airforce Station; Pacific Spaceport Complex; and the Guiana Space Centre to make solar radiation measurements in the ozone layer at an altitude of 25 km. The measurements are to be made every hour from sunrise to sunset for the longest and shortest days of the year at each location. The detectors must therefore always be oriented towards the sun. You are to generate two datafiles for each location: one for the shortest day of the year and one for the longest day of the year for each location. You are also to generate plots of the sunrise and sunset times as a function of the day of year for each location. 1. (33 points) Write a MATLAB tool to calculate sunrise and sunset times. The tool should do each of the following: (a) Generate plots of sunrise and sunset times as a function of day of the year based on the specified altitude, latitude, and longitude. Use your tool to generate plots for the locations and altitude specified above. (b) Generate one file of sunrise and sunset times for each day of the year for each of the locations. Each file should have the following columns: day of year, sunrise time, sunset time. Format the file as a tab separated file, and include a header that displays the location, altitude, latitude, and longitude corresponding to the data in the file.
ENGR 160—Engineering Software Tools II (MATLAB) Sunrise/Sunset Times Calculator Project Radiosondes are to be launched at Cape Canaveral Airforce Station; Pacific Spaceport Complex; and the Guiana Space Centre to make solar radiation measurements in the ozone layer at an altitude of 25 km. The measurements are to be made every hour from sunrise to sunset for the longest and shortest days of the year at each location. The detectors must therefore always be oriented towards the sun. You are to generate two datafiles for each location: one for the shortest day of the year and one for the longest day of the year for each location. You are also to generate plots of the sunrise and sunset times as a function of the day of year for each location. 1. (33 points) Write a MATLAB tool to calculate sunrise and sunset times. The tool should do each of the following: (a) Generate plots of sunrise and sunset times as a function of day of the year based on the specified altitude, latitude, and longitude. Use your tool to generate plots for the locations and altitude specified above. (b) Generate one file of sunrise and sunset times for each day of the year for each of the locations. Each file should have the following columns: day of year, sunrise time, sunset time. Format the file as a tab separated file, and include a header that displays the location, altitude, latitude, and longitude corresponding to the data in the file. 2. (33 points) Write a MATLAB tool to calculate solar elevation angles. The tool should do each of the following: (a) Generate a plot of solar elevation as a function of time of day from sunrise to sunset based on date and location. Use your tool to plot solar elevation as a function of time from sunrise to sunset for the longest and shortest days of the year for each of the locations specified. (b) Generate a data file of the solar elevation angles at the time of sunrise, sunset, and every hour in between. Each file should contain the following columns: time, elevation angle. Format the file as a tab separated file, and include a header that displays the location, date, altitude, latitude, and longitude corresponding to the data in the file. Use your tool to generate files for the shortest and longest days of the year for each location. 3. (34 points) Put it all together. (a) Publish a script that generates plots and files for each of the locations specified for an altitude of 25km. Save your plots and write a summary of your results in 750 words or less. Olyver Fierro NASA T M X-1646 ON THE COMPUTATION OF SOLAR ELEVATION ANGLES AND THE DETERMINATION OF SUNRISE AND SUNSET TIMES By Harold M. Woolf National Meteorological Center , ESSA Hil lcrest Heights, Md. NATIONAL AERONAUTICS AND SPACE ADMINISTRATION ~~ ~~~~~ For sale by the Clearinghouse for Federal Scientific and Technical Information Springfield, Virginia 22151 - CFSTI price $3.00 ON THE COMPUTATIOM OF SOLAR ELEXATION ANGLE3 AND THE DETERMINATION OF SUNRISE AhTD SUNSET T M S by Harold M. Woolf National Meteorological Center, ESSA Hillcrest Heights, Maryland The complete procedure for precise computation of solar elevation angle as a function of latitude, longitude, date, and time is given. Construction of a graphical a id for determining times of sunrise and sunset, w i t h a precision of one minute, as functions of latitude, longitude, date, and alt i tude is described. This Sunrise-Sunset Finder is contained i n the Appendix. iii coNTms CALCULATION OF SOLAR ELEVATION ANGLE.......................... 3 REF~CES...........o.~.e......~.........~...~.......~...~~~. 7 APPENDIX (%mise-Sunset Finder). . . . .. . . . . . . . . . . . . . . .. o . . . *. . . 8 Instructions.. . . . . . . . *. . . *. ... .. . . . . ,. . ..... . . . . , . . . . .. e . . . 8 Hour angle vs. height charts Latitudes 0' - 10' - 20' 30" 40 " 45 O 50" 55" 60" 55 " 9 10 11 12 13 14 15 18 V ON THE COMPUTATION OF SOLAR ELEVATION ANGUS AND THE DETEBMINATION OF SUNRIXF: AND SUNSET TIMES Harold M. Woolf Environmental Science Services Administration Weather Bureau National Meteorological Center INTRODUCTION Upper-atmosphere research workers often require solar elevation (or zenith) angles as input for various problems. Examples include the determination of solar-radiation corrections* fo r stratospheric radiosonde data an& the calcu- la t ion of photo-dissociation and ioniza-kton ra tes i n the mesosphere and ther- mosphere 123. Solar elevation a s a function of declination, local time, and la t i tude is presented i n convenient graphical form i n the Smithsonian Meteor- ological Tables 131. However, for many purposes the charts do not permit solar elevation t o be determined w i t h sufficient precision. In addition, many of the calculations i n which these angles are employed are performed by electronic computer. Thus it seems worthwhile t o summarize the steps required for precise determination of solar elevation. f o r computer operation; one such program has been i n daily use sinee the beginning of 1964 141. The procedure is quite readily programmed On the other hand, there are applications of earth-sun relationships i n which direct calculation i s not the optimum approach. For example, it is often necessary i n connection w i t h the planning of such experiments as chemical trail releases from rockets, t o know the t i m e of sunrise and/or sunset at a particular location and altitude. surface are readily available 151, adjustment for a l t i tude en ta i l s tedious exercises i n earth-sun geometry and computations w i t h trigonometric functions a8 i n the case of solar elevation. However, w i t h proper manipulation of the relevant astronomical parameters and formulas, it is possible t o perform the nThese corrections are based on the average differences between daytime and nighttime observations, which have been found 111 t o depend strongly on the solar elevation angle of the daylight sounding. They are needed t o achieve compatibility of data, obtained a t various local times and with many different instruments, fo r purposes of synoptic analysis 141. While tables of sunrise/sunset times at the earth 's d a3 h m k z P a P tedious calculations once and for all, and construct tables or graphs t o expedite and simplif'y the determination of sunrise/sunset times for any al t i tude and location. CALCULATION OF SOLAR ELEVATION ANGLF: I The solar elevation angle & is determined by the relation s in c4 = s in 4 sin D + cos 4 cos D cos h (1.1) .@ where # i s the latitude, D the solar declination, and h the solar hour angle. A t first glance, declination (Fig. 1) is a simple sinusoidal function of date, w i t h m a x i m u m and minimum at the summer and winter solstices, respectively, and nodes a t the equinoxes. Careful inspection of the curve, however, reveals a s l igh t asymmetry, due t o the e l l i p t i c i ty of the earth 's orbit, which is accounted for i n the following procedure for computing declination*: s i n I) = (s in 23'26'37.8'') s in cr (1.2) where cr(deg) =l+ 0.4087sin$ + 1.8'@+cos~ - 0.0182sin 21 + 0.0083~0s 2,t? (1.3a) (1 .3) 1 (deg) = 279.9348 + d, and d i s the angular fraction of a year represented by a particular date, given by [(number of day i n year)-l]x360 deg. For example, on 1 January, d=O 365 * 24.2 and on 21 March, d = Tg(0.98565) = 77.86635" = 77"52'. It i s convenient t o combine equations (1.3a) and (1.3) t o yield (r= 279.9348 + d + l.glk827sin d .. 0.079525~0~ d + o.olgg38sin 2d - 0.001620~0s 2d (1.4) The solar hour angle h, a measure of the longitudinal distance t o the sun from the point for which the calculation is being made, is given by h(deg) = 15(T-M)-L (1.5) %Equations (l.2) and (1.3) and the definition of d used here were obtained from the Nautical Almanac Office, U.S. Naval Observatory, Washington, D.C. Year- to-year variations i n the relationships involving Q, 4 , and d are negligible for atmospheric applications. where T(hr) is the time (GMT) of the calculation; M(hr) i s the time of meridian passage, or true solar noon; and L(deg) i s longitude, counted positive west of Greenwich. M, which is sham along with D i n Fig. 1, i s given by M(hr) = 12 + 0.l23570sin d - 0.004289~0s d + 0.153809sin 2d + 0.050783~0s 2d (1.6)