# Howell Jul07 - Solar insolation calculations using a QNial programming language adaptation of: # J. Laskar, P. Robutel, F. Joutel, M. Gastineau, A.C.M. Correia, B. Levrard 2004 # "A long term numerical solution for the insolation quantities of the Earth" # Astronomy & Astrophysics manuscript no. La-2004 May 23, 2004 # http://www.imcce.fr/fr/presentation/equipes/ASD/preprints/prep.2004/La_2004_prep.pdf # Solar constant assumed : 1368 # Latitude of calculations : 69 # Solar insolation average for each month (W/m2, roughly the 21st to 20th of first/second month): # ky BP 1 Dec-Jan 2 Jan-Feb 3 Feb-Mar 4 Mar-Apr 5 Apr-May 6 May-Jun 7 Jun-Jul 8 Jul-Aug 9 Aug-Sep 10 Sep-Oct 11 Oct-Nov 12 Nov-Dec a := -6012 0.1905364 19.8707420 94.6396809 228.1635927 397.3747414 534.5838697 520.9193488 367.3951587 192.1070855 64.7742405 7.1543194 0.0000000 -6011 0.3065400 21.0155881 93.7440829 219.9619263 380.5226338 519.3170422 523.4414911 381.5438161 203.9405555 69.3462721 7.7173882 0.0000000 -6010 0.4109262 22.0244234 93.2779405 212.9917429 364.0869282 500.5666049 520.7107720 394.7428368 218.8740124 76.9485746 9.1727153 0.0000000 -6009 0.4876596 22.8453472 93.3045899 207.7931937 349.7492758 480.9362514 512.9370082 404.6238625 234.8709711 87.0820392 11.6081050 0.0000000 -6008 0.5189057 23.4072130 93.8259982 204.6634022 338.5654365 462.5724920 501.3378011 409.6341067 249.7237424 98.9675772 15.2118095 -0.0001073 -6007 0.4909430 23.6435299 94.7739333 203.6676552 331.0507147 447.0814235 487.6927259 409.4012106 261.4169514 111.3602413 20.0089328 0.0407509 -6006 0.4245877 23.5281864 95.9960258 204.6825528 327.4639308 435.7539832 474.2223355 404.7016690 268.3176005 122.2876978 25.4838416 0.2030557 -6005 0.3339852 23.0619689 97.3640670 207.5256319 327.6525684 428.8551192 462.2154483 396.8241474 270.1947041 130.4141474 30.9858200 0.5526454 -6004 0.2409173 22.3232089 98.7364356 211.9095100 331.3564271 426.4644589 452.6217510 387.1671578 267.4418224 134.6902564 35.5708382 1.0901428 -6003 0.1667094 21.4519288 99.9999931 217.4252185 338.0618055 428.2150287 445.7888054 376.9318109 261.0695363 134.9185364 38.4491317 1.6233917 -6002 0.1222464 20.5892858 101.0998544 223.7011038 347.2725511 433.6127013 441.6354525 366.7764295 252.0716421 131.5112183 39.2505005 2.0278093 -6001 0.1002970 19.8759551 101.9968865 230.1429338 358.0425086 441.7190266 439.7624621 357.2859531 241.6721809 125.4818673 38.1363893 2.1684482 -6000 0.0920145 19.4078991 102.6538735 236.2179199 369.6594508 452.0565860 440.0906768 348.7672318 230.5272439 117.5180724 35.3689266 2.0126357 -5999 0.0953045 19.2054894 103.0446882 241.3288188 380.9992665 463.5638898 442.2260189 341.5693364 219.5941053 108.7672576 31.6536788 1.6533159 -5998 0.1084193 19.2565916 103.1233662 244.9519692 391.0598195 475.4604335 446.0739771 336.0691679 209.5306703 99.9852627 27.5300207 1.1997492 -5997 0.1376119 19.5181589 102.8437044 246.6716250 398.8725323 486.9829174 451.6578689 332.7211436 200.9460444 91.7856649 23.4394039 0.7709250 -5996 0.1827722 19.9134631 102.2023172 246.3264340 403.6165199 497.1828559 458.8244841 331.9477628 194.4726355 84.7612824 19.7661234 0.4201677 -5995 0.2366956 20.3695164 101.2326627 243.9810644 404.7678236 505.1528165 467.3252442 334.1253939 190.6446129 79.3172144 16.7174483 0.1992183 -5994 0.2920119 20.8253233 100.0134485 239.9940153 402.3960228 510.3205715 476.7491810 339.3183507 189.6800418 75.5857456 14.3312462 0.0791529 -5993 0.3379530 21.2130964 98.6864564 234.9524913 396.9060205 512.0005006 486.1416663 347.3041375 191.8760536 73.8545256 12.6847773 0.0175871 -5992 0.3662844 21.4961425 97.3936555 229.5033712 389.1792607 510.1335093 494.5039507 357.4314137 197.1365649 74.1712196 11.7445815 -0.0004098 -5991 0.3715023 21.6508759 96.2636486 224.3046945 380.4512632 505.3517680 500.9268375 368.5640122 204.8952604 76.3842064 11.4406356 -0.0000140 -5990 0.3486212 21.6501220 95.4041982 219.8695229 371.7422783 498.3307154 504.6576880 379.4947987 214.5971249 80.4931718 11.7966527 0.0000000 -5989 0.2995820 21.4797733 94.8595033 216.6013344 364.2007862 490.5229641 505.6704004 388.8561233 224.9518811 85.9882893 12.7312321 0.0000000 -5988 0.2319851 21.1427538 94.6106022 214.5812842 358.3297710 482.9525532 504.3709733 395.9511009 234.9386543 92.3761381 14.1846117 0.0000000 -5987 0.1593686 20.6251506 94.6359017 213.9603923 354.7120536 476.6972548 501.4501555 400.1564136 243.3403630 98.9330788 16.0605189 -0.0001715 -5986 0.1096054 19.9690627 94.8466720 214.5054764 353.2127449 472.1951157 497.7709276 401.7967243 249.6029408 104.9765023 18.1662097 -0.0007662 -5985 0.0560295 19.2082974 95.1774778 216.1302163 353.9341650 469.9680290 494.1097571 401.0974058 253.1428533 109.7112172 20.2124602 0.0071941 -5984 0.0095914 18.4111047 95.5626729 218.5282837 356.4227007 469.7628948 490.8841843 398.7225748 254.2189731 112.8778161 21.9829701 0.0430031 -5983 -0.0008042 17.6384313 95.9595928 221.4931670 360.4209563 471.4720211 488.3782445 395.1036266 253.0178659 114.2522473 23.2480621 0.0856123 -5982 -0.0002459 16.9722661 96.3211789 224.6545973 365.3619081 474.6906831 486.7786833 390.8828109 250.0750527 113.9033455 23.8475401 0.1125406 -5981 -0.0000092 16.4418949 96.6510738 227.8201888 370.8115933 478.8915966 485.8432846 386.3439051 245.9466544 112.2419957 23.8649919 0.1261361 -5980 0.0000000 16.0936106 96.9247710 230.6542369 376.1820999 483.5899509 485.5764115 381.9672954 241.1868117 109.5972191 23.3449397 0.1256722 -5979 0.0000000 15.9348664 97.1413867 232.9716063 381.0566274 488.3283402 485.8193560 377.9763250 236.2290510 106.3617420 22.4403005 0.1141744 -5978 0.0000000 15.9522977 97.3077636 234.6408416 385.0154918 492.5524895 486.3089362 374.5591845 231.5558325 103.0247604 21.3784116 0.0973082 -5977 -0.0000327 16.1323844 97.4227081 235.5756079 387.7747423 495.9135553 486.9258140 371.8710170 227.4779550 99.8866114 20.3020372 0.0785502 -5976 -0.0002543 16.4545111 97.4888726 235.7749562 389.2167328 498.2086637 487.5936234 369.9709629 224.1681133 97.1358395 19.3097366 0.0596622 -5975 -0.0006525 16.8713726 97.5359448 235.3807295 389.3560157 499.1554352 487.9635595 368.7688663 221.8268981 95.0728109 18.5651168 0.0477935 -5974 0.0002529 17.3606569 97.5700833 234.5090818 388.3838161 498.8866759 488.0179462 368.1672162 220.3582961 93.6433346 18.0524788 0.0426660 -5973 0.0194631 17.8883030 97.6131862 233.3485619 386.5783153 497.5350252 487.6235806 367.9610467 219.6524972 92.8412362 17.7910280 0.0446464 -5972 0.0488623 18.4148190 97.6949880 232.1274303 384.2907981 495.2891079 486.6169129 367.8723396 219.5534283 92.6522418 17.8045540 0.0552317 -5971 0.0795718 18.9297137 97.8120474 230.9580744 381.8556356 492.5790221 485.1715198 367.7340119 219.7463951 92.8202364 17.9932772 0.0705763 -5970 0.1055341 19.4182971 97.9663620 229.9457473 379.5396038 489.7141013 483.3908108 367.3968583 220.0018210 93.1797600 18.2998543 0.0878972 -5969 0.1289363 19.8610126 98.1637435 229.2165818 377.6343247 487.0164755 481.3497974 366.6841024 220.0746623 93.5682161 18.6732460 0.1071858 -5968 0.1609916 20.2784521 98.3649853 228.6438693 376.0786795 484.6855502 479.3982186 365.7882692 219.8981039 93.7962924 18.9982994 0.1255099 -5967 0.2001583 20.6668098 98.5596935 228.2551609 375.0106233 482.9680428 477.6920851 364.6770117 219.3140927 93.7093922 19.2053592 0.1480683 -5966 0.2432221 21.0398460 98.7202793 227.8782171 374.1259184 481.6455438 476.3377713 363.6540870 218.5890527 93.4218177 19.3014574 0.1694235 -5965 0.2899266 21.4079290 98.8220681 227.4336047 373.3682508 480.7951555 475.5226315 362.8449021 217.7145810 92.8504041 19.2285937 0.1829595 -5964 0.3408829 21.7878830 98.8351391 226.7045374 372.3136330 480.0485343 475.3075147 362.6267416 217.0784185 92.2015501 19.0299378 0.1871859 -5963 0.3921909 22.1565095 98.7794790 225.7438678 370.9177007 479.1866121 475.4761245 362.9817100 216.8564180 91.6828532 18.8046034 0.1860203 -5962 0.4525730 22.5332789 98.6251885 224.3440539 368.7815906 477.8665476 476.0919445 364.2816194 217.4091931 91.4653929 18.5798383 0.1790925 -5961 0.5122885 22.8834414 98.4145826 222.6550823 365.9839414 475.8790992 476.7910634 366.3751220 218.8781991 91.7848277 18.4782827 0.1724538 -5960 0.5624286 23.1900848 98.1747230 220.7379528 362.4935980 472.9869909 477.2962716 369.2228547 221.4624312 92.8667309 18.5962452 0.1700380 -5959 0.5950466 23.4289865 97.9417379 218.7557501 358.5301806 469.2422407 477.3728865 372.5739701 225.1059536 94.7889049 18.9897326 0.1744780 -5958 0.6018071 23.5681889 97.7638693 216.9399991 354.4468282 464.8152176 476.7469634 376.0129739 229.6082047 97.5878421 19.7243839 0.1897896 -5957 0.5749350 23.5674965 97.6918739 215.5629058 350.6961438 460.0201509 475.1972670 379.0161197 234.6157989 101.2309429 20.8666701 0.2217799 -5956 0.5164929 23.4106719 97.7352573 214.7818589 347.6810385 455.3788015 472.8814644 381.2147485 239.5952574 105.4168260 22.3660379 0.2726098 -5955 0.4330482 23.0696914 97.9072838 214.8057868 345.8757414 451.4658996 469.9863029 382.2044297 243.9187759 109.7678399 24.1620046 0.3460117 -5954 0.3423619 22.5244150 98.2064856 215.8032254 345.6919649 448.8241902 466.7680435 381.7148173 246.9827454 113.8219419 26.1415073 0.4442019 -5953 0.2459570 21.8074090 98.5752534 217.7103397 347.2623259 447.9251387 463.8029684 379.9241238 248.3714219 116.9597271 28.0094671 0.5618658 -5952 0.1570269 20.9335013 98.9930555 220.6006002 350.8420067 449.1420262 461.3646773 376.8224734 247.7454297 118.7207920 29.5311696 0.6907959 -5951 0.1016494 19.9703819 99.4084744 224.3192691 356.3468221 452.5978574 459.7901388 372.7303209 245.1101334 118.7733765 30.4178195 0.7944963 -5950 0.0539863 19.0012266 99.7776862 228.6592134 363.6107996 458.3042288 459.3172134 367.9612657 240.5929156 116.9388760 30.4258146 0.8344991 -5949 0.0149468 18.1120647 100.0690901 233.3409299 372.3076818 466.1004962 460.0312885 362.8183567 234.4845305 113.2887489 29.4546135 0.7857916 -5948 -0.0010301 17.3571622 100.2757394 238.1180410 382.0629136 475.6420279 461.7946505 357.4758422 227.1510059 108.1437447 27.6121813 0.6559954 -5947 -0.0006658 16.8294234 100.3371597 242.3864170 392.0254047 486.4472191 464.8510694 352.5194463 219.1428711 101.8209244 24.9804001 0.4720191 -5946 -0.0005346 16.5239698 100.2519907 245.8759472 401.6016554 497.9737811 468.9926999 348.1246429 210.9379185 94.8864108 21.9164208 0.2883241 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0.1685820 19.9282738 92.9400412 219.1300141 379.2068303 519.9915260 529.7554905 390.6019930 211.1302192 71.9416317 7.6103726 0.0000000 -5937 0.1925808 20.4049750 92.2840526 213.2482044 365.8454709 505.7314564 529.8692680 404.2065154 225.2966294 78.6438276 8.5663906 0.0000000 -5936 0.1943610 20.7315865 92.0628911 208.7002414 353.6456267 489.7507196 525.2979324 415.4137423 241.1158275 88.0343257 10.4229206 0.0000000 -5935 0.1716487 20.8560531 92.2888322 205.7974586 343.6276133 473.8848981 516.6515953 422.6672272 256.6917665 99.5815839 13.3649827 0.0000000 -5934 0.1368767 20.6962469 92.9418296 204.8393358 336.7016047 459.9131474 505.2405245 424.8009656 269.8098424 112.2383612 17.4969907 0.0000000 -5933 0.0891148 20.2237268 93.9110773 205.7804739 333.1553983 448.9859158 492.8666405 422.1419537 278.8068404 124.4211276 22.7622460 -0.0010711 -5932 0.0239224 19.4312219 95.0766551 208.5851326 333.2107360 441.9150727 481.0632785 415.4748883 282.6776222 134.3735150 28.5924188 0.1479485 -5931 -0.0008215 18.3784128 96.3197989 213.1201613 336.8439395 438.9995066 470.8556326 405.9509734 281.3637528 140.7082852 34.1119467 0.4215322 -5930 -0.0000057 17.1988452 97.5443879 219.1582926 343.8549408 440.1922382 462.7766313 394.6839114 275.4685544 142.6778291 38.3211320 0.8502036 -5929 0.0000000 16.0832462 98.6887265 226.3188660 353.8141620 445.1745149 456.9860069 382.6245813 265.9660884 140.2526785 40.4021570 1.3310893 -5928 0.0000000 15.1747200 99.7693573 234.3107105 366.3239068 453.3985161 453.0713772 370.1469312 253.7572670 134.0852482 40.1625962 1.6218410 -5927 0.0000000 14.6225253 100.7797343 242.4648083 380.5002035 464.1486938 450.7872791 357.8236272 239.8307095 125.0330050 37.7224363 1.6524582 -5926 0.0000000 14.4730462 101.7199680 250.1480298 395.3654343 476.5883966 449.7485174 345.9593484 225.0711878 114.2284519 33.7258262 1.4374520 -5925 0.0000000 14.7823122 102.5265460 256.5785925 409.7533066 489.9694717 449.9277800 334.9486189 210.2266307 102.5924692 28.8259452 1.0743524 -5924 -0.0001123 15.5451063 103.0839685 260.9227945 422.1827494 503.3309825 451.5096722 325.4191654 196.2124298 91.1325220 23.7564945 0.6777068 -5923 0.0082002 16.7189086 103.2326972 262.3860377 431.1379162 515.9114523 454.9961518 318.2039025 183.8164538 80.5333334 19.0023707 0.3465331 -5922 0.0876421 18.1845118 102.8586291 260.5463166 435.1998520 526.5933823 460.7630524 314.2120527 173.9552213 71.5185897 14.9875289 0.1445637 -5921 0.2262537 19.8277543 101.8879735 255.2260050 433.1885838 534.1886807 469.2656068 314.5319147 167.4625183 64.4987550 11.8455851 0.0508487 -5920 0.4688423 21.5117095 100.3698265 246.7760269 424.4576930 537.0010983 480.2292301 320.2162795 165.3355334 59.9218457 9.6374428 0.0018544 -5919 0.7923412 23.1105751 98.5170586 236.2692443 409.7317559 533.5436893 492.2372524 331.5397198 168.2916345 58.0897552 8.3238485 -0.0000858 -5918 1.1566367 24.5582099 96.6038332 224.8989093 390.4836898 522.7756678 503.0065493 348.1396980 177.0374160 59.3654737 7.8505322 0.0000000 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0.0000000 -2017 0.1335050 20.2527651 94.9514712 215.5348080 356.5725039 476.8930625 499.2184790 397.9224454 243.1558859 100.2035123 16.8402014 -0.0004811 -2016 0.1251596 20.2643172 95.5011432 215.3944252 353.0482673 469.0008106 492.0914702 397.2552820 248.3659883 106.3028127 19.5070517 0.0192533 -2015 0.1106566 20.1245973 96.2008978 216.3987044 351.7006020 463.1660070 484.7925603 394.2983982 251.1825578 111.4176425 22.2869929 0.1027720 -2014 0.0940780 19.8848227 96.9694372 218.3425566 352.4272238 459.7089220 478.1188712 389.6363218 251.4167196 114.8647406 24.7832803 0.1943482 -2013 0.0776909 19.5798994 97.7684963 221.1120873 355.1135848 458.6288322 472.3511213 383.6894913 249.2091246 116.3931033 26.7336497 0.3378294 -2012 0.0660264 19.2949068 98.5292465 224.3729578 359.3700859 459.8059422 467.8825683 377.1246389 244.9304746 115.8431639 27.8218675 0.4724895 -2011 0.0620213 19.0955599 99.2113095 227.7560839 364.5728768 462.6808919 464.7250667 370.5268587 239.3109954 113.6056775 28.0280225 0.5688566 -2010 0.0673836 19.0276993 99.7853774 231.0128073 370.3820115 467.0379404 462.8993568 364.1824092 232.7018137 109.8931563 27.3468552 0.6114681 -2009 0.0811562 19.1251611 100.2147822 233.7079441 375.9536249 472.0803162 462.2747932 358.6266818 225.9450137 105.3968734 26.0362134 0.5898181 -2008 0.1027372 19.3993619 100.4632534 235.5211452 380.6831225 477.3155964 462.8705002 354.2277685 219.5495481 100.5517448 24.2970933 0.5152451 -2007 0.1333716 19.8191881 100.5215441 236.2852069 384.0509115 482.1303060 464.4742344 351.2339519 214.0407403 95.8931757 22.4236013 0.4194763 -2006 0.1892453 20.3514144 100.3790584 235.8662207 385.5735363 485.9378860 466.9669703 349.9483734 209.9127954 91.8541035 20.6361065 0.3290767 -2005 0.2610896 20.9509111 100.0490943 234.2717554 384.9502978 488.1861716 470.0807569 350.5724975 207.5903869 88.8082489 19.1154514 0.2499775 -2004 0.3378502 21.5518941 99.5917252 231.8016972 382.3899903 488.6240779 473.3653106 352.9212087 207.1907469 86.9662737 17.9825184 0.1897357 -2003 0.4124102 22.1037654 99.0734049 228.7636636 378.1833058 487.0808590 476.3429470 356.7512418 208.7949363 86.4990568 17.3163061 0.1504061 -2002 0.4816690 22.5695155 98.5602854 225.4805074 372.7776902 483.6313483 478.5748880 361.6725875 212.3093606 87.4632420 17.1472474 0.1299108 -2001 0.5232396 22.8890935 98.1528192 222.5352145 367.2038177 478.9580148 479.5908774 366.7079624 217.0676317 89.6625977 17.4725729 0.1263722 -2000 0.5291394 23.0463493 97.8833664 220.1432917 361.9595875 473.5720680 479.3381067 371.3499258 222.6213008 92.9190493 18.2643432 0.1379299 -1999 0.4974793 23.0177890 97.7767102 218.5874518 357.7603408 468.3513739 477.9673335 374.9299147 228.1397999 96.7825870 19.4294658 0.1647338 -1998 0.4346046 22.7867469 97.8331052 218.0688870 355.1958900 464.1467569 475.8345825 376.9678183 232.7789738 100.6927137 20.8280688 0.2069053 -1997 0.3616753 22.3738448 98.0044435 218.5370656 354.4274866 461.4955241 473.5173673 377.4960323 236.0258808 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