Solar Constant
- The rate at which the solar energy arrives at the top of the atmosphere is called the solar constant Isc.
- This is the amount of energy received in unit time on a unit area perpendicular to the sun’s direction at the mean distance of the earth from the sun.
- The mean distance between the earth and sun is 1.50 * 108km
Solar Radiation reaching earth
- The distance between the earth and the sun varies a little through the year.
- Because of this variation, the extra-terrestrial(outside the earth’s atmosphere) flux also varies.
- The earth is closest to the sun in summer and farthest away in the winter.
- This variation in distance produces a nearly sinusoidal variationin the intensity of solar radiation I that reaches the earth is given by the equation \(\frac{I}{I~sc~}=1+0.033cos(\frac{360(n-2)}{365})\)
#Assigning day number to dates
days<-seq( as.Date("2020-03-22"), as.Date("2021-03-22"), by="+1 day")
ndays<-length(seq( as.Date("2020-03-22"), as.Date("2021-03-22"), by="+1 day"))
ndays
## [1] 366
#Assigning the standard value of solar constant 1353w/sq.m to Isc
Isc<-1353
#ndays<-1:365 # No.of the day ; Total no.of days 1 through 365
#Intensity of the solar radiation I that reaches the earth is given by eqn:
#I = Isc*(1+0.033*cos((360*(n-2)/365)))
#multiplied by pi/180 to convert to degrees
I<-0
for (i in 1:366){
I[i]<-Isc*(1+0.033*cos((360*(i-2)/365)*(pi/180)))
}
#plot between the days and insolation reaching earth
plot(days,I,type="l",las=1,xlab="No.of the day",ylab="Insolation on Earth(w/m2")
#Displaying minimum and maximum values of I
min(I)
## [1] 1308.353
max(I)
## [1] 1397.649
#Displaying all values of solar radiation intensity for 365 days
I
## [1] 1397.642 1397.649 1397.642 1397.623 1397.589 1397.543 1397.484 1397.411
## [9] 1397.325 1397.226 1397.114 1396.989 1396.851 1396.700 1396.536 1396.359
## [17] 1396.169 1395.966 1395.751 1395.523 1395.282 1395.029 1394.763 1394.485
## [25] 1394.195 1393.892 1393.578 1393.251 1392.913 1392.562 1392.200 1391.826
## [33] 1391.441 1391.044 1390.636 1390.217 1389.787 1389.346 1388.895 1388.432
## [41] 1387.959 1387.476 1386.983 1386.479 1385.966 1385.442 1384.909 1384.367
## [49] 1383.816 1383.255 1382.685 1382.107 1381.520 1380.924 1380.320 1379.708
## [57] 1379.088 1378.461 1377.826 1377.183 1376.533 1375.877 1375.213 1374.543
## [65] 1373.867 1373.185 1372.496 1371.802 1371.102 1370.397 1369.686 1368.971
## [73] 1368.251 1367.526 1366.797 1366.064 1365.327 1364.587 1363.843 1363.096
## [81] 1362.346 1361.593 1360.837 1360.080 1359.320 1358.558 1357.794 1357.030
## [89] 1356.264 1355.497 1354.729 1353.961 1353.192 1352.424 1351.655 1350.887
## [97] 1350.120 1349.353 1348.588 1347.824 1347.061 1346.300 1345.541 1344.785
## [105] 1344.030 1343.279 1342.530 1341.785 1341.042 1340.304 1339.569 1338.838
## [113] 1338.111 1337.389 1336.671 1335.958 1335.250 1334.548 1333.850 1333.159
## [121] 1332.473 1331.794 1331.121 1330.454 1329.794 1329.141 1328.495 1327.856
## [129] 1327.225 1326.601 1325.985 1325.377 1324.777 1324.186 1323.603 1323.029
## [137] 1322.464 1321.907 1321.361 1320.823 1320.295 1319.777 1319.268 1318.769
## [145] 1318.281 1317.803 1317.335 1316.878 1316.432 1315.996 1315.572 1315.158
## [153] 1314.756 1314.365 1313.985 1313.617 1313.261 1312.917 1312.584 1312.263
## [161] 1311.955 1311.658 1311.374 1311.102 1310.843 1310.596 1310.362 1310.140
## [169] 1309.931 1309.735 1309.551 1309.381 1309.223 1309.078 1308.947 1308.828
## [177] 1308.723 1308.630 1308.551 1308.485 1308.432 1308.392 1308.366 1308.353
## [185] 1308.353 1308.366 1308.392 1308.432 1308.485 1308.551 1308.630 1308.723
## [193] 1308.828 1308.947 1309.078 1309.223 1309.381 1309.551 1309.735 1309.931
## [201] 1310.140 1310.362 1310.596 1310.843 1311.102 1311.374 1311.658 1311.955
## [209] 1312.263 1312.584 1312.917 1313.261 1313.617 1313.985 1314.365 1314.756
## [217] 1315.158 1315.572 1315.996 1316.432 1316.878 1317.335 1317.803 1318.281
## [225] 1318.769 1319.268 1319.777 1320.295 1320.823 1321.361 1321.907 1322.464
## [233] 1323.029 1323.603 1324.186 1324.777 1325.377 1325.985 1326.601 1327.225
## [241] 1327.856 1328.495 1329.141 1329.794 1330.454 1331.121 1331.794 1332.473
## [249] 1333.159 1333.850 1334.548 1335.250 1335.958 1336.671 1337.389 1338.111
## [257] 1338.838 1339.569 1340.304 1341.042 1341.785 1342.530 1343.279 1344.030
## [265] 1344.785 1345.541 1346.300 1347.061 1347.824 1348.588 1349.353 1350.120
## [273] 1350.887 1351.655 1352.424 1353.192 1353.961 1354.729 1355.497 1356.264
## [281] 1357.030 1357.794 1358.558 1359.320 1360.080 1360.837 1361.593 1362.346
## [289] 1363.096 1363.843 1364.587 1365.327 1366.064 1366.797 1367.526 1368.251
## [297] 1368.971 1369.686 1370.397 1371.102 1371.802 1372.496 1373.185 1373.867
## [305] 1374.543 1375.213 1375.877 1376.533 1377.183 1377.826 1378.461 1379.088
## [313] 1379.708 1380.320 1380.924 1381.520 1382.107 1382.685 1383.255 1383.816
## [321] 1384.367 1384.909 1385.442 1385.966 1386.479 1386.983 1387.476 1387.959
## [329] 1388.432 1388.895 1389.346 1389.787 1390.217 1390.636 1391.044 1391.441
## [337] 1391.826 1392.200 1392.562 1392.913 1393.251 1393.578 1393.892 1394.195
## [345] 1394.485 1394.763 1395.029 1395.282 1395.523 1395.751 1395.966 1396.169
## [353] 1396.359 1396.536 1396.700 1396.851 1396.989 1397.114 1397.226 1397.325
## [361] 1397.411 1397.484 1397.543 1397.589 1397.623 1397.642
#Displaying values of I reaching earth on 20th, 40th, 165th and 360th days
I[c(71,173,265,356)]
## [1] 1369.686 1309.223 1344.785 1396.851