Cosine of Solar Zenith (θz) Embedded Excel Calculator & Lookup Table for Conversion to Surface Reflectance of Landsat (Simply use sun elevation from Landsat .Mtl file)

CALCULATOR MAY TAKE A FEW MOMENTS TO LOAD - IT IS CLOUD-BASED. IF IT IS DOWN, ENTER SOLAR ZENITH (90 - SOLAR ELEVATION) INTO A CALCULATOR FROM A WEBSITE LISTED BELOW IT.

Landsat surface reflectance (SR) can be ordered for free from the USGS. The calculator below is for converting to SR independently (as explained in tutorials and courses) - please read: Background information about USGS & GIS Ag Maps surface reflectance.

CLICK CELL AND ENTER SUN (SOLAR) ELEVATION FROM .MTL FILE (can paste or manually enter elevation), and cosine of the solar zenith will be calculated. MAY NEED TO PRESS ENTER AFTER INPUTTING SUN ELEVATION

The cosine of the solar zenith can also be calculated at the following website by entering the solar zenith (solar zenith = [90 - solar elevation]): http://www.rapidtables.com/calc/math/Cos_Calculator.htm; https://web2.0calc.com/

Cosine of Solar Zenith Lookup Table

 Sun Elevation Cos θz 0.00 0.00000 0.25 0.00436 0.50 0.00873 0.75 0.01309 1.00 0.01745 1.25 0.02181 1.50 0.02618 1.75 0.03054 2.00 0.03490 2.25 0.03926 2.50 0.04362 2.75 0.04798 3.00 0.05234 3.25 0.05669 3.50 0.06105 3.75 0.06540 4.00 0.06976 4.25 0.07411 4.50 0.07846 4.75 0.08281 5.00 0.08716 5.25 0.09150 5.50 0.09585 5.75 0.10019 6.00 0.10453 6.25 0.10887 6.50 0.11320 6.75 0.11754 7.00 0.12187 7.25 0.12620 7.50 0.13053 7.75 0.13485 8.00 0.13917 8.25 0.14349 8.50 0.14781 8.75 0.15212 9.00 0.15643 9.25 0.16074 9.50 0.16505 9.75 0.16935 10.00 0.17365 10.25 0.17794 10.50 0.18224 10.75 0.18652 11.00 0.19081 11.25 0.19509 11.50 0.19937 11.75 0.20364 12.00 0.20791 12.25 0.21218 12.50 0.21644 12.75 0.22070 13.00 0.22495 13.25 0.22920 13.50 0.23345 13.75 0.23769 14.00 0.24192 14.25 0.24615 14.50 0.25038 14.75 0.25460 15.00 0.25882 15.25 0.26303 15.50 0.26724 15.75 0.27144 16.00 0.27564 16.25 0.27983 16.50 0.28402 16.75 0.28820 17.00 0.29237 17.25 0.29654 17.50 0.30071 17.75 0.30486 18.00 0.30902 18.25 0.31316 18.50 0.31730 18.75 0.32144 19.00 0.32557 19.25 0.32969 19.50 0.33381 19.75 0.33792 20.00 0.34202 20.25 0.34612 20.50 0.35021 20.75 0.35429 21.00 0.35837 21.25 0.36244 21.50 0.36650 21.75 0.37056 22.00 0.37461 22.25 0.37865 22.50 0.38268 22.75 0.38671 23.00 0.39073 23.25 0.39474 23.50 0.39875 23.75 0.40275 24.00 0.40674 24.25 0.41072 24.50 0.41469 24.75 0.41866 25.00 0.42262 25.25 0.42657 25.50 0.43051 25.75 0.43445 26.00 0.43837 26.25 0.44229 26.50 0.44620 26.75 0.45010 27.00 0.45399 27.25 0.45787 27.50 0.46175 27.75 0.46561 28.00 0.46947 28.25 0.47332 28.50 0.47716 28.75 0.48099 29.00 0.48481 29.25 0.48862 29.50 0.49242 29.75 0.49622 30.00 0.50000 30.25 0.50377 30.50 0.50754 30.75 0.51129 31.00 0.51504 31.25 0.51877 31.50 0.52250 31.75 0.52621 32.00 0.52992 32.25 0.53361 32.50 0.53730 32.75 0.54097 33.00 0.54464 33.25 0.54829 33.50 0.55194 33.75 0.55557 34.00 0.55919 34.25 0.56280 34.50 0.56641 34.75 0.57000 35.00 0.57358 35.25 0.57715 35.50 0.58070 35.75 0.58425 36.00 0.58779 36.25 0.59131 36.50 0.59482 36.75 0.59832 37.00 0.60182 37.25 0.60529 37.50 0.60876 37.75 0.61222 38.00 0.61566 38.25 0.61909 38.50 0.62251 38.75 0.62592 39.00 0.62932 39.25 0.63271 39.50 0.63608 39.75 0.63944 40.00 0.64279 40.25 0.64612 40.50 0.64945 40.75 0.65276 41.00 0.65606 41.25 0.65935 41.50 0.66262 41.75 0.66588 42.00 0.66913 42.25 0.67237 42.50 0.67559 42.75 0.67880 43.00 0.68200 43.25 0.68518 43.50 0.68835 43.75 0.69151 44.00 0.69466 44.25 0.69779 44.50 0.70091 44.75 0.70401 45.00 0.70711 45.25 0.71019 45.50 0.71325 45.75 0.71630 46.00 0.71934 46.25 0.72236 46.50 0.72537 46.75 0.72837 47.00 0.73135 47.25 0.73432 47.50 0.73728 47.75 0.74022 48.00 0.74314 48.25 0.74606 48.50 0.74896 48.75 0.75184 49.00 0.75471 49.25 0.75756 49.50 0.76041 49.75 0.76323 50.00 0.76604 50.25 0.76884 50.50 0.77162 50.75 0.77439 51.00 0.77715 51.25 0.77988 51.50 0.78261 51.75 0.78532 52.00 0.78801 52.25 0.79069 52.50 0.79335 52.75 0.79600 53.00 0.79864 53.25 0.80125 53.50 0.80386 53.75 0.80644 54.00 0.80902 54.25 0.81157 54.50 0.81412 54.75 0.81664 55.00 0.81915 55.25 0.82165 55.50 0.82413 55.75 0.82659 56.00 0.82904 56.25 0.83147 56.50 0.83389 56.75 0.83629 57.00 0.83867 57.25 0.84104 57.50 0.84339 57.75 0.84573 58.00 0.84805 58.25 0.85035 58.50 0.85264 58.75 0.85491 59.00 0.85717 59.25 0.85941 59.50 0.86163 59.75 0.86384 60.00 0.86603 60.25 0.86820 60.50 0.87036 60.75 0.87250 61.00 0.87462 61.25 0.87673 61.50 0.87882 61.75 0.88089 62.00 0.88295 62.25 0.88499 62.50 0.88701 62.75 0.88902 63.00 0.89101 63.25 0.89298 63.50 0.89493 63.75 0.89687 64.00 0.89879 64.25 0.90070 64.50 0.90259 64.75 0.90446 65.00 0.90631 65.25 0.90814 65.50 0.90996 65.75 0.91176 66.00 0.91355 66.25 0.91531 66.50 0.91706 66.75 0.91879 67.00 0.92050 67.25 0.92220 67.50 0.92388 67.75 0.92554 68.00 0.92718 68.25 0.92881 68.50 0.93042 68.75 0.93201 69.00 0.93358 69.25 0.93514 69.50 0.93667 69.75 0.93819 70.00 0.93969 70.25 0.94118 70.50 0.94264 70.75 0.94409 71.00 0.94552 71.25 0.94693 71.50 0.94832 71.75 0.94970 72.00 0.95106 72.25 0.95240 72.50 0.95372 72.75 0.95502 73.00 0.95630 73.25 0.95757 73.50 0.95882 73.75 0.96005 74.00 0.96126 74.25 0.96246 74.50 0.96363 74.75 0.96479 75.00 0.96593 75.25 0.96705 75.50 0.96815 75.75 0.96923 76.00 0.97030 76.25 0.97134 76.50 0.97237 76.75 0.97338 77.00 0.97437 77.25 0.97534 77.50 0.97630 77.75 0.97723 78.00 0.97815 78.25 0.97905 78.50 0.97992 78.75 0.98079 79.00 0.98163 79.25 0.98245 79.50 0.98325 79.75 0.98404 80.00 0.98481 80.25 0.98556 80.50 0.98629 80.75 0.98700 81.00 0.98769 81.25 0.98836 81.50 0.98902 81.75 0.98965 82.00 0.99027 82.25 0.99087 82.50 0.99144 82.75 0.99200 83.00 0.99255 83.25 0.99307 83.50 0.99357 83.75 0.99406 84.00 0.99452 84.25 0.99497 84.50 0.99540 84.75 0.99580 85.00 0.99619 85.25 0.99657 85.50 0.99692 85.75 0.99725 86.00 0.99756 86.25 0.99786 86.50 0.99813 86.75 0.99839 87.00 0.99863 87.25 0.99885 87.50 0.99905 87.75 0.99923 88.00 0.99939 88.25 0.99953 88.50 0.99966 88.75 0.99976 89.00 0.99985 89.25 0.99991 89.50 0.99996 89.75 0.99999 90.00 1.00000