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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.

ENTER SUN (SOLAR) ELEVATION (from .MTL FILE or other source) THEN PRESS ENTER FOR COSINE OF SOLAR ZENITH (values correspond to table below).


 

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