Spatial and Temporal Variability of Solar Radiation Arriving at the Top of the Atmosphere


Based on the previously calculated insolation of the Earth, we determine the variations in solar radiation arriving at the top of the atmosphere, which are mainly connected with changes in the inclination of Earth’s rotation axis due to precession and nutation. The amplitudes of semiannual and hemispheric variations in solar radiation arriving at the top of the atmosphere were calculated. The results can be used in precise calculations of the radiative balance of Earth and its surface and atmosphere.

This is a preview of subscription content, log in to check access.

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.


  1. 1

    Bakulin, P.I., Kononovich, E.V., and Moroz, V.I., Kurs obshchei astronomii (A Course of General Astronomy), Moscow: Nauka, 1983.

  2. 2

    Budyko, M.I., Izmenenie klimata (Measurement of Climate), Leningrad: Gidrometeoizdat, 1974.

  3. 3

    Drozdov, O.A., Vasil’ev, N.V., Raevskii, A.N., et al., Klimatologiya (Climatology), Leningrad: Gidrometeoizdat, 1989.

    Google Scholar 

  4. 4

    Milankovich, M., Matematicheskaya klimatologiya i astronomicheskaya teoriya kolebanii klimata (Mathematical Climatology and Astronomical Theory of Climate Fluctuations), Moscow–Leningrad: GONTI, 1939.

  5. 5

    Monin, A.S., Vvedenie v teoriyu klimata (Introduction to the Climate Theory), Leningrad: Gidrometeoizdat, 1982.

  6. 6

    Monin, A.S. and Shishkov, Yu.A., Istoriya klimata (History of Climate), Leningrad: Gidrometeoizdat, 1979.

  7. 7

    Fedorov, V.M., Insolyatsiya Zemli i sovremennye izmeneniya klimata (The Earth’s Insolation and Current Climate Changes), Moscow: Fizmatlit, 2018.

  8. 8

    Khromov, S.P. and Petrosyants, M.A., Meteorologiya i klimatologiya (Meteorology and Climatology), Moscow: MGU, 2006.

  9. 9

    Fedorov, V.M., Interannual variability of the solar constant, Sol. Syst. Res., 2012, vol. 46, no. 2, pp. 170–176.

    ADS  Article  Google Scholar 

  10. 10

    Fedorov, V.M., Interannual variations in the duration of the tropical year, Dokl. Earth Sci., 2013, vol. 451, no. 1, pp. 750–753.

    ADS  Article  Google Scholar 

  11. 11

    Fedorov, V.M., Latitudinal variability of incoming solar radiation in various time cycles, Dokl. Earth Sci., 2015, vol. 460, no. 1, pp. 96–99.

    ADS  Article  Google Scholar 

  12. 12

    Fedorov, V.M., Periodic perturbations and small variations of the solar climate of the earth, Dokl. Earth Sci., 2014, vol. 457, no. 1, pp. 869–872.

    ADS  Article  Google Scholar 

  13. 13

    Fedorov, V.M., Spatial and temporal variation in solar climate of the earth in the present epoch, Izv., Atmos. Ocean. Phys., 2015, vol. 51, no. 8, pp. 779–791.

    Article  Google Scholar 

  14. 14

    Fedorov, V.M., Theoretical calculation of the interannual variability of the Earth’s insolation with daily resolution, Sol. Syst. Res., 2016, vol. 50, no. 3, pp. 220–224.

    ADS  Article  Google Scholar 

  15. 15

    Giorgini, J.D., Yeomans, D.K., Chamberlin, A.B., et al., JPL’s on-line solar system data service, Bull. Am. Astron. Soc., 1996, vol. 28, no. 3, p. 1158.

    ADS  Google Scholar 

  16. 16

    Hansen, J., Sato, M., Kharecha, P., and von Schuckmann, K., Earth’s energy imbalance and implications, Atmos. Chem. Phys., 2011, vol. 11, no. 24, pp. 13421–13449.

    ADS  Article  Google Scholar 

  17. 17

  18. 18

  19. 19

  20. 20

  21. 21

    Kopp, G. and Lean, J., A new lower value of total solar irradiance: Evidence and climate significance, Geophys. Res. Lett., 2011, vol. 37, L01706.

    ADS  Google Scholar 

  22. 22

    Loeb, N.G., Lyman, J.M., Johnson, G.C., et al., Observed changes in top-of-the-atmosphere radiation and upper-ocean heating consistent within uncertainty, Nature Geosci., 2012, no. 5, pp. 110–113.

  23. 23

    Raschke, E. and Ohmura, A., Radiation budget of the climate system, in Observed Global Climate, Landolt-Börnstein Group V Geophysics (Numerical Data and Functional Relationships in Science and Technology), Hantel, M., Ed., Berlin: Springer, 2005, vol. 6.

    Google Scholar 

  24. 24

    Stephens, G.L., Li, J., Wild, M., et al., An update on Earth’s energy balance in light of the latest global observations, Nature Geosci., 2012, vol. 5, pp. 691–696.

    ADS  Article  Google Scholar 

  25. 25

    Trenberth, K.E. and Fasullo, J.T., Changes in the flow of energy through the Earth’s climate system, Meteorol. Z., 2009, vol. 18, no. 4, pp. 369–377.

    Article  Google Scholar 

  26. 26

    Trenberth, K.E. and Fasullo, J.T., Tracking Earth’s energy: From El Niño to global warming, Surv. Geophys., 2012, vol. 33, nos. 3–4, pp. 413–426.

    ADS  Article  Google Scholar 

  27. 27

    Trenberth, K.E., Fasullo, J.T., and Kiehl, J., Earth’s global energy budget, Bull. Am. Meteorol. Soc., 2009, vol. 90, no. 3, pp. 311–323.

    ADS  Article  Google Scholar 

Download references

Author information



Corresponding author

Correspondence to D. M. Frolov.

Additional information

Translated by E. Petrova

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Fedorov, V.M., Frolov, D.M. Spatial and Temporal Variability of Solar Radiation Arriving at the Top of the Atmosphere. Cosmic Res 57, 156–162 (2019).

Download citation