GLOBAL DISTRIBUTION OF NET RADIATION ACCORDING TO A NEW FORMULA

ABSTRACT

A new formula for estimating net radiation has been derived from records of solar radiation, humidity, and air temperature. The formula is believed to be an improvement over the previous ones which used cloudiness instead of solar radiation. The correlation coefficient between the computed and actual values is 0.97 and the standard error of estimate is 2.57 langleys/day. The limitations of the formula, such as the use of standard values of reflection coefficients, the use of surface humidity instead of total precipitable water, and the exclusion of carbon dioxide, are discussed. The formula has been applied to 386 stations for the construction of world maps for four mid-season months as well as for the year. The distributional pattern differs somewhat from the world maps prepared by Budyko. Solar radiation retained as net radiation decreases from sixty percent in the tropics to less than twenty percent in high latitudes.

Notes

1 This study has been supported by U. S. Environmental Science Services Administration, Grant No. E-44–67 (G), and is Contribution No. 16, Water Resources Research Center, University of Hawaii.

2 J. H. Chang, “On the Study of Evapotranspiration and Water Balance,”Erdkunde, Vol. 19 (1965), pp. 141 50.

3 H. G. Houghton, “On the Annual Heat Balance of the Northern Hemisphere,”Journal of Meteorology, Vol. 11 (1954), pp. 1 9; S. I. Rasool and C. Prabhakara, “Heat Budget of the Southern Hemisphere,” in R. V. Garcia and T. F. Malone (Eds.) Problems of Atmospheric Circulation (London: McMillan Co., 1966), pp. 76–92.

4 H. E. Penman, “Natural Evaporation from Open Water, Bare Soil, and Grass,”Proceedings, Royal Society, Series A, Vol. 193 (1948), pp. 120 45; M. I. Budyko, Teplovoi Balans Zemnoi Poverkhnosti (Leningrad: Gidrometeorologicheskoe Izdatel'stvo, 1956), 255 pp. Budyko's formula was later revised for the preparation of maps in the Atlas Teplovogo Balansa (Leningrad: Gidrometeorologicheskoe Izadatel'skoe, 1963).

5 For example the correlation between solar radiation and duration of sunshine for 384 monthly values collected by Black et al, was only fair; see:J. N. Black, C. W. Bonython, and J. A. Prescott, “Solar Radiation and the Duration of Sunshine,”Quarterly Journal, Royal Meteorological Society, Vol. 80 (1954), pp. 231 35.

6 R. Fleischer, “Der Jahresgang der Strahlungsbilanz und Ihrer Komponenten,”Annalen der Meteorologie, Vol. 6 (1953/1954), pp. 357 64; R. H. Shaw, “A Comparison of Solar Radiation and Net Radiation,”Bulletin, American Meteorological Society, Vol. 37 (1958), pp. 205 06; D. W. Scholte-Ubing, “Studies on Solar Radiation and Net Radiation and on Evapo-transpiration from Grass,”Mededelingen van de Landbouwhogeschool, Wageningen, No. 59 (1959), pp. 1–93; J. H. Chang, “Microclimate of Sugarcane,”Hawaiian Planters' Record, Vol. 56 (1961), pp. 195 223; Y. Nakagawa, “Studies on the Microclimate in the Cultivated Land and on the Plant Temperature,”Bulletin, National Institute of Agricultural Science (Japan), Series A, Vol. 10 (1963), pp. 127 65; P. C. Ekern, “The Fraction of Sunlight Retained as Net Radiation in Hawaii,”Journal of Geophysical Research, Vol. 70 (1965), pp. 785 93; J. A. Davies, “A Note on the Relationship Between Net Radiation and Solar Radiation,”Quarterly Journal, Royal Meteorological Society, Vol. 93 (1967), pp. 109 15.

7 Davies, op. cit., footnote 6.

8 S. E. Jensen and H. C. Aslyng, “Net Radiation and Net Long-wave Radiation at Copenhagen, 1962–1964,”Archiv für Meteorologie, Geophysik und Bioklimatologie, Series B, Vol. 15 (1967), pp. 127 40; J. P. Funk, “Radiation Observations at Aspendale, Australia, and Their Comparison with Other Data,”Archiv für Meteorologie, Geophysik und Bioklimatologie, Series B, Vol. 13 (1963), pp. 52 70; for Florida, G. M. Prine and K. D. Butson, “Daily Total Solar Radiation and Net Radiation,” Unpublished manuscript (1958), 4 pp.; for North Carolina, U. S. Weather Bureau Climatological Summary, 1955–1959.

9 Reflection coefficients measured by airplane differ slightly from surface measurement. No firm albedo-height relationship has been established for the range from the surface to high flying altitudes; for the data on grasses in the tropics, see Chang, op. cit., footnote 6; L. S. Chia, “Albedoes of Natural Surfaces in Barbados,”Quarterly Journal, Royal Meteorological Society, Vol. 93 (1967), pp. 116 20; E. A. Fitzpatrick and W. R. Stern“Estimates of Potential Evaporation Using Alternative Data in Penman's Formula,”Agricultural Meteorology, Vol. 3 (1966), pp. 225 39. For data on the decrease at higher latitudes, see G. D. Thompson and J. P. Boyce, “Daily Measurements of Potential Evapotranspiration from Fully Canopied Sugarcane,”Agricultural Meteorology, Vol. 4 (1967), pp. 267 79; J. L. Monteith, “The Reflection of Shortwave Radiation by Vegetation,”Quarterly Journal, Royal Meteorological Society, Vol. 85 (1959), pp. 386 92; the data collected by L. Fritschen at Tempe, Arizona, cited by Davies, op. cit., footnote 6; R. G. Barry, “Albedo variations in Southern Hampshire and Dorset,”Weather, Vol. 21 (1966), pp. 60 65; H. C. Aslyng, “Evaporation, Evapotranspiration and Water Balance Investigations at Copenhagen 1955–64,”Acta Agriculturae Scandinavica, Vol. 15 (1965), pp. 284 300.

10 R. J. List, “Smithsonian Meteorological Tables, Smithsonian Miscellaneous Collections, Vol. 114 (1966), pp. 417 19; F. S. Johnson, “The Solar Constant,”Journal of Meteorology, Vol. 11 (1954), pp. 431 39. One langley is defined as one gram-calorie per square centimeter.

11 W. M. Elsasser and M. F. Culbertson, “Atmospheric Radiation Tables,”Meteorological Monographs, Vol. 4, No. 23 (1960).

12 W. D. Sellers, Physical Climatology (Chicago: University of Chicago Press, 1965), pp. 54–56.

13 Davies, op. cit., footnote 6.

14 G. O. G. Löf, J. A. Duffie, and C. O. Smith, “World Distribution of Solar Radiation,”University of Wisconsin Engineering Experiment Station Report No. 21 (Madison: University of Wisconsin, 1966); M. K. Gavrilova, Radiation Climate of the Arctic (Leningrad: Gidrometeorologicheskoe Izatel'stvo, 1963); C. C. Wallen, “Global Solar Radiation and Potential Evapotranspiration in Sweden,”Tellus, Vol. 18 (1966), pp. 786 800; L. A. Ramdas and S. Yegnanarayanan, “Solar Energy in India,” in Wind and Solar Energy, UNESCO, Proceedings of the New Delhi Symposium, 1956, pp. 188–95; B. W. Thompson, The Climate of Africa (Nairobi: Oxford University Press, 1965); T. K. Tso, Y. X. Wang, and C. X. Chen, “Characteristics of the Distribution of Total Radiation in China,”Acta Meteorologica Sinica, Vol. 33 (1963), pp. 78 95.

15 E. C. Kung, R. A. Bryson, and D. H. Lenschow, “Study of a Continental Surface Albedo on the Basis of Flight Measurements and Structure of the Earth's Surface Cover over North America,”Monthly Weather Review, Vol. 92 (1964), pp. 543 64.

16 S. S. Hwang, “Basic Factors Determining the Main Features of the General Circulation of the Atmosphere,”Acta Meteorologica Sinica, Vol. 26 (1955), pp. 35 64.

17 J. R. Mather and C. W. Thornthwaite, “Micro-climatic Investigations at Point Barrow, Alaska, 1957–1958,”Publications in Climatology, Vol. 11, No. 2 (Centerton, New Jersey: Laboratory of Climatology, 1958).

18 M. I. Budyko, “Heat Balance of the Earth's Surface,”Soviet Geography, Vol. 6 (1965), p. 311.

19 Thompson, op. cit., footnote 14. Also see: H. E. Landsberg, “Solar Radiation at the Earth's Surface,”Solar Energy, Vol. 5 (1961), pp. 95 98.

20 G. D. Thompson, “The Relationship of Potential Evapotranspiration of Sugarcane to Environmental Factors,”Proceedings of the 12th International Society of Sugarcane Technologists (Amsterdam: Elsevier Publishing Co., 1967), p. 7.

21 A. J. Dyer, “A Combined Water and Energy Balance Study at Katherine, Northern Territory,”Australian Meteorological Magazine, Vol. 15 (1967), pp. 148 55; J. L. Monteith, “An Empirical Method for Estimating Long-wave Radiation Exchanges in the British Isles,”Quarterly Journal, Royal Meteorological Society, Vol. 87 (1961), pp. 171 79.

22 Budyko, 1956, op. cit., footnote 4.

23 Cited in:F. R. Fosberg, B. J. Garnier, and A. W. Küchler, “Delimitation of the Humid Tropics,”Geographical Review, Vol. 51 (1961), p. 344.

24 Ekern, op. cit., footnote 6.

25 G. Stanhill, “The Relationship Between Climate and the Transpiration and Growth of Pastures,”Proceedings, Eighth International Grassland Congress (1960), pp. 293–96.

26 J. L. Monteith and G. Szeicz, “The Radiation Balance of Bare Soil and Vegetation,”Quarterly Journal, Royal Meteorological Society, Vol. 87 (1961), pp. 159 70.

27 For instance: G. Stanhill, G. T. Hofstede, and J. D. Kalma, “Radiation Balance of Natural and Agricultural Vegetation,”Quarterly Journal of the Royal Meteorological Society, Vol. 92 (1966), pp. 128 40.