## Black model

Black developed following quadratic equation, using data from many parts of the world.

solar energysolar fluxeuropedistributionnorth america

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Quoted from:Black J N . The Distribution of Solar Radiation over the Earth's Surface[J]. Theoretical and Applied Climatology, 1956, 7(2):165-189.

https://www.sci-hub.ren/10.1007/bf02243320

Records of total solar radiation measured on a horizontal surface (Q) on a monthly basis and of more than three years' duration are available for 88 stations. The stations are mainly concentrated in North America and Europe, and it is not possible to determine the global distribution of radiation directly from these records. Solar radiation and mean cloud amount (C) were therefore related by the quadratic regression Q = QA (0.803 -- 0.340C--0.458C2), where QA is the maximum possible radiation in the absence of an atmosphere (ANGoT's values) and the values of C were obtained from the maps printed in SHAW'S Manual of Meteorology.

Using the known distribution of QA and C, values of Q were calculated by use of the equation above for each 5°~ intersection of latitude and longitude over land, and for each 10° ~ intersection over sea. Isopleths of Q for each successive 50 gcal/cm2~ day are shown on the 12 monthly maps on which the distribution of radiation over the earth's surface is illustrated. Attention is drawn to certain features of these maps, in particular to the occurrence and movement of zones of high radiation, and a comparison is made of estimated and recorded radiation for twelve stations.

Black developed following quadratic equation, using data from many parts of the world :
$$𝐻/𝐻_0 =0.803−0.340𝐶−0.458𝐶^2 (𝐶≤0.8)$$
where C is mean total cloud cover during daytime observations in octa.

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J. N. Black (2021). Black model, Model Item, OpenGMS, https://geomodeling.njnu.edu.cn/modelItem/1684c288-6a9b-4170-98c8-35f75fcaa683

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