tailieunhanh - Short-Wave Solar Radiation in the Earth’s Atmosphere Part 7

Các công thức của phái sinh đặc biệt là chuyển đổi sang hình thức (), (5,13). Viết theo cách này, có vẻ như tách rời () trực tiếp tính toán với phương pháp Monte-Carlo theo (). | Derivative from Values of Solar Irradiance 181 The formula of the derivative is specially converted to form . Written in this way it looks as integral directly calculated with the Monte-Carlo method according to . I Ta u Ba u Wa u du Mị Ta ệ Wa ệ That is to say the calculation of the derivatives according to is reduced to the multiplying of the value written to the counter by a certain weight function Wa ệ Marchuk et al. 1980 . To construct the concrete algorithm of calculating Wa the derivative explicit form of the right part of series is obtained. For that we are using the known expression of the derivative of the product through the sum of logarithm derivatives xyz. xyz. . x x y y z z . . The following is obtained fm V _ r A T u q u A Ta qa I Ta u qa u I 1T. I J Ta u qa u J Ta K qa ị .y u qa U1 Ka U1 Uz .Ka Un u T a u q a u K a U1 U2 K a Un u x Tm -. KUU . tũũ . After writing to form as it is more convenient for the Monte-Carlo method finally derive Ta K qa y .y dudU1. .dUnTa u qa U1 Ka U1 U2 . .Ka Un u Wa u U1 U2 . Un w . . . T a u . q u . Ka u1 u2 Ka un u Wa u u1 u2 . un T. T . -yy r. T . Ta u qa u Ka U1 U2 Ka Un u As it follows from in the Monte-Carlo method the derivatives could be calculated using the same algorithms as desired values with multiplying value T ệ by special weight Wa during each writing to the counter. In addition if value T ệ depends on the current magnitude of random value ệ only i. e. of the current coordinates of the photon then Wa is the sum and depends on the whole history of its trajectory. Thus to compute the derivatives of the irradiances it is enough to differentiate the explicit expressions of functions Ta u qa u and Ka u u with respect to the retrieved parameters. Then the following elementary changes are introduced to the algorithm of irradiance calculations described in Sect. the counting of values Wa for entire set of parameters at every modeling of the