tailieunhanh - Short-Wave Solar Radiation in the Earth’s Atmosphere Part 3

Các hành vi của sự phân bố của các giá trị ngẫu nhiên ξ ↓ (z) và ξ ↑ (z) là không rõ. Tuy nhiên, sự phân bố của những kỳ vọng của nó theo các định lý giới hạn trung tâm có xu hướng phân phối bình thường như K → ∞. | 52 Theoretical Base of Solar Irradiance and Radiance Calculation in the Earth Atmosphere squares ệị z and 2 z with zeroth initial values and write together with the following z ệị z ệ z 2 z 4 z z 2 . Using the known expression for variance D ệ M 2 - M2 where M . is expectation we obtain D t 1 à z A D 1 A z - 1 A . K 2 K 1 K 2 K 1 The behavior of the distribution of random values ệt z and z is unknown. However the distribution of its expectations according to the central limit theorem tends to the normal distribution as K TO. Hence desired irradiances which are also considered as random values have the distributions asymptotically close to the normal distribution. It is known that the normal distribution is characterized with the expectation and the variance expressed by . For the standard deviation SD s . ựD . of the irradiances in accordance with the study by Marchuk et al. 1980 with taking into account the known rule for the variances addition the following is obtained s Ft z FoPo JD K s Ft z FoPo JD K . As follows from the increasing of the number of trajectories K leads to the minimization of the standard deviation SD . of the random error of the irradiances calculation. Evaluating the SD with is of great practical interest because it allows accomplishment of the calculations with the accuracy fixed in advance. Actually the calculation of the SD gives the possibility of estimating the necessary number of photon trajectories and as soon as the SD is less than the fixed value the simulating is finished. The above-considered scheme of the simulating of photon trajectories is called direct modeling Kargin 1984 as it directly reflects our implication concerning photon motion throughout the atmosphere. However direct modeling is not enough for accelerating the calculation according to the algorithm of the Monte-Carlo method or for the radiance calculation Kargin 1984 . Consider two approaches to increase the calculation