Given the second radial derivative Vrr(P) |δs of the Earth's gravitational potential V(P) on the surface δS corresponding to the satellite altitude, by using the fictitious compress recovery method, a fictitious regular harmonic field rrVrr(P)^* and a fictitious second radial gradient field V:(P) in the domain outside an inner sphere Ki can be determined, which coincides with the real field V(P) in the domain outside the Earth. Vrr^*(P)could be further expressed as a uniformly convergent expansion series in the domain outside the inner sphere, because rrV(P)^* could be expressed as a uniformly convergent spherical harmonic expansion series due to its regularity and harmony in that domain. In another aspect, the fictitious field V^*(P) defined in the domain outside the inner sphere, which coincides with the real field V(P) in the domain outside the Earth, could be also expressed as a spherical harmonic expansion series. Then, the harmonic coefficients contained in the series expressing V^*(P) can be determined, and consequently the real field V(P) is recovered. Preliminary simulation calculations show that the second radial gradient field Vrr(P) could be recovered based only on the second radial derivative V(P)|δs given on the satellite boundary. Concerning the final recovery of the potential field V(P) based only on the boundary value Vrr (P)|δs, the simulation tests are still in process. 相似文献
Environmental data seldom follow normal distributions, so how to calculate their means is a very important problem. Commonly used methods for mean calculation, such as arithmetic mean, geometric mean, and median, were evaluated. Arithmetic means should only be used when datasets follow normal distributions. Geometric means are suitable for datasets which follow log-normal distributions. Medians are a kind of robust treatment. However, their efficiency is very low. Based on the methods described, two new ideas are developed: robust and symmetric, for calculating means. As far as the symmetric feature is concerned, Box-Cox power transformation is better than logarithmic transformation. Robust statistics and Box-Cox transformation are combined to produce the robust-symmetric mean. As environmental data often follow log-normal or skewed distributions, this method is better than the previous ones and also is appropriate. 相似文献
Using more than three million Landsat satellite images, this research developed the first global impervious surface area (GISA) dataset from 1972 to 2019. Based on 120,777 independent and random reference sites from 270 cities all over the world, the omission error, commission error, and F-score of GISA are 5.16%, 0.82%, and 0.954, respectively. Compared to the existing global datasets, the merits of GISA include: (1) It provided the global ISA maps before the year of 1985, and showed the longest time span (1972–2019) and the highest accuracy (in terms of a large number of randomly selected and third-party validation sample sets); (2) it presented a new global ISA mapping method including a semi-automatic global sample collection, a locally adaptive classification strategy, and a spatio-temporal post-processing procedure; and (3) it extracted ISA from the whole global land area (not from an urban mask) and hence reduced the underestimation. Moreover, on the basis of GISA, the long time series global urban expansion pattern (GUEP) has been calculated for the first time, and the pattern of continents and representative countries were analyzed. The two new datasets (GISA and GUEP) produced in this study can contribute to further understanding on the human’s utilization and reformation to nature during the past half century, and can be freely download from http://irsip.whu.edu.cn/resources/dataweb.php.