标题： 全球总柱臭氧的空间变化 显示英文标题

标题： Spatial variation of total column ozone on a global scale

摘要： 总柱臭氧的空间相关性随着纬度的强烈变化，因此均匀模型（对所有旋转都不变）显然是不合适的。然而，轴对称假设更为合理，这意味着过程模型对地球自转轴上的旋转不变，这大大简化了建模过程。 利用TOMS（总臭氧映射光谱仪）在六天期间内测量的总柱臭氧数据，本研究探讨了在球面上用球谐函数展开来模拟轴对称过程。结果表明，在这种展开中使用相对较少数量的项就可以捕捉到空间协方差结构中的许多大规模特征，但当通过其似然性评估时，由此得到的拟合模型对数据的拟合效果非常糟糕，因为它无法准确描述过程的局部行为。 因此，开发能够捕捉这些数据的大规模和小规模结构且计算上可行的模型仍然是一个挑战。 显示英文摘要

摘要： The spatial dependence of total column ozone varies strongly with latitude, so that homogeneous models (invariant to all rotations) are clearly unsuitable. However, an assumption of axial symmetry, which means that the process model is invariant to rotations about the Earth's axis, is much more plausible and considerably simplifies the modeling. Using TOMS (Total Ozone Mapping Spectrometer) measurements of total column ozone over a six-day period, this work investigates the modeling of axially symmetric processes on the sphere using expansions in spherical harmonics. It turns out that one can capture many of the large scale features of the spatial covariance structure using a relatively small number of terms in such an expansion, but the resulting fitted model provides a horrible fit to the data when evaluated via its likelihood because of its inability to describe accurately the process's local behavior. Thus, there remains the challenge of developing computationally tractable models that capture both the large and small scale structure of these data.