Analyzing the Diurnal Cycle by Bayesian Interpolation on a Sphere

Bayesian interpolation has previously been proposed as an ideal strategy to constructmaps of radio occultation (RO) data, but that proposition did not consider the diurnaldimension of RO data. In this work, the basis functions of Bayesian interpolation areextended into the domain of the diurnal cycle, thus enabling monthly mapping of radiooccultation data in synoptic time and analysis of the atmospheric tides. The basisfunctions are spherical harmonics multiplied by sinusoids in the diurnal cycle up toarbitrary spherical harmonic degree and diurnal cycle harmonic. Bayesian interpolation requires a regularizer to impose smoothness on the fits it produces, thereby preventing the overfitting of data. In this work, a formulation for the regularizer is proposed and the most probable values of the parameters of the regularizer determined. Special care is required when obvious gaps in the sampling of the diurnal cycle are known to occur in order to prevent the false detection of statistically significant high-degree harmonics of the diurnal cycle in the atmosphere. Finally, this work probes the ability of Bayesian interpolation to generate a valid uncertainty analysis of the fit. The post-fit residuals of Bayesian interpolation are dominated not by measurement noise but by unresolved variability in the atmosphere, which is statistically non-uniform across the globe, thus violating the central assumption of Bayesian interpolation. The problem is ameliorated by constructing maps of RO data using Bayesian interpolation that partially resolve the temporal variability of the atmosphere, constructing maps for approximately every three days of RO data.

贝叶斯插值此前被提出作为构建无线电掩星（radio occultation, RO）数据地图的理想策略，但该提议未考虑RO数据的日变化维度。本研究将贝叶斯插值的基函数扩展至日循环域，从而实现RO数据的月尺度天气学时间映射及大气潮汐分析。所述基函数为球谐函数与日循环中正弦曲线的乘积，可覆盖任意球谐次数与日循环谐波。贝叶斯插值需借助正则化器保证拟合结果的平滑性，以防止数据过拟合。本研究提出了正则化器的公式，并确定了其参数的最可能值。当日循环采样存在已知明显缺口时，需特别注意，避免错误检测大气中日循环的统计显著高次谐波。最后，本研究探讨了贝叶斯插值生成拟合有效不确定性分析的能力。贝叶斯插值的拟合后残差主要并非源于测量噪声，而是大气中未解析的变率——该变率在全球范围内统计上不均匀，因此违背了贝叶斯插值的核心假设。通过使用贝叶斯插值构建RO数据地图（部分解析大气的时间变率，约每三天生成一次地图），此问题得到缓解。