Ionospheric tomography is based on the observed slant total electron content (sTEC) along different satellite‐receiver rays to reconstruct the three‐dimensional electron density distributions. Due to incomplete measurements provided by the satellite‐receiver geometry, it is a typical ill‐posed problem, and how to overcome the ill‐posedness is still a crucial content of research. In this paper, Tikhonov regularization method is used and the model function approach is applied to determine the optimal regularization parameter. This algorithm not only balances the weights between sTEC observations and background electron density field but also converges globally and rapidly. The background error covariance is given by multiplying background model variance and location‐dependent spatial correlation, and the correlation model is developed by using sample statistics from an ensemble of the International Reference Ionosphere 2012 (IRI2012) model outputs. The Global Navigation Satellite System (GNSS) observations in China are used to present the reconstruction results, and measurements from two ionosondes are used to make independent validations. Both the test cases using artificial sTEC observations and actual GNSS sTEC measurements show that the regularization method can effectively improve the background model outputs.

An α‐Chapman function with a continuously varying scale height H(h) can be used to describe the topside ionosphere electron density profile that seamlessly connects the ionosphere with the plasmasphere. Huang and Reinisch () have derived the analytic expression of the scale height from the Vary‐Chap function, which can be applied to the topside F₂ region. However, the H(h) is still difficult to obtain because H(h) is a function of the unknown value H(h) at h_mF₂. In this paper, the maximum entropy method is introduced to solve this ill‐posed problem, and the Vary‐Chap scale height for each electron density profile is derived. Then the average percentage errors that defined as the differences between the measured electron density profiles and the Vary‐Chap profiles obtained from the Vary‐Chap scale heights are calculated with the Alouette/ISIS satellites topside sounder database. The results reveal that the average percentage errors are generally less than 5% and the Vary‐Chap profiles can well represent the topside electron density profiles. What is more, the local time, seasonal, solar cycle, and latitudinal variations of the Vary‐Chap scale height are preliminarily analyzed.

在大气边界层气象中湍流黏性系数是一个很重要的参数，通过直接观测往往无法得到其准确值，仅能通过间接观测获得大致范围.本文选用随机广义Ekman动力近似模式中的湍流黏性系数进行反演研究与不确定性分析.首先利用风速观测数据，并采用基于混沌多项式的集合Kalman滤波方法对系数进行反演，降低其不确定性，缩小可能取值的范围，该方法的核心思想是将集合Kalman滤波方法中求解模式不确定性传播的方法由蒙特卡罗法改为混沌多项式展开，从而避免大规模采样带来的计算资源耗费.然后进行数值实验，结果表明该方法能够有效且快速地求解出湍流黏性的后验概率分布，从而达到降低系数不确定性的目的.根据系数的先验分布计算出风速的先验分布，从而找到风速不确定性大的区域，且揭示了在不确定性大的区域内的观测数据进行系数反演可得到十分明显的效果，这对于观测点位置的选择提供了重要的指导.

Parameter estimation in chaotic dynamical systems is an important and practical issue. Nevertheless, the high-dimensionality and the sensitive dependence on initial conditions typically makes the problem difficult to solve. In this paper, we propose an innovative parameter estimation approach, utilizing numerical differentiation for observation data preprocessing. Given plenty of noisy observations on a portion of dependent variables, numerical differentiation allows them and their derivatives to be accurately approximated. Substituting those approximations into the original system can effectively simplify the parameter estimation problem. As an example, we consider parameter estimation in the well-known Lorenz model given partial noisy observations. According to the Lorenz equations, the estimated parameters can be simply given by least squares regression using the approximated functions provided by data preprocessing. Numerical examples show the effectiveness and accuracy of our method. We also prove the uniqueness and stability of the solution.

In this paper, we propose a new method of numerical differentiation to determine the height of the top layer of the atmospheric boundary layer. In this method, a regularization technique is used to convert the problem of calculating the differential of the curve of the corners into the problem of finding the minimum value of the objective function. The two-parameter model function method is used to select the regularization parameters. Finally, the maximum gradient method is used to determine the top height of the boundary layer. Firstly, the effectiveness of the new method is validated through two numerical experiments. The experimental results show that as the noise of the occultation data increases, the fluctuation of the height of the boundary layer top obtained by the difference method and the numerical differentiation method combined with the L curve scheme increases. And the height obtained by the two-parameter model function method is very stable, which shows that the new method can filter the noise well, thereby retaining the main information about the profile. Then, based on the COSMIC angle data in January, April, July and October 2007－2011, the new method is used to analyze the seasonal characteristics of the height of the global oceanic and atmospheric boundary layer, compared with the seasonal distribution obtained by “zbalmax” with the occultation data. The results show that the seasonal distribution characteristics of the two data are very consistent: the height of the boundary layer is higher in the area where the sea surface temperature is higher than that in the surrounding sea area; on the contrary, the height of the boundary layer top is lower. In the sea area where the warm current passes, the height of the boundary layer is higher; in the sea area where the cold current passes, the height of the boundary layer is lower.