Determining Atmospheric Boundary Layer Height with the Numerical Differentiation Method Using Bending Angle Data from COSMIC

This paper presents a new method to estimate the height of the atmospheric boundary layer(ABL) by using COSMIC radio occultation bending angle(BA) data. Using the numerical differentiation method combined with the regularization technique, the first derivative of BA profiles is retrieved, and the height at which the first derivative of BA has the global minimum is defined to be the ABL height. To reflect the reliability of estimated ABL heights, the sharpness parameter is introduced, according to the relative minimum of the BA derivative. Then, it is applied to four months of COSMIC BA data(January, April, July, and October in 2008), and the ABL heights estimated are compared with two kinds of ABL heights from COSMIC products and with the heights determined by the finite difference method upon the refractivity data. For sharp ABL tops(large sharpness parameters), there is little difference between the ABL heights determined by different methods, i.e.,the uncertainties are small; whereas, for non-sharp ABL tops(small sharpness parameters), big differences exist in the ABL heights obtained by different methods, which means large uncertainties for different methods. In addition, the new method can detect thin ABLs and provide a reference ABL height in the cases eliminated by other methods. Thus, the application of the numerical differentiation method combined with the regularization technique to COSMIC BA data is an appropriate choice and has further application value.

Monte-Carlo simulation of a stochastic differential equation

For solving higher dimensional diffusion equations with an inhomogeneous diffusion coefficient,Monte Carlo（MC） techniques are considered to be more effective than other algorithms, such as finite element method or finite difference method. The inhomogeneity of diffusion coefficient strongly limits the use of different numerical techniques. For better convergence, methods with higher orders have been kept forward to allow MC codes with large step size. The main focus of this work is to look for operators that can produce converging results for large step sizes. As a first step, our comparative analysis has been applied to a general stochastic problem.Subsequently, our formulization is applied to the problem of pitch angle scattering resulting from Coulomb collisions of charge particles in the toroidal devices.

Within-Cluster Variability Exponent for Identifying Coherent Structures in Dynamical Systems

We propose a clustering-based approach for identifying coherent flow structuresin continuous dynamical systems. We first treat a particle trajectory over a finitetime interval as a high-dimensional data point and then cluster these data from differentinitial locations into groups. The method then uses the normalized standarddeviation or mean absolute deviation to quantify the deformation. Unlike the usualfinite-time Lyapunov exponent (FTLE), the proposed algorithm considers the completetraveling history of the particles. We also suggest two extensions of the method. To improvethe computational efficiency, we develop an adaptive approach that constructsdifferent subsamples of the whole particle trajectory based on a finite time interval. Tostart the computation in parallel to the flow trajectory data collection, we also developan on-the-fly approach to improve the solution as we continue to provide more measurementsfor the algorithm. The method can efficiently compute the WCVE over adifferent time interval by modifying the available data points.