The boundary layer height obtained by the spline numerical differentiation method using COSMIC GPS radio occultation data: A case study of the Qinghai-Tibet Plateau

Abstract

We apply a numerical differentiation method for gradients of bending angle (BA) vertical profiles to determine the atmospheric boundary layer (ABL) height. The basic idea to obtain profiles of BA vertical gradient is to minimize an objective functional, with the Tikhonov regularization term being the second order derivative of the function to be determined; the regularization parameter is chosen as the standard deviation of the COSMIC Radio Occultation's BA data. The optimal BA profile is in the form of cubic spline function, and its derivative is calculated, and the height with the minimum derivative is defined as the ABL height. In order to illustrate the effectiveness of this method, two numerical experiments and comparison with radio sonde data are carried out, which show that with the addition of Gaussian error, the numerical regularization method combined with cubic spline function can adequately maintain more stable and accurate results. Then, the ABL heights of the Qinghai-Tibet Plateau are obtained by the numerical differentiation method based on COSMIC radio occultation data from 2007 to 2011 (January, April, July, and October). The overall results show that the ABL height on the Qinghai-Tibet Plateau is closely related to the terrain height and the seasonal change. By comparing the results with the numerical differentiation method and “zbalmax”, it is obvious that both techniques show good consistency of spatial distribution and temporal evolution.