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.

The Variational Assimilation Experiment of GPS Bending Angle

More and more new types of observational data provide many new opportunities for improving numerical weather forecasts. Among these, the GPS (Global Positioning System) bending angle is undoubtedly very important. There are many advantages of the GPS bending angle, such as high resolution, availability in all weather conditions, and global data coverage. Thus it is very valuable to assimilate GPS bending angle data into numerical weather models. This paper introduces how to obtain and assimilate the GPS bending angle. There are two methods of assimilation: the indirect method and direct method, and they are both introduced in this paper. During the minimizing process of variational assimilation, calculation efficiency is very important and the optimal step size greatly influences the algorithm efficiency. Based on the characteristics of the minimizing algorithm, we obtain an adaptive method for calculating the optimizing step suitable for all kinds of minimization algorithms through mathematical deduction. Finally, a numerical variational assimilation experiment is performed using the GPS bending angle data of 11 October 1995. The numerical results indicate the validity of the variational assimilation method and the adaptive method introduced here.

Analysis of bending mechanism in multi-scanning laser bending process based on plastic strain development

By using multi-pass straight-line scan strategies,a larger bending angle can be achieved.There is,however,a limited understanding of the variation in bending angle per pass during multi-pass under various process parameters.In multi-pass laser scanning,the bending angle cannot always linearly increase with scanning passes and this phenomenon can be observed mostly in low heat input.Strain hardening is the common explanation for this phenomenon.However,it could not explain why this bending angle reduction phenomenon occurs at low heat input scanning rather than at high heat input scanning.In this study,this phenomenon is discussed based on strain development in experiments and numerical simulation.The different growing mechanism of plastic strain is analyzed to reveal the effects of laser power and scanning velocity.Furthermore,the opposite bending trend that occurred at larger laser power is discussed in comparison to the plastic strain development.The study shows that relatively larger heat input below 6.7 J/mm can help to avoid the bending angle reduction phenomenon and the opposite bending trend is highly dependent on the larger laser power.For achieving the expected cumulative bending angle in multi-pass laser bending,it is recommended to decrease the scanning velocity at a relatively low laser power level while increase the scanning velocity at a high level of laser power.