CMG: Use of Nonlinear Analysis to Characterize the Behavior and Predictability of the Atmospheric Boundary Layer

该项目研究了大气边界层行为与各种参数的关系，包括地面热容、Rossby数、长波辐射和加热率，以及数值模式中的行为对垂直离散化的依赖关系。所采用的方法是对描述大气边界层的一维偏微分方程组进行数值分叉分析，并将结果与水平均匀实施的MM5或WRF的积分进行比较。所使用的方法将类似于其中一名研究人员使用的方法，即考察地转风和粗糙度长度作为分叉参数的作用。在数学方面，该项目将应用和扩展使用子空间投影来扩展大型系统的延拓方案的研究。所开发的一些分叉分析工具将在其他大气和海洋研究中有用。这项工作的一个结果应该是更好地了解大气边界层的非线性行为，然后将其纳入数值天气预报模式，以产生更准确的地表温度预测，特别是在夜间。

This project is an investigation of the dependence of the behavior of the atmospheric boundary layer on a variety of parameters including surface heat capacity, Rossby number, long wave radiation and heating rate, as well as the dependence of the behavior in numerical models on vertical discretization. The approach used is that of a numerical bifurcation analysis of the one-dimensional system of partial differential equations that describe the atmospheric boundary layer and a comparison of the results to integrations of horizontally homogeneous implementations of MM5 or WRF. The approach to be used will be similar to that used by one of the investigators to look at the role of geostrophic wind and roughness length as bifurcation parameters. On the mathematical side, the project will apply and extend research on the use of sub-space projection to extend continuation schemes for large systems. Some of the bifurcation analysis tools developed will be useful in other atmospheric and oceanic studies. One consequence of this work should be a better understanding of the nonlinear behavior of the atmospheric boundary layer which can then be incorprated into numerical weather prediction models to produce more accurate predictions of surface temperatures, especially at night.