气候变化领域集成服务门户(CCPortal): Fast and Accurate Computation of Vertical Modes

CCPortal

DOI	10.1029/2019MS001939
	Fast and Accurate Computation of Vertical Modes
	Early J.J.; Lelong M.P.; Smith K.S.
发表日期	2020
ISSN	19422466
卷号	12 期号:2
英文摘要	The vertical modes of linearized equations of motion are widely used by the oceanographic community in numerous theoretical and observational contexts. However, the standard approach for solving the generalized eigenvalue problem using second-order finite difference matrices produces O(1) errors for all but the few lowest modes, and increasing resolution quickly becomes too slow as the computational complexity of eigenvalue algorithms increases as O(n3). Existing methods are therefore inadequate for computing a full spectrum of internal waves, such as needed for initializing a numerical model with a full internal wave spectrum. Here we show that rewriting the eigenvalue problem in stretched coordinates and projecting onto Chebyshev polynomials results in substantially more accurate modes than finite differencing at a fraction of the computational cost. We also compute the surface quasigeostrophic modes using the same methods. All spectral and finite difference algorithms are made available in a suite of Matlab classes that have been validated against known analytical solutions in constant and exponential stratification. ©2020. The Authors.
英文关键词	Chebyshev polynomials; internal modes; spectral methods; SQG modes
语种	英语
scopus关键词	Computational complexity; Equations of motion; MATLAB; Numerical methods; Polynomials; Accurate computations; Chebyshev polynomials; Exponential stratification; Finite-difference algorithms; Generalized eigenvalue problems; Internal modes; Spectral methods; SQG modes; Eigenvalues and eigenfunctions; algorithm; complexity; eigenvalue; finite difference method; internal wave; numerical method; numerical model; wave spectrum
来源期刊	Journal of Advances in Modeling Earth Systems
文献类型	期刊论文
条目标识符	http://gcip.llas.ac.cn/handle/2XKMVOVA/156765
作者单位	NorthWest Research Associates, Redmond, WA, United States; Center for Atmosphere Ocean Science, Courant Institute of Mathematical Sciences, New York University, New York, NY, United States
推荐引用方式 GB/T 7714	Early J.J.,Lelong M.P.,Smith K.S.. Fast and Accurate Computation of Vertical Modes[J],2020,12(2).
APA	Early J.J.,Lelong M.P.,&Smith K.S..(2020).Fast and Accurate Computation of Vertical Modes.Journal of Advances in Modeling Earth Systems,12(2).
MLA	Early J.J.,et al."Fast and Accurate Computation of Vertical Modes".Journal of Advances in Modeling Earth Systems 12.2(2020).