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DOI	10.1029/2019MS001615
	Theoretical Time Evolution of Numerical Errors When Using Floating Point Numbers in Shallow-Water Models
	Yamaura T.; Nishizawa S.; Tomita H.
发表日期	2019
ISSN	19422466
起始页码	3235
结束页码	3250
卷号	11 期号:10
英文摘要	We carried out a theoretical investigation of the impact of the numerical errors caused by using floating point numbers (FPNs) in simulations, such as rounding errors. Under the presupposition that model variables can be written as the linear sum of the true value and the numerical error, equations governing the time evolution of numerical errors due to FPNs (FPN errors) are obtained by considering the total errors of the results of simulations of shallow-water models and estimating the errors incurred by using FPNs with varying precision. We can use the time evolution equations to estimate the behavior of the FPN errors, then confirm these estimations by carrying out numerical simulations. In a geostrophic wind balance state, the FPN error oscillates and gradually increases in proportion to the square root of the number of time steps, like a random walk. We found that the error introduced by using FPNs can be considered as stochastic forcing. In a state of barotropic instability, the FPN error initially evolves as stochastic forcing, as in the case of the geostrophic wind balance state. However, it then begins to increase exponentially, like a barotropic instability wave. These numerical results are obtained by using a staggered-grid arrangement and stable time-integration method to retain near-neutral numerical stability in the simulations. The FPN error tends to behave as theoretically predicted if the numerical stability is close to neutral. © 2019. The Authors.
英文关键词	barotropic instability; geostrophic wind balance; numerical error; shallow water equations
语种	英语
scopus关键词	Digital arithmetic; Equations of motion; Meteorology; Numerical methods; Stability; Stochastic systems; Barotropic; Floating point numbers; Geostrophic winds; Numerical errors; Shallow water equations; Shallow water model; Theoretical investigations; Time evolution equations; Errors; barotropic instability; error analysis; geostrophic flow; numerical method; shallow water; shallow-water equation; temporal evolution; theoretical study; wind forcing
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/156844
作者单位	RIKEN Center for Computational Science, Japan; Research Center for Urban Safety and Security, Kobe University, Japan
推荐引用方式 GB/T 7714	Yamaura T.,Nishizawa S.,Tomita H.. Theoretical Time Evolution of Numerical Errors When Using Floating Point Numbers in Shallow-Water Models[J],2019,11(10).
APA	Yamaura T.,Nishizawa S.,&Tomita H..(2019).Theoretical Time Evolution of Numerical Errors When Using Floating Point Numbers in Shallow-Water Models.Journal of Advances in Modeling Earth Systems,11(10).
MLA	Yamaura T.,et al."Theoretical Time Evolution of Numerical Errors When Using Floating Point Numbers in Shallow-Water Models".Journal of Advances in Modeling Earth Systems 11.10(2019).