Abstract
In this paper, a frequently employed technique named the sparsity-promoting dynamic mode decomposition (SPDMD) is proposed to analyze the velocity fields of atmospheric motion. The dynamic mode decomposition method (DMD) is an effective technique to extract dynamic information from flow fields that is generated from direct experiment measurements or numerical simulation and has been broadly employed to study the dynamics of the flow, to achieve a reduced-order model (ROM) of the complex high dimensional flow field, and even to predict the evolution of the flow in a short time in the future. However, for standard DMD, it is hard to determine which modes are the most physically relevant, unlike the proper orthogonal decomposition (POD) method which ranks the decomposed modes according to their energy content. The advanced modal decomposition method SPDMD is a variant of the standard DMD, which is capable of determining the modes that can be used to achieve a high-quality approximation of the given field. It is novel to introduce the SPDMD to analyze the atmospheric flow field. In this study, SPDMD is applied to extract essential dynamic information from the 200 hPa jet flow, and the decomposed results are compared with the POD method. To further demonstrate the extraction effect of POD/SPDMD methods on the 200 hPa jet flow characteristics, the POD/SPDMD reduced-order models are constructed, respectively. The results show that both modal decomposition methods successfully extract the underlying coherent structures from the 200 hPa jet flow. And the DMD method provides additional information on the modal properties, such as temporal frequency and growth rate of each mode which can be used to identify the stability of the modes. It is also found that a fewer order of modes determined by the SPDMD method can capture nearly the same dynamic information of the jet flow as the POD method. Furthermore, from the quantitative comparisons between the POD and SPDMD reduced-order models, the latter provides a higher precision than the former, especially when the number of modes is small.
Highlights
With the rapid development of computer technology and continuous improvement of global observing system’s performance in recent decades, many new reanalysis datasets from advanced operational and research centers are built, upgraded, and opened to the meteorology community
To strike a balance between the quality of approximation and the number of modes that are used to approximate the given fields, in this paper, we focus on the advanced modal decomposition method sparsity-promoting dynamic mode decomposition (SPDMD), first proposed by Jovanovic et al [27]
Results and Discussion e data used in this paper is the ERA5 daily reanalysis dataset, the horizontal resolution of the data is 0.25° × 0.25°, and the time resolution is 1 hour [33, 34]. e SPDMD method is firstly applied to decompose a stratospheric 200 hPa jet dataset that includes 192 snapshots from 00:00 on September 24, 2009, to 24:00 on the 31st, and the analysis area is in the pan-Asian region
Summary
With the rapid development of computer technology and continuous improvement of global observing system’s performance in recent decades, many new reanalysis datasets ( known as meteorological big data) from advanced operational and research centers are built, upgraded, and opened to the meteorology community. It is very important to accurately describe and understand the structural changes and instability mechanisms of the complex atmospheric motion in both. In the instability analysis methods developed, when analyzing the stability of the atmospheric fluid motion, it is necessary to greatly simplify the Navier– Stokes equations of atmospheric motion or to calculate the inverse and eigenvalues of large matrices; it is well known that the process of calculations is complex and costly [2]. To gain a deeper understanding of the complex atmospheric fluid motion, modal decomposition methods can be utilized; among several methods, the Proper Orthogonal Decomposition (POD) and the Dynamic Mode Decomposition (DMD) have been widely used to study the dynamic mechanism of the flows in different applications [3, 4], except for the analysis of atmospheric reanalysis datasets
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