An Effective Method to Solve the Streamfunction and Velocity Potential from a Wind Field in a Limited Area

Zhu Zongshen; Zhu Guofu

Vol.19, NO.1, 2008

Article Contents

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Zhu Zongshen, Zhu Guofu. An effective method to solve the streamfunction and velocity potential from a wind field in a limited area. J Appl Meteor Sci, 2008, 19(1): 10-18.

Citation:

Zhu Zongshen, Zhu Guofu. An effective method to solve the streamfunction and velocity potential from a wind field in a limited area. J Appl Meteor Sci, 2008, 19(1): 10-18.

Zhu Zongshen, Zhu Guofu. An effective method to solve the streamfunction and velocity potential from a wind field in a limited area. J Appl Meteor Sci, 2008, 19(1): 10-18.

Citation:

Zhu Zongshen, Zhu Guofu. An effective method to solve the streamfunction and velocity potential from a wind field in a limited area. J Appl Meteor Sci, 2008, 19(1): 10-18.

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An Effective Method to Solve the Streamfunction and Velocity Potential from a Wind Field in a Limited Area

Zhu Zongshen^1,2,
Zhu Guofu^1,2

1.
State Key Laboratory of Severe Weather, Chinese Academy of Meteorological Sciences, Beijing 100081
2.
National Meteorological Center, Beijing 100081

Received Date: 2006-12-29
Rev Recd Date: 2007-07-31
Publish Date: 2008-02-29

Abstract

Abstract

The streamfunction and the velocity potential are variables commonly used in the scheme design for atmospheric data assimilation and initial field analysis of numeric weather prediction.They can be obtained in partitioning a wind field by solving the Poisson equations of the vorticity and the divergence of the horizontal components of the wind field. Difference method is usually adopted in a limited area; nevertheless, an obvious departure exits between the original wind field and the reconstructed one from the sum of the streamfunction and velocity potential components in the vicinity of the boundary of the limited area.An effective scheme is designed to solve by difference method the streamfunction and velocity potential of a wind field in an Arakawa-A grid limited area, based on analyzing detailedly the approach and characteristics in the process of the solution. The key techniques in the scheme include the following. Firstly, the solution domain is expanded by two rings by extrapolating linearly the wind field to improve a calculation of boundary values. Secondly, consistent difference schemes are introduced in the solution procedure to enhance the solution precision. And finally only two to three iterations are imposed on incremental corrections to get a satisfactorily accurate result. Experiments are carried out with real wind data and their results indicate that the streamfunction and velocity potential of a wind field can be acquired by the scheme and the reconstructed wind field is reproduced with a very high precision.
- limited area;
- streamfunction and velocity potential;
- difference scheme;
- partition and reconstruction of wind field;
- iterative method of incremental correction

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References(11)

Figures and Tables

图 1 2003年7月20日12:00的水平风速场 (单位: m·s^-1)

(a)1000 hPa u, (b)1000 hPa v, (c)500 hPa u, (d)500 hPa v, (e)150 hPa u, (f)150 hPa v

Fig. 1 Components of wind speed at 12:00 on July 20, 2003 (unit:m·s^-1)

(a) u at 1000 hPa, (b) v at 1000 hPa, (c) u at 500 hPa, (d) v at 500 hPa, (e) u at 150 hPa, (f)v at 150 hPa

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图 2 2003年7月20日12:00的流场 (单位:m·s^-1)

(a)1000 hPa, (b)500 hPa, (c)150hPa

Fig. 2 Wind fields at 12:00 on July 20, 2003(unit:m·s^-1)

(a)1000 hPa, (b)500 hPa, (c)150hPa

DownLoad: Full-Size Img PowerPoint

图 3 2003年7月20日12:00的流函数和速度势场 (单位: 10⁶m²·s^-1)

(a)1000 hPa Ψ, (b)1000 hPa χ, (c)500 hPa Ψ, (d)500 hPa χ, (e)150 hPa Ψ, (f)150 hPa χ

Fig. 3 Streamfunctions (Ψ) and velocity potentials (χ) at 12:00 on July 20, 2003 (unit:10⁶m²·s^-1)

Ψ at 1000 hPa, (b)χ at 1000 hPa, (c)Ψ at 500 hPa, (d)χ at 500 hPa, (e) Ψ at 150 hPa, (f)χ at 150 hPa

DownLoad: Full-Size Img PowerPoint

表 1 计算Poisson方程时采用3种不同差分格式方案迭代前得到的500 hPa风速绝对误差比较 (单位:m·s^-1)

Table 1 The comparison of absolute errors between wind speeds and their reconstructed ones from three difference schemes in solving the Poisson equations without any iteration correction at 500 hPa (unit:m·s^-1)

表 2 计算Poisson方程时采用3种不同差分格式方案迭代3次后得到的500 hPa风速绝对误差比较 (单位:m·s^-1)

Table 2 Same as in Table 1, but with three-iteration corrections

表 3 4种不同计算方案的500 hPa风速绝对误差比较 (单位:m·s^-1)

Table 3 Same as in Table 1, but their reconstructed ones from four difference schemes in expanding the solution domain and adding iteration corrections (unit:m·s^-1)

表 4 不扩展区域方案迭代10次计算得到的风速绝对误差 (单位:m·s^-1)

Table 4 Same as in Table 3, but for ten-iteration corrections without expanding the solution domain (unit:m·s^-1)

表 5 扩展区域方案迭代10次计算得到的风速绝对误差 (单位:m·s^-1)

Table 5 Same as in Table 4, but for ten-iteration corrections with expanding the solution domain (unit:m·s^-1)

表 6 2006年7月10—19日12:00 10 d 500 hPa风速绝对误差及统计结果 (单位:m·s^-1)

Table 6 Same as in Table 3, but for ten days from 10 to 19 July 2006 and their average, according to the scheme of expanding the solution domain and adding three-iteration corrections (unit:m·s^-1)

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