A comparison between four-dimensional variational assimilation and simplified sequential assimilation relying on three-dimensional variational analysis

We propose a dispersion-managed model with diffraction management for the stabilization of three-dimensional spatiotemporal solitons in bulk cubic–quintic media. The cubic–quintic nonlinear Schrödinger equation with periodically varying dispersion and diffraction has been studied using analytical and numerical methods. Variational analysis and the Kapitsa averaging method have been used to study the system analytically. The study has shown that periodically varying coefficients of diffraction and dispersion stabilizes the spatiotemporal solitons in cubic–quintic media.

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Three-Dimensional Variational Analysis of Small Crystal Resonators

10.1109/freq.1979.200327 ◽

1979 ◽

Cited By ~ 3

Author(s):

R.F. Milsom

Keyword(s):

Variational Analysis ◽

Three Dimensional ◽

Small Crystal

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A Space–Time Multiscale Analysis System: A Sequential Variational Analysis Approach

Monthly Weather Review ◽

10.1175/2010mwr3338.1 ◽

2011 ◽

Vol 139 (4) ◽

pp. 1224-1240 ◽

Cited By ~ 72

Author(s):

Y. Xie ◽

S. Koch ◽

J. McGinley ◽

S. Albers ◽

P. E. Bieringer ◽

...

Keyword(s):

Data Assimilation ◽

Variational Approach ◽

Variational Analysis ◽

Weather Forecasting ◽

Dimensional Space ◽

Three Dimensional ◽

Real Data ◽

Test Case ◽

Outflow Boundary ◽

Three Dimensional Space

Abstract As new observation systems are developed and deployed, new and presumably more precise information is becoming available for weather forecasting and climate monitoring. To take advantage of these new observations, it is desirable to have schemes to accurately retrieve the information before statistical analyses are performed so that statistical computation can be more effectively used where it is needed most. The authors propose a sequential variational approach that possesses advantages of both a standard statistical analysis [such as with a three-dimensional variational data assimilation (3DVAR) or Kalman filter] and a traditional objective analysis (such as the Barnes analysis). The sequential variational analysis is multiscale, inhomogeneous, anisotropic, and temporally consistent, as shown by an idealized test case and observational datasets in this study. The real data cases include applications in two-dimensional and three-dimensional space and time for storm outflow boundary detection (surface application) and hurricane data assimilation (three-dimensional space application). Implemented using a multigrid technique, this sequential variational approach is a very efficient data assimilation method.

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Assimilating Doppler radar radial velocity and reflectivity observations in the weather research and forecasting model by a proper orthogonal-decomposition-based ensemble, three-dimensional variational assimilation method

Journal of Geophysical Research Atmospheres ◽

10.1029/2012jd017684 ◽

2012 ◽

Vol 117 (D17) ◽

pp. n/a-n/a ◽

Cited By ~ 16

Author(s):

Xiaoduo Pan ◽

Xiangjun Tian ◽

Xin Li ◽

Zhenghui Xie ◽

Aimei Shao ◽

...

Keyword(s):

Radial Velocity ◽

Proper Orthogonal Decomposition ◽

Doppler Radar ◽

Three Dimensional ◽

Orthogonal Decomposition ◽

Weather Research And Forecasting ◽

Forecasting Model ◽

Variational Assimilation ◽

Proper Orthogonal ◽

Weather Research

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A THTEE-DIMENSIONAL VARIATIONAL ASSIMILATION SCHEME FOR SATELLITE AOD

ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences ◽

10.5194/isprs-archives-xlii-3-999-2018 ◽

2018 ◽

Vol XLII-3 ◽

pp. 999-1002

Author(s):

Y. Liang ◽

Z. Zang ◽

W. You

Keyword(s):

Data Assimilation ◽

Single Point ◽

Three Dimensional ◽

Quadratic Equation ◽

Size Distributions ◽

Control Variables ◽

Variational Assimilation ◽

Observation Operator ◽

Computational Resources ◽

Assimilation Scheme

A three-dimensional variational data assimilation scheme is designed for satellite AOD based on the IMPROVE (Interagency Monitoring of Protected Visual Environments) equation. The observation operator that simulates AOD from the control variables is established by the IMPROVE equation. All of the 16 control variables in the assimilation scheme are the mass concentrations of aerosol species from the Model for Simulation Aerosol Interactions and Chemistry scheme, so as to take advantage of this scheme in providing comprehensive analyses of species concentrations and size distributions as well as be calculating efficiently. The assimilation scheme can save computational resources as the IMPROVE equation is a quadratic equation. A single-point observation experiment shows that the information from the single-point AOD is effectively spread horizontally and vertically.

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