Spectral Transformation Using a Cubed-Sphere Grid for a Three-Dimensional Variational Data Assimilation System

Quart J Royal Meteoro Soc

Kang

2019

Ensemble forecast covariance plays an important role in the hybridized background error covariance framework to improve the resultant analysis quality. However, a localization of ensemble samples is needed to fully take advantage of flow-dependent error modes. In this regard, it is an interesting and practical issue as to which variables, composing the ensemble perturbation, the localization should be applied to. This study examines this issue in a boreal-summer month by comparing two experimental sets: (a) a set of model variables, and (b) another set of model wind variables and unbalanced dry mass (temperature and surface pressure) used for the control variables. In the comparison, it is shown that imposing the wind-mass balance on the ensemble perturbation improves the Antarctic lower-stratospheric temperature and tropical mid-/lower-tropospheric humidity. The nonlinear wind-mass balance relationship smooths an evolution of humidity forecast forced by the resultant analysis increments.

“…This division procedure also belongs to the parameter transform denoted by

\underline{T_{p}}

Section: Methods and Datamentioning

confidence: 99%

Effects of the wind–mass balance constraint on ensemble forecasts in the hybrid‐4DEnVar

Quart J Royal Meteoro Soc

Kang

2019

“…This division procedure also belongs to the parameter transform denoted by T p . T h is a spectral transform defined by spherical harmonic functions on cubed‐sphere grids, taking the role of a horizontal transform operator, and U h means the inverse spectral transform (Song and Kwon, ). In this study, we used a truncation wave number, 85, as a total wave number, based on the information about the limit wave number the cubed‐sphere represents (Song et al ., ).…”

Section: Numerical Model and Da Systemsmentioning

confidence: 99%

“…In this study, the version 10.2 of the RTTOV is used; the outer‐loop strategy (Lawless and Nichols, ; Song et al ., ) is not utilized; the guess field is therefore fixed to be a background state,

\underline{x^{b}}

. For the minimization of the cost function Equation 15, the preconditioning by transforming the BEC to an identity matrix, using its square‐root form, and the conjugate gradient methods (Song and Kwon, ) are utilized. The final form of the analysis,

\underline{x^{a}}

, produced by the minimization process is as follows:

\underline{x^{a}} = \underline{x^{g}} + \underline{U} (boldξ) .

…”

Section: Numerical Model and Da Systemsmentioning

confidence: 99%

“…In the same line with Kuhl et al . () and Kleist and Ide (), we use a Gaussian function in spectral space for the correlation function; however, it is based on the spherical harmonic functions defined on the cubed‐sphere grid (Song and Kwon, ; Song et al ., ); the inverse spectral transformation,

\underline{U_{h}^{α}}

, was implemented with the horizontal length‐scale of total wave‐number 10. Mitchell et al .…”

Section: Numerical Model and Da Systemsmentioning

confidence: 99%

“…H4DEV requires a correlation function to impose a specific localization on ensemble BEC to suppress the sampling error (Lorenc, 2003). In the same line with Kuhl et al (2013) and Kleist and Ide (2015a), we use a Gaussian function in spectral space for the correlation function; however, it is based on the spherical harmonic functions defined on the cubed-sphere grid (Song and Kwon, 2015;Song et al, 2017c); the inverse spectral transformation, h , was implemented with the horizontal length-scale of total wave-number 10. Mitchell et al (2002) suggested that an imbalance can occur in the analysis when they use severe localization in their ensemble DA scheme.…”

Section: Hybrid Four-dimensional Ensemble-variational Data Assimilatimentioning

confidence: 99%

See 2 more Smart Citations

Extended representation of wind–mass correlation by ensemble forecasting for data assimilation

Quart J Royal Meteoro Soc

2019

Initialization for numerical weather prediction models is of utmost importance especially in the short‐range forecast of the weather accompanying extreme events such as heavy rainfall, heatwaves, and so on. The balance relationship between wind and mass in the initialized field has been an important issue since Richardson's first attempt at numerical prediction. In a climatological framework, regressed‐linear and analytic‐nonlinear balancing methods are used to impose the wind–mass correlation onto the analysis increment, which results from data assimilation procedures. The advection of horizontal wind destroys the isotropy assumption by the regressed‐linear balance approach. The nonlinear balance equation approach including the advection process reduces this disadvantage more or less. However, it is shown that forecast ensemble correlation helps even the regressed balance approach to address the anisotropy in the hybridization framework. The regressed balance approach, in common with the nonlinear balance, experiences (a) considerable residual of the horizontal momentum conservation in the Antarctic stratosphere, and (b) lack of thermodynamic energy relationship between divergent wind and temperature in the Tropics. This study demonstrates with phenomenological examples that these weaknesses of the traditional (especially, regressed) methods are effectively resolved by forecast ensemble covariance.

The Advantages of Hybrid 4DEnVar in the Context of the Forecast Sensitivity to Initial Conditions

Shin

et al. 2017

JGR Atmospheres

Self Cite

Hybrid four‐dimensional ensemble variational data assimilation (hybrid 4DEnVar) is a prospective successor to three‐dimensional variational data assimilation (3DVar) in operational weather prediction centers currently developing a new weather prediction model and those that do not operate adjoint models. In experiments using real observations, hybrid 4DEnVar improved Northern Hemisphere (NH; 20°N–90°N) 500 hPa geopotential height forecasts up to 5 days in a NH summer month compared to 3DVar, with statistical significance. This result is verified against ERA‐Interim through a Monte Carlo test. By a regression analysis, the sensitivity of 5 day forecast is associated with the quality of the initial condition. The increased analysis skill for midtropospheric midlatitude temperature and subtropical moisture has the most apparent effect on forecast skill in the NH including a typhoon prediction case. Through attributing the analysis improvements by hybrid 4DEnVar separately to the ensemble background error covariance (BEC), its four‐dimensional (4‐D) extension, and climatological BEC, it is revealed that the ensemble BEC contributes to the subtropical moisture analysis, whereas the 4‐D extension does to the midtropospheric midlatitude temperature. This result implies that hourly wind‐mass correlation in 6 h analysis window is required to extract the potential of hybrid 4DEnVar for the midlatitude temperature analysis to the maximum. However, the temporal ensemble correlation, in hourly time scale, between moisture and another variable is invalid so that it could not work for improving the hybrid 4DEnVar analysis.