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

Abstract

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.

All‐sky microwave humidity sounder assimilation in the Korean Integrated Model forecast system

“…The H4DEV used in this study contains a wind–mass intercorrelation based on the dynamical equation as mentioned in Section 2.3 (refer to Song and Kang, 2019). We can therefore expect an improvement in the wind analysis through the flow‐dependent wind–mass relationship, which is derived from the additional humidity observations given by the cloudy MHS data.…”

“…2.2 of Song and Kang (2019): a 6‐hr analysis window is used and the ensemble trajectory, which has 50 members, is represented with seven hourly timeslots. For the static control variable, wind–mass transformation based on the temperature–wind regression (Song et al ., 2017a) is conducted, while the ensemble control variables are the same as the hydrostatic model variables (horizontal winds, temperature, water vapour mixing ratio and surface pressure; an option called “No_PT” in table 2 of Song and Kang, 2019). Although the wind–mass balance relationship is only applied to the static control variables, Song and Kang (2019) showed that the introduction of ensemble control variables into the assimilation produces a similar result to the version in which the ensemble control variables experience wind–mass transform.…”

“…A detailed description of this can be found in sect. 2.2 of Song and Kang (2019): a 6‐hr analysis window is used and the ensemble trajectory, which has 50 members, is represented with seven hourly timeslots. For the static control variable, wind–mass transformation based on the temperature–wind regression (Song et al ., 2017a) is conducted, while the ensemble control variables are the same as the hydrostatic model variables (horizontal winds, temperature, water vapour mixing ratio and surface pressure; an option called “No_PT” in table 2 of Song and Kang, 2019).…”

“…For the static control variable, wind–mass transformation based on the temperature–wind regression (Song et al ., 2017a) is conducted, while the ensemble control variables are the same as the hydrostatic model variables (horizontal winds, temperature, water vapour mixing ratio and surface pressure; an option called “No_PT” in table 2 of Song and Kang, 2019). Although the wind–mass balance relationship is only applied to the static control variables, Song and Kang (2019) showed that the introduction of ensemble control variables into the assimilation produces a similar result to the version in which the ensemble control variables experience wind–mass transform. The analysis is obtained in the form of hydrostatic model variables, which are transformed into the non‐hydrostatic model, KIM, of which the variables consist of three‐dimensional winds, potential temperature, density, pressure and water vapour mixing ratio under the hydrostatic assumption (refer to the corresponding procedure described in sect.…”

Balance conditions in variational data assimilation for a high‐resolution forecast model

“…Secondly, when a balance constraint is imposed strongly, it reduces the number of degrees of freedom that a DA problem has to deal with. Thirdly, and specifically for variational and hybrid DA schemes, balance conditions guide the definition of the control variables, which are assumed to be mutually uncorrelated, thus defining a model of (Bannister, 2008; Song and Kang, 2019).…”