Design And Application Of Dynamical Balance Constraints In A Golbal Variational Data Assimilation System

In a variational assimilation system, the incorporation of suitable dynamical balance constraints is important in order to produce balanced analysis, increase the value of each individual observation, and improve the preconditioning of the minimization problem. However, the balance constraints in GRAPES (global/regional assimilation and prediction system) global variational assimilation system (GRAPES-Var) still have many problems, which have affected the further improvement of the whole system. Therefore, there is important theoretic and practical significance to investigate dynamical balance constraints and apply the results in GRAPES-Var.Linear and nonlinear balance equations based on quasi-geostrophic theory are often adopted as dynamical balance constraints. However, in a global variational assimilation system, using those balance equations has two obvious problems. Firstly, those balance equations are calculated level by level. The vertical continuity of the atmosphere is not fully considered, which will lead to inappropriate zigzag vertical structures of analysis. Secondly, in the tropics, those equations are fallacious and will cause erroneous balance constraints. Based on GRAPES, this study focuses on researching these problems and finding reasonable solutions. The main contents and conclusions are following:1 A new multi-level statistical scheme of dynamical balance constraints has been developed in GRAPES-Var to avoid unreasonable zigzag vertical structures of temperature analysis in the linear balance equation (LBE) scheme. The multi-level scheme considers the correlation among variables at different levels and calculates the balanced mass field at each layer using the rotational wind at all model levels. The results show the following:(1) The multi-level scheme can ensure the continuity of pressure analysis at adjacent levels, reduce the magnitude of the adjustment by the initialization, and improve the temperature analysis performance. (2) The multi-level scheme can significantly improve the temperature forecast accuracy especially in the mid-and low-troposphere.2 Using equatorial wave modes and short-range forecast error samples of GRAPES global model, this study has investigated the balance characteristics of mass and wind fields in the tropics, and analyzed the problem of imposition of LBE in the tropics based on such characteristics. The results show the following:(1) Only 30-55%of the explained variance can be represented by equatorial Rossby (ER) modes, suggesting that other equatorial waves’ contributions should not be ignored. (2) Based on ER modes, introducing other equatorial waves, especially inertial-gravity and Kelvin modes, will greatly reduce the coupling between mass and wind. In this situation, the correlation between geopotential height and wind was close to zero in mid-troposphere, and the correlation between geopotential height and zonal wind in lower stratosphere was dominated by Kelvin modes. (3) The coupling between mass and wind is overestimated by using LBE in the tropics, because it mainly expresses the balance characteristics of ER modes. So when LBE is used as the balance constraints, extra steps should be taken to reduce the fallacious correlation and allow for a decoupling of mass and wind in the tropics.3 Based on the above two studies, this study has developed a LBE-regression hybrid balance constraint in GRAPES-Var. In the new scheme, after the calculation of LBE on each level, a vertical regression is introduced. The results show the following:(1) The hybrid scheme can efficiently reduce the unreasonable correlations between control variables. (2) It successfully decouples the mass/wind analyses in the tropics, and makes the structure of covariance be consistent with the theory analysis results. (3) It can improve the wind analysis and forecast accuracy in the tropics. The abnormally large tropical wind errors in the LBE scheme are dramatically suppressed. (4) Be similar with the multi-level scheme, the hybrid scheme considers the correlation among variables at different levels, so the temperature analysis and forecast performances are also improved.4 Following the settlement of the two problems, based on the hybrid scheme this study has further explored using radiosonde temperature (as a function of pressure) in place of radiosonde pressure (as a function of geopotential height). The numerical experiments indicate a clear benefit from using radiosonde temperature especially in the Northern Hemisphere and the East Asia where radiosonde observations are abundant.5 Finally, some issues related with dynamical balance constraints research have been discussed:(1) The multi-level scheme also has bright future application in regional GRAPES-Var. It can avoid the risky extrapolation over complex terrain in the original scheme. (2) Using statistical method can easily model the dynamical balance constraints between temperature and wind, which makes it possible to choose (T, ps) as the mass variable in GRAPES-Var. (3) For new hybrid variational systems, dynamical balance constraints still play a very important role.This study has deepened the understanding of the dynamical balance in the tropics, developed statistical balance constraints in GRAPES-Var for the first time, and improved the analysis and forecast performance of GRAPES. The hybrid scheme has become the operational formulation in GRAPES-Var for its better performance.