Balance conditions in variational data assimilation for a high-resolution forecast model,Quarterly Journal of the Royal Meteorological Society

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Balance conditions in variational data assimilation for a high-resolution forecast model
Quarterly Journal of the Royal Meteorological Society ( IF 3.0 ) Pub Date : 2021-05-21 , DOI: 10.1002/qj.4106
Ross N. Bannister ₁

Affiliation

This paper explores the role of balance relationships for background-error covariance modelling as the model's grid box decreases to convective scales. Data assimilation (DA) analyses are examined from a simplified convective-scale model and DA system (called ABC-DA) with a grid box size of 1.5 km in a 2D 540 km (longitude), 15 km (height) domain. The DA experiments are performed with background-error covariance matrices (

B

) modelled and calibrated by switching on/off linear balance (LB) and hydrostatic balance (HB), and by observing a subset of the ABC variables, namely

v

(meridional wind),

{\tilde{ρ}}^{'}

(scaled density, a pressure-like variable), and

b^{'}

(buoyancy, a temperature-like variable). Calibration data are sourced from two methods of generating proxies of forecast errors. One uses forecasts from different latitude slices of a 3D parent model (here called the latitude slice method), and the other uses sets of differences between forecasts of different lengths but valid at the same time (the National Meteorological Center method). Root-mean-squared errors computed over the domain from identical twin DA experiments suggest that there is no combination of LB/HB switches that give the best analysis for all model quantities. However it is frequently found that the

B

-matrices modelled with both LB and HB do perform the best. A clearer picture emerges when the errors are examined at different spatial scales. In particular it is shown that switching on HB in

B

mostly has a neutral/positive effect on the DA accuracy at ‘large’ scales, and switching off the HB has a neutral/positive effect at ‘small’ scales. The division between ‘large’ and ‘small’ scales is between 10 and 100 km. Furthermore, one hour forecast-error correlations computed between control parameters find that correlations are small at large scales when balances are enforced, and at small scales when balances are not enforced (ideal control parameters have zero cross-correlations). This points the way to modelling

B

with scale-dependent balances.

中文翻译：

高分辨率预测模型变分数据同化中的平衡条件

本文探讨了当模型的网格框减小到对流尺度时，平衡关系对背景误差协方差建模的作用。数据同化 (DA) 分析通过简化的对流尺度模型和 DA 系统（称为 ABC-DA）在 540 公里（经度）、15 公里（高度）的二维域中具有 1.5 公里的网格框大小进行检查。DA 实验使用背景误差协方差矩阵（

乙

) 通过打开/关闭线性平衡 (LB) 和流体静力平衡 (HB) 以及通过观察 ABC 变量的子集来建模和校准，即

v

(子午风),

{\overset{～}{ρ}}^{'}

（缩放密度，类似压力的变量），和

乙^{'}

（浮力，类似温度的变量）。校准数据来自两种生成预测误差代理的方法。一种使用来自 3D 父模型的不同纬度切片的预测（此处称为纬度切片方法），另一种使用不同长度但同时有效的预测之间的差异集（国家气象中心方法）。从相同的双 DA 实验计算的域上的均方根误差表明，没有 LB/HB 开关的组合可以为所有模型数量提供最佳分析。但是经常发现，

乙

- 用 LB 和 HB 建模的矩阵确实表现最好。当在不同的空间尺度上检查错误时，会出现更清晰的画面。特别是它表明，打开 HB

乙

主要对“大”尺度的 DA 精度有中性/积极影响，而关闭 HB 在“小”尺度上具有中性/积极影响。“大”和“小”尺度之间的划分在 10 到 100 公里之间。此外，控制参数之间计算的一小时预测误差相关性发现，当强制执行平衡时，相关性在大尺度上很小，而在不执行平衡时在小尺度上（理想的控制参数具有零互相关）。这为建模指明了方向

乙

与规模相关的余额。

更新日期：2021-05-21

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