A Multigrid Nonlinear Least Squares Four‐Dimensional Variational Data Assimilation Scheme With the Advanced Research Weather Research and Forecasting Model

Abstract

The motions of the atmosphere have multiscale properties in space and/or time, and the background error covariance matrix (Β) should thus contain error information at different correlation scales. To obtain an optimal analysis, the multigrid three‐dimensional variational data assimilation scheme is used widely when sequentially correcting errors from large to small scales. However, introduction of the multigrid technique into four‐dimensional variational data assimilation is not easy due to its strong dependence on the adjoint model, which has high computational costs in data coding, maintenance, and updating, especially for large‐scale, complex problems. In this study, the multigrid technique was introduced into the nonlinear least squares four‐dimensional variational assimilation (NLS‐4DVar) method, which is an advanced four‐dimensional ensemble‐variational method that can be applied without invoking the adjoint models. The multigrid NLS‐4DVar (MG‐NLS‐4DVar) scheme uses the number of grid points to control the scale, with doubling of this number when moving from coarser to finer grid levels. Furthermore, the MG‐NLS‐4DVar scheme not only retains the advantages of NLS‐4DVar but also sufficiently corrects multiscale errors to achieve a highly accurate analysis. The effectiveness and efficiency of the proposed MG‐NLS‐4DVar scheme were evaluated by one group of single‐observation experiments and one group of comprehensive evaluation experiments using the Advanced Research Weather Research and Forecasting Model. MG‐NLS‐4DVar outperformed NLS‐4DVar, with a lower computational cost.

Comprehensive Evaluation of Satellite‐Based Precipitation at Sub‐Daily Time Scales Over a High‐Profile Watershed with Complex Terrain

“…Therefore, the real-time and near real-time hourly or half-hourly data can be of great value for mountainous numerical weather prediction with a data assimilation system (Zhang & Tian, 2018). Therefore, the real-time and near real-time hourly or half-hourly data can be of great value for mountainous numerical weather prediction with a data assimilation system (Zhang & Tian, 2018).…”

“…The GPM products can reflect reasonably the rainfall characteristics for a small watershed at the subdaily time scales and can be an important supplement for the single-point monitoring for the regional scale. Therefore, the real-time and near real-time hourly or half-hourly data can be of great value for mountainous numerical weather prediction with a data assimilation system (Zhang & Tian, 2018). In addition, current GPM rainfall data also meet the demands of accuracy for some research works at regional scales, such as landscapes, ecological zoning, and atmosphere-land interactions Wilson et al, 2019).…”

Application of multigrid NLS-4DVar in radar radial velocity data assimilation with WRF-ARW

“…where k is the observation time, and Sþ1 represents the total number of observation times in the assimilation 1) at the ith grid level to calculate the analysis increment δx ðiÞ of individual levels, as described elsewhere (Xie et al 2005(Xie et al , 2011Zhang and Tian 2018a).…”

“…Equation 11describes the POD-4DVar method (Tian, Xie, and Sun 2011;Zhang and Tian 2018a). The MG_NLS-4DVar method used in this study solves the variational minimization problem through Equation (11).…”

“…Fu et al (2016) also used the Space and Time Mesoscale Analysis System to assimilate 3D Doppler radar radial velocity data, and reconstructed the 3D structure of a typhoon in an idealized experiment. Compared with NLS-4DVar, multigrid NLS-4DVar (referred to as MG_NLS-4DVar) minimizes the errors from different scales and has higher efficiency and precision in the assimilation of conventional data (Zhang et al 2017b;Zhang and Tian 2018a).…”