The improvement of GRAPES global extratropical singular vectors and experimental study

The singular vectors (SVs) based on total-energy norm are generally used to represent initial uncertainty in ensemble forecasting. The GRAEPE SV method based on the total-energy norm using the GRAPES dynamical core model has been developed. Impacts and importance of linearized physical processes on the SVs have been widely studied in the literature. To improve the GRAPES SVs, based on the recently developed GRAPES tangent linear model (TLM) and adjoint model (ADM) version 2.0, the implementation of linearized planetary boundary layer (PBL) parameterization on the calculation of extratropical SVs is conducted. The characteristics of SVs and their linear evolutions are measured by energy partition, energy spectra and spatial distribution through continuous experiments over 1-month period. The unreasonable quick energy growth near the surface that was observed previously in the structure of SVs without linearized physics has been greatly improved. Furthermore, the structures of the upgraded SVs are more consistent with those of previous studies, which exhibit the characteristics of typical total-energy based SVs, i.e., the energy maximum is located in the middle troposphere with obvious westward tilt with height in the spatial structure of SVs at initial time; during their growth, there are upward energy transfer to the upper troposphere and downward energy transfer to the surface, and an upscale energy transfer is shown in the energy spectra. The results show that the upgraded SVs are capable of capturing the baroclinic instability in the troposphere. In order to improve the computation efficiency of GRAPES SVs, the ADM that is most computationally expensive is optimized by reducing the use of GCR (Generalized Conjugate-Residual) in the ADM and increasing computational memory. As a result, the total computation time of GRAPES SVs can be reduced by up to 25%. Overall, the upgraded GRAPES SVs are able to meet the expectation for constructing the initial perturbation for GRAPES global ensemble prediction.