Abstract: The singular vectors (SV) based on linearized physical processes have been applied in the Global and Regional Assimilation PrEdiction System (GRAPES) global ensemble forecast system to generate initial perturbations. However, the nonlinear integration of some singular vectors may occasionally break down. This means that there exist discordances between different perturbed variables and the method for SV computation should be improved, which could further improve the SV-based initial perturbations and the GRAPES global ensemble forecasts. Based on the original computation scheme for the GRAPES global SV, when computing SV, the pressure perturbation component at the initial time is obtained through the potential temperature perturbation component according to the hydrostatic equilibrium relation, and others remain the same. Since the tropical cyclone SV (TCSV) are sensitive to the linearized physical processes, one single case that consisted of two typhoon processes is selected for the present study (the initial time is 12:00 UTC 8 August 2019). TCSV are respectively computed with the original SV computation scheme and the improved computation scheme of SV based on the hydrostatic equilibrium, and the nonlinear integrations of the TCSV are given to analyze the stability of the nonlinear integrations for the TCSV. The structure characters of the TCSV and the initial perturbations are further analyzed, the ensemble forecasting experiments are conducted, and the influences of the improved computation method of SV on the GRAPES global ensemble prediction skills are investigated. The experiments show that by generating coordinated pressure perturbation and potential temperature perturbation, the improved computation method of SV based on the hydrostatic equilibrium solves the breakdown problem of the nonlinear integrations of SV and eliminates the original small-scale structure that is too local and may result in nonlinear integration instability. The improved computation method of SV based on the hydrostatic equilibrium has slight effects on the structures of potential perturbation and zonal wind perturbation. It makes the maximum value of pressure perturbation locate near the tropical cyclone, which can better describe the initial uncertainty of the tropical cyclone and make the pressure perturbation and the potential temperature perturbation more coordinating. Using the improved computation method of SV based on the hydrostatic equilibrium in the GRAPES global ensemble forecasts, the Northern and Southern isobaric variables ensemble forecasts and the probability forecast skill of 24 h accumulated precipitation in China can be improved, and the tropical cyclone track ensemble spread is also increased.