Abstract: The GRAPES global four-dimensional variational data assimilation system (4D-Var) requires tangent and adjoint schemes of deep convection cumulus parameterization scheme. It is not practical to directly linearize the original complicated deep convection cumulus parameterization scheme. Simplified smoothing scheme is needed to reduce the nonlinearity and discontinuity. The GRAPES global model adopts the New Simplified Arakawa-Schubert (NSAS) cumulus parameterization scheme developed in NCEP. Deep convection feedback to the environment is mainly achieved by compensating subsidence. In this paper, the contribution from compensating subsidence is addressed and the contributions of precipitation evaporation and momentum feedback are ignored to form a simplified scheme. By adding small amplitude perturbations to the input temperature and specific humidity profiles, the sensitivity of temperature and specific humidity tendencies calculated by the parameterization scheme to input perturbations is evaluated, and the non-linear and discontinuous characteristics of the scheme are tested. Based on the simplified scheme, a simplified smoothing scheme is proposed by using a method of avoiding or reducing discontinuous "switches". Compared with the original deep convection cumulus parameterization scheme, the simplified smoothing NSAS scheme is consistent in convection triggering, and the potential temperature and specific humidity tendencies are comparable with those from the original scheme, while the precipitation time series simulation is better. The simplified smoothing NSAS also has obvious advantages in reducing non-linearity and avoiding discontinuity. The tangent linear scheme based on the simplified smoothing scheme shows that when the perturbation amplitude is less than 2 times of the analysis increment, it can well simulate the difference of the nonlinear schemes. The above results clearly demonstrate the rationality and practicability of the simplified smoothing scheme developed in this paper.