In this work we present an approach toward the sensitivity analysis of optimal economic growth to a negative environmental impact driven by random natural hazards that damage the  production output. We use a simplified model of the GDP growth. We assume that production leads to th increase of the atmospheric GHG provided investment in cleaning is insufficient. The hypothesis of the Poisson probability distribution of the frequency of natural hazards is used at the this research stage. We apply the standard utility function-the discounted integral  consumption and construct an optimal investment policy in production and cleaning together with optiml GDP trajectories. We calibrate the model in the global scale and analyze the sensitivity of obtained optimal growth scenarios with respect to uncertain parameters of the Poisson distribution.