Predictability is an important aspect of model ability to forecast. Predictability measures the divergence rate of infinitestimal close trajectories. In this paper, a new predictability measurement, supremum Lyapunov exponent (SLE) is proposed. This method is based on the Lyapunov exponent (LE). The SLE is applied to 2 cases of the Asian northeast monsoon forecast under a global warming scenario by a shallow water model. The results show that the forecasts from slightly different initial conditions converge after 3-day forecasts. That is, the shallow water model is not suitable for the purpose of climate downscaling.