First passage time analysis for climate prediction

Climate prediction experiences various input uncertainties such as initial condition errors (predictability of the first kind), boundary condition (or model parameter) errors (predictability of the second kind), and combined errors (predictability of the third kind). Quantification of model predictability due to input uncertainties is a key issue leading to successful climate prediction. The first passage time (FPT), defined as the time period when the prediction error first exceeds a predetermined criterion (i.e. the tolerance level) can be used to quantify the model predictability. A theoretical framework on the basis of the backward Fokker–Planck equation is developed to determine the probability distribution function of FPT. Furthermore, the FPT analysis can also be used for climate index prediction.