Error Sensitivity Analysis in 10–30-Day Extended Range Forecasting by Using a Nonlinear Cross-Prediction Error Model

Extended range forecasting of 10–30 days, which lies between medium-term and climate prediction in terms of timescale, plays a significant role in decision-making processes for the prevention and mitigation of disastrous meteorological events. The sensitivity of initial error, model parameter error, and random error in a nonlinear cross-prediction error (NCPE) model, and their stability in the prediction validity period in 10–30-day extended range forecasting, are analyzed quantitatively. The associated sensitivity of precipitable water, temperature, and geopotential height during cases of heavy rain and hurricane is also discussed. The results are summarized as follows. First, the initial error and random error interact. When the ratio of random error to initial error is small (10^–6–10^–2), minor variation in random error cannot significantly change the dynamic features of a chaotic system, and therefore random error has minimal effect on the prediction. When the ratio is in the range of 10^–1–2 (i.e., random error dominates), attention should be paid to the random error instead of only the initial error. When the ratio is around 10^–2–10^–1, both influences must be considered. Their mutual effects may bring considerable uncertainty to extended range forecasting, and de-noising is therefore necessary. Second, in terms of model parameter error, the embedding dimension m should be determined by the factual nonlinear time series. The dynamic features of a chaotic system cannot be depicted because of the incomplete structure of the attractor when m is small. When m is large, prediction indicators can vanish because of the scarcity of phase points in phase space. A method for overcoming the cut-off effect (m > 4) is proposed. Third, for heavy rains, precipitable water is more sensitive to the prediction validity period than temperature or geopotential height; however, for hurricanes, geopotential height is most sensitive, followed by precipitable water.