Extended Range(10–30 Days) Heavy Rain Forecasting Study Based on a Nonlinear Cross-Prediction Error Model

Extended range （10-30 d） heavy rain forecasting is difficult but performs an important function in disaster prevention and mitigation. In this paper, a nonlinear cross prediction error （NCPE） algorithm that combines nonlinear dynamics and statistical methods is proposed. The method is based on phase space reconstruction of chaotic single-variable time series of precipitable water and is tested in 100 global cases of heavy rain. First, nonlinear relative dynamic error for local attractor pairs is calculated at different stages of the heavy rain process, after which the local change characteristics of the attractors are analyzed. Second, the eigen-peak is defined as a prediction indicator based on an error threshold of about 1.5, and is then used to analyze the forecasting validity period. The results reveal that the prediction indicator features regarded as eigenpeaks for heavy rain extreme weather are all reflected consistently, without failure, based on the NCPE model; the prediction validity periods for 1-2 d, 3-9 d and 10-30 d are 4, 22 and 74 cases, respectively, without false alarm or omission. The NCPE model developed allows accurate forecasting of heavy rain over an extended range of 10-30 d and has the potential to be used to explore the mechanisms involved in the development of heavy rain according to a segmentation scale. This novel method provides new insights into extended range forecasting and atmospheric predictability, and also allows the creation of multi-variable chaotic extreme weather prediction models based on high spatiotemporal resolution data.

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 met- eorological 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 1 0-30-day extended range fore- casting, 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＂5-10-2）, minor vari- ation in random error cannot significantly change the dynamic features of a chaotic system, and therefore random er- ror has minimal effect on the prediction. When the ratio is in the range of 10-1-2 （i.e., random error dominates）, at- tention 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 forecast- ing, 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 depic- ted 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 temperat- ure or geopotential height; however, for hurricanes, geopotential height is most sensitive, followed by precipitable water.

DOWNSCALING FORECAST OF MONTHLY PRECIPITATION OVER GUANGXI BASED ON BP NEURAL NETWORK MODEL

Variables fields such as enstrophy, meridional-wind and zonal-wind variables are derived from monthly 500 hPa geopotential height anomalous fields. In this work, we select original predictors from monthly 500-hPa geopotential height anomalous fields and their variables in June of 1958 - 2001, and determine comprehensive predictors by conducting empirical orthogonal function (EOF) respectively with the original predictors. A downscaling forecast model based on the back propagation (BP) neural network is built by use of the comprehensive predictors to predict the monthly precipitation in June over Guangxi with the monthly dynamic extended range forecast products. For comparison, we also build another BP neural network model with the same predictands by using the former comprehensive predictors selected from 500-hPa geopotential height anomalous fields in May to December of 1957 - 2000 and January to April of 1958 - 2001. The two models are tested and results show that the precision of superposition of the downscaling model is better than that of the one based on former comprehensive predictors, but the prediction accuracy of the downscaling model depends on the output of monthly dynamic extended range forecast.