南水北调与水利科技（中英文）2025，Vol.23Issue(2)：343-353,11.DOI:10.13476/j.cnki.nsbdqk.2025.0036
基于Prony算法和卡尔曼滤波的月降水随机预报模型
A stochastic forecasting model for monthly precipitation based on the Prony algorithm and Kalman filter
摘要
Abstract
Precipitation forecasting plays a crucial role in the early warning of water hazards and the allocation of water resources,however,it is often confronted with extreme challenges in achieving accuracy due to the complex and variable nature of the climatic environment and weather systems.Despite the fact that the traditional seasonal autoregressive integrated moving average(SARIMA)model is capable of handling the seasonal fluctuations and long-term trends within precipitation sequences,it still suffers from inherent limitations when it comes to dealing with nonlinear relationships and adapting to real-time data. Two refined models grounded in Kalman filter(KF)data fusion are devised by synergizing the advantages of three methodologies:time series analysis,signal processing technology,and Kalman filter algorithm.The first model adopts the autoregressive(AR)model as the state transition matrix within the Kalman filter framework.The second model employs the Prony all-pole AR model,with its order ascertained by the MUSIC algorithm,as the state transition matrix for Kalman filter Subsequently,both models,by capitalizing on the recursive estimation mechanism intrinsic to the filtering process,carry out real-time updates of the prediction sequences yielded by the SARIMA model.These two models are respectively labeled as the SARIMA-AR-KF model and the SARIMA-PAR-KF model.The monthly precipitation data spanning from 1960 to 2014,obtained from 15 meteorological stations in the Weihe River basin,were utilized as research samples for validation of the forecasting models on the preprocessed data. The model validation results show that the SARIMA-AR-KF model improves the coefficient of determination(R2)by 6.8％ to 21.5％ and the Nash efficiency coefficient(ENS)by 6.4％ to 19.4％ as compared to the SARIMA model.The SARIMA-PAR-KF model improves the R2 by 7.3％ to 22.1％ as compared to the SARIMA-AR-KF model,the ENS improvement of 6.8％ to 19.8％.The prediction accuracy of the SARIMA-AR-KF model is higher than that of the SARIMA model at all sites,and the prediction accuracy of the SARIMA-PAR-KF model is again significantly higher than that of the SARIMA-AR-KF model at all sites. In summary,the SARIMA-PAR-KF model can effectively improve the accuracy of monthly precipitation forecasts and open up a new way for precipitation and runoff forecasts.However,the model still has deficiencies in dealing with nonlinear,non-Gaussian precipitation series,which can be further optimized in the future by applying nonlinear models and improved filtering techniques.关键词
SARIMA模型/MUSIC算法/Prony算法/卡尔曼滤波/降水预报/渭河流域Key words
SARIMA model/MUSIC algorithm/Prony algorithm/Kalman filter/precipitation forecasting/Weihe River basin分类
建筑与水利引用本文复制引用
张航,宋松柏,刘允龙,栾伟琦..基于Prony算法和卡尔曼滤波的月降水随机预报模型[J].南水北调与水利科技（中英文）,2025,23(2):343-353,11.基金项目
国家自然科学基金项目(52379026 （）
52079110) （）
