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Precipitation Forecast Correction in South China Based on SVD and Machine Learning
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摘要: 降水是在多种天气系统和复杂物理过程共同影响下形成的，因此降水预报难度较大。由于数值预报模式的局限性，使得模式预报产品存在一定误差。为探讨更加有效的模式预报产品误差订正方法，基于奇异值分解（SVD）与机器学习（多元线性回归、套索回归、岭回归）构建订正模型，对2007—2019年4月1日—6月30日华南前汛期欧洲中期天气预报中心（EC）模式降水预报产品进行误差订正试验。结果表明：基于SVD与机器学习相结合的订正模型能有效降低EC模式降水预报产品在华南的预报误差，均方根误差最大优化率达4.2%，累计超过69%的站点得到不同程度的优化；SVD与机器学习相结合的订正模型能很好地处理因子间共线性问题，具有更好的鲁棒性；而对多个订正模型加权集成，均方根误差优化率达5.7%，累计超过77%的站点得到优化，显然加权集成方法订正效果不仅优于EC模式预报产品，也优于参与集成的任一订正模型。Abstract:
Precipitation can be induced by various weather systems and a series of complex physical processes, so its prediction is relatively difficult in weather forecasting. Due to the limitation of numerical model, the prediction error is inevitable. It is a hot topic in meteorological research and operation to explore a more effective method to correct the model product, and to improve the interpretation and applicability. To explore a more effective model product error correction method, a combination of correction methods is put forward, based on singular value decomposition (SVD) and machine learning, including multiple linear regression, LASSO regression and Ridge regression. The results are compared with the traditional matrix coefficient method, and then correction models are tested in pre-flood season precipitation forecast in South China, by correcting European Centre for Medium-Range Weather Forecasts (EC) product. The result shows that the proposed correction models combining SVD and machine learning can effectively reduce the error of EC product. The maximum optimization rate root mean square error is 4.2%, and more than 69% of the stations are optimized to different degrees. These correction models have better robustness to deal with the problem of collinearity between factors, and the correction effect is better than that of the traditional matrix coefficient method. Furthermore, the weighted integration of multiple correction models is carried out by assigning different weights to different models, and the root mean square error by the integrated approach in South China is smaller than EC product and any single correction model. It shows that the weighted ensemble method can better integrate the advantages of multiple correction models and enlarge the advantages. For the weighted ensemble of multiple correction models, it is not only better than the precipitation prediction results of EC product, but also better than any one of the integrated correction models. Its optimization rate of root mean squared error can achieve 5.7%, and more than 77% of the stations are optimized to different degrees.
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图 4 不同模型(方法)与EC模式预报产品均方根误差差值对比
(a)模型Ⅰ, (b)模型Ⅱ, (c)模型Ⅲ，(d)模型Ⅳ, (e)加权集成方法
Fig. 4 Comparison of root mean square error difference of different models, method to EC product before and after correction
(a)model Ⅰ, (b)model Ⅱ, (c)model Ⅲ, (d)model Ⅳ, (e)weighted ensemble
图 5 正负订正幅度站点数占比
(a)模型Ⅰ, (b)模型Ⅱ, (c)模型Ⅲ, (d)模型Ⅳ, (e)加权集成方法
Fig. 5 Ratio of positive and negative sites to the correction amplitude
(a)model Ⅰ, (b)model Ⅱ, (c)model Ⅲ, (d)model Ⅳ, (e)weighted ensemble
图 7 正、负订正单站对比
(RMSE1为EC模式预报产品的均方根误差，RMSE2为加权集成订正后的均方根误差)
Fig. 7 Comparison of positive and negative correction sites
(RMSE1 is root mean square error of the EC product, RMSE2 is root mean square error of weighted ensemble)
图 8 2018年6月12日和2019年5月9日两次降水个例订正
Fig. 8 Comparison of two precipitation cases on 12 Jun 2018 and 9 May 2019 before and after correction
表 1 前10个模态累计方差贡献
Table 1 Cumulative variance contribution of the top 10 modes
模态序号 累计方差贡献 1 0.5162 2 0.6220 3 0.6763 4 0.7220 5 0.7516 6 0.7716 7 0.7888 8 0.8014 9 0.8112 10 0.8197 
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表 2 不同模型(方法)订正效果
Table 2 Correction effect in different models and method
模型 均方根误差/(mm·d-1) 优化率/% 模型Ⅳ 13.26 4.1 模型Ⅱ 13.26 4.1 模型Ⅲ 13.24 4.2 模型Ⅰ 13.24 4.2 加权集成方法 13.01 5.7
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