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Application of Machine Learning to Statistical Evaluation of Artificial Rainfall Enhancement
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摘要: 利用福建省古田人工增雨试验基地2014年1月—2023年1月小时自然降水数据, 结合线性拟合、多项式回归和样条回归等多种数学统计方法, 开展决策树、支持向量机(SVM)和卷积神经网络(CNN)3种机器学习方法在估测目标区自然降水中的应用研究。目标区和对比区自然雨量关系模型对比结果表明:以区域平均面雨量为统计变量时, CNN和四项式回归效果相对较好, 其中CNN的确定系数为0.516, 均方根误差为1.097 mm;对平均面雨量进行六次方根变换后, 各模型的精准度大幅提升, CNN表现最优, 确定系数为0.658, 其次为SVM;为克服目标区和对比区雨量时间序列效应及空间分布不均等问题, 以面雨量空间格点数据作为研究对象, 采用CNN 3种优化器(自适应矩估计、均方根传递和梯度随机下降)算法进行对比, 发现基于自适应矩估计优化器建立目标区和对比区雨量关系模型最优, 其降水估测值与实测值更接近, 均方根误差最小, 为0.61 mm。因此, 利用CNN方法能够进一步优化目标区和对比区雨量关系模型, 可为定量评估人工增雨效果提供参考。Abstract: As an important part of weather modification operation, the scientific effectiveness evaluation of artificial rainfall enhancement has gradually attracted attentions of government and public. In order to evaluate effects of artificial rainfall enhancement objectively and quantitatively, combing linear fitting, polynomial regression, spline regression and 3 other machine learning methods including decision tree, support vector machine and neural network, the relationship model between the rainfall in the target area and the contrast area is established based on rainfall data and operation information of recent 10 years in Fujian. Different historical regression statistical test schemes of rainfall enhancement effects are compared and analyzed, aiming to further optimize the best natural rainfall estimation algorithm based on alterable contrast area with statistical method, which can provide reference for the assessment of artificial rainfall enhancement effects. Results show that historical rainfall data samples are mainly concentrated in the weak rainfall grade. Using multiple regression methods (linear regression, polynomial regression and spline regression), the piecewise statistics of rainfall data does not significantly improve the linear regression model between two regions, and its root mean square error (RMSE) is generally higher than the statistical results. By comparing various machine learning and linear regression models, it is found that CNN and quomial regression perform relatively well when the regional average surface rainfall is taken as the statistical variable, with the determination coefficient of CNN being 0.516 and RMSE being 1.097 mm. Each statistical model is greatly improved after six root square transformations of rainfall data. The performance of the model established by CNN method is relatively optimal, with determination coefficient R2 up to 0.658 and RMSE only
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图 1 福建省古田人工增雨效果检验基地
Fig. 1 Gutian artificial rainfall effect evaluation base in Fujian
图 2 目标区与对比区地形相似度与降水相似度拟合关系
Fig. 2 Fitting relationship between topography similarity and rainfall correlation coefficient in target area and contrast area
图 3 古田随机试验目标区、浮动对比区与最佳对比区设置
Fig. 3 Artificial rainfall target area, floating contrast area and the best-contrast area of Gutian
图 5 不同雨强下各模型的降水估测均方根误差对比
Fig. 5 Root mean square error of rainfall estimation for different rainfall intensity by different models
图 6 基于总样本的不同模型降水估测的均方根误差和确定系数
Fig. 6 Root mean square error and determination coefficient of rainfall estimation based on total samples by different models
图 7 目标区和对比区格点化及区域自动气象站分布
Fig. 7 Regional grid and automatic weather station in target area and contrast area
图 8 2016年4月9日19:00不同插值方法得到的面雨量分布
Fig. 8 Area rainfall distribution with different methods at 1900 BT 9 Apr 2016
图 9 3种优化器降水估测对比
Fig. 9 Comparison of rainfall estimation among 3 machine learning optimizers
表 1 2014—2023年不同等级降水样本量
Table 1 Sample size of different rainfall categories in 2014-2023
降水等级 雨强/(mm·h-1) 样本量 样本比例/% 弱降水 [0.1, 5) 25207 95.98 一般降水 [5, 10) 780 2.97 中等降水 [10, 25) 269 1.02 强降水 [25, +∞) 7 0.03 
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