基于太阳黑子的邵阳地区月降水量预报
doi: 10.11728/cjss2026.05.2025-0220 cstr: 32142.14.cjss.2025-0220
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赵海娟 女, 1977年4月出生于河北省滦南县, 现为国家卫星气象中心(国家空间天气监测预警中心)高级工程师, 主要研究方向为太阳活动预报及空间天气预报. E-mail: zhaohj@cma.cn -
孙飞飞 男, 1985年5月出生于江苏省灌南县, 现为中水北方勘测设计研究有限责任公司高级工程师, 主要研究方向为中长期降水预报及工程安全等. E-mail: f556sun@163.com
作者简介:
通讯作者:
Monthly Precipitation Forecast in Shaoyang Region Based on Sunspots
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摘要: 开展邵阳地区月降水量的精准预报研究, 构建太阳黑子相对数年滑月均值(RSSNy)指数, 基于该指数构建径向基函数(RBF)神经网络预报模型; 以RSSNy指数的预测结果为核心输入变量, 构建多层感知器(MLP)月降水量预报模型, 实现从太阳活动信号到降水量的关联建模; 定义降水量丰枯指数(RAI), 通过该指数的构建有效克服预报模型优化过程中局部最优与全局最优的矛盾, 进而采用MLP模型开展RAI预测研究. 研究结果表明, 基于RSSNy指数的RBF预报模型性能优异, 在率定期、验证期及预测期均呈现良好的稳定性与精度, 其中t+1月预测结果中, 93%样本的相对误差小于10%; MLP月降水量预报模型拟合与泛化能力突出, 训练集与测试集的决定系数(R2)均达到0.99, 满足高精度预报要求; 定义的RAI指数为降水量丰枯状态的量化评估提供了有效工具, 具有进一步深化研究与推广应用的价值; MLP月RAI预报模型的预测精度达到满足相关规范规定的精度标准要求, 可有效实现降水量丰枯状态的提前预判. 综上研究结果, 突破了传统降水预报仅依赖局地气象因子的局限, 为月尺度降水预报提供了新的技术路径与理论支撑.Abstract: The prediction of monthly precipitation is of great significance for water resource utilization and water conservancy project scheduling. The core work of this study includes: proposing a new sunspot RSSNy index and constructing an RBF forecasting model; construct a Multilayer-Perceptron (MLP) monthly precipitation forecast model based on the RSSNy index prediction value; construct the Rainfall Abundance Index (RAI) to overcome the contradiction between local and global optima, and using MLP for RAI prediction. The results show that: the Radial Basis Function network (RBF) forecasting model of RSSNy index performs well in the calibration, validation, and prediction stages, with a relative error of less than 10% for 93% of the predicted values in month t+1; the training and testing sets of the MLP monthly precipitation forecast model have good performance, with R2 values of 0.99 for both sets; the defined RAI index provides an effective tool for the quantitative assessment of precipitation abundance and scarcity states, and holds value for further research deepening and application promotion; the MLP monthly RAI forecast model performs well and meets the accuracy requirements. The research on monthly precipitation forecast based on sunspots has pioneering significance.
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Key words:
- Sunspot number /
- RSSNy index /
- Monthly precipitation /
- Forecasting model /
- Rainfall abundance index
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图 1 基于太阳黑子数的月降水量预报方法
Figure 1. Framework of monthly precipitation forecasting method based on sunspot number
图 2 极值系列实例(以1960年1月的预测RSSNy指数和率定的$ {f}_{\text{B}} $模型计算)
Figure 2. Example of extreme value series (calculated based on the RSSNy and calibrated $ {f}_{\text{B}} $ model for January 1960)
图 3 1950年1月至2026年5月RSSNy指数未来第一个月的预测、实测及误差
Figure 3. One-month lead prediction, observation, and error of RSSNy index from January 1950 to May 2026
图 4 1950年1月至2026年5月RSSNy指数未来第二个月的预测、实测及误差
Figure 4. Two-month lead prediction, observation, and error of RSSNy index from January 1950 to May 2026
图 5 $ {f}_{\text{B}} $模型降水量预测. (a)训练集的相对误差, (b)测试集的相对误差, (c)模拟值与实测值的散点图
Figure 5. $ {f}_{\text{B}} $ model-predicted precipitation. (a) relative error (training set), (b) relative error (test set), (c) scatter plot of simulated versus observed values
图 6 1960－2023年期间最优RAI整数值在各月的出现次数
Figure 6. Number of occurrences of the optimal RAI value in each month during 1960－2023
图 7 1960－2023年RAI整数值与每月出现次数的关系
Figure 7. Relationship between the RAI and the occurrence quantity during 1960－2023
图 8 (a) RAI年值与年降水量的关系, (b) RAI月均值与月降水量的关系
Figure 8. (a) Relationship between RAI annual value and annual precipitation, (b) relationship between RAI monthly mean and monthly precipitation
图 9 RAI_id1模型和RAI_id2模型预测值各月平均合格率
Figure 9. Average qualification rate in each month of RAI_id1 model and RAI_id2 model
表 1 PSO参数设置依据
Table 1. Basis for setting PSO parameters
参数 推荐值 设定依据 邵阳市案例适配调整 粒子数量 50～100 文献实证: Kennedy 等研究[29]表明, 粒子数量大于30时可有效避免早熟收敛, 保障解空间的覆盖度
计算效率: 邵阳市降水数据采用月度尺度, 数据维度较低, 无需过多粒子即可覆盖潜在解空间, 减少计算冗余设定为60, 既满足解的精度要求, 又控制计算成本, 单次迭代耗时控制在合理范围 惯性权重ω 0.4→0.9
线性递减理论基础: Shi 等提出[30], 高惯性权重可增强粒子的全局探索能力, 帮助跳出局部最优; 低惯性权重则可加速粒子向局部最优解收敛, 提升调优精度
动态策略: 初始阶段采用高ω扩大搜索范围, 避免错过全局最优解; 迭代末期采用低ω进行精细调优, 提升解的稳定性迭代公式: $ {\omega }_{t}=0.9-0.5×(t/{T}_{\max }) $, 其中$ t $为当前迭代次数, $ {T}_{\max } $为最大迭代次数, 实现惯性权重的动态自适应调整 认知系数c1 1.5～2.0 个体学习权重: 认知系数控制粒子对自身历史最优位置的学习能力, >2.0时, 易导致粒子轨迹振荡, 降低收敛效率; <1.0时, 则会使粒子学习能力不足, 收敛速度过慢
实验验证: 通过参数扫描实验发现, 当c1=1.7时, 目标函数NSE较其他取值提升12%, 适配性最优固定为1.7, 通过网格搜索法确定, 确保粒子个体学习能力与收敛稳定性的平衡 社会系数c2 1.5～2.0 群体协作权重: 社会系数控制粒子对群体最优位置的学习能力需与认知系数协同作用, 共同控制粒子轨迹的合理性
敏感性分析: 通过正交实验验证, 当c2=1.8时, 粒子群多样性最优, 可有效避免早熟收敛, 同时保障收敛速度固定为1.8, 经正交实验验证, 与c1=1.7组合时, 目标函数值达到最优 速度限幅 ±20%解
空间范围防止粒子速度过快导致轨迹振荡, 避免粒子跳出合理解空间; 结合邵阳市降水序列特性, 降水值域为0～400 mm, 20%的限幅可兼顾探索性与稳定性 动态约束: $ {v}_{\max }=0.2×({x}_{\max }-{x}_{\min }) $, 其中$ {x}_{\max } $, $ {x}_{\min } $分别为降水序列的最大值与最小值, 即$ {v}_{\max }=80 $ mm·month–1, 适配邵阳降水数据范围 
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表 2 1960－2023年期间最优RAI整数值出现次数
Table 2. Occurrence of the RAI value in each month during 1960－2023
RAI 1月 2月 3月 4月 5月 6月 7月 8月 9月 10月 11月 12月 出现次数 1 41 35 19 9 7 3 22 25 40 32 38 52 323 2 16 20 23 15 8 15 17 14 10 13 13 7 171 3 5 8 14 21 26 20 15 11 11 12 9 5 157 4 2 1 6 14 14 10 5 12 1 3 4 0 72 5 0 0 2 5 6 14 5 2 2 4 0 0 40 6 0 0 0 0 2 1 0 0 0 0 0 0 3 7 0 0 0 0 1 1 0 0 0 0 0 0 2 合格率/(%) 81.3 76.6 93.8 92.2 90.6 87.5 95.3 90.6 82.8 82.8 78.1 71.9 85.3
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