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Daily Maximum Air Temperature Forecast Based on Fully Connected Neural Network
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摘要: 为了考察辅助变量、时间滞后变量设置的重要性和神经网络中嵌入层对分类变量处理的有效性，利用2015年1月15日—2020年12月31日欧洲中期天气预报中心（European Centre for Medium-Range Weather Forecasts，ECMWF）高分辨率模式（high resolution，HRES）输出产品及中国2238个国家级地面气象站基本气象要素数据集，在全连接神经网络基础上设计4个试验，构建24 h最高气温预报神经网络模型。结果表明：加入辅助变量、时间滞后变量的特征和带有嵌入层的全连接神经网络结构的深度学习神经网络模型对HRES日最高气温预报误差均有订正效果，均方根误差降低29.72%~47.82%，温度预报准确率提高16.67%~38.89%。加入经过嵌入层处理的辅助变量后，可显著提高青藏高原中南部和西南地区东部的平均绝对偏差不超过2℃的正技巧站点比例（比仅用HRES预报因子建模分别提高21.74%和14.17%），在此基础上加入时间滞后变量显著提高上述两个地区的平均绝对偏差不超过2℃的正技巧站点比例（比仅用HRES预报因子建模分别提高40.98%和20.33%），且预报性能更加稳定。Abstract:
Objective forecast of maximum temperature is an important part in numerical weather prediction(NWP). The forecast uncertainty of near-surface meteorological elements is greater than that of upper atmospheric elements due to the impact of uncertainty in numerical forecasting models for sub-grid and boundary layer schemes.In recent years, meteorological observations expand rapidly, making traditional error correct method difficult to deal with the massive data. As a result, artificial intelligence has an increasingly obvious advantage in processing big data. Based on the fully connected neural network, four sensitivity experiments are designed in order to investigate the importance of auxiliary variable, time-lagged variable and the effectiveness of embedding layer in the neural network. The output products of high resolution(HRES) model of European Centre for Medium-Range Weather Forecasts(ECMWF) and the observations of basic meteorological elements of totally 2238 basic weather stations from 15 January 2015 to 31 December 2020 are employed. The training period is from 15 January 2015 to 31 December 2019, and the rest part is test period.The results show that the forecast error of daily maximum air temperature from the HRES in test period is reduced greatly by the sensitivity experiments, which add auxiliary variables, daily maximum air temperature with 1-2 lag days and embedding layer structures and their combination. The root mean square error is reduced by 29.72%-47.82% and the accuracy of temperature forecast are increased by 16.67%-38.89%, and the effects for Qinghai-Tibet Plateau is especially remarkable where the forecast error of HRES model is very high. It is preliminarily proved that the fully connected neural network with embedding layer has better overall performance than the raw fully connected neural network, and the features also affect the forecast errors and forecast skills of the model. Besides, the prediction error of neural network model with embedding layer is more stable when auxiliary variables and lag time variables are added. Positive forecasting techniques are available for almost all stations in the study, and it is possible to reduce the mean absolute error to less than 1℃ at many stations.
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图 1 研究区域地形高度(填色)及站点(黑色圆点)分布
Fig. 1 Topography(the shaded) of the target area and distribution of stations(black dots)
图 3 日最高气温预报值与观测值散点图及核密度
(红色实线为对角线，黑色虚线为拟合线)
Fig. 3 Scatter plot and kernel density of daily maximum air temperature between observation and forecasting
(the red solid line denotes the diagonal, the black dashed line denotes the fitting line)
图 4 日最高气温预报技巧评分(单位：%)
Fig. 4 Prediction skill score for forecasted daily maximum temperature(unit: %)
图 5 测试集中HRES和各试验预报的1—12月均方根误差箱线图
Fig. 5 Box plot of root mean square error of HRES and each test in test dataset during Jan-Dec
表 1 不同特征和嵌入层对全连接神经网络结构影响试验设计
Table 1 Experiments of features and embedding layers on the structure of multi-input neural network
试验 特征 辅助变量 嵌入层 时间滞后变量 1 有 无 无 无 2 有 有 无 无 3 有 有 有 无 4 有 有 有 有 
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表 2 各试验不同区域的正技巧站点比例(单位：%)
Table 2 Ratio of positive skills in different regions(unit: %)
试验 东北 新疆 西北地区东部 华北 青藏高原中南部 西南地区东部 长江中下游 华南 1 96.35 87.50 79.38 91.45 89.87 85.64 96.71 97.46 2 78.54 66.67 73.75 76.92 83.54 78.10 84.87 87.31 3 99.09 94.79 96.88 98.72 98.73 98.78 99.18 97.97 4 99.54 98.96 98.13 98.93 100.00 99.76 99.34 100.00
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表 3 各试验不同区域平均绝对偏差不超过2℃的正技巧站点比例(单位：%)
Table 3 Positive skill ratio of mean absolute error no more than 2℃ in different regions(unit: %)
试验 东北 新疆 西北地区东部 华北 青藏高原中南部 西南地区东部 长江中下游 华南 1 98.58 89.29 96.85 99.07 57.75 78.69 97.96 97.92 2 97.09 82.81 95.76 98.89 51.52 78.82 97.48 97.67 3 99.54 97.80 100.00 99.57 79.49 92.86 99.67 99.48 4 100.00 100.00 100.00 100.00 98.73 99.02 99.83 100.00
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表 4 各试验不同区域平均绝对偏差不超过1℃的正技巧站点比例(单位：%)
Table 4 Positive skill ratio of mean absolute error no more than 1℃ in different regions(unit: %)
试验 东北 新疆 西北地区东部 华北 青藏高原中南部 西南地区东部 长江中下游 华南 1 17.54 17.86 14.17 39.72 5.63 0.00 29.25 6.25 2 0.58 4.69 5.93 8.89 4.55 0.00 6.59 4.07 3 24.42 19.78 20.65 39.18 8.97 1.97 23.38 5.70 4 43.12 48.42 48.41 70.41 37.97 11.95 43.71 22.34
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表 5 各试验不同区域平均正技巧评分(单位：%)
Table 5 Average positive skill scores in different regions(unit: %)
试验 东北 新疆 西北地区东部 华北 青藏高原中南部 西南地区东部 长江中下游 华南 1 19.19 23.38 35.86 23.46 57.81 33.38 25.31 28.44 2 10.84 20.05 34.72 17.60 57.16 32.47 16.14 21.17 3 20.75 27.78 36.85 23.84 64.97 39.74 26.88 30.56 4 27.20 37.40 43.47 30.72 71.04 46.46 33.18 37.53
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