Construction and Verification of DAM Model
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摘要: 根据热层物理、经验模型原理和代码分析，研究模型构建方法。进而剖析国内热层大气探测和热层模型构建现状，提出存在的困难和未来的发展思路。以GOST模型为基础，分析模型的工作机制、地磁扰动期大气密度预报误差来源和密切相关的模型系数，推导模型密度对相关模型系数的偏导数矩阵。利用天基实测密度，有针对性地构建磁暴期大气模型(DAM)。并通过独立于建模的实测密度数据，验证DAM模型性能。统计发现，地磁活动指数Ap介于100～132时GOST, MSIS00和DAM模型的相对误差均值依次为64.32%，–176.72%，–14.83%。Ap指数80～132时，相对误差均值对应为77.44%，–136.74%，–14.14%，DAM模型性能较GOST和MSIS00均有明显提升。证明通过搭建大气模型框架和实测密度数据估计模型参数的建模方法是可行和有效的。Abstract: The physical model of the thermosphere and the empirical and semi-empirical model of the thermosphere are analyzed. The basic theory and code analysis of the empirical thermosphere model are used to clarify the model construction methods. Based on the current situation of atmospheric modeling in China, the difficulties are analyzed and development suggestions are given. Based on the GOST model, the prediction performance of atmospheric model in geomagnetic disturbed period was analyzed, and the construction of atmospheric model in geomagnetic storm period was studied. The Disturbed Atmospheric Model (DAM) was constructed based on the measured density data, and its validity was verified. It is found that the mean relative errors of GOST, MSIS00 and DAM models are 64.32%, –176.72% and –14.83%, respectively, within the range of geomagnetic index Ap 100～132. As Ap is within the range of 80～132, the relative error mean of each model is 77.44%, –136.74%, –14.14% respectively, DAM model is significantly improved compared with GOST and MSIS00. It is proved that the modeling method of estimating model parameters by building an atmospheric model framework and measured density data is feasible and effective.
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Key words:
- Thermosphere models /
- Model construction /
- DAM model /
- Evaluation
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图 1 GOST, DAM和MSIS00模型预报残差(a)和误差百分比(b)
Figure 1. Prediction residual (a) and error percentage (b) of GOST, DAM and MSIS00 model
图 2 GOST，DAM，MSIS00模型预报与实测密度
Figure 2. GOST, DAM, MSIS00 model prediction and measured density
图 3 基于数据集 1 评估的各模型预报残差 (a) 与误差百分比 (b)
Figure 3. Prediction residual (a) and error percentage (b) of each model based on evaluation data set 1
图 4 数据集2评估的GOST，DAM和MSIS00模型预报残差(a)和误差百分比(b)
Figure 4. Prediction residual (a) and error percentage (b) of GOST, DAM and MSIS00 model with evaluation data set 2
表 1 GOST模型参数（180<h<600 km）
Table 1. Parameters of GOST model
F0 75 100 125 150 175 200 250 a1 –1.5560×101 –1.5640×101 –1.522×101 –1.69752×101 –1.7304×101 –1.8266×101 –1.92782×101 a2 8.248×10–1 7.754×10–1 7.569×10–1 6.736×10–1 6.382×10–1 5.797×10–1 5.118×10–1 a3 7.69132×101 6.79162×101 5.58165×101 8.5444×101 8.19596×101 1.009417×101 1.165792×101 d1 –1.721×10–1 –1.721×10–1 –1.721×10–1 –1.721×10–1 –1.721×10–1 –1.721×10–1 –1.721×10–1 d2 5.756×10–3 5.756×10–3 5.756×10–3 5.756×10–3 5.756×10–3 5.756×10–3 5.756×10–3 d3 –3.635×10–6 –3.635×10–6 –3.635×10–6 –3.635×10–6 –3.635×10–6 –3.635×10–6 –3.635×10–6 b1 –8.607×10–1 –7.54×10–1 –5.7×10–1 –4.76×10–1 –2.92×10–1 –3.113×10–1 –3.307×10–1 b2 7.861×10–3 6.85×10–3 5.25×10–3 4.4×10–3 2.80×10–3 2.839×10–3 2.878×10–3 b3 –5.711×10–6 –4.6×10–6 –3.0×10–6 –2.40×10–6 –8.0×10–6 –1.089×10–6 –1.378×10–6 c1 1.2791 1.2791 1.2903 1.2903 2.057×10–1 2.057×10–1 1.499×10–3 c2 –1.576×10–2 –1.576×10–2 –1.547×10–2 –1.547×10–2 –2.912×10–3 –2.911×10–3 –2.399×10–4 c3 6.499×10–5 6.499×10–5 5.964×10–5 5.964×10–5 1.739×10–5 1.739×10–5 7.006×10–6 c4 –5.145×10–8 –5.145×10–8 –4.503×10–8 –4.503×10–8 –8.565×10–9 –8.565×10–9 –5.999×10-10 e1 –2.152×10–1 –2.162×10–1 –1.486×10–1 –1.495×10–1 –8.19×10–2 –8.286×10–2 –2.048×10–1 e2 4.167×10–3 4.086×10–3 3.263×10–3 3.182×10–3 2.358×10–3 2.278×10–3 3.596×10–3 e3 1.587×10–6 1.27×10–6 3.143×10–6 2.825×10–6 4.698×10–6 4.381×10–6 –1.587×10–6 e4 –1.651×10–9 –1.587×10–9 –3.429×10–9 –3.365×10–9 –5.206×10–9 –5.143×10–9 3.175×10-10 e5 –1.2×10–1 –1.2×10–1 –1.0×10–1 –1.0×10–1 –1.3×10–1 –1.1×10–1 –9.0×10–2 e6 5.0×10–3 2.5×10–2 2.083×10–2 2.75×10–2 4.389×10–2 3.81×10–2 3.117×10–2 e7 1.5×10–2 7.5×10–3 6.25×10–3 3.75×10–3 1.821×10–3 1.178×10–3 9.662×10–4 l1 –1.698×10–2 –1.249×10–2 –7.879×10–3 –4.882×10–3 –5.195×10–3 –5.017×10–3 –5.455×10–3 l2 1.448×10–4 1.111×10–4 7.258×10–5 4.692×10–5 4.664×10–5 4.282×10–5 4.273×10–5 l3 –9.535×10–8 –7.706×10–8 –3.658×10–8 –1.742×10–8 –2.164×10–8 –2.132×10–8 –2.273×10–8 
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表 2 GOST模型半周年效应相关参数
Table 2. Parameters related to the semi-annual effect
d A(d) d A(d) d A(d) 0 –0.028 130 0.013 260 0.015 10 –0.045 140 –0.037 270 0.07 20 –0.047 150 –0.086 280 0.115 30 –0.035 160 –0.128 290 0.144 40 –0.011 170 –0.162 300 0.155 50 0.022 180 –0.185 310 0.145 60 0.057 190 –0.199 320 0.120 70 0.090 200 –0.202 330 0.084 80 0.114 210 –0.193 340 0.044 90 0.125 220 –0.173 350 0.006 100 0.118 230 –0.140 360 –0.023 110 0.096 240 –0.096 370 –0.04 120 0.060 250 –0.042 － －
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表 3 GOST与DAM模型系数
Table 3. Parameters comparison of GOST and DAM
参数 $ \mathrm{G}\mathrm{O}\mathrm{S}\mathrm{T} $ $ \mathrm{D}\mathrm{A}\mathrm{M} $ 参数 $ \mathrm{G}\mathrm{O}\mathrm{S}\mathrm{T} $ $ \mathrm{D}\mathrm{A}\mathrm{M} $ a1 18.266 –17.37078425 n0 1.5 1.5 a2 0.5797 0.54020803 n1 0.006 0.006 a3 10.09417 10.09417 e1 –0.08286 –0.086750778 d1 –0.1721 –0.1721 e2 0.002278 0.002907369 d2 0.005756 0.005756 e3 4.38×10–6 5.43×10–6 d3 –3.64×10–6 –3.64×10–6 e4 –5.14×10–9 –3.98×10–9 l1 –0.005017 –0.005017 e5 –0.11 –0.11880196 l2 4.28×10–5 4.28×10–5 e6 0.0381 0.030412034 l3 –2.13×10–8 –2.13×10–8 e7 0.001178 0.000911514 c1 0.2057 0.2057 b1 –0.3113 –0.385954838 c2 –0.002911 –0.002911 b2 0.002839 0.002566231 c3 1.74×10–5 1.74×10–5 b3 –1.09×10–6 –1.34×10–6 c4 –8.57×10–9 –8.57×10–9 $ {\varphi }_{B} $ 0.5585 0.5585 注 黑色字体表示建模确定的 12 个待估参数。
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表 4 基于校正数据集评估的地磁扰动期模型预报性能
Table 4. Performance of each model in disturbed period based on correction data set
模型名称 相对误差均值μ/(%) 相对误差标准差σ/(%) GOST 84.99 7.66 MSIS00 –57.84 108.20 DAM 24.94 38.38
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表 5 基于数据集 1 评估的地磁扰动期各模型预报性能
Table 5. Performance of each model in disturbed period based on evaluation data set 1
模型名称 相对误差均值μ/(%) 相对误差标准差σ/(%) GOST 64.32 20.22 MSIS00 –176.72 161.35 DAM –14.83 63.70
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表 6 基于数据集 2 评估的地磁扰动期各模型预报性能
Table 6. Performance of each model in disturbed period based on evaluation data set 2
模型名称 相对误差均值μ/(%) 相对误差标准差σ/(%) GOST 77.44 11.10 MSIS00 –136.74 155.91 DAM –14.14 56.31
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