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空间结构函数在北京地区气象观测站网设计中的应用
The Application of Spatial Structure Functions to the Design of Weather Station Networks in Beijing Area
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摘要: 通过统计1978—2000年北京东南低地形区有关台站在春季、夏季、秋季、冬季的逐日平均气温和水汽压的结构函数, 分季节分析了该地区这两个二类气象要素的线段及平面内插精度和台站间距的对应关系, 并根据内插标准误差不超过观测标准误差的原则, 对上述两要素在北京东南低地形区的合理布站方案及间距进行了估算, 可以为2008年北京奥运会气象服务系统建设中气象台站布网建设提供一定的依据。结果表明, 正三角形排列方案为北京东南地区二类气象台站的最佳布站方案, 且布站精度应小于等于16 km。Abstract: Using the data of daily air temperature and water-vapor pressure from 1978 to 2000 over the southeast Beijing, the spatial structure functions of the two elements are regressed for different seasons. Furthermore, based on the structure functions, the relationships between the error of linear and plane interpolation and distance are established. Finally, according to the principle that the standard error of interpolation should not exceed the standard error of observation, the maximum admissible spacing between stations of second group meteorological networks are estimated over the area.It is found that the equilateral triangle distributing is the best scheme to use, and the distance between stations should be less than 16 km. Firstly, the regressed spatial structure functions to the distances of the air temperature and water-vapor pressure are linear or close to linear. Over the southeast Beijing, the spatial structure functions increase monotonously with the distances, and have different values in different seasons. The season sequences in which the spatial structure functions of air temperature varies from largest to least are winter, autumn, spring and summer, and they are just opposite for the structure functions of water-vapor pressure. It illustrates that the temperature gradient is largest in winter, least in summer, and larger in autumn than in spring over the southeast Beijing, and the water-vapor pressure gradient varies from the largest to the least sequentially in summer, spring, autumn and winter, just oppositely to the condition of temperature gradient. The standard error of interpolation, maximum admissible error, and maximum admissible spacing all vary with seasons and distributing schemes, and the season sequences according to the standard error values is the same with that for the structure functions. When the standard error of interpolation is less than the standard error of observation, in all seasons, the equilateral triangle distributing has the least interpolation error, the largest maximum admissible error and admissible spacing between stations for the both elements. So the equilateral triangle distributing is the best scheme to use. With this distributing scheme, the distance between stations should be less than 16 km for temperature and 88 km for water-vapor pressure. So in a word, based on these two elements, the equilateral triangle distributing is the best scheme to use, and the distance between stations should be less than 16 km for the second group meteorological networks over the southeast Beijing.Further investigation shows that if consider the northwest high altitude region together with the southeast low lying region of Beijing, the equilateral triangle distributing is still the best scheme, but the distance between stations should be less than 4 km for the second group meteorological networks over the whole Beijing region. This is not consistent with the request of the second group meteorological networks. So the second group meteorological networks over the southeast and northwest region of Beijing should be designed separately, or some resource would be wasted.
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图 1 北京地区边界 (虚线)、地形高度 (实线, 单位:m) 及台站 (实心圆点) 分布
Fig. 1 The outline (dashed line), the topographic altitude of Beijing (solid line, unit:m) and the location of the observation stations (thick dots)
图 2 北京东南低地形区1978—2000年1, 4, 7, 10月日平均气温 (a) 和日平均水汽压 (b) 的结构函数与距离的关系
Fig. 2 The spatial structure functions of daily average air temperature (a) and water vapor pressure (b) varying with the distance between stations over the southeast Beijing for different seasons during 1978 to 2000
图 3 北京东南低地形区1978—2000年1, 4, 7, 10月日平均气温在3种布站方案下的内插标准误差与距离的关系
Fig. 3 The interpolation error of daily average air temperature for linear, equilateral triangle and equilateral rectangle distributing schemes varying with the distance between stations over the southeast Beijing for different seasons during 1978 to 2000
图 4 北京东南低地形区1978—2000年1, 4, 7, 10月日平均水汽压在3种布站方案下的内插标准误差与距离的关系
Fig. 4 The interpolation error of daily water vapor pressure for linear, equilateral triangle and equilateral rectangle distributing schemes varying with the distance between stations over the southeast Beijing for different seasons during 1978 to 2000
表 1 北京东南低地形区1978—2000年1, 4, 7, 10月日平均气温和水汽压的结构函数对于距离的回归方程
Table 1 The equations of regressed spatial structure functions of daily average air temperature and water vapor pressure to the distance between stations over the southeast Beijing for different seasons during 1978 to 2000
表 2 北京低地形区1978—2000年各代表月份气温及水汽压在不同布站方案下的最大容许误差及最大容许距离
Table 2 The maximum admissible error and maximum admissible spacing of daily average air temperature and water vapor pressure for different distributing schemes over the southeast Beijing for different seasons during 1978 to 2000
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