不同时间尺度、季节的气温数据空间平稳特征及其对插值结果的影响

doi:10.11821/dlyj201509006

摘要/Abstract

摘要：

不同时间尺度、季节的气温数据表现出不同的空间平稳特征。为探讨分析空间平稳性对气温插值的影响规律,采用趋势线法对气温数据进行空间平稳性探索,并对比分析不同空间平稳性条件下,普通线性回归、普通克里格、回归克里格的气温插值精度及插值结果的空间分布特点。结果显示：冬季日均、月均气温与年均气温呈现空间非平稳,插值精度随时间序列的增长而提高,随着气温数据逐渐趋于稳定,精度提高的幅度逐渐下降;夏季日均、月均气温呈现空间平稳,随时间序列的增长,插值精度的提高并不显著;夏季日均气温各插值方法的插值精度普遍高于冬季日均气温。与普通克里格相比,回归克里格能有效提高空间非平稳数据的插值精度。时间序列的增长削弱了不同插值算法之间的插值精度差异和插值结果空间分布差异。

关键词: 气温, 空间平稳性, 时间尺度, 季节, 空间插值

Abstract:

Spatial stationary is a hypothesis for most geo-statistical processes. In order to explore the influence of spatial non-stationary on air temperature interpolation performance, a set of air temperature data in different time scales (including daily average air temperature, monthly average air temperature of January and July and annual average air temperature in 2010) are used. First of all, stepwise regression analysis is adopted to select the most important regression parameters for each data set of temperature. Then trend line analysis is used to estimate whether the air temperature data meets the assumption of spatial stationary. Finally, ten-cross validation is carried out by using the interpolation methods of ordinary linear regression, ordinary kriging, and regression kriging respectively. According to the results, the conclusion can be summarized as follows: 1) Daily average, monthly average air temperature of January, and annual average air temperature data present spatial non-stationary characteristic and an obvious change trend in the north-south direction; while daily average and monthly average air temperature of July are spatial stationary. Interpolation accuracy of daily average air temperature in July, which is spatial stationary, is significantly higher than that in January, which is spatial non-stationary. 2) In general, all the three interpolation methods obtain the best prediction results on annual dataset, then monthly datasets, worst on daily datasets, because the spatial structure of the daily air temperature dataset is more non-stationary than that of the monthly and annual temperature datasets. In terms of time series, the interpolation error reduces with the decrease of the degree of reduction. 3) Regression kriging achieves higher interpolation accuracy on each dataset in general than ordinary kriging, furthermore the improvement of interpolation accuracy achieved by regression kriging is more obvious on non-stationary datasets than on stationary datasets. 4) Distribution of air temperature interpolated by various techniques presents significantly difference in daily time scale, but in monthly and annual scales, there is no significant difference. Values in long time series, which are the means of values in short time series, weaken the occurrence probability of extreme values. Thus the distribution ranges of air temperature in January and July decrease, compared with daily average air temperature in corresponding seasons.

Key words: air temperature, spatial stationary, time scales, season, spatial interpolation

郭春霞, 诸云强, 孙伟. 不同时间尺度、季节的气温数据空间平稳特征及其对插值结果的影响[J]. 地理研究, 2015, 34(9): 1675-1684.

Chunxia GUO, Yunqiang ZHU, Wei SUN. Analysis of spatial stationary characteristics of air temperature data in different time scales, seasons and its influence on interpolation performance[J]. GEOGRAPHICAL RESEARCH, 2015, 34(9): 1675-1684.

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统计量	平均气温（℃）
统计量	2010.01.01	2010.07.01	2010.01	2010.07	2010
平均值	-2.18	24.59	-1.51	24.50	11.76
中位数	0.70	24.80	-1.10	25.70	12.50
最小值	-41.80	5.10	-29.40	7.70	-4.60
最大值	22.50	33.60	20.90	33.30	25.50
标准差	11.90	5.59	10.27	4.75	6.4
峰度系数	0.32	0.14	-0.65	0.94	-0.82
偏度系数	-0.90	-0.72	-0.31	-1.16	-0.26

插值方法	1月1日平均气温(℃)			7月1日平均气温(℃)
插值方法	RMSE		MAE	RMSE	MAE
普通线性回归	4.454	3.470		2.790	2.192
普通克里格	4.032	3.064		2.537	1.752
回归克里格	2.559	1.816		2.061	1.388

插值方法	1月平均气温(℃)			7月平均气温(℃)
插值方法	RMSE		MAE	RMSE	MAE
普通线性回归	2.929	2.139		2.332	1.706
普通克里格	2.490	1.809		2.533	1.731
回归克里格	1.750	1.195		1.964	1.265

插值方法	2010年平均气温(℃)
插值方法	RMSE	MAE
普通线性回归	1.981	1.408
普通克里格	2.361	1.625
回归克里格	1.784	1.133