一种融合时空特性的气温缺失记录重建方法

doi:10.13249/j.cnki.sgs.2014.09.1125

摘要/Abstract

摘要：

针对气象记录缺失的普遍现象以及现实中对完整记录的迫切需求,提出一种新的融合时空特性的气温缺失记录重建方法,并与线性插值、基于DEM的普通克里金以及标准比率法等进行对比。实验结果表明：线性插值法和基于DEM的普通克里金法仅考虑气温的时间或空间特性,重建精度较差;标准比率法部分地考虑气温的时空分布特性,因此在部分月份具有较高的重建精度;然该方法稳健性较差,致使其整体重建精度较低。

关键词: 气象缺失记录, 克里金, 气温缺失记录, 气温

Abstract:

Data missing is frequently encountered in climate variables due to many reasons, such as instrument failures in the observatory, meteorological extremes, and observation recording errors. However, several types of climatic analysis require the availability of data not only covering a long enough period of time, but also forming a complete and homogeneous series. This paper presented a novel imputation method for missing air temperature records by merging their spatio-temporal characteristics. On the basis of extending Kriging model, a nonstationary Kriging method which assumes that the mean is known and varying in study area was proposed. Firstly, the trend of air temperature in each station was attained by analyzing its time series data, and linear interpolation was adopted in this study. Then, geostatistical analysis were performed on the errors between the trend and observed values. Finally, the spatio-temporal information of air temperature was integrated into the proposed Kriging model. Three other imputation methods, including linear interpolation, ordinary Kriging based on DEM (OKD) and normal ratio, were introduced to compare with. The results show that: 1) Besides OKD, the imputation accuracy of the other three methods varies obviously in 12 months. For linear interpolation, its imputation accuracy in May and July-October is much higher than that in the rest of the month. Normal ratio has higher imputation accuracy in April-November. The proposed method has higher imputation accuracy in March-October, with mean absolute error (MAE) less than 0.2℃. 2) Normal ratio has the largest MAE (4.17℃) in December and the least MAE (0.18℃) in October, this means that it has poor robustness. Compared with linear interpolation, the difference between the maximum and minimum MAE values of OKD is much less (0.25℃), thus it has better robustness. With the difference being 0.1℃ only, the proposed method has the strongest robustness. 3) Air temperature contains the temporal and spatial characteristics together. Linear interpolation only considers its temporal characteristics but ignores its spatial characteristics, while OKD only considers its spatial characteristic but ignores its temporal characteristics. Therefore, they don't attain the satisfactory imputation results. With partly taking the spatio-temporal characteristics of air temperature into account, normal ratio can attain higher imputation accuracy in March-November. However, this method has poor robustness. When air temperature in study area varies sharply or fluctuates around 0℃, normal ratio has lower imputation accuracy. As a result, its overall imputation accuracy is still lower. Among these methods, the proposed method has the smallest MAE and root mean square error in each month and produces the best imputation results.

Key words: missing meteorological records, Kriging, missing air temperature, air temperature

中图分类号:

P456.8

陈锋锐, 刘宇, 李熙. 一种融合时空特性的气温缺失记录重建方法[J]. 地理科学, 2014, 34(9): 1125-1133.

Feng-rui CHEN, Yu LIU, Xi LI. A Novel Imputation Method of Missing Air Temperature Records Based on Merging Spatio-temporal Characteristics[J]. SCIENTIA GEOGRAPHICA SINICA, 2014, 34(9): 1125-1133.

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月份（月）	最大值（0.1℃）	最小值（0.1℃）	平均值（0.1℃）	标准差（0.1℃）	变异系数（%）	偏度	Moran's I
1	2.6	-27.4	-10.2	4.1	-	-0.70	0.68^**
2	-12.6	-58.2	-35.2	6.9	-	-0.08	0.65^**
3	1.0	-20.6	-11.1	4.1	-	0.55	0.57^**
4	22.2	-0.2	11.3	4.7	41.6	-0.52	0.52^**
5	6.4	-14.6	-3.7	4.4	-	-0.36	0.37^**
6	21.8	-3.4	12.9	5.4	41.8	0.88	0.34^**
7	20.0	-10.4	6.4	5.8	90.6	0.06	0.42^**
8	6.2	-28.4	-5.9	7.2	-	-0.38	0.50^**
9	23.0	-5.2	5.2	6.2	119.2	0.40	0.54^**
10	7.0	-14.4	-4.2	3.9	-	0.86	0.62^**
11	22.6	-3.2	10.9	5.0	45.9	-0.51	0.69^**
12	2.6	-38.2	-17.9	8.1	-	0.00	0.69^**

月份（月）	变异模型	块金（C₀）	基台（C₀+C）	变程(A) (km)	结构方差/基台[C/(C₀+C)]	R²
1	指数模型	1.96	21.12	1013	0.91	0.94
2	指数模型	5.22	65.02	1450	0.92	0.96
3	球面模型	1.73	19.25	858	0.91	0.99
4	高斯模型	5.79	19.88	521	0.71	0.95
5	高斯模型	5.36	19.76	531	0.73	0.99
6	高斯模型	4.96	34.90	694	0.86	0.99
7	高斯模型	5.60	52.20	1039	0.89	0.99
8	高斯模型	6.90	84.80	1105	0.92	0.99
9	高斯模型	5.80	50.47	668	0.89	0.99
10	球面模型	1.10	18.89	913	0.94	0.98
11	高斯模型	11.63	29.80	678	0.61	0.91
12	高斯模型	10.71	82.42	868	0.87	0.98

月份（月）	线性插值		OKD		NR		提出方法
月份（月）	MAE	RMSE	MAE	RMSE	MAE	RMSE	MAE	RMSE
1	10.2	10.9	7.5	10.3	15.4	17.9	2.3^a	3.2^b
2	35.2	35.9	6.3	9.9	20	41	2.9^a	4.1^b
3	11.1	11.8	7.3	10.9	8.2	15.8	1.6^a	2.1^b
4	11.2	12.2	8.1	11.2	2.0	2.6	1.9^a	2.4^b
5	4.5	5.7	7.0	10.0	2.0	2.6	1.8^a	2.4^b
6	13.1	13.9	7.4	10.5	2.2	2.9	1.8^a	2.3^b
7	7.1	8.7	6.4	9.3	1.9^a	2.5^b	1.9^a	2.5^b
8	7.1	9.3	5.6	8.1	2.1	2.7	1.9^a	2.5^b
9	6.4	8.1	6.0	8.5	2.1	2.8	1.8^a	2.3^b
10	5.1	5.7	6.7	8.4	1.8	2.4	1.6^a	2.1^b
11	10.9	11.9	7.5	9.4	4.4	7.5	2.5^a	3.4^b
12	17.9	19.6	7.2	9.2	41.7	81.9	2.6^a	3.6^b
平均	11.6	12.8	6.9	9.6	8.7	15.4	2.1^a	2.7^b