﻿ 克里金日降水插值的不同变异函数比较分析 Comparison and Analysis of Different Variogram Functions Models in Kriging Interpolation of Daily Rainfall

Journal of Water Resources Research
Vol.05 No.05(2016), Article ID:18788,9 pages
10.12677/JWRR.2016.55054

Comparison and Analysis of Different Variogram Functions Models in Kriging Interpolation of Daily Rainfall

Qingjing Wang1, Chongyu Xu1,2, Hua Chen1

1State Key Laboratory of Water Resources and Engineering Science, Wuhan University, Wuhan Hubei

2Department of Geosciences, University of Oslo, Oslo Norway

Received: Oct. 4th, 2016; accepted: Oct. 23rd, 2016; published: Oct. 26th, 2016

Copyright © 2016 by authors and Hans Publishers Inc.

ABSTRACT

Ordinary Kriging is a wide-used method of geostatistical interpolation. However, it is only one variogram function that is often used to calculate the estimated value depending on one’s experience. Meanwhile, there is lesser study about daily rainfall comparison of different variogram functions in ordinary Kriging because most of the recent researches emphasize yearly and monthly rainfall. To obtain the better fitted variogram function in ordinary Kriging for daily rainfall interpolation within four different variogram functions (exponential, spherical, gauss, linear). The study leans on 16-year (1990-2005) daily rainfall data at 43 raingages in and around Mishui Basin. According to the comparison of three aspects including the correlation coefficients, examine index, accuracy of different precipitation grade, the result of cross- validation shows that: 1) exponential and spherical functions can fit the daily rainfall interpolation better in ordinary Kriging; 2) the estimated value in ordinary Kriging is generally smaller than observed value on days of heavy rainfall; 3) the error of daily rainfall interpolation increases with the precipitation grade.

Keywords:Ordinary Kriging, Variogram Function, Daily Rainfall, Spatial Interpolation, Cross-Validation

1武汉大学水资源与水电工程科学国家重点实验室，湖北 武汉

2挪威奥斯陆大学地学系，挪威 奥斯陆

1. 引言

2. 研究方法

2.1. 插值方法

2.1.1. 变异函数

(1)

(2)

(3)

(4)

(5)

2.1.2. 普通克里金法

(6)

(7)

2.2. 评判方法

(8)

(9)

(10)

3. 研究区域及资料

4. 结果与讨论

4.1. 变异函数参数的选择

Figure 1. DEM and distribution of rainfall stations in Mishui Basin

4.2. 交叉验证结果与分析

4.2.1. 相关系数比较

Figure 2. The correlation coefficients and comparison of four different variogram functions between estimated and observed value for daily rainfall (a) Exponential function; (b) Spherical function; (c) Gauss function; (d) Linear function

4.2.2. 不同检验指标比较

4.2.3. 不同降水级别的插值准确率比较

Table 1. The cross-validation results of four different variogram functions between estimated and observed value

Table 2. The cross-validation results of four different functions between estimated and observed values (daily rainfall ≥ 10 mm)

Figure 3. Accuracy of different precipitation grade of four different variogram functions

5. 结论

1) 指数和球型函数对于普通克里金日降水插值的适应性较好。指数函数在日降水量级较小时适应性更好；在日降水量级增大时，指数和球型函数对普通克里金插值的适应性均较好。

2) 普通克里金法的插值结果在降水量大的日子普遍偏小。

3) 随着降水量级的增大，日降水的误差明显增大。

Comparison and Analysis of Different Variogram Functions Models in Kriging Interpolation of Daily Rainfall[J]. 水资源研究, 2016, 05(05): 469-477. http://dx.doi.org/10.12677/JWRR.2016.55054

1. 1. FAURÈS, J. M., GOODRICH, D. C., WOOLHISER, D. A., et al. Impact of small-scale spatial variability on runoff modeling. Journal of Hydrology, 1995, 173(1): 309-326. http://dx.doi.org/10.1016/0022-1694(95)02704-S

2. 2. CHAUBEY, I., HAAN, C. T., GRUNWALD, S., et al. Uncertainty in the model parameters due to spatial variability of rainfall. Journal of Hy-drology, 1999, 220(1-2): 48-61. http://dx.doi.org/10.1016/S0022-1694(99)00063-3

3. 3. 易湘生, 李国胜, 尹衍雨, 彭景涛. 土壤厚度的空间插值方法比较——以青海三江源地区为例[J]. 地理研究, 2012, 31(10): 1793-1805. YI Xiangsheng, LI Guosheng, YIN Yanyu and PENG Jingtao. Comparison on soil depth prediction among different spatial in-terpolation methods: A case study in the Three-River Headwaters Region of Qinghai Province. Geographical Research, 2012, 31(10):1793-1805. (in Chinese)

4. 4. BORGA, M., VIZZACCARO, A. On the interpolation of hydrologic variables: Formal equivalence of multiquadratic surface fitting and kriging. Journal of Hydrology, 1997, 195(1-4): 160-171. http://dx.doi.org/10.1016/S0022-1694(96)03250-7

5. 5. CHEN, D., OU, T., GONG, L., et al. Spatial interpolation of daily precipitation in China: 1951-2005. Advances in Atmospheric Sciences, 2010, 27(6): 1221-1232. http://dx.doi.org/10.1007/s00376-010-9151-y

6. 6. LY, S., CHARLES, C. and DEGRÉ, A. Geostatistical interpolation of daily rainfall at catchment scale: The use of several variogram models in the Ourthe and Ambleve catchments, Belgium. Hy-drology & Earth System Sciences, 2011, 15(7): 2259- 2274. http://dx.doi.org/10.5194/hess-15-2259-2011

7. 7. LIN, G. F., CHEN, L. H. A spatial interpolation method based on radial basis function networks incorporating a semivariogram model. Journal of Hydrology, 2004, 288(288): 288-298. http://dx.doi.org/10.1016/j.jhydrol.2003.10.008

8. 8. DIRKS, K. N., HAY, J. E., STOW, C. D., et al. High-resolution Studies of rainfall on norfolk island part II: Interpolation of rainfall data. Journal of Hydrology, 2012, 208(3): 187-193.

9. 9. 张余庆, 陈昌春, 尹义星, 杨绪红. 江西多年平均降水量空间插值模型的选取与比较[J]. 水土保持研究, 2013, 20(4): 69- 74. ZHANG Yuqing, CHEN Changchun, YIN Yixing and YANG Xuhong. Spatial interpolation model selection of multi-year av-erage precipitation in Jiangxi Province. Research of Soil and Water Conservation, 2013, 20(4): 69-74. (in Chinese)

10. 10. 王常森, 陶月赞, 方必和. 淮北平原年降水量空间插值模型的比选[J]. 水文, 2012, 32(2): 49-53. WANG Changsen, TAO Yuezan and FANG Bihe. Comparison of spatial interpolation models for annual precipitation in Huaibei Plain. Journal of China Hydrology, 2012, 32(2): 49-53. (in Chinese)

11. 11. 张康聪. 地理信息系统导论[M]. 电子工业出版社, 2014. CHANG K.-T. Introduction to geographic information systems. Electronic Industry Publishing House, 2014.

12. 12. DEUTSCH, C. V. Correcting for negative weights in ordinary kriging. Computers & Geosciences, 1996, 22(7): 765-773. http://dx.doi.org/10.1016/0098-3004(96)00005-2