基于贝叶斯最大熵的甘肃省多年平均降水空间化研究

摘要/Abstract

摘要： 贝叶斯最大熵方法可以对具有一定不确定性的“软数据”和认为没有误差的“硬数据”进行插值。对甘肃省1961—1990年52个气象站点的多年平均降水数据进行空间化研究。通过比较普通克里格、共协克里格、三元回归建模后残差插值以及基于贝叶斯最大熵的3种不同软硬数据参与情况下的插值结果,发现考虑降水30 a时间序列不完整性以及辅助变量经验模型不确定性的插值结果的MAE和RMSE,比直接使用多年平均降水数据直接插值的MAE和RMSE小,表明贝叶斯最大熵方法通过对不确定性的考虑可以有效降低预测结果的绝对误差。从降水的空间分布来看,考虑辅助变量DEM的插值结果能相对较好的体现高程对降水的地形影响,尤其分区将辅助变量转换为软数据可以有效体现不同区域高程对降水的不同影响问题。综合误差评价以及降水插值结果的空间分布,认为BME插值过程中可以考虑数据本身以及辅助数据利用的不确定性,使降水空间化的结果更加真实客观,同时为合理利用辅助信息提供了一个新思路。

关键词: 贝叶斯最大熵, 地统计学, 不确定性, 软数据, 降水

Abstract: Bayesian Maximum Entropy (BME) is a spatio-temporal mapping method which can use the soft data with uncertainty and accurate hard data to perform the spatial interpolation. Spatial interpolation of multi-yearly average precipitation was conducted in Gansu Province based on precipitation data from 52 meteorological stations of Gansu Province during 1961-1990 and BME and traditional interpolation methods. Interpolation accuracy of ordinary Kriging interpolation, Cokriging interpolation, residual Kriging interpolation after triple regression modeling and three BME interpolation methods incorporating different soft and hard data were compared. Results showed that MAE and RMSE values of interpolations with soft data incorporation were smaller than those with hard data only. This result indicated BME could effectively reduce the absolute error by taking account of data uncertainty from missing records and relationship model between the interest variable and secondary variable. Based on the fact that the altitude played different roles in different regions, so the DEM was converted into different soft data in different sub regions and the interpolation results showed the effect of elevation on precipitation was better. We can see that BME can perform precipitation interpolation objectively from the error evaluation and spatial distribution of precipitation interpolation results, and provide a new way to integrate the secondary information.

Key words: Bayesian Maximum Entropy, geostatistics, uncertainty, soft data, precipitation

中图分类号:

P426.6

李爱华, 柏延臣. 基于贝叶斯最大熵的甘肃省多年平均降水空间化研究[J]. 中国沙漠, 2012, 32(5): 1408-1416.

LI Ai-hua, BAI Yan-chen. Spatial Interpolation of Mean Yearly Precipitation in Gansu Province Based on Bayesian Maximum Entropy[J]. JOURNAL OF DESERT RESEARCH, 2012, 32(5): 1408-1416.

参考文献

[1]时兴合,赵燕宁,戴升,等.柴达木盆地40多年来的气候变化研究[J].中国沙漠,2005,25(1):123-128.

[2]丁荣,王伏村,王静,等. 近47 a来黑河流域的降水时空特征分析及预报评估[J].中国沙漠,2009,29(2):335-341.

[3]张立杰,赵文智.黑河流域日降水格局及其时间变化[J].中国沙漠,2008,28(4):741-747.

[4]林忠辉,莫兴国,李宏轩,等.中国陆地区域气象要素的空间插值[J].地理学报,2002,57(1):47-56.

[5]Lam N S-N.Spatial interpolation methods:A review[J].Cartography and Geographic Information Science,1983,10(2):129-150.

[6]徐成东,孔云峰,仝文伟.线性加权回归模型的高原山地区域降水空间插值研究[J].地球信息科学,2008,10(1):14-19.

[7]刘劲松,陈辉,杨彬云,等.河北省年均降水量插值方法比较[J].生态学报.2009,9(7):3493-3500.

[8]Goovaerts P.Geostatistics in soil science:State of the art and perspectives[J].Geoderma,1999,89(1-2):1-45.

[9]Goovaerts P.Geostatistical approaches for incorporating elevation into the spatial interpolation of rainfall [J].Journal of Hydrology,2000,228(1-2):113-129.

[10]王政权.地统计学及在生态学中的应用[M].北京:科学技术出版社,1999:35-74.

[11]Allard D.Geostatistical classification and class Kriging [J].Journal of Geographic Information and Decision Analysis,1998,2(2):77-90.

[12]Todini E,Ferraresi M.Influence of parameter estimation uncertainty in Kriging[J].Journal of Hydrology,1996,175:555-566.

[13]王海军,张勃,靳晓华,等.基于GIS的祁连山区气温和降水的时空变化分析[J].中国沙漠,2009,29(6):1196-1201.

[14]刘新安,于贵瑞,范辽生,等.中国陆地生态信息空间化技术研究（Ⅲ）——温度降水等气象要素[J].自然资源学报,2004,19(6):818-825.

[15]董国涛,罗格平,许文强,等.三工河流域下游绿洲土壤微量元素的空间变异特征[J].中国沙漠,2010,30（4）:862-869.

[16]杨红梅,徐海量,樊自立,等.塔里木河下游表层土壤盐分空间变异和格局分析[J].中国沙漠,2010,30（3）:564-569.

[17]穆振侠,姜卉芳,刘丰,等.天山西部区降雨量空间分布的研究[J].新疆农业大学学报,2007,30(1):75-77.

[18]朱会义,刘述林,贾绍凤.自然地理要素空间插值的几个问题[J].地理研究,2006,23(4):425-432.

[19]Christakos G,Li X.Bayesian Maximum Entropy analysis and mapping-A farewell to Kriging estimators[J].Mathematical Geology,1998,30(4):435-462.

[20]Christakos G.Modern Spatiotemporal Geostatistics[M].New York:Oxford University Press,2000:71-130.

[21]Christakos G.A Bayesian Maximum-Entropy view to the spatial estimation problem[J].Mathematical Geology,1990,22(7):763-777.

[22]Bogaert P,Christakos G,Jerrett M.Spatiotemporal modelling of ozone distribution in the state of California[J].Atmospheric Environment,2009,43(5):2471-2480.

[23]Lee S,Balling R,Gober P.Bayesian Maximum Entropy mapping and the soft data problem in urban climate research[J].Geographers,Annals of the Association,2008,98(2):309-322.

[24]Yu H,Chen J,Christakos G,et al.BME estimation of residential exposure to ambient PM10 and ozone at multiple time scales[J].Environmental Health Perspectives,2009,117(4):537-544.

[25]Pang W,Christakos G,Wang J F.Comparative spatiotemporal analysis of fine particulate matter pollution[J].Environmetrics,2010,21(3-4):305-317.

[26]D'Or D.Spatial Prediction of Soil Properties:The Bayesian Maximum Entropy Approach[D].Belgium:Université catholique de Louvain,2003.

[27]邹松兵.基于GIS的甘肃中部地区气温降水分布模式研究[D].兰州:兰州大学,2002.

[28]谭启后,褚友余.甘肃省干旱半干旱地区降水的研究[J].干早区资源与环境,1991,5(2):50-59.

[29]徐晓桃,颉耀文,马金辉.兴隆山地区气温与降水的面域化处理[J].遥感技术与应用,2006,21(4):317-321.