基于贝叶斯最大熵和多源数据的作物需水量空间预测
|
摘要
作物需水量是灌溉工程规划、设计和管理的重要基础数据,充分利用多源数据和先验知识,快速经济地获取精度较高的区域作物需水量对于区域水资源的优化配置具有重要意义。为精确预测作物需水量,该文以长系列实际监测和校核作物系数后计算得到的作物需水量为硬数据,利用硬数据确定获得最大熵的约束条件,根据软数据获取渠道的不同(部分年份缺失的站点数据、文献中获得的数据、利用灌溉试验数据库中的作物需水量资料,采用协同克立格方法获得的数据、考虑主要地形因子和主要气象要素的影响,采用主成分分析和地理加权回归(geographically weighted regression,GWR)方法获得作物需水量数据以及遥感数据),提出不同来源软数据的概率密度函数表达方法,采用贝叶斯最大熵(Bayesian maximum entropy,BME)方法对不同来源的作物需水量信息进行有机整合。结果表明:除硬数据+文献软数据外,其他数据整合呈现一致结果。华北地区冬小麦作物需水量在豫南地区较小,中部地区黄河北岸有连片的相对高值区,山东需水量相对较高,冀东北的乐亭、唐山附近有相对低值区。除硬数据+文献软数据比不整合的精度低9.41%外,其他软数据源均可不同程度地提高整合效果,硬数据+克立格软数据、硬数据+GWR软数据和硬数据+除文献数据外的其他软数据分别比不整合的精度提高85.33%、85.75%和91.69%。对考虑地形、气象等要素的多源数据进行整合可更好地反映冬小麦作物需水量空间分布的细节,显著提高估算精度,为稀疏监测站点地区水土资源的精准管理和优化配置提供数据支撑。
Crop water requirement is an important basic data for planning,design and management of irrigation engineering.Obtaining high-precision regional crop water requirement prediction using multi-source data and the priori knowledge has great significance for optimal allocation of regional water resources.In the paper,multisource data was integrated using the Bayesian maximum entropy(BME) method for crop water requirement prediction.A long series of crop water requirement measured and calculated by using the crop coefficients adjusted for actual measurement,were taken as the hard data.The soft data included the missing data in partial years for some stations,literature data,the Kriging interpolation data considering the main influence elements of crop water requirement,the crop water requirement data based on the principal component analysis(PCA) and geographically weighted regression(GWR) method,and the remote sensing data.For the soft data from different sources,the expression method of probability density function was put forward and the crop water requirement information from different sources was well integrated using the BME method.Hard data for the period of 1954-2013 were collected from measurements from the irrigation stations in North China.Soft data for winter wheat in North China were also collected by searching literatures and the others.The results showed that spatial distribution of crop water requirement in North China was almost consistent for the hard data,hard data + Kriging soft data,hard data + GWR soft data and hard data + the soft data except for literature data.In the southern Henan had smaller crop water requirement,but the middle part(northern part of the Yellow River) of the North China was relatively high.The crop water requirement was relatively high in Shandong but low in the northeast of Hebei such as Leting,Tangshan.The results from hard data + literature soft data were slightly different from the others and the difference might be because the time periods used were different.In general,the integration accuracy of hard data + literature soft data was 9.41%lower than that based on hard data only.Hard data integrated with the other soft data could improve the integration effect.In particular,the integration accuracy of hard data + Kriging soft data,hard data + GWR soft data and hard data + the soft data except for literature data increased by 85.33%,85.75%and 91.69%,respectively.The integration of multi-source data through considering the terrain,meteorological factors and etc,can could better reflect the spatial distribution of crop water requirements for winter wheat,and significantly improve the estimation accuracy of crop water requirement for winter wheat.The presented method provided the most important basic data for the precise management and optimization of water and soil resources in the region with sparse monitoring stations.In the paper,we need pay attention to some questions in the soft data processing.The partially missing data of some stations need amend the variance calculation results.In order to avoid the agglomeration phenomenon,the selection of interpolation data need adopt the method of random sampling,and at the same time,the distance between adjacent samplings must be limited,should not be too far or near,and 20 km was advisable.In order to avoid too big error and uncertainty,the literature data must be screened and pretreatment,otherwise,the integration effect may be affected.
Crop water requirement is an important basic data for planning,design and management of irrigation engineering.Obtaining high-precision regional crop water requirement prediction using multi-source data and the priori knowledge has great significance for optimal allocation of regional water resources.In the paper,multisource data was integrated using the Bayesian maximum entropy(BME) method for crop water requirement prediction.A long series of crop water requirement measured and calculated by using the crop coefficients adjusted for actual measurement,were taken as the hard data.The soft data included the missing data in partial years for some stations,literature data,the Kriging interpolation data considering the main influence elements of crop water requirement,the crop water requirement data based on the principal component analysis(PCA) and geographically weighted regression(GWR) method,and the remote sensing data.For the soft data from different sources,the expression method of probability density function was put forward and the crop water requirement information from different sources was well integrated using the BME method.Hard data for the period of 1954-2013 were collected from measurements from the irrigation stations in North China.Soft data for winter wheat in North China were also collected by searching literatures and the others.The results showed that spatial distribution of crop water requirement in North China was almost consistent for the hard data,hard data + Kriging soft data,hard data + GWR soft data and hard data + the soft data except for literature data.In the southern Henan had smaller crop water requirement,but the middle part(northern part of the Yellow River) of the North China was relatively high.The crop water requirement was relatively high in Shandong but low in the northeast of Hebei such as Leting,Tangshan.The results from hard data + literature soft data were slightly different from the others and the difference might be because the time periods used were different.In general,the integration accuracy of hard data + literature soft data was 9.41%lower than that based on hard data only.Hard data integrated with the other soft data could improve the integration effect.In particular,the integration accuracy of hard data + Kriging soft data,hard data + GWR soft data and hard data + the soft data except for literature data increased by 85.33%,85.75%and 91.69%,respectively.The integration of multi-source data through considering the terrain,meteorological factors and etc,can could better reflect the spatial distribution of crop water requirements for winter wheat,and significantly improve the estimation accuracy of crop water requirement for winter wheat.The presented method provided the most important basic data for the precise management and optimization of water and soil resources in the region with sparse monitoring stations.In the paper,we need pay attention to some questions in the soft data processing.The partially missing data of some stations need amend the variance calculation results.In order to avoid the agglomeration phenomenon,the selection of interpolation data need adopt the method of random sampling,and at the same time,the distance between adjacent samplings must be limited,should not be too far or near,and 20 km was advisable.In order to avoid too big error and uncertainty,the literature data must be screened and pretreatment,otherwise,the integration effect may be affected.
引文
[1]陈玉民,郭国双,王广兴,等.中国主要作物需水量与灌溉[M].北京:水利电力出版社,1995.
[2]孙景生,熊运章,康绍忠.农田蒸发蒸腾的研究方法与进展[J].灌溉排水,1993,13(4):36-38.Sun Jingsheng,Xiong Yunzhang,Kang Shaozhong.Progress and research method in evapotransipiration in cropland[J].Irrigation and Drainage,1993,13(4):36-38.(in Chinese with English abstract)
[3]许迪,刘钰.测定和估算田间作物腾发量方法研究综述[J].灌溉排水,1997,16(4):54-59.Xu Di,Liu Yu.Review of study on calculating and estimating methods on crop evapotanspiration[J].Irrigation and Drainage,1997,16(4):54-59.(in Chinese with English abstract)
[4]Rana G,Katerji N.Measurement and estimation of actual evapotranspiration in the field under Mediterranean climate:A review[J].European Journal of Agronomy,2000,13(23):125-153.
[5]王景雷,孙景生,付明军,等.区域作物需水量估算存在的主要问题及可能的解决途径[J].节水灌溉,2005(3):4-7.Wang Jinglei,Sun Jingsheng,Fu Mingjun,et al.Existing problems and solving methods of regional crop water requirements evaluation[J].Water Saving Irrigation,2005(3):4-7.(in Chinese with English abstract)
[6]Lin Wenjing,Su Zhongbo,Dong Hua,et al.Regional evapotranspiration estimation based on MODIS products and surface energy balance system(SEBS)in Hebei plain Northeastern China[J].Journal of Remote Sensing,2008,12(4):663-672.
[7]王景雷,孙景生,刘祖贵,等.作物需水量观测站点的优化设计[J].水利学报,2005,36(2):225-231.Wang Jinglei,Sun Jingsheng,Liu Zugui,et al.Optimal arrangement of observation stations for crop water requirement[J].Journal of Hydraulic Engineering,2005,36(2):225-231.(in Chinese with English abstract)
[8]雷志栋,罗毅,杨诗秀,等.利用常规气象资料模拟计算作物系数的探讨[J].农业工程学报,1999,15(3):119-122.Lei Zhidong,Luo Yi,Yang Shixiu,et al.Calculation of crop coefficient with meteorological data[J].Transactions of the Chinese Society of Agricultural Engineering(Transactions of the CSAE),1999,15(3):119-122.(in Chinese with English abstract)
[9]刘元波.遥感反演区域蒸散的不确定性研究[C]//2009第五届苏皖两省大气探测、环境遥感与电子技术学术研讨会专辑.江苏省气象学会、安徽省气象学会,2009:2.
[10]Christakos G.A Bayesian/maximum-entropy view to the spatial estimation problem[J].Mathematical Geology,1990,22(7):763-777.
[11]Christakos G,Li X.Bayesian maximum entropy analysis and mapping:A farewell to kriging estimators?[J].Mathematical Geosciences,1998,30(4):435-462.
[12]Serre M L,Christakos G.Modern geostatistics:Computational BME analysis in the light of uncertain physical knowledge-the Equus Beds study[J].Stochastic Environmental Research and Risk Assessment,1999,13(1):1-26.
[13]Christakos G,Serre M L.BME analysis of spatiotemporal particulate matter distributions in North Carolina[J].Atmospheric Environment,2000,34(20):3393-3406.
[14]Douaik A,Van Meirvenne M,Toth T.Soil salinity mapping using spatio-temporal kriging and Bayesian maximum entropy with interval soft data[J].Geoderma,2005,128(23):234-248.
[15]徐英,夏冰.综合BME和BNN法的农田土壤水分与养分分布空间插值[J].农业工程学报,2015,31(16):119-127.Xu Ying,Xia Bing.Spatial interpolation of soil moisture and nutrients using BME combined with BNN[J].Transactions of the Chinese Society of Agricultural Engineering(Transactions of the CSAE),2015,31(16):119-127.(in Chinese with English abstract)
[16]Lee S J,Balling R,Gober P.Bayesian maximum entropy mapping and the soft data problem in urban climate research[J].Annals of the Association of American Geographers,2008,98(2):309-322.
[17]Yu H L,Wang C H,Liu M C,et al.Estimation of fine particulate matter in Taipei using land use regression and Bayesian maximum entropy methods[J].International Journal of Environmental Research and Public Health,2011,8(6):2153-2169.
[18]Zhang Fushen,Yang Zhitao,Zhong Shaobo,et al.Exploring mean annual precipitation values(2003-2012)in a specific area(36°N-43°N,113°E-120°E)using meteorological,elevational,and the nearest distance to coastline variables[J].Advances in Meteorology,2015,2016(4):1-13.
[19]灌溉与排水工程设计规范:GB 50288-99[S].北京:中国计划出版社,1999.
[20]Douaik A.Evaluation of the Space-time Variability of Soil Salinity by Statistical,Geostatistical and Bayesian Maximum Entropy Methods[D].Ghent:Ghent University,2005.
[21]张楚天.贝叶斯最大熵方法时空预测关键问题研究与应用[D].武汉:华中农业大学,2016.Zhang Chutian.Research on Key Issues of Bayesian Maximum Entropy Spatiotemporal Prediction and Its Application[D].Wuhan:Huazhong Agricultural University,2016.(in Chinese with English abstract)
[22]Tesar M L L.A Comparison of Spatial Prediction Techniques Using Both Hard and Soft Data[D].Lincoln:University of Nebraska-Lincoln,2011.
[23]Serre M L.Environmental Spatiotemporal Mapping and Groundwater Flow Modeling Using the BME and ST Methods[D].Chapel Hill:University of North Carolina,1999.
[24]Lee S J.Models of Soft Data in Geostatistics and Their Application in Environmental and Health Mapping[D].Chapel Hill:University of North Carolina,2005.
[25]Shannon C E.A mathematical theory of communication[J].The Bell System Technical Journal,1948,27:379-423.
[26]Manly B F J.Statistics for Environmental Science and Management[M].Boca Raton:CRC Press,2008.
[27]Wang J L,Kang S Z,Sun J S,et al.Estimation of crop water requirement based on principal component analysis and geographically weighted regression[J].Science Bulletin,2013,58(27):3371-3379.
[28]吴炳方,熊隽,闫娜娜,等.基于遥感的区域蒸散量监测方法:ETWatch[J].水科学进展,2008,19(5):671-678.Wu Bingfang,Xiong Jun,Yan Nana,et al.ET-Watch for monitoring regional evapotranspiration with remote sensing[J].Advances in Water Sciences,2008,19(5):671-678.(in Chinese with English Abstract)
[29]茌伟伟,刘钰,刘玉龙,等.基于SWAT模型的区域蒸散发模拟及遥感验证[J].中国水利水电科学研究院学报,2013,11(3):167-175.Chi Weiwei,Liu Yu,Liu Yulong,et al.SWAT-based simulation for regional evapotranspiration and verification by means of remote sensing[J].Journal of China Institute of Water Resources and Hydropower Research,2013,11(3):167-175.(in Chinese with English abstract)
[30]陈鹤,杨大文,刘钰,等.基于遥感模型的华北平原农田区蒸散发量估算[J].灌溉排水学报,2014,33(4):21-25.Chen He,Yang Dawen,Liu Yu,et al.Cropland evapotranspiration estimation based on remote sensing model in the north china plain[J].Journal of Irrigation and Drainage,2014,33(4):21-25.(in Chinese with English abstract)
[31]于雷,洪永胜,耿雷,等.基于偏最小二乘回归的土壤有机质含量高光谱估算[J].农业工程学报,2015,31(14):103-109.Yu Lei,Hong Yongsheng,Geng Lei,et al.Hyperspectral estimation of soil organic matter content based on partial least squares regression[J].Transactions of the Chinese Society of Agricultural Engineering(Transactions of the CSAE),2015,31(14):103-109.(in Chinese with English abstract)
[32]陈鹏飞,杨飞,杜佳.基于环境减灾卫星时序归一化植被指数的冬小麦产量估测[J].农业工程学报,2013,29(11):124-131.Chen Pengfei,Yang Fei,Du Jia.Yield forecasting for winter wheat using time series NDVI from HJ satellite[J].Transactions of the Chinese Society of Agricultural Engineering(Transactions of the CSAE),2013,29(11):124-131.(in Chinese with English abstract)
[33]陈丹丹,李国强,张杰,等.基于DSSAT模型的河南省冬小麦需水量分析[J].河南农业科学,2017,46(2):153-160.Chen Dandan,Li Guoqiang,Zhang Jie,et al.Analysis on water demand of winter wheat in henan province based on DSSAT model[J].Journal of henan agricultural sciences,2017,46(2):153-160.(in Chinese with English abstract)
[34]孙现领.基于冬小麦产量与蒸发量相关性研究的安阳节水农业探讨[D].重庆:西南大学,2012.Sun Xianling.Studies Based on Winter Wheat Yield and the Evaporation Correlation Water-saving Agriculture in Anyang[D].Chongqing:Southwest University,2012.(in Chinese with English abstract)
[35]梁薇.冬小麦经济节水灌溉制度的研究[D].邯郸:河北工程大学,2007.Liang Wei.Study on Economical Water-saving Irrigation Schedule for Winter Wheat[D].Handan:Hebei University of Engineering,2007.(in Chinese with English abstract)
[36]杨计刚.河北省临漳县冬小麦科学灌溉制度研究[D].邯郸:河北工程大学,2010.Yang Jigang.The Study of Winter Wheat Science Irrigation in Linzhang City Heibei Province[D].Handan:Hebei University of Engineering,2010.(in Chinese with English abstract)
[2]孙景生,熊运章,康绍忠.农田蒸发蒸腾的研究方法与进展[J].灌溉排水,1993,13(4):36-38.Sun Jingsheng,Xiong Yunzhang,Kang Shaozhong.Progress and research method in evapotransipiration in cropland[J].Irrigation and Drainage,1993,13(4):36-38.(in Chinese with English abstract)
[3]许迪,刘钰.测定和估算田间作物腾发量方法研究综述[J].灌溉排水,1997,16(4):54-59.Xu Di,Liu Yu.Review of study on calculating and estimating methods on crop evapotanspiration[J].Irrigation and Drainage,1997,16(4):54-59.(in Chinese with English abstract)
[4]Rana G,Katerji N.Measurement and estimation of actual evapotranspiration in the field under Mediterranean climate:A review[J].European Journal of Agronomy,2000,13(23):125-153.
[5]王景雷,孙景生,付明军,等.区域作物需水量估算存在的主要问题及可能的解决途径[J].节水灌溉,2005(3):4-7.Wang Jinglei,Sun Jingsheng,Fu Mingjun,et al.Existing problems and solving methods of regional crop water requirements evaluation[J].Water Saving Irrigation,2005(3):4-7.(in Chinese with English abstract)
[6]Lin Wenjing,Su Zhongbo,Dong Hua,et al.Regional evapotranspiration estimation based on MODIS products and surface energy balance system(SEBS)in Hebei plain Northeastern China[J].Journal of Remote Sensing,2008,12(4):663-672.
[7]王景雷,孙景生,刘祖贵,等.作物需水量观测站点的优化设计[J].水利学报,2005,36(2):225-231.Wang Jinglei,Sun Jingsheng,Liu Zugui,et al.Optimal arrangement of observation stations for crop water requirement[J].Journal of Hydraulic Engineering,2005,36(2):225-231.(in Chinese with English abstract)
[8]雷志栋,罗毅,杨诗秀,等.利用常规气象资料模拟计算作物系数的探讨[J].农业工程学报,1999,15(3):119-122.Lei Zhidong,Luo Yi,Yang Shixiu,et al.Calculation of crop coefficient with meteorological data[J].Transactions of the Chinese Society of Agricultural Engineering(Transactions of the CSAE),1999,15(3):119-122.(in Chinese with English abstract)
[9]刘元波.遥感反演区域蒸散的不确定性研究[C]//2009第五届苏皖两省大气探测、环境遥感与电子技术学术研讨会专辑.江苏省气象学会、安徽省气象学会,2009:2.
[10]Christakos G.A Bayesian/maximum-entropy view to the spatial estimation problem[J].Mathematical Geology,1990,22(7):763-777.
[11]Christakos G,Li X.Bayesian maximum entropy analysis and mapping:A farewell to kriging estimators?[J].Mathematical Geosciences,1998,30(4):435-462.
[12]Serre M L,Christakos G.Modern geostatistics:Computational BME analysis in the light of uncertain physical knowledge-the Equus Beds study[J].Stochastic Environmental Research and Risk Assessment,1999,13(1):1-26.
[13]Christakos G,Serre M L.BME analysis of spatiotemporal particulate matter distributions in North Carolina[J].Atmospheric Environment,2000,34(20):3393-3406.
[14]Douaik A,Van Meirvenne M,Toth T.Soil salinity mapping using spatio-temporal kriging and Bayesian maximum entropy with interval soft data[J].Geoderma,2005,128(23):234-248.
[15]徐英,夏冰.综合BME和BNN法的农田土壤水分与养分分布空间插值[J].农业工程学报,2015,31(16):119-127.Xu Ying,Xia Bing.Spatial interpolation of soil moisture and nutrients using BME combined with BNN[J].Transactions of the Chinese Society of Agricultural Engineering(Transactions of the CSAE),2015,31(16):119-127.(in Chinese with English abstract)
[16]Lee S J,Balling R,Gober P.Bayesian maximum entropy mapping and the soft data problem in urban climate research[J].Annals of the Association of American Geographers,2008,98(2):309-322.
[17]Yu H L,Wang C H,Liu M C,et al.Estimation of fine particulate matter in Taipei using land use regression and Bayesian maximum entropy methods[J].International Journal of Environmental Research and Public Health,2011,8(6):2153-2169.
[18]Zhang Fushen,Yang Zhitao,Zhong Shaobo,et al.Exploring mean annual precipitation values(2003-2012)in a specific area(36°N-43°N,113°E-120°E)using meteorological,elevational,and the nearest distance to coastline variables[J].Advances in Meteorology,2015,2016(4):1-13.
[19]灌溉与排水工程设计规范:GB 50288-99[S].北京:中国计划出版社,1999.
[20]Douaik A.Evaluation of the Space-time Variability of Soil Salinity by Statistical,Geostatistical and Bayesian Maximum Entropy Methods[D].Ghent:Ghent University,2005.
[21]张楚天.贝叶斯最大熵方法时空预测关键问题研究与应用[D].武汉:华中农业大学,2016.Zhang Chutian.Research on Key Issues of Bayesian Maximum Entropy Spatiotemporal Prediction and Its Application[D].Wuhan:Huazhong Agricultural University,2016.(in Chinese with English abstract)
[22]Tesar M L L.A Comparison of Spatial Prediction Techniques Using Both Hard and Soft Data[D].Lincoln:University of Nebraska-Lincoln,2011.
[23]Serre M L.Environmental Spatiotemporal Mapping and Groundwater Flow Modeling Using the BME and ST Methods[D].Chapel Hill:University of North Carolina,1999.
[24]Lee S J.Models of Soft Data in Geostatistics and Their Application in Environmental and Health Mapping[D].Chapel Hill:University of North Carolina,2005.
[25]Shannon C E.A mathematical theory of communication[J].The Bell System Technical Journal,1948,27:379-423.
[26]Manly B F J.Statistics for Environmental Science and Management[M].Boca Raton:CRC Press,2008.
[27]Wang J L,Kang S Z,Sun J S,et al.Estimation of crop water requirement based on principal component analysis and geographically weighted regression[J].Science Bulletin,2013,58(27):3371-3379.
[28]吴炳方,熊隽,闫娜娜,等.基于遥感的区域蒸散量监测方法:ETWatch[J].水科学进展,2008,19(5):671-678.Wu Bingfang,Xiong Jun,Yan Nana,et al.ET-Watch for monitoring regional evapotranspiration with remote sensing[J].Advances in Water Sciences,2008,19(5):671-678.(in Chinese with English Abstract)
[29]茌伟伟,刘钰,刘玉龙,等.基于SWAT模型的区域蒸散发模拟及遥感验证[J].中国水利水电科学研究院学报,2013,11(3):167-175.Chi Weiwei,Liu Yu,Liu Yulong,et al.SWAT-based simulation for regional evapotranspiration and verification by means of remote sensing[J].Journal of China Institute of Water Resources and Hydropower Research,2013,11(3):167-175.(in Chinese with English abstract)
[30]陈鹤,杨大文,刘钰,等.基于遥感模型的华北平原农田区蒸散发量估算[J].灌溉排水学报,2014,33(4):21-25.Chen He,Yang Dawen,Liu Yu,et al.Cropland evapotranspiration estimation based on remote sensing model in the north china plain[J].Journal of Irrigation and Drainage,2014,33(4):21-25.(in Chinese with English abstract)
[31]于雷,洪永胜,耿雷,等.基于偏最小二乘回归的土壤有机质含量高光谱估算[J].农业工程学报,2015,31(14):103-109.Yu Lei,Hong Yongsheng,Geng Lei,et al.Hyperspectral estimation of soil organic matter content based on partial least squares regression[J].Transactions of the Chinese Society of Agricultural Engineering(Transactions of the CSAE),2015,31(14):103-109.(in Chinese with English abstract)
[32]陈鹏飞,杨飞,杜佳.基于环境减灾卫星时序归一化植被指数的冬小麦产量估测[J].农业工程学报,2013,29(11):124-131.Chen Pengfei,Yang Fei,Du Jia.Yield forecasting for winter wheat using time series NDVI from HJ satellite[J].Transactions of the Chinese Society of Agricultural Engineering(Transactions of the CSAE),2013,29(11):124-131.(in Chinese with English abstract)
[33]陈丹丹,李国强,张杰,等.基于DSSAT模型的河南省冬小麦需水量分析[J].河南农业科学,2017,46(2):153-160.Chen Dandan,Li Guoqiang,Zhang Jie,et al.Analysis on water demand of winter wheat in henan province based on DSSAT model[J].Journal of henan agricultural sciences,2017,46(2):153-160.(in Chinese with English abstract)
[34]孙现领.基于冬小麦产量与蒸发量相关性研究的安阳节水农业探讨[D].重庆:西南大学,2012.Sun Xianling.Studies Based on Winter Wheat Yield and the Evaporation Correlation Water-saving Agriculture in Anyang[D].Chongqing:Southwest University,2012.(in Chinese with English abstract)
[35]梁薇.冬小麦经济节水灌溉制度的研究[D].邯郸:河北工程大学,2007.Liang Wei.Study on Economical Water-saving Irrigation Schedule for Winter Wheat[D].Handan:Hebei University of Engineering,2007.(in Chinese with English abstract)
[36]杨计刚.河北省临漳县冬小麦科学灌溉制度研究[D].邯郸:河北工程大学,2010.Yang Jigang.The Study of Winter Wheat Science Irrigation in Linzhang City Heibei Province[D].Handan:Hebei University of Engineering,2010.(in Chinese with English abstract)