Evapotranspiration estimation methods in hydrological model

第44卷第2期测绘与空间地理信息Vol.44，No.2Feb.，2021 2021年2月GEOMATICS&SPATIAL INFORMATION TECHNOLOGY基于Penman-Monteith Leuning模型的遥感蒸散发估算——以四川省马尔康县为例王力涛1，高伟2，庄春晓1（1.天津市勘察院，天津300110；2.湖北省建筑科学研究设计院，湖北武汉430071）摘要：蒸散发作为地表水分消耗和参与水文生态循环的重要参数，是生态应用研究的重点。

尤其对于植被恢复和水资源管理的领域而言，区域蒸散发估算的准确性十分重要。

本文以野外实测（气象和蒸散发）数据为基础，利用实测数据对遥感PML模型进行参数优化，基于Landsat-8遥感影像数据对四川省马尔康县蒸散发进行估算。

研究结果表明：马尔康县模型模拟蒸散发与实测蒸散发拟合程度较好，PML模型优化的土壤湿度系数为1，气孔导度为0.0165m/s,模型验证系数RMSE为0.15mm/d。

研究区域内不同土地利用类型的蒸散发差异较大。

马尔康县日平均蒸散发为1.05mm/d，马尔康县区域蒸散发呈现空间异质性，并受到地形、气象以及土地利用类型等因子的影响。

关键词：区域蒸散发；Landsat-8;Penman-Monteith公式；参数优化中图分类号：P237文献标识码：A文章编号：1672-5867（2021）02-0137-04Remote Sensing Evapotranspiration Estimation Based onPenman-M onteith Leuning Model:Take Maerkang County,Sichuan Province as an ExampleWANG Litao1,GAO Wei2,ZHUANG Chunxiao1(1.Tianjin Institute of Geotechnical Investigation&Surveying,Tianjin300110,China；2.Hubei Provincial Academy of Building Research and Design,Wuhan430071,China)Abstract:Evapotranspiration,as an important parameter of surface water consumption and participation in hydrological ecological cy­cle,is the focus of ecological application research.Especially for the field of vegetation restoration and water resources management, the accuracy of regional evapotranspiration estimation is very important and of great significance.In this paper,based on the field data (weather and evapotranspiration),the parameters of the remote sensing PML model are optimized using the measured data,and the e­vapotranspiration in Maerkang County,Sichuan Province is estimated based on the Landsat-8remote sensing image data.The research results show that the simulated evapotranspiration of the Maerkang County model fits well with the measured evapotranspiration.The optimized soil moisture coefficient of the PML model is1,the stomatal conductance is0.0165m/s,and the model verification coeffi­cient RMSE is0.15mm/d.The evapotranspiration of different land use types in the study area is quite different.The daily average e­vapotranspiration in Maerkang County is1.05mm/d,and the regional evapotranspiration in Maerkang County presents spatial hetero­geneity and is affected by factors such as topography,meteorology,and land use types.Key words：evapotranspiration；Landsat-8；Penman-Monteith equation；parameter optimization0引言由于遥感卫星航片成本低，基于遥感技术估算蒸散发逐渐成为经济实用的技术手段。

基于Shuttleworth-Wallace模型的水稻蒸散组分模拟及其特征分析王宇;周莉;贾庆宇;王磊;徐军亮【摘要】The simulation of evapotranspiration (ET) and its components in croplands is critical for the precise irrigation and accurate estimation of ecosystem productivity. Based on the eddy-covariance flux measurement and ancillary data during 2013-2015, evapotranspiration and its components were simulated using the Shuttleworth-Wallace model (S-W model) in a rice paddy field in Panjin. The controlling mechanism of the ratio of soil evaporation to evapotranspiration (ES/ET) was analyzed with the structural equation modeling (SEM) method. The results showed that: (1) the simulated ET was close to the observed ET in the late growing season, however, it was lower than the observed ET in the early growing season and higher in the peak growing season. (2) As for the seasonal variation, the simulated ET showed a drastic day-to-day fluctuation (0.5-10.4mm·d-1) but no clear seasonal pattern; the plant transpiration (TR) was higher in the peak growing season and lower at the start and the end of the growing season, with the range of 0.1-8.4mm·d-1; ES showed a U-type curve, with the range of 0.1-4.7mm·d-1. (3) The simulated mean annual ET was 892mm during 2013-2015. TR was equal to ES at the annual scale. As for the growing season scale, TR was the main consumer of the ET: TR was close to ES in the transplanting-tillering stage, while in the other growth stages and the whole growing season, TR was more than twice as ES. (4)The SEM results indicated that air temperature (Ta) was the primary controlling factor of the ES/ET (total effect=-0.82). Ta was shown to influence ES/ET both directly (direct effect=-0.50) and indirectly through its regulation on leaf area index (LAI, indirect effect=-0.32). In addition, the LAI and wind speed (WS) were also shown to have significant effects on ES/ET. ES/ET decreased with LAI (total effect=-0.39) and increased with WS (total effect=0.38).%农田蒸散(ET)及其组分的模拟是精准灌溉及准确估算生产力的基础.基于2013-2015年的涡度相关通量观测及辅助观测资料,利用Shuttleworth-Wallace模型(S-W模型)对盘锦水稻的蒸散及其组分进行模拟,并利用结构方程模型分析土壤蒸发占蒸散比例(ES/ET)的控制机制.结果表明:(1)S-W模型模拟蒸散值在生长季前期偏低,在生长旺季总体偏高;而在生长季后期与观测蒸散基本吻合.(2)就季节变化过程而言,水稻蒸散模拟值呈现明显的日间波动(0.5~10.4mm·d-1),但季节总体变化趋势不明显;蒸腾(TR)则先增大后降低,变化范围为0.1~8.4mm·d-1;土壤蒸发(ES)呈U型曲线,变化范围为0.1~4.7mm·d-1.(3)模拟水稻蒸散3a均值为892mm.在年尺度上,TR与ES各占ET的50%;但在生长季,TR是ET的主要消耗方式:在移栽分蘖期,水稻的植物蒸腾与土壤蒸发较接近,而在其它各生育期及全生育期,水稻的植物蒸腾均达土壤蒸发的2倍以上.(4)结构方程模型分析结果表明,气温是ES/ET最重要的影响因子,ES/ET随气温上升而下降(总影响系数为-0.82).气温不仅对ES/ET有显著的直接影响(直接影响系数为-0.50),还通过叶面积指数(LAI)对ES/ET产生显著的间接影响(间接影响系数为-0.32).除气温外,LAI和风速也是ES/ET的重要影响因子,ES/ET随LAI增大而下降(总影响系数为-0.39),随风速增大而增大(总影响系数为0.38).【期刊名称】《中国农业气象》【年(卷),期】2017(038)011【总页数】11页(P709-719)【关键词】结构方程模型;涡度相关;土壤蒸发;植物蒸腾【作者】王宇;周莉;贾庆宇;王磊;徐军亮【作者单位】河南科技大学林学院,洛阳 471023;中国气象科学研究院,北京100081;中国气象局沈阳大气环境研究所,沈阳 110016;河南科技大学林学院,洛阳471023;河南科技大学林学院,洛阳 471023【正文语种】中文蒸散（ET）是水分及能量平衡的重要组成部分，是连接生态与水文过程的重要纽带[1]。

基于IDL的MODIS影像地表蒸散发参数反演系统邓世赞;张友静;张子衡;谢丽军;王文种【摘要】针对水文水资源分析计算所需要的地表蒸散发参数难以荻取的问题,利用MODIS遥感影像数据和气象观测数据,采用SEBAL(地表能量平衡)模型,并结合ENVI/IDL二次开发语言构建了流域陆面蒸散发反演系统.以黄河三花间(三门峡一花园口区间)流域为例,编程实现了地表温度、植被指数、水体指数、不透水面指数等蒸散发计算所需相关地表参数的提取和日陆面蒸散发量的计算,并利用IDL的统计分析功能,通过随机采样,综合分析了地表参数与蒸散发量的关系.应用结果表明,该系统具有平台无关性特点,人机交互友好,可作为独立模块加入水文分析等专业系统,有效解决了通用遥感软件缺乏专业信息提取功能的问题.【期刊名称】《河海大学学报（自然科学版）》【年(卷),期】2010(038)004【总页数】5页(P447-451)【关键词】地表蒸散发参数;反演系统;SEBAL模型;MODIS影像;ENVI/IDL;黄河三花间流域【作者】邓世赞;张友静;张子衡;谢丽军;王文种【作者单位】河海大学水文水资源学院,江苏,南京,210098;河海大学水文水资源学院,江苏,南京,210098;河海大学水文水资源与水利工程科学国家重点实验室,江苏,南京,210098;河海大学水文水资源学院,江苏,南京,210098;河海大学水文水资源学院,江苏,南京,210098;河海大学水文水资源学院,江苏,南京,210098【正文语种】中文【中图分类】P426.2;P237地表蒸散发参数是涉及多个圈层水热交换与平衡的重要参数.利用气象数据,采用彭曼蒙特斯模型、彭曼组合模型和基于太阳辐射的日蒸散发模型等,计算点尺度的蒸散发,已有许多研究[1-2],但由于这些研究局限于离散的点观测与估算,存在插值外延精度低、大范围高密度观测成本大等缺陷.随着多时相、多分辨率卫星遥感数据的应用,通过遥感信息提取来估算地表蒸散发方法的应用越来越广.在地表蒸散发遥感反演方法中,SEBAL(地表能量平衡)模型[3-4]是目前应用较多的模型之一.但蒸散发计算中所需要的地表参数众多,流程复杂,需要遥感专业人员进行重复性的演算,不利于长时间序列的蒸散发反演.Wang J等[5]改进了SEBAL模型,并利用C++语言对农作物——山核桃的消费性用水量进行了计算,但模型参数局限于产品数据,无法从原始影像中反演得到.吴炳方等[6]利用能量平衡余项式方法和Penman-Monteith模型相结合的方法开发了区域蒸散发遥感监测系统,该系统利用逐日气象数据与遥感反演参数,能动态反映区域蒸散发的时空变化规律,但其简化了地表与大气由于温度差引起的热量传输过程,使反演的蒸散发量具有一定的不确定性.针对以上问题,本文利用MODIS遥感数据并结合地面气象观测数据,应用SEBAL模型,通过ENVI/IDL二次开发语言实现了日蒸散发量的批处理,并给出了该方法的应用实例.1 SEBAL(地表能量平衡)模型SEBAL模型的优点是可充分利用由遥感图像反演得到的地表参数,结合少量的常规气象资料就能得到区域地表蒸散发量.该模型建立的基础是能量平衡方程[7],即式中:R n——地表净辐射通量;G——土壤热通量,即下垫面土壤中的热交换量;H——下垫面到大气的显热通量(也称感热通量);λ——水的汽化潜热;E——蒸散发量;λ E——下垫面到大气的潜热通量.计算得到各通量后,再利用能量平衡方程就可以反演日蒸散发量.1.1 地表净辐射通量地表净辐射通量是地表接收到的太阳辐射和大气长波辐射减去地表面反射的太阳辐射和发射的长波辐射后得到的辐射差值.它是地表能量、动量、水分输送与交换过程中的主要能量来源.地表辐射平衡方程为[8]式中:Q——太阳总辐射;a——反照率;εα——地表反射率;εs——地表比辐射率;σ——斯蒂芬-波尔兹曼常数;Tα——空气温度;T s——地表温度.1.2 土壤热通量土壤热通量是指用于土壤热交换的那部分能量,表征土壤表层和深层的热量传递.对于植被覆盖区域,土壤热通量与地表净辐射通量的比值为[9]式中b为归一化植被指数.不同地物类型,土壤热交换不同:非植被-裸土,G=0.2R n;水体,G=0.9R n-40.1.3 显热通量显热通量表征下垫面与大气间湍流形式的热交换,又称感热通量,其表达式为[10]式中:ρ——空气密度;Cp——空气定压质量热容;r a——空气动力学阻抗.1.4 日蒸散发量由于遥感所获得的是瞬时蒸散发量,需推算到日蒸散发量.本文采用谢贤群的正弦公式[11],考虑到1 d中不可避免地会有云的出现,而气象站观测到的日照时数可以反映1d中云的出现时长,因而在进行时间尺度扩展的过程中,加入日照时数来进行校正[12].式中:a,b——系数,一般分别取0.25和0.50;n——气象站观测日照时数;N E——理论日照时数,可以通过地理纬度计算得出;t——影像接收时间;E t——瞬时蒸散发量;E d——日蒸散发量.2 日蒸散发量算法的IDL实现2.1 气象数据插值SEBAL模型蒸散发反演过程中部分地表参数的计算必须依靠气象站实测数据,而由于气象站数据往往是离散的,必须通过插值方法获取该区域任意点的数据.本系统通过IDL语言自动交互读取气象站矢量文件,利用griddata函数中反距离插值方法实现气象数据的插值.2.2 地表参数反演SEBAL模型涉及地表参数较多,其中大气透过率、地表反照率、地表比辐射率等大多数参数通过经验模型求出[13].本文以地表温度为例,采用劈窗算法,简述其IDL的实现过程.算法的实现主要利用地表辐射率和大气透过率2个因子.在计算大气透过率时不仅要利用MODIS的B31和B32波段对其进行温度校正,还要结合MODIS 原始影像中Sensor Zenith数据集对传感器进行视角纠正,具体实现流程见图1. 为提高系统运行效率,将众地表参数合成一个文件,每个地表参数相当于其中1个波段,需要该数据时可直接读取该波段数据.对本模块而言,用户可以通过界面选择不同的参数和计算方法,并可以方便地按不同渲染方式输出地表参数影像,如图2所示. 图1 地表温度反演算法流程Fig.1 Flow chart of inversion of surface temperature2.3 SEBAL模型各通量IDL的实现图2 地表参数查询窗口Fig.2 Interface for querying surface parameters2.3.1 净辐射通量考虑到地形起伏导致的阳坡和阴坡太阳辐射不同,将对太阳辐射进行地形校正.本系统考虑了DEM及所反映的地形特征参数如坡度、坡向的太阳天顶角校正,校正时只需输入影像获取时间、DEM、经纬度波段等初始条件.2.3.2 土壤热通量计算土壤热通量时,将地表分为水体、植被和裸土3类,并利用IDL提供的where判别函数来判断地物类型.计算某类型地表土壤热通量时,首先计算归一化植被指数NDVI(以I NDV表示),然后分别查找I NDV＞0.25-I NDV＜0和 I NDV=0～0.25之间所包含的像元并获取各个像元所在的位置,最后再计算这些像元的土壤热通量.裸土地表土壤热通量IDL实现算法为2.3.3 显热通量显热通量的计算最为复杂.SEBAL模型引入了“干点”和“湿点”概念,利用“干点”处蒸散发量基本为0,而“湿点”处蒸散发量达到最大的假设,结合近地表面温度差的线性函数,并考虑大气稳定度,通过Monin-Obukhov方法[14]求得不同状态条件下的摩擦风速、动力学粗糙度和阻抗等参数[15],从而计算获得显热通量H.本文通过IDL语言并以显热通量的变化小于1%作为循环终止条件,实现了整个循环迭代过程.在程序实现过程中,“干点”和“湿点”根据地表温度参数来选取(图3).为保证“干点”和“湿点”选取的合理性,应考虑研究区局部云层覆盖导致的地表温度降低而引起的误差.利用云层的高反射低温度特点,通过多波段合成方法将云层检测出来,获取其所在像元位置,并进行掩膜处理.3 SEBAL模型日蒸散发量反演黄河三花间(三门峡—花园口区间)是我国中部地区主要的半干旱区,该系统的研究区包括陕西、山西、河南3省的部分地区.该区域地表类型复杂,春季易干旱,夏季多暴雨.本研究采用的遥感影像是Terra卫星的2002年3月8日、4月18日和6月12日3期MODIS影像.3.1 日蒸散发量IDL批处理结果充分利用ENVI/IDL二次开发函数,实现了日蒸散发量反演的批处理.运算过程中,仅需要人工选择预处理后的MODIS影像、对应日期的气象shapefile文件以及DEM数据和初始条件,经系统运算就可得到日蒸散发量分布,如图4所示.图3 显热通量计算显示窗口Fig.3 Interface for calculating sensib le heat flux 图4 黄河三花间日蒸散发量分布(单位:mm)Fig.4 Distribution of daily evapotranspiration in Sanmenxia-Huayuankou watershed of YellowRiver(unit:mm)分析图4可知,日蒸散发量高值区分布在研究区西南熊耳山地带以及北部植被覆盖度较高的山区及有灌溉的农业区,一般在4mm以上,而植被覆盖相对较少的裸土和城镇,蒸发量相对较小,一般在1.0～2.5mm之间.不同下垫面具有不同的地表特征和水热性状,有植被覆盖区明显大于周围无植被区和少植被区.日蒸散发量的空间分布基本符合实际.图5 日蒸散发量与各地表参数相关分析显示窗口(2002-04-18)Fig.5 Interface for corrlation between daily evapotranspiration and surface parameters(April 18,2002)3.2 日蒸散发量与地表参数相关分析IDL语言在数据处理、统计分析与图形显示方面具有强大的优势,可以使开发者通过较少的命令完成大量的数据预处理、变换及统计分析等工作.通过对日蒸散发量与地表参数的统计计算和相关分析(图5),可以知道各参数对蒸散发量的影响程度. 分析结果表明:日蒸散发量与地表温度相关性最好,整体呈线性负相关关系,相关系数R达到0.95,这是由于地表温度高的区域多为植被覆盖相对比较少的地区;植被覆盖度高的地区由于植被蒸腾作用造成冠层温度降低;日蒸散发量与地表温度差和植被指数的相关系数分别为0.63和0.61.4 参数计算结果存取为了将日蒸散发量反演过程中计算获得的地表参数和其他参数进行影像匹配,可以将其结果保存为ENVI标准格式或指定格式,并定义好地理坐标投影.应用时,通过自定义map-info函数读取校正后的影像坐标并赋予参数影像就可以实现了.具体代码如下:5 结语本文基于SEBAL模型,在IDL环境下编程建立了地表蒸散发反演系统.该系统界面友好,操作简单,运算速度快,可进行批量、快速的日蒸散发量计算,统计分析功能可用于精度评价、蒸散发与地表参数回归分析等.由于该系统具有平台无关性特点,因而可将其作为独立模块加入水文分析等专业系统,从而可有效解决通用遥感软件缺乏专业信息提取功能的问题.参考文献:【相关文献】[1]PETER W.A discussion on and alternative to the Penman-Monteithequation[J].Agricultural Water M 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Estimating reference evapotranspiration (ETo)using numerical weather forecast data in central ChileDaniel Silva a ,Francisco J.Meza a,b,*,Eduardo Varas caFacultad de Agronomía e Ingeniería Forestal,Pontificia Universidad Católica de Chile,Chile bCentro Interdisciplinario de Cambio Global UC,Pontificia Universidad Católica de Chile,Chile cEscuela de Ingeniería,Departamento de Ingeniería Hidráulica y Ambiental,Pontificia Universidad Católica de Chile,Chilea r t i c l e i n f o Article history:Received 17March 2009Received in revised form 16November 2009Accepted 12December 2009This manuscript was handled byK.Georgakakos,Editor-in-Chief,with the assistance of kshmi,Associate Editor Keywords:MM5dataMOS correctionsReference evapotranspiration Maipo river basins u m m a r yWater demand at a basin level is influenced by many factors such meteorological variables,soil moisture,vegetation type and irrigation system.Among them,climate is the major driver,because weather condi-tions determine energy balances and vapor pressure deficits that affect the magnitudes of vapor flux from surface to atmosphere.Monitoring evaporation is a great challenge since specific and costly equipments are required.As an alternative,agronomists and engineers use semi-empirical equations such as the Penman–Monteith for-mula to estimate potential evapotranspiration based on surface weather observations.Unfortunately weather stations are scarce and do not always have the instrumentation to measure relevant variables for its calculation.In this work,we evaluate the use of numerical weather forecasts,obtained from MM5model,as proxy for surface meteorological data with the specific objective of using them to estimate reference evapo-transpiration (ETo)in the Maipo river basin.We compared three procedures to obtain ETo:(a)Raw MM5estimates of latent heat flux;(b)calculation of ETo from Penman–Monteith equation,using raw MM5outputs of weather variables;and (c)calculation of ETo from Penman–Monteith using MOS-cor-rected MM5weather data.We used class A pan evaporation data and estimates of ETo using observed daily surface data to evaluate the precision of each method.We found that the estimation of ETo based on MOS-corrected weather variables is usually the most effective method to estimate reference evapotranspiration.Since MM5outputs in this region are avail-able at 25km grids,the number of monitoring sites can be increased substantially,improving the ability to capture spatial variability of water demands in the basin.Ó2009Elsevier B.V.All rights reserved.IntroductionIn modern societies,potential water resource conflicts arise as a consequence of current multiple uses (i.e.industrial,agriculture,ecosystems,and human consumption)as well as increasing de-mand due to population growth (Rosegrant et al.,2000).In Medi-terranean regions,the situation could become more critical since current imbalances between water supply and demand are aggra-vated as a consequence of climate change.Several models predict that precipitation is likely to be reduced in the next decades affect-ing runoff processes.In addition,temperature increases will pro-duce changes in seasonality of streamflow associated with early snowmelt (Vicuña and Dracup,2007;Bates et al.,2008).For these reasons,it is necessary to develop systems that allow efficient operation of water resources,and water allocation policies that consider the increasing demand and multiple uses of water,climatic and spatial variability of water resources and climate change impacts on supply and seasonality.Irrigated agriculture is one of the largest consumers of water resources (Ward and Trimble,2004).For this reason,the knowl-edge of evaporation rates in a region is a critical issue that allows managers to develop strategies for efficient operation of water resources.Unfortunately measurements of evapotranspiration are scarce and expensive.Real measurements of vapor fluxes require special-ized instruments such as lysimeters (López-Urrea et al.,2006),Bowen ratio equipments (Jara et al.,1998)or specific instrumenta-tion to calculate instantaneous fluxes of momentum and vapor to apply methods such as ‘‘Eddy covariance”(Rana et al.,2005).Some equations have been developed to estimate vapor fluxes as a function of routine meteorological observations.These equations0022-1694/$-see front matter Ó2009Elsevier B.V.All rights reserved.doi:10.1016/j.jhydrol.2009.12.018*Corresponding author.Address:Facultad de Agronomía e Ingeniería Forestal,Pontificia Universidad Católica de Chile,Casilla 306-22,Santiago,Chile.Tel.:+5623547911;fax:+5625534130.E-mail address:fmeza@uc.cl (F.J.Meza).Journal of Hydrology 382(2010)64–71Contents lists available at ScienceDirectJournal of Hydrologyj o u r n a l h o m e p a g e :w w w.e l s e v i e r.c o m /l o c a t e /j h y d r olintroduce specific assumptions regarding the status and behavior of vegetation surfaces(generally under well watered conditions).At regional level,there are methods that use satellite images and surface meteorological data to calculate both reference evapo-transpiration and actual evapotranspiration.An example of these methods is SEBAL(Surface Energy Balance Algorithm for Land;Bas-tiaanssen et al.,1998,2005),which has been used in regional water balance studies(Allen et al.,2007).In any case,the correct estimation of crop evapotranspiration and therefore irrigation needs relies on the availability of routine meteorological information.Unfortunately weather stations are scarce and do not always have the instrumentation needed to mea-sure all relevant variables.Over the last years there have been improvements in objective weather forecasting based on mesoscale numerical models.These models not only provide forecast for commonly used variables such as temperature and precipitation.They also give information regarding other relevant variables such as pressure,wind speed and direction,specific humidity and solar radiation.All of these variables are required to calculate reference evapotranspiration, representing a potentially valuable source of information for water resources management.The objective of this research is to evaluate the use of mesoscale model results as proxy for surface weather variables in places where there is no meteorological stations,and use these variables to estimate reference evapotranspiration.Determining evapotranspirationBecause of its theoretical basis and effectiveness in assessing evapotranspiration rates,the Penman–Monteith equation(Mon-teith,1965;Monteith and Unsworth,1990)has been recom-mended by FAO as the most appropriate method to determine crop water requirements(Allen et al.,1998).The equation is:k E¼DðR NÀGÞþq c p ðe sÀeÞr hDþc1þr c r hð1ÞHere,k is the latent heat of vaporization(2,500,000J kgÀ1),D is the rate of change of vapor pressure with temperature(Pa KÀ1).R N cor-responds to net radiation(J mÀ2dayÀ1),G is the soil heatflux (J mÀ2dayÀ1).q is air density(kg mÀ3).c p is the specific heat at constant pressure(J kgÀ1KÀ1).e s and e are the saturation vapor pressure and the actual vapor pressure of air(Pa).r h is the aerody-namic resistance to heatflow(days mÀ1).c is the psycrometric constant(Pa KÀ1).r c is the canopy resistance(days mÀ1).When the crop experiences water stress,active mechanisms of regulation are trigged and vapor exchange is restricted via stomata closure.In Eq.(1)this is represented by increasing canopy resis-tance,which in turn reduces evapotranspiration.However,canopy resistance is very difficult to measure,unless soil water content is high enough so stomata are fully open and the resistance reaches its minimum value.Reference evapotranspiration(ETo)Due to the difficulties associated with the estimation of can-opy resistances,environmental scientists have preferred to de-fine a variable called reference evapotranspiration(ETo),which is the amount of water transpired by a short,dense vegetation growing under total satisfaction of its water requirements.Pen-man–Monteith equation is applied assuming that the canopy resistance is set to a known value close to zero.Allen et al. (1998)present this equation as a function of daily routine mete-orological data.ETo¼0:408ÁDÁðR NÀGÞþc900Áu2Áðe sÀeÞc2ð2ÞIn this case,net radiation(R N)and soil heatflux(G)are expressed in MJ mÀ2dayÀ1.Mean temperature is in Celsius(°C),and wind speed at2m height(u2)is in m sÀ1.Reference evapotranspiration is regarded as a process that oc-curs without water stress,and represents the upper limit of grass water requirements when exposed to the observed meteorological conditions.Empirical work(mostly carried on using lysimeters)has shown that water requirements of any crop are proportional to reference evapotranspiration.Therefore one can obtain crop po-tential evapotranspiration multiplying reference evapotranspira-tion by a crop coefficient(kc).As in the case of reference evapotranspiration,the application of this method is only possi-ble when the crop does not experience water stress.To model ac-tual evapotranspiration it is necessary to represent changes in canopy resistance as a function of water availability(Jarvis, 1976;Stewart,1988).In some cases it is possible to model the crop coefficient value as a function of soil water content to repre-sent impacts of water shortages on canopy resistance.Examples of this approach are found in Allen et al.(1994,1998),and Meza (2005).Class A evaporation panAn alternative method to obtain reference evapotranspiration corresponds to the use of class A evaporation pan(Eb).This instru-ment has been standardized allowing the user to determine water evaporation measuring variations of the water table(Jensen et al., 1990;Allen et al.,1998).Since evaporation form an open source differs form the one occurring in crops,it is necessary to apply an empirical coefficient denominated pan coefficient(Kp).This va-lue depends on wind speed and relative humidity in the surround-ing environment.For a class A evaporation pan,Allen et al.(1998) give an equation to determine its value.Kp¼0:108À0:0286Áu2þ0:0422lnðdÞþ0:1434lnðRHÞÀ0:000631ðlnðdÞÞ2ÁlnðRHÞð3ÞHere,RH corresponds to relative humidity(%),d is the distance be-tween the instrument and crop(m),and u2corresponds to the wind speed measured at2m height.Once this value has been deter-mined,reference evapotranspiration can be calculated as:ETo¼EbÁKpð4ÞMM5modelIt is clear that surface weather observations are needed to cal-culate reference evapotranspiration either using Penman–Mon-teith or class A evaporation pan.Since it is not always possible to have these values,the use of other sources of information such as weather forecasts from numerical models appears as an inter-esting alternative.MM5is a non-hydrostatic,sigma coordinate,mesoscale model developed by the National Center for Atmospheric Research (NCAR)and Pennsylvania State University(PSU).The model has been designed to simulate and predict atmospheric circulation, based on the work of Anthes and Warner(1978).It is composed by a series of sub-models which represent several processes in the atmosphere such as conservation of mass and momentum, atmospheric thermodynamics,advection and divergence.In recent years,it has been possible to operate MM5in a nested mode improving its spatial resolution(Dudhia et al.,2005).D.Silva et al./Journal of Hydrology382(2010)64–7165The use of MM5based forecasts for individual meteorological variables such as temperature,wind speed,and precipitation has been documented previously(Hart et al.,2004;Falvey,2007;Onc-ley and Dudhia,1995)and it has been used in several countries as a fundamental tool for objective weather forecasting.However,there is a rich body of information in MM5simulations that can befit within the framework of predicting evapotranspiration,since most of the variables requested in Eq.(2)are found in regular MM5out-puts.Moreover,MM5gives information about latent heatflux(k E) at the surface,so it will be possible to use both,the direct assess-ment of evaporation and the one obtained combining surface meteorological information.MM5uses a Land Surface Model (LSM;Chen and Dudhia,2001)to represent feedback mechanisms between vegetation and the atmosphere,and calculates soil heat flux(G),sensible heatflux(H)and latent heatflux(k E),using a Pen-man-based energy balance approach with an stability-dependent aerodynamic resistance(Mahrt and Ek,1984).Although this fea-ture is recognized as a significant improvement in the ability of MM5to represent land–atmosphere interactions,MM5-computed latent heatfluxes show important discrepancies with observed data when are applied to large regions(Marx et al.,2008).MOSIt is widely recognized that MM5forecasts(i.e.raw data)are far from perfect,and that the model has some limitations related to the coarse representation of the terrain,the numerical representa-tion of the differential equations,and lack of high resolution upper air data for initialization.In some cases there are systematic errors that can be removed using statistically based post processing rou-tines,training equations to obtain a better estimation of meteoro-logical variables in specific locations.These types of procedures receive the common denomination of Model Output Statistics (MOS;Glahn and Lowry,1972;Wilks,1995)and have been used to obtain forecasts of daily surface weather variables form Numer-ical Weather Prediction models(NWP)for more than30years(So-kol and Rezacova,2000).The method was proposed by Glahn and Lowry(1972),and it is described by the authors as an objective numerical weather forecasts technique that is based on determin-ing the statistical associations between variables obtained from the numerical model(predictors)and the climatic variable of interest (predictand)for a specific time period.The application of MOS to outputs of any Numerical Weather Prediction model(NWP)reduces forecasts errors,because the sys-tematic deviation is removed and/or forecast variance is corrected (Neilley et al.,2002).The general format of this procedure corresponds to a multiple linear regression model in which several NWP variables are in-cluded to obtain the best estimation of the forecasted variable (Eq.(6)).Y p¼a0þa1Áp1þa2Áp2þa3Áp3þÁÁÁþa nÁp nð5ÞHere,Y p is the MOS corrected predictand,a i are the regression coef-ficients(I=1,2,...,n),and p i correspond to the predictors from a NWP model(Antolik,2000).The optimum number of predictors is obtained using a screening procedure called stepwisefit regression. Basically this method chooses the predictor with highest correla-tion,then the pair of variables,including the predictor selected in the step before,with highest correlation and then the triplet,and so on.The process is repeated until the reduction of the root mean square error is no longer significant(Glahn and Lowry,1972;Anto-lik,2000;Wilks,1995).One disadvantage of MOS is that it requires a fairly long record of NWP outputs and observations to produce robust estimations (Antolik,2000).It is also very likely that specific MOS equations have to be developed for different locations,making spatial gener-alization are very difficult task(Clark and Hay,2004).Even though there are evident limitations in mesoscale models and that MOS corrected forecast do not always achieve good re-sults,it is important to recognize that these models contain infor-mation that can be used,especially in places where there is an insufficient network of meteorological stations and situation where only few meteorological variables are recorded.Methods and proceduresLocationThe area under study corresponds to the Maipo basin,located between latitudes32°550and34°150south,and longitudes70–72 west.The basin has a surface of15,157km2,33%of that surface corresponds to mountains(Andes),45%shows native forests,30% is irrigated agriculture and the rest corresponds to urban areas (DGA,2007).The climate is regarded as Mediterranean with mean annual temperature of14°C and total precipitation of350mm in the val-ley.Rainfall shows strong seasonality with80%of annual precipita-tion falling in austral winter.Snow accumulation occurs above 1500m during winter.Reference evapotranspiration varies from6.5mm dayÀ1in the austral summer to1.5mm dayÀ1in mid winter.The strong sea-sonal pattern is a consequence of the variability of solar radiation and temperature.High frequency variability(i.e.day to day)re-mains constant over the year,with a slight reduction in winter and a peak in the beginning of spring.Fig.1shows mean and stan-dard deviations of reference evapotranspiration for the region un-der study.Interannual variability is rather small.For instance, mean values for reference evapotranspiration in the month of Jan-uary(the month that exhibits the highest intensities)are around 6.8mm dayÀ1with a coefficient of variation of only3%.Previous work(Meza,2005)has shown a significant ENSO footprint in the evaporation regime of the Maipo basin(central Chile),but the greater differences among ENSO phases are observed in winter and fall seasons.Meteorological dataWe collected daily data for the period2004–2007.MM5outputs were provided by the department of geophysics(Universidad de Chile).Each time the model is run it provides forecast for meteoro-logical conditions up to144h ahead.To ensure we would work with the data with a minimum of uncertainty,we only used the values that represent the period from0to24h in the future,select-ing the variables that are equivalent to the surfacerecords.Fig.1.Seasonal variation of reference evapotranspiration in central Chile.66 D.Silva et al./Journal of Hydrology382(2010)64–71Surface weather information was collected form different sources.One of them is a network of automatic weather stations called AGROCLIMA,the other sources were the Directorate General of Waters (DGA)and the Chilean National Weather Service (DMC).Within the existing network of meteorological stations in the ba-sin,only five (Pudahuel,Los Panguiles,Talagante,Quinta Normal and Pirque)recorded the meteorological variables needed to calcu-late reference evapotranspiration according to Penman–Monteith formula.Two stations (Quinta Normal and Pirque)had also data from class A pan evaporation,allowing us to have an alternative estimate of reference evapotranspiration.Fig.2shows the geo-graphic distribution of weather stations (control points)and MM5grid points within the Maipo basin.We removed outliers and inconsistent data from both series (i.e.MM5forecasts and weather observations).We used the series from 2004to 2006to fit the coefficients of a MOS for each location and left the year 2007as an independent validation data set.Since grid points of MM5forecasts do not coincide with the sites of observation we interpolate values from the closest four grid points using a three dimensional inverse distance algorithm.Although MM5can give information in 29sigma coordinate levels,we only used surface values as proxy for meteorological data.The variables used were:surface pressure,precipitation,temperature,shortwave radiation,longwave radiation,wind speed,latent heat flux and specific humidity.MOS equationsIn this case,we develop specific MOS equations for each station and applied this procedure for raw outputs of MM5model (i.e.maximum temperature,minimum temperature,mean tempera-ture,specific humidity,daily sum of shortwave radiation,and daily mean wind speed)as well as the estimation of ETo using latent heat data from MM5.Since MM5variables and observed meteorological data show marked seasonality,we fit a Fourier series to each variable and re-move the seasonality,working only with anomalies.In this way we reduced the probability of choosing a predictor that shows high correlation only because it varies over time following a similar mode of the predictand.The general Fourier series equation is:F W ;t¼b 0þb 1Ásin 2Áp Átþb 2Ácos2Áp Átð6ÞF W ,t corresponds to the value of the Fourier series for variable W intime t (1,...,365),b 0is the annual mean of the variable,b 1and b 2are the coefficients associated to the firstharmonic.Fig.2.Geographic distribution of meteorological stations and MM5grid point.D.Silva et al./Journal of Hydrology 382(2010)64–7167Once seasonality is being removed we used a stepwisefit proce-dure included in Matlab to select the predictors for each variable and location.Thus the general MOS equation is:ðY tÀF Y;tÞ¼a0þa1ÁðX1tÀF X1;tÞþa2ÁðX2tÀF X2;tÞþÁÁÁþa nÁðX ntÀF Xn;tÞð7ÞHere,Y represents the predictand,and X i(i=1,...,n)the selected MM5predictors.The performance of MOS equations for individual meteorologi-cal variables(i.e.temperature,relative humidity,wind speed and solar radiation)is discussed in Silva et al.(2009).Comparison of resultsSince the objective is to evaluate the use of MM5forecasts to estimate reference evapotranspiration we compare three different methods.Method1corresponds to direct use of latent heatfluxes obtain from MM5.Dividing this value by the latent heat of vapor-ization(k)one obtains an estimate of evapotranspiration.Method2 corresponds to the calculation of ETo by means of Penman–Mon-teith equation,using raw data from MM5(without MOS).Method 3calculates ETo using Penman–Monteith equation,but in this opportunity the formula is fed with MOS-corrected MM5outputs.To compare the accuracy of the estimates from all methods,in each station we calculated Penman–Monteith reference evapo-transpiration using observed weather data,and in two of them we calculated reference evapotranspiration using class A evapora-tion pan.We computed root mean square error,maximum absolute devi-ance and the coefficient of determination between observed and predicted values of reference evapotranspiration.We also con-ducted a T-test for observed and predicted values with the null hypothesis that there are no differences between the two data sets. This procedure has been used in similar studies(Jacovides and Kontoyiannis,1995),but in this case is necessary to apply a vari-ance inflation factor(Wilks,1995)since observed and predicted data show significant autocorrelation coefficients.Results and discussionSeasonal variationOne of the most important sources of variability in almost all variables(i.e.calculated ETo and MM5forecast data)corresponds to seasonality.Table1shows the results of a single harmonic Fou-rier seriesfit to the data to model the behavior of each variable throughout the year.Even tough the analyses of variance were sta-tistically significant in all cases;wind speed and pressure did not show seasonal variations that can be represented using sinusoidal functions.In those cases the anomalies were comparatively larger than in the case of temperature and solar radiation.In the case of reference evapotranspiration,the use of Fourier series allowed us to capture up to75%of the variability.The strong seasonality ob-served is a consequence of the characteristic pattern of variation of temperature,relative humidity,and clear skies found in semi-arid and Mediterranean regions.MOS proceduresMOS data contains a number of different predictors that can be used to obtain the best representation of real weather data.We performed a MOS procedure using stepwise regression to choose only the ones that achieve better results in terms of variance ex-plained.Table2shows an example of selected predictors for max-imum and minimum temperature.Even tough some predictors may have no direct connection with the meteorological variable from the biophysical standpoint, the main advantage of this method is that usually the bias is re-moved and variance of the error is reduced.Table3shows a com-parison of goodness offit indices for selected variables,with and without MOS.It is clear that MOS procedures outperform raw MM5data in the ability to represent daily surface weather obser-vations.A complete evaluation of the use of MOS-corrected MM5 data as proxy for daily weather variables is presented in Silva et al.(2009).Estimation of EToDaily data from2004to2006was used to calibrate MOS equa-tions and later on used to calculate reference evapotranspiration using Eq.(2).Note that reference evapotranspiration shows a very strong seasonal behavior.Even though the harmonic analysis car-ried out here does not represent a forecast method by itself,given the proportion of the variance captured by the Fourier series,we have considered it as a baseline for comparison,so a good method to assess reference evapotranspiration must not only outperform the others,but also show improvements over simple seasonal models such as the ones obtained using Fourier series.Table4shows a comparison between methods in terms of their ability to represent reference evapotranspiration.Except for the case of class A evaporation Pan at Pirque,maximum absolute devi-ation was substantially reduced in all cases where ETo is estimated Table1Fourier series coefficients(b0,b1,b2)and summary statistics of goodness offit for reference evapotranspiration(PM-ETo and A-ETo)and MM5variables.b0b1b2R2RMSE PudahuelPM-ETo(mm) 2.39À0.03 1.550.680.67 Maximum temperature(°C)24.46 1.227.390.77 2.67 Minimum temperature(°C)8.02 1.53 5.080.66 2.54 Solar radiation(MJ mÀ2)16.73À1.429.040.89 2.03 Wind(m sÀ1) 2.94À0.03À0.240.030.89 Pressure(kPa)94.56À0.10À0.110.160.24 Quinta NormalPM-ETo(mm) 2.80À0.02 1.970.750.75 A-ETo(mm) 3.320.59 2.860.63 1.44 Maximum temperature(°C)24.23 2.457.350.79 2.70 Minimum temperature(°C)7.65 2.67 4.430.66 2.63 Solar radiation(MJ mÀ2)16.52À1.079.340.88 2.09 Wind(m sÀ1) 2.800.01À0.720.200.89 Pressure(kPa)94.13À0.05À0.230.290.23 Los PanguilesPM-ETo(mm) 4.410.37 1.050.31 1.15 Maximum temperature(°C)23.64 1.217.320.780.78 Minimum temperature(°C)8.53 1.56 4.920.67 2.50 Solar radiation(MJ mÀ2)16.68À1.519.150.88 2.12 Wind(m sÀ1) 2.77À0.11À0.070.010.81 Pressure(kPa)94.90À0.08À0.150.260.20 PirquePM-ETo(mm) 3.19À0.17 1.520.490.96 A-ETo(mm) 3.880.71 3.040.71 1.27 Maximum temperature(°C)23.05 1.69 6.450.78 2.29 Minimum temperature(°C)7.64 1.82 4.320.65 2.26 Solar radiation(MJ mÀ2)16.40À0.919.340.87 2.22 Wind(m sÀ1) 3.21À0.02À0.840.430.60 Pressure(kPa)92.10À0.05À0.100.170.16 TalagantePM-ETo(mm) 2.37À0.14 1.340.600.68 Maximum temperature(°C)23.53 1.127.410.77 2.71 Minimum temperature(°C)8.60 1.57 4.910.65 2.59 Solar radiation(MJ mÀ2)16.54À1.519.250.88 2.22 Wind(m sÀ1) 2.85À0.06À0.180.01 1.00 Pressure(kPa)94.89À0.07À0.140.230.2168 D.Silva et al./Journal of Hydrology382(2010)64–71with MOS-corrected MM5data.Root mean squared error also shows important reductions,ranging from10%to20%,and conse-quently the percentage of the observed variance that is explained by the estimates increases.As in the case of routine meteorological data(i.e.precipitation, temperature and wind speed),the estimation of ETo using raw MM5values do not produce satisfactory results.In some cases the coefficient of determination gives values that are even smaller than zero.This result implies that either original variables used or the estimates of ETo must be statistically corrected to achieve some degree of predictability.It is interesting to note that estimates of ETo using latent heat fluxes from MM5(Method1)provide results that are better than the ones obtained using the set of meteorological variablesTable2List of MOS predictors used to represent maximum and minimum temperature at each location.LocationPudahuel Quinta Normal Los Panguiles Pirque TalaganteMaximum temperatureMM5total solar radiation xMM5maximum solar radiation xMM5maximum temperature x X x x x MM5maximum wind speed x X xMM5maximum specific humidity x x x MM5minimum specific humidity XMM5mean specific humidity xMinimum temperatureMM5total solar radiation XMM5maximum solar radiation xMM5minimum temperature x x x x MM5mean temperature X xMM5surface pressure X xMM5maximum wind Speed x x MM5maximum specific humidity XMM5minimum specific humidity xMM5mean specific humidity X xTable3Comparison of goodness offit indicators for some selected variables,with and without MOS.aLocation Without MOS With MOSR2RMSE n m MAD R2RMSE n m MADMaximum temperaturePirque0.74 2.90À0.85 1.0213.700.79 2.640.00 1.0112.52 Talagante0.63 3.69 2.090.8513.200.69 3.380.03 1.008.80 Quinta Normal0.80 2.86À1.370.9912.600.84 2.590.00 1.008.87Minimum temperaturePirque0.48 2.490.590.6310.300.74 1.760.00 1.00 5.89 Talagante0.46 2.59 3.180.5511.500.57 2.310.00 1.00 6.75 Quinta Normal0.63 2.41 3.850.7010.400.84 1.600.00 1.00 6.33Mean temperaturePirque0.85 1.57 1.450.8410.110.88 1.410.00 1.007.35 Talagante0.75 2.05 3.580.7110.740.84 1.650.00 1.00 5.20 Quinta Normal0.83 1.98 3.130.85 6.450.90 1.510.00 1.00 4.90a R2is the determination coefficient,RMSE corresponds to root mean square error,MAD corresponds to the maximum absolute deviation and m and n are the slope and intercept of the observed vs.predicted regression,respectively.Table4Comparison between methods a to estimate reference evapotranspiration from MM5outputs.Bold values of RMSE represent cases where the null hypothesis of a T-test for autocorrelated data is not rejected at the5%significance level.MAD(mm)RMSE(mm)R2M1M2M3M1M2M3M1M2M3FSPudahuel 2.77 4.34 2.680.780.990.630.570.300.710.68 Quinta Normal 3.97 4.20 2.070.960.990.660.520.480.770.75 Quinta Normal(pan) 5.66 5.23 3.19 1.21 1.160.980.440.490.630.63 Los Panguiles8.717.86 5.13 1.34 1.54 1.220.21À0.060.350.31 Pirque 6.42 6.47 5.00 1.39 1.51 1.170.380.270.560.49 Pirque(pan) 3.57 3.46 3.81 1.00 1.130.920.670.590.730.71 Talagante 3.89 4.70 2.340.74 1.150.650.52À0.150.630.60a M1estimates ETo using latent heatflux,M2uses raw MM5variables,and M3uses MOS-corrected MM5variables.FS corresponds to a single harmonic Fourier series, representing seasonal variation.D.Silva et al./Journal of Hydrology382(2010)64–7169。

三江源温性草原蒸散量计算方法的比较赵双喜;张耀生;赵新全;冯承彬【摘要】[目的]对比分析了三江源温性草原蒸散量的计算方法,为牧区蒸散量的合理使用提供依据.[方法]以小型自动气象站气象观测资料为基础,采用FAO Penman-Monteith(FAO P-M)、Penman1948(P-48)、Priestley-Tay-lor(P-T)和FAO Penman 1979(F-79)4种不同方法,估算了三江源温性草原参考作物蒸散量,并对计算结果进行了对比分析.[结果]三江源温性草原的参考作物蒸散量季节分布极不均匀,表现出春季、夏季、秋季、冬季依次减小的趋势.并且FAO P-M公式的计算结果与其他3种方法(P-48、P-T和F-79)的计算结果呈正相关,但与F-79公式计算结果间差异不大,与另两种方法计算结果间的差异显著.通过偏差分析可知,P-48公式计算的结果偏大,P-T公式计算的结果偏小,造成偏差的主要原因是4种模型各自选用了不同的辐射项和动力项.[结论]在利用气象数据计算蒸散量的过程中,要根据当地需要采用不同的公式.在三江源温性草原,可采用F-79修正式代替标准的FAO P-M公式计算参考作物蒸散量.【期刊名称】《西北农林科技大学学报（自然科学版）》【年(卷),期】2009(037)001【总页数】5页(P79-83)【关键词】三江源;温性草原;参考作物蒸散量【作者】赵双喜;张耀生;赵新全;冯承彬【作者单位】中国科学院,西北高原生物研究所,高原生物适应与进化重点实验室,青海,西宁,810001;中国科学院研究生院,北京,100001;中国科学院,西北高原生物研究所,高原生物适应与进化重点实验室,青海,西宁,810001;中国科学院,西北高原生物研究所,高原生物适应与进化重点实验室,青海,西宁,810001;中国科学院,西北高原生物研究所,高原生物适应与进化重点实验室,青海,西宁,810001;中国科学院研究生院,北京,100001【正文语种】中文【中图分类】S812.1作物需水预测对合理利用和节约用水，缓解水资源的供需矛盾具有重要意义。

水稻作物系数与稻田渗漏模型参数的同步估算石艳芬;缴锡云;罗玉峰;虞晓彬【摘要】Based on a water balance model, a multivariate nonlinear programming approach was employed to synchronously estimating the crop coefficients for rice and the seepage model parameters for paddy fields, with the objective function being to minimize the sum of square-error between the simulated face water depth and the observed one. Then, the model efficiency coefficient, the average relative error and the average absolute error were calculated to evaluate the simulation results of the approach. Case study shows that the simulated values for crop coefficients and seepage model parameters are both close to the empirical ones, and the simulated value for face water depth is in good agreement with the measured one. Hence, the approach presented in this paper can be used to estimate the crop coefficient for rice and the seepage model parameters for paddy fields.% 根据田间水量平衡模型，以田面水层深度误差平方和最小为目标函数，采用多变量非线性规划方法同步估算水稻作物系数和稻田渗漏模型参数，并利用统计学方法中的模型效率系数、平均相对误差、平均绝对误差等指标对模拟效果进行评价。

基于温度资料估算参考作物腾发量的方法比较张倩;段爱旺;高阳;申孝军;蔡焕杰【摘要】以Penman-Monteith方法计算的参考作物腾发量ETo为标准,与采用温度法和辐射法的Penman-Monteith温度法(PMT)、修正的PMT (PMT-cor)、Hargreaves-Samain (HG)、修正的HG公式(HG-M1,HG-M2)、Thornthwaite 公式、Irmak公式、修正的Irmak公式(Irmak-eor)、McGuinness Bordne公式(M-B)的估算值进行对比分析,同时引入干旱指数对温度法中的PMT公式进行修正,采用多元线性拟合对辐射法中的Irmak公式进行修正.结果表明:温度法中的PMT 公式、PMT-cor公式、HG公式和辐射法中Irmak公式、Irmak-cor公式的计算值与PM法计算值间的回归系数b都接近于1.0,相关系数R2大于0.80,相对误差RE小于20％,一致性指数d大于0.95.通过交叉比较发现,Irmak-cor公式精度较高(b=1.00、R2=0.98、RMSE=0.17 mm/d、RE=7％、d=1.00),其次是Irmak公式(b=1.03、R2=0.95、RMSE=0.31 mm/d、RE=12％、d=0.99),再次是PMT、PMT-cor、HG方法.考虑计算结果的精确度,该地区首选Irmak-eor公式估算ETo;如果考虑计算简便,该地区可选HG公式估算ETo.【期刊名称】《农业机械学报》【年(卷),期】2015(046)002【总页数】6页(P104-109)【关键词】温度资料;参考作物蒸发蒸腾量;Penman-Monteith公式;PMT公式【作者】张倩;段爱旺;高阳;申孝军;蔡焕杰【作者单位】西北农林科技大学旱区农业水土工程教育部重点实验室,陕西杨凌712100;中国农业科学院农田灌溉研究所农业部作物需水与调控重点实验室,新乡453002;中国农业科学院农田灌溉研究所农业部作物需水与调控重点实验室,新乡453002;中国农业科学院农田灌溉研究所农业部作物需水与调控重点实验室,新乡453002;西北农林科技大学旱区农业水土工程教育部重点实验室,陕西杨凌712100;西北农林科技大学旱区节水农业研究院,陕西杨凌712100【正文语种】中文【中图分类】S274.1参考作物蒸发蒸腾量(ETo)是计算作物需水量的重要参数，它的精确估算是灌溉管理、水资源评价和流域管理的重要依据[1-4]。

叶面积指数间接测量方法分析熊万彩;邱权;陈天华;郑文刚【摘要】Leaf area index (LAI) is defined as the ratio of the total blade surface area of the plant and the area occupied by the plant.It is an important parameter for describing the growth situation of plants.Two dominating branches of the indirect LAI measuring methods were summarized:remote sensing quantitative analysis and LIDAR measurements,and three methods under the two branches were introduced in detail:statistical model method,optical model method and LIDAR measurement,the principle and research progress were elaborated.On the basis of this,the advantages and disadvantages and development trends of LAI measurement methods were discussed.%叶面积指数(LAI)被定义为植物所有叶片表面积总和与植株所占的土地面积的比值,是表征植物生长趋势的重要参数.总结了当前LAI间接测量研究中的2个重要分支:遥感定量法和LIDAR测量法；详细地介绍了这2个分支下的3种方法:统计模型法、光学模型法、LIDAR测量法,阐述了各自的原理和研究进展；在此基础上,讨论了3种方法的优缺点及未来的发展趋势.【期刊名称】《安徽农业科学》【年(卷),期】2013(041)015【总页数】3页(P7022-7024)【关键词】LAI;统计模型;光学模型;LIDAR【作者】熊万彩;邱权;陈天华;郑文刚【作者单位】北京工商大学,北京100048;北京农业智能装备技术研究中心,北京100097;北京农业智能装备技术研究中心,北京100097;北京工商大学,北京100048;北京农业智能装备技术研究中心,北京100097【正文语种】中文【中图分类】S126;Q945生物学研究表明，叶面积指数(Leaf Area Index，LAI)是衡量植物生长状态的一个重要因素。