涡动相关能量闭合问题的研究进展

doi:10.11867/j.issn.1001-8166.2018.09.0898

地球科学进展 ›› 2018, Vol. 33 ›› Issue (9): 898 -913. doi: 10.11867/j.issn.1001-8166.2018.09.0898

涡动相关能量闭合问题的研究进展

周彦昭 ^1, ²(

), 李新 ^3, ^4, ^*(

)

1.中国科学院西北生态环境资源研究院甘肃省遥感重点实验室,甘肃兰州 730000
2.中国科学院大学,北京 100049
3.中国科学院青藏高原地球科学卓越创新中心,北京 100101
4.中国科学院青藏高原研究所,北京 100101

出版日期:2018-10-20
通讯作者: 李新 E-mail:zhouyanzhao@lzb.ac.cn;lixin@lzb.ac.cn
基金资助:
?国家自然科学基金项目“黑河流域水—生态—经济系统的集成模拟与预测”(编号: 91425303)中国科学院交叉创新团队“水文数据同化交叉团队”(编号: XXH13505-06)资助.

Progress in the Energy Closure of Eddy Covariance Systems

Yanzhao Zhou ^1, ²( ), Xin Li ^3, ^4, ^*( )

1.Key Laboratory of Remote Sensing of Gansu Province, Northwest Institute of Eco-Environment and Resources,Chinese Academy of Sciences, Lanzhou 730000, China
2.University of Chinese Academy of Sciences,Beijing 100049, China
3.CAS Center for Excellence in Tibetan Plateau Earth Sciences, Chinese Academy of Sciences, Beijing 100101, China
4.Institute of Tibetan Plateau Research,Chinese Academy of Sciences, Beijing 100101, China

Online:2018-10-20 Published:2018-10-24
Contact: Xin Li E-mail:zhouyanzhao@lzb.ac.cn;lixin@lzb.ac.cn
About author:
First author:Zhou Yanzhao(1989-), male, Xingtai City, Hebei Province, Ph.D student. Research areas include applications of remote sensing and GIS in hydrology and numerical simulations in atmospheric boundary layer. E-mail:zhouyanzhao@lzb.ac.cn
Supported by:
Foundation item:Project supported by the National Natural Science Foundation of China "Integrated modeling and prediction of the water-ecosystem-economy in the Heihe River Basin"(No.91425303);The Inter-disciplinary Innovation Team of the Chinese Academy of Science "The inter-disciplinary innovation team of data assimilation in hydrology"(No.XXH13505-06).

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涡动相关系统(EC)观测的湍流通量总是低于有效能量(净辐射与地表热储量之差),两者的差值可达有效能量的10%~30%。这种EC观测的湍流通量低估的现象,称之为“EC能量闭合问题”,已成为微气象学研究中的一大瓶颈。过去的几十年间大量学者对此问题进行了深入研究,积累了丰富的认知。系统介绍了EC能量闭合问题的成因,总结了学者对于EC能量闭合问题的认识以及基于这些认识提出的可能的修正方案,并详细评述了这些修正方案的优劣。与之前的综述不同,重点介绍了基于大涡模拟(LES)研究EC能量闭合问题的方法和进展。指出目前缺少高精度且时间连续、空间密集(如矩阵式观测)的地表通量观测数据集、LES尚不足以完全表征真实的EC观测、大尺度湍涡影响EC能量闭合的机制尚不清楚等问题。今后应加强大尺度湍涡影响EC能量闭合的机制研究,同时开展空间矩阵式观测,验证LES的结果。

关键词: EC, 能量闭合, 大涡模拟, 陆面过程, 微气象

The sum of turbulent fluxes measured by the eddy-covariance method is often 10%~30% lower than available energy (i.e., the net radiation minus the ground heat flux). This systematic bias in the EC method is called the "EC energy closure problem" and has been one of the biggest challenges in micrometeorology. In the past decades, lots of studies have focused on this problem and have found extensive knowledge about it. In this paper, we introduced the reasons to the EC energy closure problem and systematically summarized the understandings on this problem with a discussion regarding the merits and limitations of possible correction methods. Compared with previous overview studies, our study focused on the methods and progresses on the EC energy closure problem using the Large Eddy Simulation (LES). The existing problem, e.g., the lack of high quality and high spatial density of "surface true fluxes" observations (e.g., matric observations), the failure of fully emulating the EC using the LES and how to mechanistically understand that large eddies affect turbulence structures and lead to non-closure problem, hinder the further understanding of the EC energy closure problem. Thus, in the future, focus should be put on the mechanistic understanding of how large eddies affect the non-closure problem and some dense field observations to obtain the high quality "surface true fluxes".

Key words: Eddy Covariance, Energy Closure, Large Eddy Simulation, Land Surface Progress, Micrometeorology.

中图分类号:

P433

表1 主要野外观测试验中能量闭合情况(据参考文献[ 13 ]修改)

Table 1 The energy residuals in field observations (modified after reference[13])

试验名称	不闭合率/%	天数/d	下垫面类型	参考文献
FIFE-89	0~10	40	草地	[14]
Vancouver Island-90	17	9	落叶林	[15]
TARTEX-90	33	24	裸地	[16]
KUREX-91	38	27	农田	[17]
LINEX-96/2	21	3	草地	[18]
LITFASS-98	14	21	裸地	[19]
EBEX-2000	10	约30	玉米	[13]
GAME-Tibet/TIPEX	10~20	约150	高原草地	[1]
LITFASS-2003	20~30	30	玉米和草地	[9]
金塔试验	28	6	小麦	[20]
WATER-2008	18	6	玉米	[21]
HiWATER-2012	8	约100	玉米、荒漠、戈壁、沙漠、果园	[7]
HiWATER-STEWC	12	约100	胡杨、柽柳、耕地、裸地	[4]

表1 主要野外观测试验中能量闭合情况(据参考文献[ 13 ]修改)

Table 1 The energy residuals in field observations (modified after reference[13])

试验名称	不闭合率/%	天数/d	下垫面类型	参考文献
FIFE-89	0~10	40	草地	[14]
Vancouver Island-90	17	9	落叶林	[15]
TARTEX-90	33	24	裸地	[16]
KUREX-91	38	27	农田	[17]
LINEX-96/2	21	3	草地	[18]
LITFASS-98	14	21	裸地	[19]
EBEX-2000	10	约30	玉米	[13]
GAME-Tibet/TIPEX	10~20	约150	高原草地	[1]
LITFASS-2003	20~30	30	玉米和草地	[9]
金塔试验	28	6	小麦	[20]
WATER-2008	18	6	玉米	[21]
HiWATER-2012	8	约100	玉米、荒漠、戈壁、沙漠、果园	[7]
HiWATER-STEWC	12	约100	胡杨、柽柳、耕地、裸地	[4]

表1 主要野外观测试验中能量闭合情况(据参考文献[ 13 ]修改)

Table 1 The energy residuals in field observations (modified after reference[13])

试验名称	不闭合率/%	天数/d	下垫面类型	参考文献
FIFE-89	0~10	40	草地	[14]
Vancouver Island-90	17	9	落叶林	[15]
TARTEX-90	33	24	裸地	[16]
KUREX-91	38	27	农田	[17]
LINEX-96/2	21	3	草地	[18]
LITFASS-98	14	21	裸地	[19]
EBEX-2000	10	约30	玉米	[13]
GAME-Tibet/TIPEX	10~20	约150	高原草地	[1]
LITFASS-2003	20~30	30	玉米和草地	[9]
金塔试验	28	6	小麦	[20]
WATER-2008	18	6	玉米	[21]
HiWATER-2012	8	约100	玉米、荒漠、戈壁、沙漠、果园	[7]
HiWATER-STEWC	12	约100	胡杨、柽柳、耕地、裸地	[4]

表1 主要野外观测试验中能量闭合情况(据参考文献[ 13 ]修改)

Table 1 The energy residuals in field observations (modified after reference[13])

试验名称	不闭合率/%	天数/d	下垫面类型	参考文献
FIFE-89	0~10	40	草地	[14]
Vancouver Island-90	17	9	落叶林	[15]
TARTEX-90	33	24	裸地	[16]
KUREX-91	38	27	农田	[17]
LINEX-96/2	21	3	草地	[18]
LITFASS-98	14	21	裸地	[19]
EBEX-2000	10	约30	玉米	[13]
GAME-Tibet/TIPEX	10~20	约150	高原草地	[1]
LITFASS-2003	20~30	30	玉米和草地	[9]
金塔试验	28	6	小麦	[20]
WATER-2008	18	6	玉米	[21]
HiWATER-2012	8	约100	玉米、荒漠、戈壁、沙漠、果园	[7]
HiWATER-STEWC	12	约100	胡杨、柽柳、耕地、裸地	[4]

图1 EC控制体积方法示意图 ^[31] u, v, w 分别为顺风向速度、侧风向速度和垂直速度; c为测定的标量

Fig.1 The sketch of control volume method ^[31]The u, v, w are the horizontal, lateral and vertical velocity,respectively; The c is the interested scalar

图1 EC控制体积方法示意图 ^[31] u, v, w 分别为顺风向速度、侧风向速度和垂直速度; c为测定的标量

Fig.1 The sketch of control volume method ^[31]The u, v, w are the horizontal, lateral and vertical velocity,respectively; The c is the interested scalar

表2 基于LES和野外实测数据研究EC能量闭合问题的优缺点

Table 2 The advantages and disadvantages of the methods based on LES and filed observations

方法	优点	缺点
基于野外实测数据	方法简单;结果可靠	大气环境多变,观测仪器易受环境因子和电磁因素干扰;难以进行控制实验分析某一变量对EC能量闭合问题的影响
基于LES 数据	便于进行控制实验,分析某一变量对EC能量闭合问题的影响;避免观测仪器噪声的干扰,便于理论分析和解释EC能量闭合问题	边界条件不易选取;计算量大,目前很难进行实际EC观测高度处的高精度的LES模拟

表2 基于LES和野外实测数据研究EC能量闭合问题的优缺点

Table 2 The advantages and disadvantages of the methods based on LES and filed observations

方法	优点	缺点
基于野外实测数据	方法简单;结果可靠	大气环境多变,观测仪器易受环境因子和电磁因素干扰;难以进行控制实验分析某一变量对EC能量闭合问题的影响
基于LES 数据	便于进行控制实验,分析某一变量对EC能量闭合问题的影响;避免观测仪器噪声的干扰,便于理论分析和解释EC能量闭合问题	边界条件不易选取;计算量大,目前很难进行实际EC观测高度处的高精度的LES模拟

表2 基于LES和野外实测数据研究EC能量闭合问题的优缺点

Table 2 The advantages and disadvantages of the methods based on LES and filed observations

方法	优点	缺点
基于野外实测数据	方法简单;结果可靠	大气环境多变,观测仪器易受环境因子和电磁因素干扰;难以进行控制实验分析某一变量对EC能量闭合问题的影响
基于LES 数据	便于进行控制实验,分析某一变量对EC能量闭合问题的影响;避免观测仪器噪声的干扰,便于理论分析和解释EC能量闭合问题	边界条件不易选取;计算量大,目前很难进行实际EC观测高度处的高精度的LES模拟

表2 基于LES和野外实测数据研究EC能量闭合问题的优缺点

Table 2 The advantages and disadvantages of the methods based on LES and filed observations

方法	优点	缺点
基于野外实测数据	方法简单;结果可靠	大气环境多变,观测仪器易受环境因子和电磁因素干扰;难以进行控制实验分析某一变量对EC能量闭合问题的影响
基于LES 数据	便于进行控制实验,分析某一变量对EC能量闭合问题的影响;避免观测仪器噪声的干扰,便于理论分析和解释EC能量闭合问题	边界条件不易选取;计算量大,目前很难进行实际EC观测高度处的高精度的LES模拟

图2 控制体积示意图(据参考文献[ 72 ]修改)

Fig.2 Scheme describing control volume for the sensible heat flux (modified after reference[72])

图2 控制体积示意图(据参考文献[ 72 ]修改)

Fig.2 Scheme describing control volume for the sensible heat flux (modified after reference[72])

表3 基于控制面和控制体的方法的优缺点

Table 3 The advantages and disadvantages between the control face and volume methods

方法	优点	缺点
控制面方法	方法简单,便于数值分析,对数值模拟分辨率要求较低	只能用于均匀和一维异质性下垫面
控制体方法	便于理论分析和解释EC能量闭合问题,可用于复杂下垫面,便于数值分析	实际中控制体积的选取较为复杂,不易于实际应用;对数值模拟分辨率和精度要求较高

表3 基于控制面和控制体的方法的优缺点

Table 3 The advantages and disadvantages between the control face and volume methods

方法	优点	缺点
控制面方法	方法简单,便于数值分析,对数值模拟分辨率要求较低	只能用于均匀和一维异质性下垫面
控制体方法	便于理论分析和解释EC能量闭合问题,可用于复杂下垫面,便于数值分析	实际中控制体积的选取较为复杂,不易于实际应用;对数值模拟分辨率和精度要求较高

表3 基于控制面和控制体的方法的优缺点

Table 3 The advantages and disadvantages between the control face and volume methods

方法	优点	缺点
控制面方法	方法简单,便于数值分析,对数值模拟分辨率要求较低	只能用于均匀和一维异质性下垫面
控制体方法	便于理论分析和解释EC能量闭合问题,可用于复杂下垫面,便于数值分析	实际中控制体积的选取较为复杂,不易于实际应用;对数值模拟分辨率和精度要求较高

表3 基于控制面和控制体的方法的优缺点

Table 3 The advantages and disadvantages between the control face and volume methods

方法	优点	缺点
控制面方法	方法简单,便于数值分析,对数值模拟分辨率要求较低	只能用于均匀和一维异质性下垫面
控制体方法	便于理论分析和解释EC能量闭合问题,可用于复杂下垫面,便于数值分析	实际中控制体积的选取较为复杂,不易于实际应用;对数值模拟分辨率和精度要求较高

表4 基于LES的EC能量闭合的研究

Table 4 The studies about the EC energy closure based on LES

地表	水平分辨率/m	垂直分辨率/m	模型	SGS	参考文献
均匀	50	50	PALM	1.5阶TKE	[46]
均匀	100	50	北大LES	K闭合	[70]
均匀	10,50,2	10,50,2	PALM	1.5阶TKE	[45]
均匀	50	20	NCAR LES	1.5阶TKE	[44]
均匀	100,25	30~70,8~40	GALES	1.5阶TKE	[43]
不均匀	50	50	PALM	1.5阶TKE	[47]
不均匀	20	20	PALM	1.5阶TKE	[72]
不均匀	10	10	PALM	1.5阶TKE	[71]
均匀和不均匀	50	6~50	WRF LES	1.5阶TKE	[42]

表4 基于LES的EC能量闭合的研究

Table 4 The studies about the EC energy closure based on LES

地表	水平分辨率/m	垂直分辨率/m	模型	SGS	参考文献
均匀	50	50	PALM	1.5阶TKE	[46]
均匀	100	50	北大LES	K闭合	[70]
均匀	10,50,2	10,50,2	PALM	1.5阶TKE	[45]
均匀	50	20	NCAR LES	1.5阶TKE	[44]
均匀	100,25	30~70,8~40	GALES	1.5阶TKE	[43]
不均匀	50	50	PALM	1.5阶TKE	[47]
不均匀	20	20	PALM	1.5阶TKE	[72]
不均匀	10	10	PALM	1.5阶TKE	[71]
均匀和不均匀	50	6~50	WRF LES	1.5阶TKE	[42]

表4 基于LES的EC能量闭合的研究

Table 4 The studies about the EC energy closure based on LES

地表	水平分辨率/m	垂直分辨率/m	模型	SGS	参考文献
均匀	50	50	PALM	1.5阶TKE	[46]
均匀	100	50	北大LES	K闭合	[70]
均匀	10,50,2	10,50,2	PALM	1.5阶TKE	[45]
均匀	50	20	NCAR LES	1.5阶TKE	[44]
均匀	100,25	30~70,8~40	GALES	1.5阶TKE	[43]
不均匀	50	50	PALM	1.5阶TKE	[47]
不均匀	20	20	PALM	1.5阶TKE	[72]
不均匀	10	10	PALM	1.5阶TKE	[71]
均匀和不均匀	50	6~50	WRF LES	1.5阶TKE	[42]

表4 基于LES的EC能量闭合的研究

Table 4 The studies about the EC energy closure based on LES

地表	水平分辨率/m	垂直分辨率/m	模型	SGS	参考文献
均匀	50	50	PALM	1.5阶TKE	[46]
均匀	100	50	北大LES	K闭合	[70]
均匀	10,50,2	10,50,2	PALM	1.5阶TKE	[45]
均匀	50	20	NCAR LES	1.5阶TKE	[44]
均匀	100,25	30~70,8~40	GALES	1.5阶TKE	[43]
不均匀	50	50	PALM	1.5阶TKE	[47]
不均匀	20	20	PALM	1.5阶TKE	[72]
不均匀	10	10	PALM	1.5阶TKE	[71]
均匀和不均匀	50	6~50	WRF LES	1.5阶TKE	[42]

表5 EC能量闭合相关的影响因子

Table 5 The factors related to the flux imbalance of EC during daytime

影响因子	与I关系	参考文献
滤波方法	去趋势,I较大;去平均I较小	[42,43,45,77]
平均时间	平均时间越短,I越大	[31,42,43,45,46,70,78]
高度	高度越高,I越大	[42~46,70]
水平风速	风速越小,I越大	[42~46,49,58,70,79,80]
相位差	地表热储存量与净辐射的相位差越大,I越大;垂直速度脉动与所测标量脉动相位差越大,I越大	[81,82]
地表异质性	地表异质性越强,I越大	[7,27,47,49]
u_/w_	u_/w_越小,I越大	[44]
z_i/L	-z_i/L越大,I越大	[43]
z/L	-z/L越大,I越大	[80,83]
湍流强度	相对垂直湍越弱,I越大;湍流动能越小,I越大	[27,42]
垂直速度	垂直速度越高,I越大	[84]

表5 EC能量闭合相关的影响因子

Table 5 The factors related to the flux imbalance of EC during daytime

影响因子	与I关系	参考文献
滤波方法	去趋势,I较大;去平均I较小	[42,43,45,77]
平均时间	平均时间越短,I越大	[31,42,43,45,46,70,78]
高度	高度越高,I越大	[42~46,70]
水平风速	风速越小,I越大	[42~46,49,58,70,79,80]
相位差	地表热储存量与净辐射的相位差越大,I越大;垂直速度脉动与所测标量脉动相位差越大,I越大	[81,82]
地表异质性	地表异质性越强,I越大	[7,27,47,49]
u_/w_	u_/w_越小,I越大	[44]
z_i/L	-z_i/L越大,I越大	[43]
z/L	-z/L越大,I越大	[80,83]
湍流强度	相对垂直湍越弱,I越大;湍流动能越小,I越大	[27,42]
垂直速度	垂直速度越高,I越大	[84]

表5 EC能量闭合相关的影响因子

Table 5 The factors related to the flux imbalance of EC during daytime

影响因子	与I关系	参考文献
滤波方法	去趋势,I较大;去平均I较小	[42,43,45,77]
平均时间	平均时间越短,I越大	[31,42,43,45,46,70,78]
高度	高度越高,I越大	[42~46,70]
水平风速	风速越小,I越大	[42~46,49,58,70,79,80]
相位差	地表热储存量与净辐射的相位差越大,I越大;垂直速度脉动与所测标量脉动相位差越大,I越大	[81,82]
地表异质性	地表异质性越强,I越大	[7,27,47,49]
u_/w_	u_/w_越小,I越大	[44]
z_i/L	-z_i/L越大,I越大	[43]
z/L	-z/L越大,I越大	[80,83]
湍流强度	相对垂直湍越弱,I越大;湍流动能越小,I越大	[27,42]
垂直速度	垂直速度越高,I越大	[84]

表5 EC能量闭合相关的影响因子

Table 5 The factors related to the flux imbalance of EC during daytime

影响因子	与I关系	参考文献
滤波方法	去趋势,I较大;去平均I较小	[42,43,45,77]
平均时间	平均时间越短,I越大	[31,42,43,45,46,70,78]
高度	高度越高,I越大	[42~46,70]
水平风速	风速越小,I越大	[42~46,49,58,70,79,80]
相位差	地表热储存量与净辐射的相位差越大,I越大;垂直速度脉动与所测标量脉动相位差越大,I越大	[81,82]
地表异质性	地表异质性越强,I越大	[7,27,47,49]
u_/w_	u_/w_越小,I越大	[44]
z_i/L	-z_i/L越大,I越大	[43]
z/L	-z/L越大,I越大	[80,83]
湍流强度	相对垂直湍越弱,I越大;湍流动能越小,I越大	[27,42]
垂直速度	垂直速度越高,I越大	[84]

表6 EC能量闭合修正公式

Table 6 The correctional equations for the EC flux imbalance

公式	备注	参考文献
NEE= $∫ 0 h ? c - ? t$ dz+ $w'c' ˉ h$ + $w - h c - h - 1 h ∫ 0 h c - d z$	一维质量守恒方程推导;单个站点验证; 理论推导	[58]
EBR=K $z 0 eff L eff$ +C	经验公式;4个站点以及Eder等^{[ 85 ]}独立验证	[17]
[I]= $exp a + b u * w * + c 1.1 + d z z i + f 2 0.5$	基于LES的经验公式; Eder等^{[ 86 ]}独立验证	[44]
H= $w'θ' ˉ h$ =-ρc_pK_θ $? θ ? z$ +ρc_pK_Wθ $∫ 0 h ? h · V →$ dz LE=-ρλ_vK_q $? q ? z$ +ρλ_vK_Wq $∫ 0 h ? h · V →$ dz	尚未得到验证	[86]
LE= $L E EC H EC + L E EC$ (R_n-G) H= $H EC H EC + L E EC$ (R_n-G)	Twine等^{[ 12 ]}和Foken等^{[ 25 ]}建议使用	[12]
H=H_EC LE=R_n-G-H_EC	一些学者基于此,修正EC能量闭合问题	[12]

表6 EC能量闭合修正公式

Table 6 The correctional equations for the EC flux imbalance

公式	备注	参考文献
NEE= $∫ 0 h ? c - ? t$ dz+ $w'c' ˉ h$ + $w - h c - h - 1 h ∫ 0 h c - d z$	一维质量守恒方程推导;单个站点验证; 理论推导	[58]
EBR=K $z 0 eff L eff$ +C	经验公式;4个站点以及Eder等^{[ 85 ]}独立验证	[17]
[I]= $exp a + b u * w * + c 1.1 + d z z i + f 2 0.5$	基于LES的经验公式; Eder等^{[ 86 ]}独立验证	[44]
H= $w'θ' ˉ h$ =-ρc_pK_θ $? θ ? z$ +ρc_pK_Wθ $∫ 0 h ? h · V →$ dz LE=-ρλ_vK_q $? q ? z$ +ρλ_vK_Wq $∫ 0 h ? h · V →$ dz	尚未得到验证	[86]
LE= $L E EC H EC + L E EC$ (R_n-G) H= $H EC H EC + L E EC$ (R_n-G)	Twine等^{[ 12 ]}和Foken等^{[ 25 ]}建议使用	[12]
H=H_EC LE=R_n-G-H_EC	一些学者基于此,修正EC能量闭合问题	[12]

表6 EC能量闭合修正公式

Table 6 The correctional equations for the EC flux imbalance

公式	备注	参考文献
NEE= $∫ 0 h ∂ c - ∂ t$ dz+ $w'c' ¯ h$ + $w - h c - h - 1 h ∫ 0 h c - d z$	一维质量守恒方程推导;单个站点验证; 理论推导	[58]
EBR=K $z 0 eff L eff$ +C	经验公式;4个站点以及Eder等^{[ 85 ]}独立验证	[17]
[I]= $exp a + b u * w * + c 1.1 + d z z i + f 2 0.5$	基于LES的经验公式; Eder等^{[ 86 ]}独立验证	[44]
H= $w'θ' ¯ h$ =-ρc_pK_θ $∂ θ ∂ z$ +ρc_pK_Wθ $∫ 0 h ∇ h · V →$ dz LE=-ρλ_vK_q $∂ q ∂ z$ +ρλ_vK_Wq $∫ 0 h ∇ h · V →$ dz	尚未得到验证	[86]
LE= $L E EC H EC + L E EC$ (R_n-G) H= $H EC H EC + L E EC$ (R_n-G)	Twine等^{[ 12 ]}和Foken等^{[ 25 ]}建议使用	[12]
H=H_EC LE=R_n-G-H_EC	一些学者基于此,修正EC能量闭合问题	[12]

表6 EC能量闭合修正公式

Table 6 The correctional equations for the EC flux imbalance

公式	备注	参考文献
NEE= $∫ 0 h ∂ c - ∂ t$ dz+ $w'c' ¯ h$ + $w - h c - h - 1 h ∫ 0 h c - d z$	一维质量守恒方程推导;单个站点验证; 理论推导	[58]
EBR=K $z 0 eff L eff$ +C	经验公式;4个站点以及Eder等^{[ 85 ]}独立验证	[17]
[I]= $exp a + b u * w * + c 1.1 + d z z i + f 2 0.5$	基于LES的经验公式; Eder等^{[ 86 ]}独立验证	[44]
H= $w'θ' ¯ h$ =-ρc_pK_θ $∂ θ ∂ z$ +ρc_pK_Wθ $∫ 0 h ∇ h · V →$ dz LE=-ρλ_vK_q $∂ q ∂ z$ +ρλ_vK_Wq $∫ 0 h ∇ h · V →$ dz	尚未得到验证	[86]
LE= $L E EC H EC + L E EC$ (R_n-G) H= $H EC H EC + L E EC$ (R_n-G)	Twine等^{[ 12 ]}和Foken等^{[ 25 ]}建议使用	[12]
H=H_EC LE=R_n-G-H_EC	一些学者基于此,修正EC能量闭合问题	[12]

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