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地球信息科学学报 >

2016 , Vol. 18 >Issue 1: 106 - 116

DOI: https://doi.org/10.3724/SP.J.1047.2016.00106

遥感科学与应用技术

热红外地表方向性辐射温度与半球辐射温度关系研究

  • 彭硕 , 1, 2 ,
  • 唐伯惠 , 1, * ,
  • 李召良 1 ,
  • 吴骅 1 ,
  • 唐荣林 1
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  • 1. 中国科学院地理科学与资源研究所 资源与环境信息系统国家重点实验室,北京 100101
  • 2. 中国科学院大学,北京 100049
*通讯作者：唐伯惠（1973-）,男,湖南永州人,博士,副研究员,研究方向为地表参数的遥感定量反演及地表净辐射、蒸散发和土壤水分的遥感估算方法与应用研究。E-mail:

作者简介：彭硕（1989-）,女,内蒙古呼和浩特人,硕士生,研究方向为热红外方向性辐射。E-mail:

收稿日期: 2015-03-09

  要求修回日期: 2015-04-21

  网络出版日期: 2016-01-10

基金资助

国家自然科学基金重点项目（41231170）

中国科学院地理科学与资源研究所可桢杰出青年学者计划项目（2012RC101）

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Study of the Relationship Between Thermal Infrared Directional and Hemispherical Radiative Temperatures

  • PENG Shuo , 1, 2 ,
  • TANG Bohui , 1, * ,
  • LI Zhaoliang 1 ,
  • WU Hua 1 ,
  • TANG Ronglin 1
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  • 1. State Key Laboratory of Resources and Environmental information System, Institute of Geographic Sciences and Natural Resources Research, CAS, Beijing 100101, China
  • 2. University of Chinese Academy of Sciences, Beijing 100049, China
*Corresponding author: TANG Bohui, E-mail:

Received date: 2015-03-09

  Request revised date: 2015-04-21

  Online published: 2016-01-10

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《地球信息科学学报》编辑部 所有
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摘要

地表温度是陆面过程的一个重要影响因素,利用地表温度的遥感反演算法只能获取卫星传感器观测角度条件下的地表温度（即某个方向上的辐射温度）,但地球表面普遍存在非同温像元,反演得到的像元地表辐射温度具有方向性特征。本文利用热红外辐射传输模型4 SAIL（Scattering by Arbitrarily Inclined Leaves）,以及方向性热辐射参数化模型,针对非同温均匀冠层,考虑冠层结构、太阳位置和观测角等因素的影响,模拟得到方向性辐射温度数据,与半球辐射温度数据比较,得到估算半球辐射温度的最佳观测角度。此外,开展热红外地面观测试验,对热红外地表辐射温度的角度效应,以及利用模拟数据得到的半球辐射温度最佳观测角度进行了验证。结果表明,当太阳高度角较低时,均匀草地的地表辐射温度,会随着观测天顶角的增大而增加,受观测方位角的影响较小,当观测天顶角为75°时,倾斜观测与垂直观测得到的辐射温度差值达到2.7 K,说明热辐射存在明显的方向性特征。同时,将热红外地表方向性辐射温度与同步观测的半球辐射温度进行对比分析,当叶面积指数小于1.0时,半球辐射温度的最佳替代角度为51°,与模拟结果相符。

关键词： 4 SAIL模型; 方向性热辐射参数化模型; 方向性辐射温度; 多角度观测试验; 半球辐射温度

本文引用格式

彭硕 , 唐伯惠 , 李召良 , 吴骅 , 唐荣林 . 热红外地表方向性辐射温度与半球辐射温度关系研究[J]. 地球信息科学学报, 2016 , 18(1) : 106 -116 . DOI: 10.3724/SP.J.1047.2016.00106

Abstract

Land surface temperature (LST) is one of the key parameters in land surface processes, and hemispherical radiative surface temperature is also an important input parameter for land surface models. However, notably the LST derived from satellite scale data is affected by the variation of viewing zenith angles. Therefore, it is necessary to develop methods to estimate the hemispherical radiative temperature from the satellite-derived LST before inputting the hemispherical radiative temperature into land surface models. This paper firstly analyzes the relationship between the directional and hemispherical radiative temperatures simulated by a thermal-infrared radiative transfer model and a parameterized model for flat and homogeneous canopy, considering leaf inclination distribution function (LIDF), leaf area index (LAI), solar zenith angle and viewing azimuth angle. Then, a best directional radiative temperature is proposed to substitute the hemispherical radiative temperature. In addition, this paper also briefly describes the angular effect of the radiative surface temperature via field experimental study. The experiments were conducted over a homogenous and flat grassy lawn using two KT-15.85D infrared radiometers mounted on a multi-angle observation device. The grass radiative surface temperature under different viewing angles was measured by one radiometer through rotating the arm of the multi-angle observation device. The radiative surface temperature at nadir was measured by the other radiometer on a fixed arm. The results reveal that the radiative surface temperature increases with the increase of viewing zenith angle and it depends slightly on the variation of viewing azimuth angle. Comparing the off-nadir radiative temperatures to those measured at nadir, it exhibits a maximum difference of 2.7 K when the viewing zenith angle is at 75°, which implies that the angular effect of infrared radiation does exist. Comparing and analyzing the directional and hemispherical radiative temperatures, we found that the directional radiative temperature measured at a viewing zenith angle of 51° can be the best substitute for the hemispherical radiative temperature when the LAI is below 1.0.

Key words： 4 SAIL model; parameterized model for directional thermal radiation; directional radiative temperature; angular measurement; hemispherical radiative temperature

1 引言

在碳循环、水循环、能量交换等领域中,地表温度都发挥着重要作用[1-2]。目前,其可从卫星传感器上获取不同观测角度下的亮温数据,利用遥感地表温度反演算法得到地表温度[3]。真实地表温度不具有方向性,但是,由于普遍存在非同温混合像元现象,且地物的发射率也会随观测角发生变化,所以,反演得到的地表温度并不是真实的地表温度,而是某个方向上的辐射温度[4]。从1967年Fuchs等[5]在野外实验中发现,植被热辐射会随观测角发生变化开始,科学家就热辐射方向性这一问题展开了一系列观测实验。如Kimes等[6]通过实验发现当作物冠层顶层和底层温差为4.1 K时,天顶与水平方向的作物冠层的有效辐射温度差异可达2 K;Balick等则对同一片阔叶林在夏天和秋天都进行了观测,在夏天叶子茂盛的时候辐射温度的方向差别仅有1 K,热辐射方向性不明显,而秋天落叶后观测到的辐射温度的方向差别可达7 K,具有强烈的方向性现象[7-8];Chehbouni等[9]的研究也指出天顶方向的亮温和倾斜方向的亮温会相差5 K,特别在植被冠层温度和裸土表面温度差别大的地区,角度效应更加明显,这些观测实验说明热辐射存在很强的方向性效应。众所周知,传统气候模式研究中一般使用天顶方向的辐射温度代表整个半球的热红外辐射温度,Harries等[10]研究指出,这将会带来1~2 K的误差。此外,为了提高模型的可靠性和稳定性,现阶段的各种陆面过程模型和水文过程模型等,都需要整个半球的热红外辐射温度作为模型输入参数。
卫星传感器从一定的角度且具有一定的视场角对地观测,不能覆盖整个半球空间,但可建立方向性辐射温度与半球辐射温度之间的关系,利用方向性辐射温度得到半球辐射温度。所以,通过对像元的热辐射方向性建模,进一步了解热辐射的方向性,得到半球空间的方向性辐射温度数据。方向性热辐射模型主要分为几何光学模型、辐射传输模型和混合模型,本文选用了一个热红外辐射传输模型4 SAIL,以及一个参数化模型来对热辐射的方向性进行模拟,并对模型进行了详细的介绍,同时,利用模拟数据建立方向性辐射温度与半球辐射温度之间的关系,提出替代半球辐射温度的方向性辐射温度的观测角度,并为了验证热辐射的方向性,以及方向性辐射温度与半球辐射温度的关系进行了地面观测试验。

2 模型与方法

2.1 4 SAIL模型

Verhoef等[11]提出了适用于非同温均匀冠层的热红外辐射传输模型4 SAIL,该模型是将SAIL模型拓展到热红外区域,并将冠层分为光照土壤、阴影土壤、光照植被和阴影植被4部分。SAIL模型是对辐射传输方程的4通量近似,是一个4流9参数线性微分方程组。其中,4通量分别为太阳直接辐射 E s ,下行散射光辐射 E - ,上行散射光辐射 E + 和观测方向的辐射 E 0 [12]。而4 SAIL模型则在SAIL模型中添加了叶片的热辐射项,变为一个4流11参数线性微分方程,同时,也进一步提高了模型的鲁棒性和解的稳定性,方程组如式（1）所示。
d Ldx E s = k E s d Ldx E - = - s ' E s + a E - - σ E + - ε v H v d Ldx E + = s E s + σ E - - a E + + ε v H v d Ldx E 0 = w E s + v E - + v ' E + - K E 0 + K ε v H v （1）
式中：L是冠层叶面积指数LAI;x是相对高度,是微分方程的自变量,这里定义x在冠层底部为-1,在冠层顶部为0,即x向上为正方向;k是太阳入射方向的衰减系数;a表示下行（或上行）散射光的衰减系数; σ 表示经散射作用后上行光辐射转变为下行辐射（或下行辐射转变为上行辐射）的比例; s ' 和 s 分别为太阳直接辐射转变为下行和上行散射辐射的比例; w 、 v 和 v ' 分别为太阳直射辐射、下行散射辐射和上行散射辐射向观测方向散射的比例,在朗伯体的假设下, w = v + v ' 。 ε v H v 和 K ε v H v 为增加的叶片的热辐射项, ε v H v 为叶片的热辐射对上行和下行散射辐射的增强, K ε v H v 为叶片热辐射对观测方向辐射的增强,其中, ε v 是叶片的发射率, H v 是在叶片温度为 T v 时,利用普朗克函数得到的黑体辐射的半球积分,如式（2）所示。
H v = πB ( T v ) （2）
通过求解微分方程组的系数,以及利用冠层顶和下垫面的边界条件,可求解微分方程组。4 SAIL模型虽然将太阳光照、观测角的变化、叶倾角和叶面积指数等的变化计入模型,可用来模拟方向性辐射数据,但对于观测方位角及太阳位置并不敏感。

2.2 方向性热辐射参数化模型

Ren等[13]提出了同样适用于非同温均匀冠层的方向性热辐射参数化模型,该模型考虑了土壤与植被层及植被层内部的多次散射,如式（3）所示。
L = ∑ i = 1 N f i ∙ ε i ∙ B i ( T i ) + L multi （3）
L multi = σ f ∙ L leaf ∙ 1 - ε g ) ∙ b ( θ ) + ( 1 - α ) [ 1 - b ( θ ) ∙ 1 - σ f ) ] [ 1 - b ( θ ) ] ( 1 - ε v ) ∙ L leaf （4）
式中： L 为冠层的方向性热辐射; f i 是冠层中不同组分所占冠层的比例; ε i 是不同组分的发射率; B i ( T i ) 是不同组分的真实温度为 T i 时的普朗克函数,只考虑3种组分,分别为叶片、光照土壤和阴影土壤。 L multi 表示多次散射,式（4）中右侧第1项表示土壤对下行植被热辐射 L leaf 的多次散射;第2项表示植被层内部的多次散射,其中, σ f 为半球遮挡率, ε g 和 ε v 分别为土壤和植被的发射率, b ( θ ) 为植被的方向性间隙率, α 为空腔效应因子。
方向性热辐射参数化模型和4 SAIL模型各有侧重,方向性热辐射参数模型虽弥补了4 SAIL模型观测方位角,以及太阳位置不敏感的缺陷,但本身对不同叶倾角分布类型不敏感,且为了简化模型,没有考虑大气的影响。所以,本文将2种模型结合使用,以探讨不同条件下热红外方向性辐射温度的变化。

3 热红外方向性辐射温度与半球辐射温度数据模拟

3.1 模型输入参数

分别用4 SAIL模型和热辐射方向性参数化模型,对方向性辐射温度进行模拟研究,表1分别列出了4 SAIL模型和参数化模型,模拟方向性辐射温度所需的主要输入参数。
Tab. 1 Input variables for the two simulation models

表1 利用模型进行模拟所需的主要输入参数

参数 4 SAIL模型 参数化模型
太阳天顶角(SZA) 88° 20°,60°
太阳方位角(SAA) 267° 120°
观测天顶角(VZA) 0~90° 0~90°
观测方位角(VAA) 0° 0~360°
叶面积指数(LAI) 0.5,1,2,3 0.5,1,2
叶倾角分布函数(LIDF) 喜直型,球面型 平均叶倾角=0.7854
光照叶片温度(Th) 21° 17°
阴影叶片温度(Tc) 19° 17°
光照土壤温度(Ts) 19.5° 32°
阴影土壤温度(Td) 16° 22°
天空温度(Tsky) -30° -
叶片发射率(εv) 0.985 0.985
土壤发射率(εg) 0.95 0.95
研究中4 SAIL模型选用喜直型（Erectophile）和球面型（Spherical）2种叶倾角分布函数,如图1所示,能代表一部分植被的叶子分布,有一定的代表性,而参数化模型中叶倾角分布函数使用平均叶倾角（ALA）代替。由于参数化模型不区分光照叶片和阴影叶片,故光照叶片温度与阴影叶片温度相等。
Fig. 1 Modeled cumulative LIDFs

图1 叶倾角分布函数示意图

3.2 热红外方向性辐射温度模拟

利用4 SAIL模型,输入表1中对应的参数,模拟叶倾角分布函数为喜直型和球面型,叶面积指数分别为0.5、1.0、2.0、3.0时的方向性辐射温度,如图2所示。需要指出的是,输出的辐射温度为9.6~11.5 μm波谱范围内的辐射温度。
Fig. 2 Simulated directional radiative temperature profiles for four LAI values and two LIDFs using 4 SAIL model

图2 利用4 SAIL模型模拟的不同叶倾角分布函数下的4种叶面积指数对应方向性辐射温度曲线图

如图2所示,方向性辐射温度明显受到叶倾角分布函数及叶面积指数变化的影响。当叶倾角分布函数为喜直型时,随着观测天顶角的增大,辐射温度明显增大,而当叶倾角分布函数为球面型时,辐射温度在观测天顶角为0~50°的范围内变化不大,之后随天顶角的增大明显增加,辐射温度曲线呈碗状。
接下来利用方向性热辐射参数化模型,输入表1中对应的参数,模拟太阳天顶角为20°、40°、60°,叶面积指数为0.5、1.0、2.0时的方向性辐射温度。
图3中3列依次对应太阳天顶角为20°、40°和60°,3行依次对应叶面积指数为0.5、1.0和2.0。如图3所示,在表1的模拟条件下,冠层辐射温度在 半球空间有明显的方向性特征,这种方向性导致的差异最大可达到7°C。冠层辐射温度在半球空间的分布也有类似可见光波段存在的热点效应,因为光照部分要比阴影部分获得更多的太阳辐射,所以温度更高,与其他观测方向相比,在热点方向也更容易观测到光照部分,所以,在热红外范围虽然太阳辐射被忽略,但是也会存在热点效应。热点位置与太阳天顶角与方位角有关,当观测天顶角和方位角与太阳位置相同时,温度会达到峰值,出现热点效应。
Fig. 3 Simulated directional radiative temperature for three SZA values and three LAI values using a parameterized model

图3 利用方向性热辐射参数化模型模拟的不同太阳天顶角条件及3种叶面积指数条件下的冠层方向性辐射温度的半球空间分布

3.3 热红外半球辐射温度最佳替代角度分析

利用4 SAIL模型和方向性热辐射参数化模型,模拟得到的方向性辐射温度数据,以及半球空间内的方向性辐射温度数据积分得到半球辐射温度数据,通过对二者的分析比较,得到半球辐射温度的最佳替代角度。
图4和图5分别为利用4 SAIL模型,根据表1的输入参数,当叶倾角分布函数分别为喜直型和球面型时,4种叶面积指数条件下方向性辐射温度与半球辐射温度差值的曲线,差值最小时对应的方向性辐射温度即认为可替代半球辐射温度。
Fig. 4 Simulated differences profiles between the directional radiative temperature and the hemispherical radiative temperature under four LAI values and the erectophile LIDF by 4 SAIL model

图4 利用4 SAIL模型模拟的叶倾角分布函数为喜直型,4种不同叶面积指数条件下方向性辐射温度与半球辐射温度差值曲线

Fig. 5 Simulated differences profiles between the directional radiative temperature and the hemispherical radiative temperature under four LAI values and the spherical LIDF by 4 SAIL model

图5 利用4 SAIL模型模拟的叶倾角分布函数为球面型,4种不同叶面积指数条件下方向性辐射温度与半球辐射温度差值的曲线

如图4所示,在观测天顶角0~50°左右的范围内,方向性辐射温度与半球辐射温度差值随着观测天顶角的增大逐渐减小,在0°天顶角时达到最大,为0.6 °C左右;超过50°之后随着观测天顶角的增加而增大,在90°时差值最大可达1.4 °C。在观测天顶角为0~50°左右的范围内,随着叶面积指数的增大,方向性辐射温度与半球辐射温度差值变化不明显,而在50°左右到90°的范围内,差值随叶面积指数增大有了明显的降低。根据图4中的差值曲线可得到半球辐射温度最佳观测角,当叶面积指数分别为0.5、1、2和3时,能替代半球辐射温度的最佳观测天顶角约为51°、48°、43°和40°。由上述分析可以得出,叶倾角分布函数为喜直型时,随叶面积指数的增大,能最佳替代半球辐射温度的方向性辐射温度的观测天顶角有减小的趋势。
如图5所示,叶倾角分布函数为球面型时的方向性辐射温度与半球辐射温度的差值曲线趋势与叶倾角分布函数为喜直型时大致相同,在观测天顶角从0~50°左右的范围内,差值逐渐减小,之后逐渐增大。不同的是叶倾角分布函数为喜直型时,随叶面积指数的增大,在天顶角从0~50°左右的范围内,差值相差不大,在天顶角从50°左右到90°的范围内,差值明显减小。而叶倾角分布函数为球面型时,观测天顶角从0~90°左右的范围内,随叶面积指数的增大,差值都是减小的。根据图5中方向性辐射温度与半球辐射温度的差值,当叶面积指数分别为0.5、1、2和3时,最佳半球辐射观测天顶角约为54°、52°、48°和45°。可见,当叶倾角分布函数为球面型时,随叶面积指数的增大,替代半球辐射温度的方向性辐射温度观测天顶角也有减小的趋势。
为进一步考察观测方位角、太阳天顶角等参数对方向性辐射温度的影响,利用方向性热辐射参数化模型进行模拟。
图6中为不同观测方位角,不同太阳天顶角和不同叶面积指数条件下,方向性辐射温度与半球辐射温度之差。图6中3行依次对应叶面积指数为0.5、1.0和2.0,2列对应太阳天顶角为20°和60°。如图6所示,由于热点效应的存在,在与太阳方位角相等的观测方位角曲线上,方向性辐射温度与半球辐射温度的差值,会出现一个明显的峰值,即小范围内的差值最大值。峰值的出现的位置与热点位置有关,通常出现在与太阳方位角有相同值的观测方位角差值曲线上,且随着太阳天顶角的增加向与太阳天顶角相同大小的观测天顶角方向增加,而在其他方位角观测到的差值所对应的峰值较小。当观测方位角变化或太阳天顶角变化时,差值最小时对应的观测天顶角（即最佳半球辐射温度观测天顶角）基本不变。当叶面积指数分别为0.5、1和2时最佳半球辐射观测天顶角约为55°、50°和48°,与上文中4 SAIL模型模拟的结果相同,随叶面积指数的增大,替代半球辐射温度的方向性辐射温度观测天顶角有减小的趋势。
Fig. 6 Simulated differences profiles between the directional radiative temperature and the hemispherical radiative temperature under three viewing azimuth angles, two solar zenith angles and three LAI values by a parameterized model with SZA=20° and SZA=60°

图6 参数化模型模拟的不同观测方位角及不同太阳天顶角和不同叶面积指数条件下方向性辐射温度与半球辐射温度差值曲线

4 热红外方向性辐射地面观测试验

为了验证辐射温度的方向性,以及半球辐射温度的最佳替代观测角,利用多角度观测装置在均匀草地上开展了初步的多角度观测试验。
（1） 多角度观测装置
多角度观测装置如图7所示,由一个多角度观测架和架设在观测架上的2个KT-15.85热红外辐射计组成,通过旋转、移动等运动对地表进行多角度观测。
Fig. 7 Photo of the automatic multi-angle observation device setup for multi-angle thermal infrared measurements

图7 多角度观测装置

多角度观测架主要由一个半径为1 m的半圆形轨道、一个1 m高的升降机、一个旋转臂和一个固定臂组成[14]。旋转臂和固定臂一起固定在升降机上,可随升降机垂直升降改变对地表观测的高度,也可跟随升降机在半圆形轨道上移动,改变对地观测的方位角。在升降机底部安装有电机,电机控制旋转臂以升降机底部为轴心,通过旋转来改变对地观测的天顶角,其范围可以达到-90~90°;固定臂则一直对准半圆形轨道的圆心位置对地表进行垂直观测。
在多角度观测架的旋转臂和固定臂上,分别固定一个KT-15.85热红外辐射计（已利用面型差分黑体进行了标定）。KT-15.85辐射计观测面积的直径是观测距离的函数,根据本次试验中对地观测距离为1.5 m,对应的观测面积直径大约为65 mm。该辐射计具有快速响应,且小巧轻便的特点,光谱响应范围为9.6~11.5 μm,测温范围为-50~200 °C,精度可达到±0.5 °C,温度分辨率为±0.2 °C,响应时间为1 s。
在试验区内架设一台4分量净辐射传感器CNR 4,CNR 4有向上的短波、长波及向下的短波和长波4个输出,长波辐射传感器光谱范围为4.5~42 μm,传感器向下和向上的视场角分别为150°和180°,观测值近似为半球空间的辐射。
（2） 观测试验
选择中国科学院奥运园区附近草地（116.37°E,40.00°N,海拔36 m）进行观测试验,草叶新鲜,平均8~10 cm高,叶倾角分布类型为喜直型,土壤类型为粉砂质壤土。
搭建多角度观测架,半圆形轨道的缺口正对太阳,避免样本在测量时被观测架的阴影遮挡,在旋转臂和固定臂上各安装一个热红外辐射计。操纵升降机到方位角0°位置,以步长30°改变方位角直至方位角180°位置,每改变一次方位角,升降机在此停顿,等待旋转臂上的辐射计以5°或10°为步长,随旋转臂自动旋转连续完成天顶角从75~-75°的对地观测,固定臂上的辐射计则始终在天顶角0°位置垂直向下观测,具体观测顺序如图8所示。在每个天顶角位置都作短暂停留,使辐射计可进行3次测量,取3次测量的平均值作为这个角度下的观测值。按照上述方法,10 min即可完成半球空间的方向性亮度温度观测。同时,利用4分量净辐射传感器在试验区内相同草地上进行同步观测,得到地表的上行长波辐射,利用斯蒂芬-玻尔兹曼定律,可获得对应的半球辐射温度。
Fig. 8 Schematic representation of the hemispheric measurement in polar coordinate. (Each point represents a measurement at the corresponding viewing zenith and azimuth angle)

图8 极坐标下的半球观测示意图（在每点对应的观测天顶角和观测方位角进行一次观测）

在进行试验时,保证样本在测量过程中始终处于太阳照射下,避免观测样本受到阴影遮挡。因为天气晴朗无云、无风,且测量时间较短,即可近似为在完成一个半球空间的测量过程中,样本温度没有发生变化[15-16]。但周围环境在测量周期内仍会有对温度轻微的扰动,除了在每个角度位置测量3次取平均值,将倾斜观测值与同步进行的垂直观测值作差,利用差值来比较各个观测角的数据,以消除测量周期内样本温度发生变化对方向性的影响。
（3）观测数据的处理与分析
为尽量消除在一个半球观测周期地表温度的变化,定义倾斜观测亮度温度与同步垂直观测亮度温度的差值为 ΔT [17]。
ΔT ( θ , φ ) = T ̅ ( θ , φ ) - T ̅ ( 0 θ , φ ) （5）
式中： T ̅ ( θ , φ ) 代表倾斜观测时在观测天顶角θ,观测方位角 φ 处3次观测的亮度温度均值; T ̅ ( 0 θ , φ ) 代表与在 ( θ , φ ) 位置进行倾斜观测同步进行的3次垂直观测的亮度温度均值。
利用式（5）计算得到半球空间的多角度亮度温度差值如图9、10所示。图9和图10中X轴分别表示观测方位角和观测天顶角,Y轴均表示相对亮温。
Fig. 9 ΔT of grassy lawn for different viewing azimuth angles

图9 不同观测方位角下草地的亮度温度差值曲线

Fig. 10 ΔT of grassy lawn for different viewing zenith angles

图10 不同观测天顶角下草地的亮度温度差值曲线

图9中12条曲线代表在12个观测天顶角下,亮温差随观测方位角的变化可看出,亮温受观测方位角的影响小,且没有观测到明显的热点现象。图10中7条曲线对应在7个观测方位角下,亮温差随观测天顶角变化。亮温差曲线在垂直观测两侧呈对称分布,随观测天顶角的增加,亮温差明显增大,在观测天顶角为75°时可达到最大2.7 K。这一结果与相关研究观测到的亮度温度会随着观测天顶角的增大而减小的结果相反[17],但同时,Lagouarde等[18]也曾提出,当太阳高度角较低时,在平坦均匀的草地观测得到的ΔT是正数,即ΔT会随着观测天顶角的增大而增加。
本实验结果与Lagouarde等的实验结果对比如图11所示。红色实线代表本文的实验结果,蓝色虚线为Lagouarde等的实验结果,圆形和三角形分别代表方位角为0°和90°。图11可看出,2次实验的结果相同,方向亮温均随观测天顶角的增加而增大,倾斜观测的亮温值与垂直观测的亮温值之差,均在观测天顶角60°达到1 K左右。
Fig. 11 Comparison of ΔT between the results of Lagouarde et al. and this paper at 0° and 90° viewing azimuth angles

图11 方位角0°和方位角90°时倾斜测量的亮度温度与垂直测量的亮度温度差值随观测天顶角的变化曲线

实际上,本试验在傍晚进行,此时太阳高度角较低,亮度温度随观测天顶角的增加而增大的现象与草叶的垂直结构有关。在正午的时候,太阳高度角高,太阳能直射土壤和草叶,使土壤和草叶温度升高且土壤的温度要高于草叶,垂直观测时,辐射计的视场内占主要比重的是温度较高的土壤,倾斜观测时,视场内占比重较大的主要是温度较低的草叶,所以,当太阳高度角较高时,亮度温度一般会随观测天顶角的增大而减小。当下午太阳高度角降低时,虽然土壤和草叶的温度都降低,但草叶的上端仍然会受到太阳照射,垂直观测时,阴影及降温的土壤占据了主要的视场,倾斜观测时,则仍在加热的草叶上端占据主要的视场。所以会出现实验结果中随观测天顶角增大,亮温增加的现象。根据本文实验可看出,地表的辐射温度具有明显的方向性特征。

5 结果与分析

利用4 SAIL模型进行模拟时输入的组分温度、组分发射率、太阳天顶角和太阳方位角等参数为观测试验时实测数据,所以,模拟数据与实测数据具有一定的可比性,可利用实测数据对模拟数据进行验证。如图12所示,选择叶倾角分布函数为喜直型,叶面积指数为1.0时的模拟数据,对模拟得到的方向性辐射温度与观测得到的方向性亮温数据进行对比。
Fig. 12 Comparison between the simulated directional radiative temperature and the measured radiative temperature

图12 针对草地模拟的方向性辐射温度与测量的方向性辐射温度比较

如图12所示,模拟结果与测量结果相比较,辐射温度随观测天顶角的变化趋势相同,且在75°之内,实测数据均值与模拟数据相差不到0.41 °C,说明利用模型模拟能代表真实的冠层植被热辐射方向性。
根据上述分析叶面积指数、叶倾角分布函数、观测方位角和太阳天顶角等参数,对半球辐射最佳替代观测角的影响发现,最佳替代观测角主要随着叶面积指数的变化而变化,所以,分为叶面积指数较小和较大2种情况考虑。当叶面积指数值较小时,能替代半球平均辐射温度的最佳角度比较大,为51°左右;当叶面积指数值较大时,最佳替代角比较小,为44°左右。
为了验证这一结果,利用了地面试验观测得到的不同观测方位角条件下的方向性辐射温度数据,与半球辐射温度作差。图13为从中选择的4个方位角条件下差值的曲线图。
Fig. 13 Measured differences profiles between the directional radiative temperature and the hemispherical radiative temperature under 4 viewing azimuth angles

图13 不同观测方位角条件下方向性辐射温度与半球辐射温度差值曲线

进行观测的草地比较稀疏,叶面积指数值为1.0左右,根据上文的分析,最佳替代观测角应 为51°左右。如图13所示,观测得到的方向性辐射温度与半球辐射温度差值,主要受到观测天顶 角的影响,差值最小值主要出现在50°左右,即能最佳替代半球辐射温度的观测天顶角约为50°左右,与上文模拟结果相符,对模拟结果进行了有效的验证。

6 结论和展望

本文选取热红外辐射传输模型4 SAIL,以及方向性热辐射参数化模型,针对非同温均匀冠层的方向性辐射温度进行研究,同时计算了相应场景的半球辐射温度,将其与方向性辐射温度进行了比较,给出了最佳的估算半球辐射温度的观测角度。此外,本文还分析了叶倾角分布函数、叶面积指数、太阳天顶角、观测天顶角和观测方位角等参数,对方向性辐射温度及最佳的替代半球辐射温度的观测角度的影响。研究指出,太阳天顶角及观测方位角的变化,对最佳替代观测角度影响不大,而当叶面积指数值小于1.0时,最佳替代角度为51°左右,当叶面积指数大于1.0小于3.0时,最佳替代角为44°左右。同时,开展了多角度观测试验,得到了太阳高度角较低时的方向性辐射温度和同步的半球辐射温度。试验结果表明,辐射温度随着观测天顶角的增大而增加,受观测方位角的影响较小。当观测天顶角为75°时,倾斜观测与垂直观测得到的辐射温度差值达到2.7 K,表明热辐射存在明显的方向性,在利用卫星数据反演地表温度时,要对这种方向性予以考虑。试验也对提出的最佳估算半球辐射温度的观测角度进行了验证,当叶面积指数小于1.0时,最佳替代半球辐射温度的观测角为51°左右。
本研究仅考虑了2种叶倾角分布函数,如果在输入参数中加入更多的叶倾角类型,可使结果更具代表性。为了简便化,研究中使用的2种模型均设植被组分和土壤组分的发射率没有方向性,对组分发射率进行改进,加入方向参数,可进一步提高模型的真实性。本文只在叶面积指数较小且太阳高度角较低时,进行了多角度辐射温度和半球辐射温度观测试验,后续应进一步针对叶面积指数较大和其他太阳高度角的多角度观测试验,对提出的最佳替代角度进行完整的验证。

The authors have declared that no competing interests exist.

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DOI

[4]
Norman J M, Becker F.Terminology in thermal infrared remote sensing of natural surfaces[J]. Remote Sensing Reviews, 1995,12(3-4):159-173.A consistent nomenclature for thermal infrared remote sensing of natural surfaces is outlined in this paper. Terms such as ‘canopy temperature’ and ‘surface temperature’ should be confined to general, qualitative descriptions and terms such as directional radiometric temperature, hemispherical emissivity, aerodynamic temperature, or hemispherical-directional reflectance used for technical precision. Some discussion also is included on the relation between hemispherical-directional thermal reflectance and directional thermal emissivity. A distinction is made between two kinds of emissivity; e-emissivity and r-emissivity. Through use of detailed models of directional thermal emissivity and bidirectional reflectance, we suggest that the influence of temperature gradients in vegetation on directional emissivity usually will cause uncertainties of less than 0.005. In addition, uncertainties that occur in estimating surface temperature, which arise because an ensemble of black bodies each at a different temperature does not have a black body radiance distribution with temperature, will not always be negligible for purposes of remote sensing of natural surfaces. Differences between mean thermodynamic and ensemble radiometric temperatures of 1 K or larger are possible even though differences in ensemble radiometric temperatures for different wavelength bands in the atmospheric window (8–14 μm) usually will be less than 0.1 K.

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[5]
Fuchs M, Kanemasu E T, Kerr J P, et al.Effect of viewing angle on canopy temperature measurements with infrared thermometers[J]. Agronomy Journal, 1967,59(5):494-496.Crop surface temperatures were measured with infrared thermometers at various viewing angles and for a range of solar zenith angles. The temperature readings of crops with continuous and uniform canopies were not related to the above angles. In the case of open row crops, the side of the row facing the sun was 1 to 3 C warmer than the shaded side.

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[6]
Kimes D S, Kirchner J A.Directional radiometric measurements of row-crop temperatures[J]. International Journal of Remote Sensing, 1983,4(2):299-311.Incomplete vegetation canopies are complex remote-sensing targets. The directional variability of sensor response when viewing a cotton row crop with 48 per cent ground cover was documented for the thermal infrared region. The geometric structure of the canopy was described and radiometric temperatures of four components, sunlit and shaded vegetation and soil, were measured. These data were used to validate and verify a geometric, row projection model. The model predicts the thermal infrared response of a sensor as a function of sensor view angle, component temperature and geometry structure of the canopy. The field data showed sensor response differentials as great as 16.2°C when going from a zenith view angle of 0° to one of 80° in a plane normal to the row direction. The root-mean-square deviation between the model prediction and measured sensor response for all measurement periods and view angles (n = 90) was 0.96°C. The model serves as a sound mathematical basis for interpreting remotely-sensed data from row crops, and optimizing the directional view for specific canopy structures and environments.

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[7]
Balick L K, Hutchinson B A.Directional thermal infrared exitance distributions from a leafless deciduous forest[J]. Geoscience and Remote Sensing, IEEE Transactions on, 1986,5:693-698.The directional thermal infrared exitance distributions of a 21.5-m-tall leafless deciduous forest were measured using a rotating 7-detector array suspended 33 m above the forest floor. These distributions are presented for several illumination conditions. Strong directional thermal infrared distributions were observed at high solar elevations on a clear day. Temperature gradients frequently exceeded 3°C per 10-degree change of view angle. At low sun angles and the early evening, change of observed temperature with nadir angle was more moderate and was negligible with azimuth angle. At night and on a cloudy morning, uniform temperature distributions were observed. An interpretation of these directional temperature distributions is given.

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[8]
Balick L K, Hutchison B A, Smith J A, et al.Directional thermal infrared exitance distributions of a deciduous forest in summer[J]. IEEE transactions on geoscience and remote sensing, 1987,3(GE-25): 410-412.Directional measurements of effective radiant temperatures (ERT) were made from a rotating mount suspended above an Oak-Hickory canopy. A directional ERT distribution is presented showing fairly weak trends with view angle. Additional data are presented to illustrate the character of spatial variations of ERT as a function of view and sun angle.

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[9]
Chehbouni A, Nouvellon Y, Kerr Y H, et al.Directional effect on radiative surface temperature measurements over a semiarid grassland site[J]. Remote Sensing of Environment, 2001,76(3):360-372.

[10]
Harries J E, Russell J E, Hanafin J A, et al.The geostationary earth radiation budget project[J]. Bulletin of the American Meteorological Society, 2005,86(7):945-960.This paper reports on a new satellite sensor, the Geostationary Earth Radiation Budget (GERB) experiment. GERB is designed to make the first measurements of the Earth's radiation budget from geostationary orbit. Measurements at high absolute accuracy of the reflected sunlight from the Earth, and the thermal radiation emitted by the Earth are made every 15 min, with a spatial resolution at the subsatellite point of 44.6 km (north09outh) by 39.3 km (east09est). With knowledge of the incoming solar constant, this gives the primary forcing and response components of the top-of-atmosphere radiation. The first GERB instrument is an instrument of opportunity on Meteosat-8, a new spin-stabilized spacecraft platform also carrying the Spinning Enhanced Visible and Infrared (SEVIRI) sensor, which is currently positioned over the equator at 3.500°W. This overview of the project includes a description of the instrument design and its preflight and in-flight calibration. An evaluation of the instrument performance after its first year in orbit, including comparisons with data from the Clouds and the Earth's Radiant Energy System (CERES) satellite sensors and with output from numerical models, are also presented. After a brief summary of the data processing system and data products, some of the scientific studies that are being undertaken using these early data are described. This marks the beginning of a decade or more of observations from GERB, as subsequent models will fly on each of the four Meteosat Second Generation satellites.

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[11]
Verhoef W, Jia L, Xiao Q, et al.Unified optical-thermal four-stream radiative transfer theory for homogeneous vegetation canopies[J]. IEEE Transactions on Geoscience and Remote Sensing, 2007,45(6):1808-1822.Foliage and soil temperatures are key variables for assessing the exchanges of turbulent heat fluxes between vegetated land and the atmosphere. Using multiple-view-angle thermal-infrared (TIR) observations, the temperatures of soil and vegetation may be retrieved. However, particularly for sparsely vegetated areas, the soil and vegetation component temperatures in the sun and in the shade may be very different depending on the solar radiation, the physical properties of the surface, and the meteorological conditions. This may interfere with a correct retrieval of component temperatures, but it might also yield extra information related to canopy structure. Both are strong reasons to investigate this phenomenon in some more detail. To this end, the relationship between the TIR radiance directionality and the component temperatures has been analyzed. In this paper, we extend the four-stream radiative transfer (RT) formalism of the Scattering by Arbitrarily Inclined Leaves model family to the TIR domain. This new approach enables us to simulate the multiple scattering and emission inside a geometrically homogenous but thermodynamically heterogeneous canopy for optical as well as thermal radiation using the same modeling framework. In this way top-of-canopy thermal radiances observed under multiple viewing angles can be related to the temperatures of sunlit and shaded soil and sunlit and shaded leaves. In this paper, we describe the development of this unified optical-thermal RT theory and demonstrate its capabilities. A preliminary validation using an experimental data set collected in the Shunyi remote sensing field campaign in China is briefly addressed

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[12]
Verhoef W.Light scattering by leaf layers with application to canopy reflectance modeling: the SAIL model[J]. Remote sensing of environment, 1984,16(2):125-141.The scattering and extinction coefficients of the SAIL canopy reflectance model are derived for the case of a fixed arbitrary leaf inclination angle and a random leaf azimuth distribution. The SAIL model includes the uniform model of G. H. Suits as a special case and its main characteristics are that canopy variables such as leaf area index and the leaf inclination distribution function are used as input parameters and that it provides more realistic angular profiles of the directional reflectance as a function of the view angle or the solar zenith angle.

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[13]
Ren H, Liu R, Yan G, et al.Angular normalization of land surface temperature and emissivity using multiangular middle and thermal infrared data[J]. IEEE Transactions on Geoscience and Remote Sensing, 2014,52(8):4913-4931.This paper aimed at the case of nonisothermal pixels and proposed a daytime temperature-independent spectral indices (TISI) method to retrieve directional emissivity and effective temperature from daytime multiangular observed images in both middle and thermal infrared (MIR and TIR) channels by combining the kernel-driven bidirectional reflectance distribution function (BRDF) model and the TISI method. Four groups of angular observations and two groups of MIR and TIR channels with narrow and broad bandwidths were used to investigate the influence of angular observations and bandwidth on the retrieval accuracy. Model sensitivity analysis indicated that the new method can generally obtain directional emissivity and temperature with an error less than 0.015 and 1.5 K if the noise included in the measured directional brightness temperature (DBT) and atmospheric data was no more than 1.0 K and 10%, respectively. The analysis also indicated that 1) large-angle intervals among the angular observations and a larger viewing zenith angle, with respect to nadir direction, can improve the retrieval accuracy because those angle conditions can result in significant difference for components' fractions and DBT under different viewing directions; 2) narrow channels can produce better results than broad channels. The new method was finally applied to a multiangular MIR and TIR data set acquired by an airborne system, and a modified kernel-driven BRDF model was used for angular normalization to the surface temperature for the first time. The difference of the retrieved emissivity and Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) emissivity was found to be approximately 0.012 in the study area.

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[14]
Li Z L, Zhang R, Sun X, et al.Experimental system for the study of the directional thermal emission of natural surfaces[J]. International Journal of Remote Sensing, 2004,25(1):195-204.A new automatic experimental system was designed to improve the accuracy of multidirectional thermal infrared measurements. This experimental system mainly consists of two identical thermal cameras operating at 8-13 08 m, one metal ring to keep the constant view area for different view angles and a goniometer, which is composed of: (1) a semicircular roadway of 2 m diameter to change the observation angle in the azimuth direction; (2) an elevator of 1 m height to adjust the measuring level to the target level; (3) a rotating arm equipped with one thermal camera for changing the observation angle in the zenith direction; and (4) a fixed arm equipped with another thermal camera to record at nadir the target temperature variation with time during the measurements. The system can be disassembled for easy transport and all of the data acquisition procedures are automatically monitored. For a given azimuth angle, the system needs about 2 minutes to make the directional measurements from about 6170° to 70°, and for completing one hemispheric measurement it needs about 20 minutes if the multidirectional measurements are conducted by a step of 30° in the azimuth direction. The preliminary data acquired using our new system on bare soil and winter wheat are displayed and analysed. The results show that the angular variation of surface brightness temperature is measurable and presents some regular directional distribution and can be used quantitatively to study the directional thermal emission of the natural surfaces.

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[15]
Cuenca J, Sobrino J A.Experimental measurements for studying angular and spectral variation of thermal infrared emissivity[J]. Applied Optics, 2004,43(23):4598-4602.One condition for precise multiangle algorithms for estimating sea and land surface temperature with the data from the Advanced Along Track Scanning Radiometer is accurate knowledge of the angular variation of surface emissivity in the thermal IR spectrum region. Today there are very few measurements of this variation. The present study is conducted to provide angular emissivity measurements for five representative samples (water, clay, sand, loam, gravel). The measurements are made in one thermal IR broadband (8-13 microm) and three narrower bands (8.2-9.2, 10.3-11.3, and 11.5-12.5 microm) at angles of 0 degrees-60 degrees (at 5 degrees increments) to the surface normal. The results show a general decrease in emissivity with increasing viewing angles, with the 8.2-9.2-microm channel the most sensitive to this dependence and sand the sample showing the greatest variation.

DOI PMID

[16]
Sobrino J A, Cuenca J.Angular variation of thermal infrared emissivity for some natural surfaces from experimental measurements[J]. Applied Optics, 1999,38(18):3931-3936.Abstract Multiangle algorithms for estimating sea and land surface temperature with Along-Track Scanning Radiometer data require a precise knowledge of the angular variation of surface emissivity in the thermal infrared. Currently, few measurements of this variation exist. Here an experimental investigation of the angular variation of the infrared emissivity in the thermal infrared (8-14-microm) band of some representative samples was made at angles of 0 degrees-65 degrees (at 5 degrees increments) to the surface normal. The results show a decrease of the emissivity with increasing viewing angle, with water showing the highest angular dependence (approximately 7% from 0 degrees to 65 degrees views). Clay, sand, slime, and gravel show variations of approximately 1-3% for the same range of views, whereas a homogeneous grass cover does not show angular dependence. Finally, we include an evaluation of the impact that these data can produce on the algorithms for determining land and sea surface temperature from double-angle views.

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[17]
Cuenca J, Sobrino J A, Soria G.An experimental study of angular variations of brightness surface temperature for some natural surfaces[C]. MERIS (A) ATSR Workshop, 2005,597: 33.

[18]
Lagouarde J P, Kerr Y H, Brunet Y.An experimental study of angular effects on surface temperature for various plant canopies and bare soils[J]. Agricultural and Forest Meteorology, 1995,77(3):167-190.Surface temperature is a key parameter for assessing fluxes at the surface-atmosphere interface. Proper estimation of radiative surface temperature requires corrections for perturbating factors such as atmospheric contributions and angular effects. Several models have been derived to address angular effects, but relevant data for validating such models is still scarce. This paper describes a field experiment dedicated to collecting angular measurements of brightness surface temperature over several types of surfaces (bare soils with different roughnesses, corn, grass, alfalfa), using a unique measurement protocol with simultaneous temperature readings at two angles. For each surface zenithal and azimuthal angular effects are quantified. In some cases (unstressed, fully-covering alfalfa) the difference between oblique and vertical brightness temperatures is within 0.5 K. Over stressed corn the temperature measured at angles of 60 is about 4 K less than the nadir looking temperature, but it is 3.5 K higher over a ploughed bare soil, when the inclined radiometer faces the sunlit side of the furrows. Over a bare smooth soil the observed angular variations are shown to be compatible with those due to possible angular variations in emissivity. All the results are discussed in terms of surface geometry and microclimatic conditions, and compared to previous studies. Implications are deduced for the interpretation of satellite measurements of surface temperature.

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