基于Monte Carlo方法的水体二向反射分布函数（BRDF）模拟
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摘要
水体的二向反射特征是表征海洋光学特性的重要因素之一,对应用遥感系统进行水色参数准确定量反演及海洋水色遥感技术的发展有着重要意义,是进行水质监测、水体温度、海洋生产力估产等方面定量遥感必须解决的问题之一
二向反射是自然界中最基本的宏观现象之一。水体表面光场的方向分布携带有水体的一些重要的属性信息(如水体各组成含量、类型、粒径分布以及表面粗糙度等),忽略其方向性会带来一定的误差。然而早期的遥感应用,通常假定物体反射表面是朗伯反射,认为反射辐射强度、反射方向与入射辐射方向无关,在各方向上均匀分布。随着定量遥感技术的不断发展,遥感的定量化要求传感器获取的信息能准确反映目标特征,同时对由卫星遥感信号中提取的离水辐亮度的精度要求也越来越高。
目前,植被、土壤的二向反射特性及模拟模型得到了大量的研究,取得了不少进展,但水体二向反射特性的研究相对较少,能够推广应用的二向反射函数模型则更少。这主要是由于影响海洋光谱因素较多,难以精确模拟；海上原位测量困难较大,风浪、阴影、天空状况等影响因素众多,都可以对结果引起较大误差,难以通过实验测量。而通过构建蒙特卡罗模型模拟计算辐射传输模型则可以很好地解决以上困难。由此可见,开展水体的BRDF的模拟模型及模型验证研究将会成为海洋水色遥感定量研究的热点和难点。
本研究基于一定的假设,通过采用蒙特卡罗方法模拟追踪光子在水中的运动碰撞,采用散射相函数、单次散射率、衰减系数,并通过随机数选取碰撞的位置和散射角度,建立包含高吸收和高散射水体、分子的散射和大颗粒的散射、太阳入射角度、天空光影响的蒙特卡罗二向反射模型。在此基础上,模拟结果基于四边形网格统计技术,统计大量入射光子在水体表面空间所形成的出射光场,并使用圆柱坐标图,实现出射光场的三维展示。
通过对模型结果的分析与计算发现,太阳入射角度、天空光所占比例、散射相函数、单次散射率等因素共同决定着二向反射分布函数的数值和形状。具体研究结果如下：
(1)太阳入射角度,特别是太阳天顶角能改变水体二向反射分布函数的形状。在以悬浮颗粒物散射为主的水体,能量大都集中在后向热点方向,且后向热点的位置与太阳入射方向密切相关,也即后向热点的位置均出现在太阳入射光的反方向上；
(2)天空光所占比例,本研究采用简单的各向同性天空光,当加入天空光后,二向反射分布函数峰值降低,并随着天空光比例的增大,二向反射分布函数的形状趋于对称,后向热点逐渐消失；
(3)单次散射率主要影响二向反射分布函数的数值大小。同一条件下,单次散射率越大,水体表面反射光场越强烈,二向反射分布函数值越大；反之,越小。
(4)散射相函数是影响二向反射分布函数形状的主导因素。水分子散射占主导的水体,其散射相函数采用瑞利相函数,光场能量较分散,其二向反射分布函数形状基本不随入射天顶角的变化而变化。而颗粒散射占主导的水体,其散射相函数为Petzold相函数,光子在水中碰撞之后,前向散射非常强烈,经多次散射逃出水面的光子较少,其能量集中在后向热点位置。
Bi-directional Reflectance Distribution Function (BRDF) of water is one of the most important factors to describe the optical characteristics of ocean, It also plays important roles in the research of remote sensing modelling and inversion. Study of this BRDF of water is meaningful to the quantitative remote sensing and the development of remote sensing technology, which need to be solved for monitoring the quality and temperature of water and assess the ocean productivity.
BRDF is the most basic macroeconomic phenomenon in nature. The directional distribution of light field on water surface carry the important information of water properties such as the composed of water, concentration of component, minerals, the distribution of particle size and surface roughness. It can bring some errors if we ignoring its direction. However, early applications of remote sensing are usually assumed that the object surface is a Lambert. It is uniformly distributed in all directions and the intensity of reflected radiation, reflection direction are nothing to do with the direction of incident radiance. With the continuous development of quantitative remote sensing technology, it's urgent to obtain the more accurately information.
Now, The BRDF is widely implemented in land remote sensing, especially for quality assessment of vegetation and soil. However, it has only been occasionally applied in marine optics to date. This is mainly because many factors affect the marine spectrum and it is not easy to simulate accurately; It is very difficult to measure BRDF in situ. Sea waves, shadows, sky conditions can lead to large errors on the results. The Monte Carlo model by constructing simulation of radiation transfer model can solve these problems well. Thus, building the mathematical model and validate the models will become the hot and difficult point in ocean color remote sensing.
This research was based on certain assumptions, by using Monte Carlo method to track a large number of photon collisions in the water. We use random number to select the location of the collision and the scattering angle of photons by the knowledge of scattering phase function, single scattering albedo, and attenuation coefficient. The Monte Carlo model was built to treat those problems such as highly absorbing and highly scattering waters, scattering by molecules and by particulates, incident sun-zenith, sky light. Based on this, the result was through statistical a large number of the photon which formed the light field using quad-averaged techniques, and present in three-dimensional coordinate.
Through analysis of the results of the model, both single scattering albedo, solar incident angle, the ratio between sky light and whole light and scattering phase function have an impact on shape and quantity of BRDF. The results are as follows:
(1) Solar incident angle, especially zenith angle can change the shape of BRDF. When the major scattering particle of water was suspended particles, most of the power was concentrated and the maximum appear near the direction of light incidence (backscattering light).
(2) The results showed that the ratio of sky to total radiance can also change the shape of BRDF. The peak of BRDF decreased with increasing ratio and the shape tend to be axial symmetrical, the axial of symmetry was identical to the line perpendicular to the horizontal plane. The backward hot spot was gradually disappearing.
(3) The single scattering albedo has an impact on the BRDF quantity, the number of BRDF increased with the raise of single scattering albedo at the same conditions. On the contrary, BRDF became smaller.
(4) Scattering phase function was a dominant factor to affect the shape of the BRDF. When the major scattering material was water molecules, a Rayleigh phase function was used to describe the angular scattering properties of the water. The distribution of photon was not concentrated and nothing to do with the incident zenith angle. But for water which major scattering material of water was suspended particles was used to describe the angular scattering properties use Petzold phase function. The Petzold phase function was characterized by a intense forward scattering. So most of photon seldom escaped the water. The picture of BRDF also showed that the most power was concentrated in the backword hot spot.
二向反射是自然界中最基本的宏观现象之一。水体表面光场的方向分布携带有水体的一些重要的属性信息(如水体各组成含量、类型、粒径分布以及表面粗糙度等),忽略其方向性会带来一定的误差。然而早期的遥感应用,通常假定物体反射表面是朗伯反射,认为反射辐射强度、反射方向与入射辐射方向无关,在各方向上均匀分布。随着定量遥感技术的不断发展,遥感的定量化要求传感器获取的信息能准确反映目标特征,同时对由卫星遥感信号中提取的离水辐亮度的精度要求也越来越高。
目前,植被、土壤的二向反射特性及模拟模型得到了大量的研究,取得了不少进展,但水体二向反射特性的研究相对较少,能够推广应用的二向反射函数模型则更少。这主要是由于影响海洋光谱因素较多,难以精确模拟；海上原位测量困难较大,风浪、阴影、天空状况等影响因素众多,都可以对结果引起较大误差,难以通过实验测量。而通过构建蒙特卡罗模型模拟计算辐射传输模型则可以很好地解决以上困难。由此可见,开展水体的BRDF的模拟模型及模型验证研究将会成为海洋水色遥感定量研究的热点和难点。
本研究基于一定的假设,通过采用蒙特卡罗方法模拟追踪光子在水中的运动碰撞,采用散射相函数、单次散射率、衰减系数,并通过随机数选取碰撞的位置和散射角度,建立包含高吸收和高散射水体、分子的散射和大颗粒的散射、太阳入射角度、天空光影响的蒙特卡罗二向反射模型。在此基础上,模拟结果基于四边形网格统计技术,统计大量入射光子在水体表面空间所形成的出射光场,并使用圆柱坐标图,实现出射光场的三维展示。
通过对模型结果的分析与计算发现,太阳入射角度、天空光所占比例、散射相函数、单次散射率等因素共同决定着二向反射分布函数的数值和形状。具体研究结果如下：
(1)太阳入射角度,特别是太阳天顶角能改变水体二向反射分布函数的形状。在以悬浮颗粒物散射为主的水体,能量大都集中在后向热点方向,且后向热点的位置与太阳入射方向密切相关,也即后向热点的位置均出现在太阳入射光的反方向上；
(2)天空光所占比例,本研究采用简单的各向同性天空光,当加入天空光后,二向反射分布函数峰值降低,并随着天空光比例的增大,二向反射分布函数的形状趋于对称,后向热点逐渐消失；
(3)单次散射率主要影响二向反射分布函数的数值大小。同一条件下,单次散射率越大,水体表面反射光场越强烈,二向反射分布函数值越大；反之,越小。
(4)散射相函数是影响二向反射分布函数形状的主导因素。水分子散射占主导的水体,其散射相函数采用瑞利相函数,光场能量较分散,其二向反射分布函数形状基本不随入射天顶角的变化而变化。而颗粒散射占主导的水体,其散射相函数为Petzold相函数,光子在水中碰撞之后,前向散射非常强烈,经多次散射逃出水面的光子较少,其能量集中在后向热点位置。
Bi-directional Reflectance Distribution Function (BRDF) of water is one of the most important factors to describe the optical characteristics of ocean, It also plays important roles in the research of remote sensing modelling and inversion. Study of this BRDF of water is meaningful to the quantitative remote sensing and the development of remote sensing technology, which need to be solved for monitoring the quality and temperature of water and assess the ocean productivity.
BRDF is the most basic macroeconomic phenomenon in nature. The directional distribution of light field on water surface carry the important information of water properties such as the composed of water, concentration of component, minerals, the distribution of particle size and surface roughness. It can bring some errors if we ignoring its direction. However, early applications of remote sensing are usually assumed that the object surface is a Lambert. It is uniformly distributed in all directions and the intensity of reflected radiation, reflection direction are nothing to do with the direction of incident radiance. With the continuous development of quantitative remote sensing technology, it's urgent to obtain the more accurately information.
Now, The BRDF is widely implemented in land remote sensing, especially for quality assessment of vegetation and soil. However, it has only been occasionally applied in marine optics to date. This is mainly because many factors affect the marine spectrum and it is not easy to simulate accurately; It is very difficult to measure BRDF in situ. Sea waves, shadows, sky conditions can lead to large errors on the results. The Monte Carlo model by constructing simulation of radiation transfer model can solve these problems well. Thus, building the mathematical model and validate the models will become the hot and difficult point in ocean color remote sensing.
This research was based on certain assumptions, by using Monte Carlo method to track a large number of photon collisions in the water. We use random number to select the location of the collision and the scattering angle of photons by the knowledge of scattering phase function, single scattering albedo, and attenuation coefficient. The Monte Carlo model was built to treat those problems such as highly absorbing and highly scattering waters, scattering by molecules and by particulates, incident sun-zenith, sky light. Based on this, the result was through statistical a large number of the photon which formed the light field using quad-averaged techniques, and present in three-dimensional coordinate.
Through analysis of the results of the model, both single scattering albedo, solar incident angle, the ratio between sky light and whole light and scattering phase function have an impact on shape and quantity of BRDF. The results are as follows:
(1) Solar incident angle, especially zenith angle can change the shape of BRDF. When the major scattering particle of water was suspended particles, most of the power was concentrated and the maximum appear near the direction of light incidence (backscattering light).
(2) The results showed that the ratio of sky to total radiance can also change the shape of BRDF. The peak of BRDF decreased with increasing ratio and the shape tend to be axial symmetrical, the axial of symmetry was identical to the line perpendicular to the horizontal plane. The backward hot spot was gradually disappearing.
(3) The single scattering albedo has an impact on the BRDF quantity, the number of BRDF increased with the raise of single scattering albedo at the same conditions. On the contrary, BRDF became smaller.
(4) Scattering phase function was a dominant factor to affect the shape of the BRDF. When the major scattering material was water molecules, a Rayleigh phase function was used to describe the angular scattering properties of the water. The distribution of photon was not concentrated and nothing to do with the incident zenith angle. But for water which major scattering material of water was suspended particles was used to describe the angular scattering properties use Petzold phase function. The Petzold phase function was characterized by a intense forward scattering. So most of photon seldom escaped the water. The picture of BRDF also showed that the most power was concentrated in the backword hot spot.
引文
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