REMOTE SENSING EM Radiation Interactions with Earth Surface Features

REMOTE SENSING EM Radiation Interactions with Earth Surface Features
Professor Ke-Sheng Cheng Department of Bioenvironmental Systems Engineering National Taiwan University

Outline Remote sensing using energy of solar energy paths
Spectral reflectance of Earth surface features Remote sensing using energy of thermal energy paths 7/21/2018 Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

Remote sensing using energy of solar energy paths
Solar radiation passing through the atmosphere will come into contact with features on the Earth surface. Although absorption, reflection and transmission may occur when solar radiation is incident on Earth surface, for most applications the amount of radiances reflected from the target on Earth surface is of major concern. Radiant energy absorbed by or transmitted through the target is not measured by the sensor. 7/21/2018 Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

Solar irradiance at the Earth surface
7/21/2018 Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

Downwelled radiance Assume that a volumetric element dV of one unit volume in the atmosphere receives direct solar irradiance. Fraction of the incident energy is scattered into direction  and onto a target area dA1 on the Earth surface. 7/21/2018 Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

The volumetric element has a unit area perpendicular to the incident ray and a unit length along the ray travel direction. Let r be the distance between dV and dA1 and  be the azimuthal angle of dV when viewed from dA1. The irradiance at the target element dA from dV is calculated as 7/21/2018 Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

Thus, 7/21/2018 Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

Considering all downwelled scattering from a whole overcast hemisphere, the total irradiance on the target is 7/21/2018 Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

Surface roughness and types of reflection
Natural reflecting surfaces can be divided into two general categories – specular reflectors and diffuse reflectors, depending on the relative roughness of the surface with respect to wavelength of the incident radiation. A natural surface may appear to be rough with respect to radiation of one wavelength, while smooth with respect to radiation of another longer wavelength. 7/21/2018 Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

A perfect specular surface reflects radiation according to Snell's Law which states that the angle of incidence θi is equal to the angle of reflectance θr. Radiation impinging on a diffuse surface tends to be reflected in many directions (scattered). A perfect diffuse surface yields the same reflected radiance in all directions. 7/21/2018 Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

An important characteristic of reflection is that the incident radiation, the reflected radiation and the normal of the reflecting surface all lie in the same plane. Fig Geometric illustration of the specular reflection (a) and diffuse reflection (b). The incident and reflected radiations and the surface normal are in the same plane. 7/21/2018 Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

Rayleigh roughness criteria

It is important to note that the Rayleigh roughness parameter is dependent on the incident angle .
A surface may be considered smooth with respect to radiation of a specific wavelength when the ray direction is perpendicular to the surface ( ), whereas it may appear to be rough with respect to radiation of the same wavelength if the incident angle is large. 7/21/2018 Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

Lambertian surface and the Lambertian cosine law
A perfect diffuse surface which reflects equal amount of radiance into any direction of the hemisphere above the surface is called a Lambertian surface. An important property of the Lambertian surface is that the reflected radiant intensity in any direction from a point on the surface varies as a cosine function of the angle between that direction and the normal vector of the surface. 7/21/2018 Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

Fig. 1.19 Schematic illustration of a Lambertian surface (a) and the Lambertian cosine law (b).

Since the radiance is anisotropic, i.e. , we have

Relationship between the total exitance and radiance from a Lambertian surface
Few natural objects are specular reflectors. In fact, there are many natural surfaces that are more closely approximate Lambertian surfaces. Thus, it is often convenience for us to treat natural surfaces which are less well-behaved as Lambertian surfaces. 7/21/2018 Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

Fig. 1.20 Radiances reflected from a Lambertian surface into the hemisphere above the surface.

The total exitance M from a Lambertian surface element dA is equally distributed into a hemisphere over the element. Thus the total exitance can be calculated by integrating the radiance L over the hemisphere, i.e., 7/21/2018 Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

Thus, for Lambertian surfaces, the radiance and the total exitance are related by a factor of . Many natural surfaces show Lambertian characteristics up to , and some (such as snow and desert) are Lambertian up to Most naturally occurring surfaces depart significantly from the Lambertian case for greater than about 60 (Slater, 1980). 7/21/2018 Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

Bidirectional reflectance distribution function
For a non-Lambertian surface, various proportions of the incident radiation are reflected into different directions. The dependence of amount of reflected energy on the direction of incident radiation and direction of exitance to be measured is represented by the bidirectional reflectance distribution function (BRDF) defined as 7/21/2018 Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

Fig Geometric illustration of the irradiance and reflected radiance which define the bidirectional reflectance distribution function. 7/21/2018 Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

Unlike the reflectance , the bidirectional reflectance function has a unit of .
Reflectance is not associated to direction of incident or reflected radiation, whereas BRDF is dependent on both directions. The reflectance can assume any value between 0 and 1, while the BRDF can take values between 0 and infinity. 7/21/2018 Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

In the following we will derive the relationship between the BRDF and surface reflectance r under two different cases of incident radiation. Primary solar irradiance case Downwelled solar radiance case 7/21/2018 Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

Primary solar irradiance case

Thus, the value of BRDF of a Lambertian surface being exposed to a beam of parallel incident rays from a point source of radiation is calculated as 7/21/2018 Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

Downwelled solar radiance case
Now let’s consider another case of having a hemisphere of overcastting irradiance of uniform flux density Ei on a Lambertian surface element. The uniform downwelled radiance from the atmosphere onto a surface element is an example of such case. 7/21/2018 Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

The total radiant flux arriving at dA is calculated by integrating radiant flux over the hemisphere, i.e., 7/21/2018 Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

The total irradiance reaching dA is
The reflected radiance due to the overcastting irradiance is 7/21/2018 Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

Thus, the total reflected radiant flux is
Therefore, the dimensionless reflectance is 7/21/2018 Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

Nomenclature of reflectance quantities
Until now, we have discussed two different quantities describing the reflectivity of a surface element. The reflectance is defined as the ratio of reflected to incident radiant flux (or flux density). The BRDF describes the reflectance anisotropy of a surface as a function of a parallel beam of incident radiation from a single direction into another direction of the hemisphere. 7/21/2018 Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

However, we have not explicitly specified the nature of incident and reflected radiation in terms of their angular characteristics and measurable amounts. Although conceptually we can consider incident and reflected radiant flux of infinitesimal elements of solid angle, these quantities are not practically measurable since unlimited small source of radiation and sensor field of view do not exist. 7/21/2018 Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

All measurable amounts of radiant flux involve conical or hemispherical domain of geometrical considerations. Depending on the geometrical domain of the incoming and reflected radiances, Nicodemus et al. (1970) recommended the nomenclature shown in Table 1.6 for proper definition of reflectance quantities. 7/21/2018 Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

Table 1.6 Relation of incoming and reflected radiance terminology used to describe reflectance quantities. 7/21/2018 Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

Depending on the geometrical domain of the incident and reflected radiances, nine cases of reflectance quantities can be defined. Among these cases, only radiant fluxes of cases 5, 6, 8 and 9 are measurable. Radiant fluxes of other cases are merely conceptually quantities. Specifically, the BRDF is a Case-1 reflectance quantity. 7/21/2018 Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

Bidirectional reflectance factor (BDRF)
Another dimensionless quantity of reflectivity is the reflectance factor defined as the ratio of the radiant flux reflected by a surface to that reflected into the same reflected-beam geometry by a perfect (energy lossless) Lambertian surface. 7/21/2018 Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

The nomenclature proposed by Nicodemus also applies to reflectance factor. For example, the bidirectional reflectance factor (BDRF) is the ratio of the radiance reflected into a particular direction by a surface element under directional incidence to the radiance that would be reflected into the same direction by a perfect (energy lossless) Lambertian radiator illuminated in an identical fashion. 7/21/2018 Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

Fig Designations for denoting incident and reflected (collected) beam geometry. (Adapted from Nicodemus et al., 1977.) 7/21/2018 Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

Relationships between reflectance quantities

Furthermore, if the object of interest is Lambertian with a constant reflectance rd (i.e. a diffuse reflector), we have It indicates that for a Lambertian surface the reflectance is equivalent to the bidirectional reflectance factor which is itself isotropic. 7/21/2018 Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

Topographic effect on downwelled solar irradiance
Thus far we have implicitly assumed that the target point is on a horizontal and unobstructed plane such that the entire hemisphere above the target is sky. However, if the target is on a sloped plane or if there are adjacent objects obstructing the sky dome, the downwelled irradiance will be reduced. 7/21/2018 Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

F : Shape factor 7/21/2018 Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

Obstruction by adjacent objects

Reflected solar radiance from the Earth surface

Fig The source-target-sensor geometry for target on a sloped terrain. The target receives radiant fluxes from two sources – the direct solar irradiance and the dowelled radiance of the atmosphere. 7/21/2018 Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

Solar radiance reaching the sensor
The solar radiance reaching the sensor is the sum of the solar radiance reflected into the target-sensor direction from the Earth surface multiplied by the spectral transmittance of the atmosphere and the upwelled solar radiance (path C-C). Similar to the treatment of downwelled solar radiance, the upwelled solar radiance can be expressed as: 7/21/2018 Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

Schematic illustration of the upwelled solar radiance.

Integration in the above equation should be carried out over the Zp range along the target-sensor direction. The total amount of solar radiance reaching the sensor is therefore expressed as 7/21/2018 Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

Za and Zs are respectively the depth of the Earth atmosphere and vertical distance from the target to the sensor altitude. For satellite remote sensing for which the sensor is in space, the Sun-target path and the target-sensor path have the same vertical distances (i.e. Za = Zs), and as a result, 7/21/2018 Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

For a Lambertian surface of constant reflectance rd, it reduces to
A more complete form of the solar radiance reaching the sensor can be expressed as For a Lambertian surface of constant reflectance rd, it reduces to 7/21/2018 Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

Outline Propagation of EM radiation in the atmosphere
Remote sensing using energy of solar energy paths Spectral reflectance of Earth surface features Remote sensing using energy of thermal energy paths 7/21/2018 Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

Spectral reflectance of Earth surface features
Reflectance of a feature on Earth surface is a function of the wavelength of incident radiation. Such a function is often referred to as the spectral reflectance curve or spectral response pattern of the surface feature. From the concept of bidirectional reflectance distribution function, reflectance is a characteristic of a surface feature which not only is dependent on the spectral wavelength of radiation but also the directions and geometric domain of the incident and reflected radiances. 7/21/2018 Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

Similarly, the spectral reflectance curves also depend on the directions and geometrical domain of the incident and reflected radiances, and the Nicodemus nomenclature should apply. 7/21/2018 Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

Field measurements of spectral reflectance curves of various Earth surface features can be conducted using a spectroradiometer. Figure 1.26 demonstrates typical spectral reflectance curves of selected Earth surface features. These curves should be considered as average reflectance representation of individual features as they may vary with field condition of surface features. 7/21/2018 Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

Fig. 1.26 Spectral reflectance curves of selected Earth surface features. (After Jensen, 2007)

Spectral Signature Typical spectral reflectance curves for urban–suburban phenomena in the region 0.4 – 0.9 mm. 7/21/2018 Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

Spectral reflectance curves represent spectral characteristics of specific features. Although it may not be feasible to define unique patterns for specific features, distinctive differences in spectral response between different feature classes can be observed. For example, vegetation has a peak reflectance in green spectral range and an even higher reflectance in near infrared range, whereas reflectance of clear water is low in visible range and nearly zero in near infrared range. 7/21/2018 Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

In addition, spectral response of a given object may change over time (for examples, due to changes in growth condition of vegetation or moisture content in soils). Thus, many studies have used the spectral response patterns for classification of landcover types on Earth surface, identifying physiological condition of vegetation, geological exploration, etc. 7/21/2018 Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

Outline Propagation of EM radiation in the atmosphere
Remote sensing using energy of solar energy paths Spectral reflectance of Earth surface features Remote sensing using energy of thermal energy paths 7/21/2018 Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

Remote sensing using energy of thermal energy paths
From the Stefan-Boltzmann law, any object with higher-than-zero absolute temperature is a source of EM radiation. Thus, in addition to the Sun, the Earth atmosphere and the Earth itself also emit EM radiation. As a result, a target on the Earth surface not only receives solar radiation but also thermal radiation from the atmosphere (path G-G). Likewise, a sensor in space receives thermal radiances from the Earth (paths E and G-G) and the atmosphere (path F). 7/21/2018 Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

Figure 1.5 shows that within the visible and near infrared spectral range solar irradiance at the top of the atmosphere is much higher than radiant emittance of the Earth whereas in the thermal infrared range (8 – 9.5 and 10 – 14 m) earth emittance dominates. 7/21/2018 Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

In practical remote sensing applications, sensors are designed and utilized to detect radiant energy within certain spectral ranges. Thus, a sensor designed to detect radiant flux within the thermal infrared range will receive radiance mostly from the Earth (including the atmosphere) emission. This is why the term “thermal infrared” is coined for this spectral range. In this section we discuss the amount of thermal radiance leaving the Earth surface, i.e. radiances arisen from paths E and G-G’. 7/21/2018 Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

Kirchhoff’s law Emissivity is a measure of emittance capability of an object as compared to a blackbody. A blackbody is an ideal body which absorbs all radiation incident on it, and then re-emit all absorbed energy (zero reflectance and unity absorptance). Radiation emitted by a blackbody is isotropic (independent of direction) and, at a given wavelength, depends only on the temperature. In general, an object that absorbs radiant energy may also emit radiant energy at the same wavelength. 7/21/2018 Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

The relationship between emissivity and absorptance of an object can be described by the Kirchhoff’s law. 7/21/2018 Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

Emissivity The above definition of emissivity is a hemispherical quantity, i.e. the total emittance into a hemisphere above the object need to be considered. Such definition does not describe the dependence of emissivity on angular directions. 7/21/2018 Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

Thermal emission from the target of interest

Downwelled thermal radiance

Illustration of downwelled thermal radiance calculation

Thermal radiance reaching the sensor
The total amount of thermal radiance reaching the sensor is the sum of thermal radiance leaving the target multiplied by the transmittance along the target-sensor path and the upwelled thermal radiance (path F). Upwelled thermal radiance represents the amount of thermal radiation emitted by the atmosphere directly into the target-sensor direction. Similar to the treatment in calculating the downwelled thermal radiance, the atmosphere is again considered as having N homogeneous layers, except that the layer index increases downward. 7/21/2018 Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

Illustration of upwelled thermal radiance calculation

Split-Windows Technique (SWT) for LST estimation

Examples of SWT equations used for AVHRR channels 4 and 5

REMOTE SENSING EM Radiation Interactions with Earth Surface Features

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REMOTE SENSING EM Radiation Interactions with Earth Surface Features

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