Lesson 1, Topic 1
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# Geometric Parameters

## Overview of geometrical parameters

### Which parameters influence the radar backscatter?

The Earthâ€™s surface is a complex target. Multiple parameters play a significant role in the strength of the radar echoes as they are received by the SAR sensor. This strength of the returning signal is referred to as backscatter intensity. So-called â€˜ground parametersâ€˜ comprise those variables that describe the composition of objects on the Earthâ€™s surface and influence the backscatter intensity drastically are given below:

• Geometric properties
• Dielectric properties

### Which geometrical parameters influence the radar backscatter?

• Surface roughness
• Topography
• Object geometry
• Object orientation

As object geometry and orientation are strongly related to the physics happening in topographical and surface related effects, this topic will focus on the three main geometric parameters: surface roughness, topography and the geometric appearance and density of the vegetation.

## Sensing a rough world â€¦

The surface roughness is a major parameter influencing our radar backscatter signal. Natural surfaces can generally be considered to be â€˜roughâ€™, even though this term should always be considered to be relative. Surface roughness is not only defined by an objectâ€™s geometry but also depends on the properties of an EM wave hitting that same target such as the wavelength.

What is â€˜roughâ€™?

To determine what is considered as â€˜roughâ€™, the wavelength needs to be considered as youâ€™ve learned in previous topics. If we want to quantify what roughness means, we can use the standard deviation (or root means square, RMS) h of a mean height (h) of the respective surface. The area over which this measurement is done, of course, is greater than the wavelength.

Dependence of wavelength and surface roughness

The relation between wavelength Î» and surface roughness s can be described through the parameter k(s). The equation of k is given as,

k = 2Ï€ / Î»

This equation means, that with increasing wavelength, the relative roughness decreases. As wavelength exceeds the size of a scatter target, the surface seems smoother than compared to the same object sensed at smaller wavelength.

When do we consider a surface to be â€˜roughâ€™?

A surface is considered â€˜roughâ€™, when h exceeds a certain threshold. So how do we define, where this value is located?

One idea is to find out what the phase difference Î”Î¦ between two points on a surface is, which are separated by one h. This separation is large enough, when it is similar to the scale of the wavelength that is being used by the radar sensor. If this is the case, the backscattered waves will start to interfere, making it less predictable.

## Criteria to define surface roughness

The question of how surface roughness can be calculated can be answered by using two common criteria.

The Rayleigh criterion

This criterion was defined by the British scientist John W. Strutt and is widely used for the specification of the minimum separation between a smooth and rough surface. It states that a smooth surface, is characterized by a phase difference due to h that is less than 1/4 of a wavelength (e.g. for C-Band = 6 cm).
If the change of phase would exceed this threshold, scattered radiation would not be coherent (on average) and therefore scattered waves become more diffuse. The definition of a smooth surface hsmooth is given on the right.

The factor 8 by which this term is divided arises from the two-way path the emitted energy has to take to reach the sensor again after being scattered.

Î» represents the wavelength of the incoming radiation and Î¸ the incidence angle. Latter, influences the path difference the is associated with the surface roughness.

The Fraunhofer criterion

While the Rayleigh criterion is sufficient to perform first order classifications whether a surface is considered â€˜roughâ€™ or not, it is not quite suitable to model the behaviour of scattered microwaves on natural surfaces.
Here, Î» is often of the same extent of h and therefore asks for a stricter threshold to define smoothness.

Consequently, the threshold of phase difference that needs to be satisfied to consider a surface â€˜smoothâ€™ is Î”Î¦ < Ï€/8.

## Effects of imaging geometry

Now you know that a radar system is looking to the side, away from the nadir line below the sensor. This has very unique effects on how objects appear in a radar image. While this situation enables unique analysis techniques, it also introduces some challenges when looking at complex objects on the Earthâ€™s surface.

Due to the slanted lateral observation geometry of SAR systems, we can observe several effects in our SAR images that originate from the existence of topography. When interpreting radar images it is crucial to understand the processes behind these geometric distortions.

In this topic you will learn which effects are created by the radarâ€™s side looking geometry.

## The Radar imaging effects

Youâ€™ve just heard about the effects that are produced by the imaging geometry. Letâ€™s take a look at them in more detail to consolidate these concepts.

Elevation displacement

Elevation displacement, also referred to as geometric distortion, is the image displacement in a remote sensing image toward the nadir point, in radar imagery due to sensor/target imaging geometries. In a radar image the displacement is toward the sensor and can become quite large when the sensor is nearly overhead. The displacement increases with decreasing incidence angle. The characteristics resulting from the geometric relationship between the sensor and the terrain that are unique to radar imagery are foreshortening, layover, and shadowing.

Topographic features like mountains, and artificial targets like tall buildings, will be displaced from their desired orthographic position in an image. The effect can be removed through independent knowledge of the terrain profile.

Foreshortening

Foreshortening is the spatial distortion whereby terrain slopes facing a side-looking radarâ€™s illumination are mapped as having a compressed scale relative to its appearance, as if the same terrain were level. Foreshortening is a special case of elevation displacement. The effect is more pronounced for steeper slopes and for radars that use steeper incidence angles.

Layover

Layover is an extreme form of elevation displacement or foreshortening in which the top of a reflecting object, such as a mountain, is closer to the radar (in slant range) than the lower parts of the object. The image of such a feature appears to have fallen over towards the radar. Also defined as the displacement of the top of an elevated feature with respect to its base on the radar image.
The peaks look like dip-slopes. The effect is more pronounced for radars having smaller incidence angle.

A radar shadow is the absence of radar illumination due to intervening reflecting or absorbing objects. The occurrence, shape and amount of radar shadow caused by either concave or convex relief features depend on several factors. These include radar look direction, incidence angle and platform altitude, as well as terrain configuration, slope angle and slope orientation. Shadow effects are common with large incidence angle illumination and they occur in down-range direction. Thus, they serve as a good indicator of radar illumination direction, topography, and height.

In high relief terrain, radar shadow effects may obscure a significant amount of surface area, which is most obvious in large incidence angle (e.g. >50Â°) airborne SAR imagery. Satellite-based radar tends to produce far less radar shadow effects. There is no measurable target return signal in radar shadows (other than noise).

Explore the hotspots in the image to obtain a glimpse of the radar imaging effects.

Click on the individual Icons to learn more. Use the full screen mode on the image to get the best learning experience.

## Interactions of microwaves with vegetation

The relation between different types of vegetation and the resulting scattering processes are complex and quite diverse. This can be attributed to the fact the geometric appearance and density of plants are subject to strong variations across the globe. Scattering elements can be leaves, tree trunks, blades of grass or bushes in countless shapes. As a rule of thumb, the longer the wavelength is, the deeper the radiation can penetrate the vegetation.

## Influences on the backscatter signal from vegetation

### Sensor

• wavelength & frequency
• polarisation
• cell size
• viewing geometry (incidence angle, etc.)

### Ground Parameters

• topographic features
• surface roughness
• geometric target properties
• dielectric constant (moisture content)

As visualised in the figure below, the backscatter response from vegetation (in this case trees and grasses of different height) depends on a list of parameters, which are also related to one another. For example, will a temporal flooding within a forest strongly change the signal in contrast to the same area being imaged during dry conditions (non-flooded). As mentioned earlier you can see how differently varying wavelengths interact with the tree canopy. Similarly, smaller crops or grasses change the scattering behaviour with respect to the wavelength that is used.

## Different scattering mechanisms in tree stands

Within a single tree, depending on the wavelength and canopy composition, different scattering processes can occur. As given on the right side, we can see that a portion of incoming EM radiation is scattered back to the sensor. This is the case when short wavelengths such as C- or X-Band are used. Here the signal is not â€˜long enoughâ€™ to penetrate the canopy and reach the stem. The radiation entering the canopy (typically L-Band or larger) can then either be scattered within the volume (volume scattering) or it can interact with the tree trunk to be finally scattered back to the sensor after hitting the ground (double bounce). In most cases, tree canopies tend to exhibit degrees of high complexity so that they can be modelled as random volumes.

While L-Band sensors are generally regarded to be more suitable for forest monitoring, Sentinel-1 C-Band data has also proven to be a good choice for a variety of forest applications, especially with regards to its dense time series and the number of successful applications is most likely to grow in the future.