# SuperDARN Mapping

Details and examples of the problems associated with our current techniques used to map SuperDARN backscatter to a particular location. There are two main problems. The first affects the range of the backscatter along a particular beam direction and the second affects the actual direction the beam is pointed for non-zero elevation angles.

## Range Mapping

There are currently two techniques for mapping scatter along a particular beam direction: the standard technique and the Chisham virtual height model. The latter was described in a paper but never put into use. A third technique is shown below. It has many similarities to the Chisham technique, but does not use unrealistic virtual heights.

### Fixed Range: 800 km range

**click**image to step through ranges

**click**image to step through ranges

### Fixed Range: 1000 km range

**click**image to step through ranges

**click**image to step through ranges

### Fixed Range: 1200 km range

**click**image to step through ranges

**click**image to step through ranges

### Fixed Range: 1400 km range

**click**image to step through ranges

**click**image to step through ranges

### Fixed Range: 1600 km range

**click**image to step through ranges

**click**image to step through ranges

### Fixed Range: 1800 km range

**click**image to step through ranges

**click**image to step through ranges

### Fixed Range: 2000 km range

**click**image to step through ranges

**click**image to step through ranges

This set of figures shows the 1.5 hop path compared to the 0.5 hop path used in the standard algorithm. The elevation angle and, therefore, the virtual height are changed for fixed ranges of 1800 km, 2400 km, 3000 km, 3600 km, 4200 km and 4800 km. Click on a figure to see the range of elevation angles.

### Fixed Range: 600 km Leg (1800 km range)

**click**image to step through ranges

**click**image to step through ranges

### Fixed Range: 800 km Leg (2400 km range)

**click**image to step through ranges

**click**image to step through ranges

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### Fixed Range: 1000 km Leg (3000 km range)

**click**image to step through ranges

**click**image to step through ranges

### Fixed Range: 1200 km Leg (3600 km range)

**click**image to step through ranges

**click**image to step through ranges

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### Fixed Range: 1400 km Leg (4200 km range)

**click**image to step through ranges

**click**image to step through ranges

### Fixed Range: 1600 km Leg (4800 km range)

**click**image to step through ranges

**click**image to step through ranges

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This set of figures shows the 1.5 hop path compared to the 0.5 hop path used in the standard algorithm. The range is changed in these examples and the virtual height is held fixed at 400 km, 500 km and 600 km.

### Fixed Virtual Height: 400 km; 1.5 hop

**click**image to step through ranges

**click**image to step through ranges

### Fixed Virtual Height: 500 km; 1.5 hop

**click**image to step through ranges

**click**image to step through ranges

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### Fixed Virtual Height: 600 km; 1.5 hop

**click**image to step through ranges

**click**image to step through ranges

Summary figures showing the errors in range associated with the standard model.

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One example showing 2.5 hop scatter, which is only likely to be possible for far ranges and low elevation angles.

### 400 km; 2.5 hop

**click**image to step through ranges

**click**image to step through ranges

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## Beam Angle Mapping

Although it has been known for more than a decade that the beam direction
depends on the elevation angle (the so-called *coning angle*) little
has been done to improve the state of the elevation angle determination of
the network nor has any attempt to incorporate this fact into the mapping of
SuperDARN data.

The figures below show the impact of using the proper beam direction on the mapping of several example range-gates. 45 km range resolution is chosen for simplicity. The beam direction set by the phasing matrix is defined as phi_0 and corresponds to the beam direction for zero elevation angle. The beam direction for non-zero elevation angles is defined as phi.

### Fixed Elevation Angle

An illustration of the difference in beam direction for a fixed elevation angle and varying phi_0.

**click**image to step through values of beam direction

### Fixed Beam Direction

An illustration of the difference in beam direction for a fixed phi_0 and varying elevation angle.

**click**image to step through values of elevation angle

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## Coning Angle Correction

Illustrations of the impact of using the correct beam direction.

### 24 Beam FOV

**click**image to step through values of elevation angle

### 16 Beam FOV

**click**image to step through values of elevation angle

## Chisham Virtual Height Correction

Illustrations of the impact of using the Chisham virtual height algorithm.

### 24 Beam FOV

**click**image to step through values of height

### 16 Beam FOV

**click**image to step through values of height

## Full Solution

Correct solution for different altitudes of scatter.

### 24 Beam FOV

**click**image to step through values of height

### 16 Beam FOV

**click**image to step through values of height