Refraction
To model atmospheric refraction:
- Select and configure a refraction model, and
- Opt whether to have refraction considered in Access calculations.
Background: Atmospheric Refraction
Atmospheric refraction is the bending of an RF signal as it travels through the atmosphere, caused by the changing refractive index at different altitudes. Normally, the refractive index is a decreasing function of altitude, with the bending most pronounced at lower altitudes. Refracted elevation is measured from the tangent to the bent signal path, rather than from the straight line-of-sight vector. We term the difference between the refracted elevation and the line-of-sight elevation the refraction angle.
Here is an illustration of the refracted path:
Let L and H be two objects exchanging a signal, where L is the object lower in the atmosphere and H is the higher object. The unrefracted path lies along the line LH. When light time delay is being considered, the distance along LH is related to the time delay of the transmitted signal. The actual signal travels along the refracted path that is bent at L and H. The line LK is tangent to the refracted path at L; the refraction angle ε at L is the angle between LK and LH. The line HK is tangent to the refracted path at H; the refraction angle δ at H is the angle between KH and LH. We term point K as the knee point of the refracted path.
Computing Refraction
The most precise methods for computing the refraction angle involve numerical quadrature along the signal path between objects (see reference, below). The refraction angle at each endpoint, as well as the curved path of the signal, can be found in this manner. The integrand is a function of the refractive index that itself is a function of altitude. Usually, the atmosphere is partitioned into different altitude bands with differing refractive index models, though exponential models are typical. In general, each refractive index model depends on the weather characteristics in its respective altitude band.
Less precise refraction models use simplified models of the refractive index, avoiding any dependence on weather. They also may provide an analytical formula that approximates the results of the numerical quadrature.
Typically, refraction models are developed using a spherical Earth approximation, where both altitude and elevation angle are measured centrically (using radials from the Earth center) rather than detically (using the surface normal of an oblate spheroid). Because STK uses an oblate spheroid to model the Earth, with altitude and elevation angle measured using a surface normal, the refraction models are not used directly but are instead adapted for use in STK by using detic elevation rather than centric.
Auer, Lawrence H. and E. Myles Standish, "Astronomical Refraction: Computational Method for all Zenith Angles," The Astronomical Journal, 119:2472-2474, 2000 May.
Refraction Models
Select among the following atmospheric refraction models:
Effective Radius Model
The effective radius model approximates the effects of refraction by assuming that the refractive index decreases linearly with altitude. This is only valid for objects at low altitude, typically less than 8-10 km. This approximation leads to a very simple formula for the refracted elevation angle that is akin to computing the elevation angle relative to a scaled Earth surface. The Earth's radius is scaled by the effective radius factor, typically a value between 0.3 and 2 -- the most common value is 4/3. (Previous versions of STK used the term "4/3 Earth Radius model" and did not allow you to set the effective radius directly.) Note that the model does not provide a manner for computing the effect of refraction on the signal path length.
The following parameters can be set for this model:
| Parameter | Description |
|---|---|
| Effective Radius Factor | The multiplicative factor that scales the Earth's size in the model. |
| Refraction Ceiling | The maximum altitude of the lower object for which the refraction angle will be computed. Whenever the lower object's altitude is above the refraction ceiling, the refraction angle is considered to be 0.0 deg, because little atmosphere is present above this altitude to cause appreciable refraction. |
| Max Target Altitude | For objects at higher altitudes (e.g., launch vehicles and satellites), the refraction angle computed by the effective radius model is a poor approximation to reality (because the refraction angle is too large). If the higher object's altitude is above the maximum target altitude, then the effective radius model does not apply. In such cases, if extrapolation is turned off, then the refraction angle is set to 0.0 deg. |
| Extrapolate Above Max Altitude | If extrapolation is enabled, then the refraction angle will still be computed when the higher object exceeds the maximum target altitude using a modified approach. In this approach, the higher object H will be replaced in the computation by the point P, located along the line LH at the point where the (approximate) altitude is the maximum target altitude. This extrapolated model ignores any refraction occurring along the relative path LH above the maximum target altitude. |
ITU-R P.834-4
P.834-4 is the ITU recommendation concerning "Effects of tropospheric refraction on radiowave propagation." The recommendation provides an analytical formula for the refracted elevation at the ground. The higher object is assumed to be a satellite. More information is available at http://www.itu.int/ITU-R target="_blank". Note that the model does not provide a manner for computing the effect of refraction on the signal path length.
The model does not provide a method for determining the refraction angle δ at the higher object H. Rather than performing ray tracing to determine δ, a simple approximation is used to locate the knee point K. After the refraction angle ε at the lower object L is determined, the direction from L toward K is known, although the distance to K is not. Let R be the distance along LH and let d be x% of that distance, where x% is the knee bend distance factor (a percentage you specify). Since most of the bending occurs near L, x is small, say 10-20%. The distance d is then used to compute K. If, however, the altitude of K exceeds the atmospheric altitude A, then d is reduced so that the altitude of K is (approximately) A. This ensures that the knee point K lies within the atmosphere. The value of δ computed in this way is likely to be an over-estimate of the actual refraction angle at H.
The following parameters can be set for this model:
| Parameter | Description |
|---|---|
| Refraction Ceiling | The maximum altitude of the lower object for which the refraction angle will be computed. Whenever the lower object's altitude is above the refraction ceiling, the refraction angle is considered to be 0.0 deg, because little atmosphere is present above this altitude to cause appreciable refraction. |
| Atmospheric Altitude | The maximum altitude of the knee point K. |
| Knee Bend Factor | The factor used in computing the approximate location of the knee point K. |
SCF
The SCF (Satellite Control Facility) refraction model is based upon the paper "Refraction Correction, 'RC, Refraction Addition, 'RA, Milestone 4, Model 15.3A" by A. M. Smith, Aug 1978. The 'RC model (pronounced tick-R-C) provides analytical formulas for computing the refraction angle and the refracted range (i.e., the effect of refraction on the signal path) of an observer on the ground to a satellite target. The formulas depend on the surface refractivity at the ground site.
The SCF method uses different ways of determining the refraction angle, depending on the elevation. For elevation angles between 90 and 1.5 deg refraction is computed analytically, while between 1.5 and -0.72 deg a table interpolation is performed. For elevation angles less than -0.72 deg, the refraction value for -0.72 deg elevation is used.
At the transitions between these elevation angle ranges, the SCF model may show small discontinuities in the refraction angle.
Like the ITU model, the model does not provide a manner for computing the refraction angle δ at the higher object H. The same approximation method as used by the ITU model is used for computing δ.
The following parameters can be set for this model:
| Parameter | Description |
|---|---|
| Use Constant Refraction Index |
Select this option to use a constant surface refractivity instead of using a polynomial (see below). |
| Refraction Polynomial | Use 10th order polynomial η = C0 + C1t + C2t2 + ... + C10t10 to approximate the surface refractivity over time, where t is the current epoch, expressed as a fraction of the current year (so that t is 0.0 at the start of the year and 1.0 at the end of the year). |
| Refraction Ceiling | The maximum altitude of the lower object for which the refraction angle will be computed. Whenever the lower object's altitude is above the refraction ceiling, the refraction angle is considered to be 0.0 deg, because little atmosphere is present above this altitude to cause appreciable refraction. |
| Atmosphere Altitude | The maximum altitude of the knee point K. |
| Knee Bend Factor |
The factor used in computing the approximate location of the knee point K. |
| Min Target Altitude | For objects at low altitudes (e.g., less than 5 km), the refraction angle computed by the SCF model is a poor approximation to reality. If the higher object's altitude is below the minimum target altitude, then the SCF model does not apply. In such cases, if extrapolation is turned off, then the refraction angle is set to 0.0 deg. |
| Extrapolate Below Min Altitude | If extrapolation is enabled, then the refraction angle will still be computed when the higher object is below the minimum target altitude using a modified approach. In this approach, the higher object H will be replaced in the computation by the point P, located along the line LH at the point where the (approximate) altitude is the minimum target altitude (P will be located past H along LH). |
Refraction in Access
By default, refraction is not considered when performing the relative apparent position computation in Access. You can turn this capability on by selecting Use Refraction in Access Computations. Refraction is applied after the light time delay computation, but before aberration is applied (if any).
When refraction is used in Access, all constraints that depend on the relative position and/or velocity of the two objects involved will be affected, including Line of Sight and Elevation Angle. However, in order to account for refraction when computing Access between a Sensor and another object, the Line of Sight constraint for that other object must be disabled.
Refraction is embedded in the STK Access Line of Sight (LOS) visibility computations. Access computes geometric LOS or Radio LOS based on whether Use Refraction in Access Computations is enabled. Each end computes independently; therefore, Use Refraction in Access Computations needs to be disabled on the other end or set on both ends.
Currently, the refraction models are Earth-specific models. Thus, refraction cannot be considered in Access for objects on other central bodies.