Gamma Radiation Skyshine Calculator

A schematic of the geometry

The following images show top, side and 3D views of the geometry set up for the skyshine calculator data entry. As noted in the images, and explained further later below, horizontal measurements are taken from the inner wall (the calculation does not need wall thickness). All vertical measurements are taken from the top of the wall, so enclosure wall height is not required.  

Radiation skyshine geometry inputs

The calculator uses the following geometry. For version V1.1b all dimensional inputs are in meters (m). 

L  = enclosure length
W  = enclosure width
A  = source setback (distance) from the front wall
B  = source offset (distance) from the left wall
D  = detector distance from the front wall (i.e. calculation point)
S  = sideways detector offset from the source line
SD = source depth below the wall top
DD = detector depth below the wall top

The vertical quantities are measured relative to the top of the wall. The horizonal quantities are measured from the inner surfaces of the vertical walls. 

A positive value of SD means the source is below the wall top. A positive value of DD means the detector is below the wall top. A negative value of DD means the detector is above the wall top (this is restricted as noted below). 

Interpretation for real life facilities - if you want to try this calculator with a real life facility then proceed as follows. Suppose the shielding wall height is 5 m - then setting SD and DD to 5 m would place the source and detector at ground level (and reducing either would raise them above the floor). If the real thickness of vertical walls is 1 m, and a detector (calculation point) is located 5m from the outer surface of the enclosure, then the dimension A will be (5 m + 1 m = 6m), since all horizontal dimensions are measured from the inner surface as already described. 

For version V1, the calculator applies supported input ranges to avoid unvalidated geometries. In particular:

• SD must be between 0.1 m and 5 m
• DD must be between -1 m and +5 m
• S must remain within the front-wall projection: -B ≤ S ≤ W - B

These limits do not suggest other geometries are impossible, they simply define the range over which this V1 skyshine calculator is intended to be used.

Sensitivity analysis and result plotting

If the detector-distance sensitivity plot is enabled,  this varies D (the detector distance from the front wall / calculation point), while keeping the other inputs fixed. The solid line shows the Ionactive skyshine estimate. The dashed inverse-square curve is normalised to the first plotted skyshine point and is included only as a shape comparison; it is not a separate direct-radiation calculation. The marker shows the current calculator result. The image below provides an example of its use. 

How gamma skyshine can be calculated

A formal gamma skyshine calculation does not use an inverse-square calculation. The scattered photons do not travel directly from the source to the detector. Instead, the problem involves photons escaping upwards, scattering in air, changing direction and energy, and then reaching the detector point. The simple assumption is that air is only in the way, although as shown above, physical features can significantly change a predicted dose rate near ground level.  

The established SKYDOSE / MicroSkyshine family of methods is based on the integral line-beam method and the line-beam response function. SKYDOSE reference can be found here - SKYDOSE: A Code for Gamma Skyshine Calculations Using the Integral Line-Beam Method . Details of the MicroSkyshine software can be found here: MicroSkyShine code by Grove Software (Ionactive as a full license for this - just renewed until 26 May 2027). 

In simple terms, a line-beam response function describes the dose or air kerma at a detector (calculation) point from photons emitted into a specific direction and energy, after scatter in the atmosphere. SKYDOSE describes this in terms of a line-beam response function R(z,E,ϕ), where the response depends on source-to-detector distance, photon energy and emission angle. The skyshine dose is then found by integrating that response over the photon energies and over the emission directions allowed by the geometry.

A simplified way of writing this idea is as follows (the understanding of this is not required in order to use the Ionactive skyshine calculator!). 

\[
D(s) =
\int_E
\int_{\Omega}
S(E,\Omega)\,
R(z,E,\phi)\,
d\Omega\,dE
\]

where:

For an isotropic monoenergetic point source, SKYDOSE reduces the expression to an angular integral over the directions allowed by the source collimation or shielding geometry. The permitted angular limits depends on the particular geometry, such as a silo, wall or rectangular building.

The important part in the above expression is the response function. SKYDOSE uses analytical approximations to the line-beam response function, with fitted parameters tabulated by photon energy and emission angle. To run the code the user needs to access auxiliary data files which contain the response parameters used for interpolation between energies and angles.

MicroSkyshine is described in the literature as a commercial, substantially updated version of SKYDOSE, and it also uses the integral line-beam skyshine method from the line-beam response function, while allowing more extensive source and source-to-detector geometries. Ionactive has no access to the line-beam response functions, as far as we can tell they are not freely available. [Update 26 May 2026 - we have found them, stay tuned!]. 

What Ionactive would like vs what we have available

The full line-beam method requires response-function data tables over photon energy, angle and distance - this data is not available in a convenient open form for Ionactive use in a simple web based calculator. We could go down the route of trying to reproduce them using MCNP or similar, but this is out of scope for a freely available skyshine calculator.  For that reason, the Ionactive Skyshine calculator does not attempt to reproduce SKYDOSE or MicroSkyshine internally. It is not a cut-down copy of MicroSkyshine and serves a different purpose. It is a freely available educational tool allowing those interested in (or working in) radiation protection to experiment with skyshine, without needing expensive and / or professional software.

[Ionactive comment: OpenMC is a professional level Monte Carlo radiation transport code which is freely available, and could be used to evaluate skyshine. However, it has a considerable and steep learning curve which is not compatible with the objectives of our freely available calculators. ]

If you need to evaluate skyshine professionally, then use the Ionactive Radiation Protection Adviser service, or buy MicroSkyshine or MCNP (etc).  

What is the Ionactive approach to the gamma skyshine calculator

The Ionactive calculator has three main parts.

Radionuclide-specific distance response

For each radionuclide, the calculator uses a fitted distance response of the form:

\[
D(r)=D_{15}
\left(\frac{r}{15}\right)^{-n}
e^{-\mu(r-15)}
\]

where:

This is not an inverse-square law. Skyshine is produced by photons escaping upwards and scattering in air, so the fall-off with distance is different from direct radiation from an unshielded point source (which has been shown to be the case in the Se-75 real life monitoring example given earlier). 

Each radionuclide has its own fitted values because Co-60, Cs-137, Ir-192 and Se-75 have different photon energies and emission probabilities.

Angular open-top geometry factor

The Ionactive calculator then estimates how favourable the enclosure geometry is for photons to escape through the open top. It samples upward directions from the source and checks which directions can geometrically escape through the top of the enclosure. Those directions are then weighted according to their alignment with the detector-side geometry. This calculation will change significantly with the geometry settings available as specified earlier. 

This gives an angular geometry factor. A value greater than 1 means the geometry is more favourable for skyshine than the internal reference geometry. A value less than 1 means it is less favourable. This part of the calculator is geometry-based (we have not stored a table of geometry data based on inputs). 

Source-depth and detector-depth corrections

The angular model alone does not capture all trends in a typical benchmark skyshine calculation. Therefore, the Ionactive calculator also applies modest calibrated corrections for:

• source depth below wall top
• detector depth below wall top

These corrections are radionuclide-specific and were fitted against selected benchmark cases (we ran many cases!). 

Under the hood

We have included an under the hood check box, which if checked will provide significant additional information about the skyshine calculation. This feature is mostly for Ionactive internal development purposes, but we thought we would include in the public V1 calculator release. 

Angular geometry factor

The angular geometry factor represents how favourable the enclosure geometry is for photons to escape through the open top and contribute to skyshine at the detector position. A source near the middle of a large opening has a different skyshine opportunity compared with a source close to a wall, close to a corner, or deep below the wall top. A value greater than 1 means the angular geometry is more favourable than our reference case. A value less than 1 means it is less favourable.

q value

The q value is an internal shape parameter used by the angular model. It controls how strongly the Ionactive calculator weights photon directions that are more favourably aligned with the detector (calculation) position. It is not a physical attenuation coefficient, shielding factor or dose conversion factor.

Escaped upward fraction

The escaped upward fraction is the fraction of sampled upward directions from the source that can geometrically escape through the open top of the enclosure. A source deep below the wall top, or close to a wall or corner, may have fewer open upward paths than a source near the centre of a large opening. This is significantly affected by the geometric inputs of the Ionactive calculator. 

Current angular sum and reference angular sum

The angular sum is a weighted version of the escaped upward fraction. It includes both whether a sampled direction escapes, and whether it is favourably aligned with the detector-side geometry. The current angular sum applies to the Ionactive calculator input geometry. The reference angular sum applies to the internal reference geometry. Their ratio contributes to the angular geometry factor.

Distance response factor

The distance response factor accounts for how the skyshine field changes with horizontal source-to-detector distance. This is not a simple inverse-square factor since  skyshine involves air scatter, so the distance dependence is different from direct radiation.

Source-depth correction

The source-depth correction accounts for the source being below the top of the wall.

A source closer to the open top usually has a greater opportunity to contribute to skyshine. A source deeper below the wall top is more geometrically restricted by the enclosure walls. Note that is still assumes perfect air scatter and does not account for a building roof above the enclosure, cranes or other objects. These can significantly impact skyshine dose rates at ground level (as has been shown with our Se-75 example earlier). 

Detector-depth correction

The detector-depth correction accounts for the detector position relative to the wall top.

Both source depth and detector depth are measured from the top of the wall. A negative detector depth means the detector is above the wall top. For this V1 calculator, detector depth is restricted to the supported range shown in the input checks.

Sampling grid

The sampling grid shows how many upward directions are sampled by the Ionactive angular model. The current setting is chosen to give stable results while keeping the calculator responsive in a web browser. Ionactive will tweak this considerably during development, but it is fixed for the V1 calculator release. 

Important limitations of the Ionactive V1 gamma radiation skyshine calculator

This Ionactive calculator is primarily an educational tool. It is intended to help users understand approximate skyshine behaviour and the effect of changing geometry. It does not replace the requirement to use professional  software / codes or to seek the formal advice of a Radiation Protection Adviser. 

The V1 Ionactive skyshine calculator does not include:

• direct radiation through walls
• wall shielding transmission
• roof shielding or partial covers
• cranes or overhead structures
• building roofs
• nearby plant or equipment
• ground reflection
• detailed energy degradation after scatter
• detector energy/angular response
• source self-shielding or container shielding
• complex extended-source geometries

It should therefore not be used as the sole basis for:

• formal shielding design
• regulatory compliance
• HSE consent submissions
• critical dose assessments
• controlled area or supervised area decisions

Real-world measurements and why they may differ (from MicroSkyshine or Ionactive)

Real-world skyshine measurements may differ from calculated values (as we have seen with the Se-75 example). This does not necessarily mean the calculation is wrong.

At low dose rates, for examples below a few µSv/h, a 5–10% difference between two calculation methods may be smaller than the variability observed when making workplace measurements with a handheld radiation dose rate monitor. Detector orientation, averaging time, background subtraction, nearby scatter, local structures and instrument response can all produce variations of this order or larger.

In real industrial environments, the situation can be even more complex. A factory may contain roof steelwork, overhead cranes, plant, tanks, pipework, vehicles, source containers and other scattering or absorbing structures. These can reduce, enhance or redistribute the skyshine field.

Therefore, the Ionactive skyshine calculator should be treated as an indicative open-air screening estimate, not a promise of the exact dose rate that will be measured at a particular point in a real facility. However, the evidence so far suggests that both MicroSkyshine and the Ionactive skyshine calculator will over estimate real world likely dose rates.