Propagation and terrain¶
Code: radarsim/physics/atmospheric.py, rain.py, terrain.py.
Gaseous absorption¶
Specific attenuation of oxygen and water vapour follows the line-by-line method of ITU-R P.676-13 Annex 1 (44 oxygen and 35 water-vapour lines plus the dry continuum), valid from 1 to 1000 GHz. The test suite reproduces the ITU validation workbook to 12 significant digits. The Recommendation is written in terms of the dry-air pressure \(p\); scenarios give the barometric pressure, and the engine passes \(p = P - e\) with the water-vapour pressure \(e = \rho T / 216.7\).
The path loss is \(2\gamma R\) for the two-way path. Below 1 GHz gaseous absorption is negligible and is set to zero.
Rain¶
Specific attenuation \(\gamma_R = k R^{\alpha}\) uses the ITU-R P.838-3 coefficients for the radar's frequency and polarisation tilt. Rain only fills the layer below the rain height \(h_R = h_0 + 0.36\) km (ITU-R P.839-4, \(h_0 = 3\) km by default), so the attenuated length is the part of the slant path below \(h_R\). A target above the rain layer sees less attenuation and no rain clutter in its own cell.
Rain also returns power: the volume reflectivity from the Marshall–Palmer Z–R relation, \(Z = 200 R^{1.6}\), \(\eta = \pi^5 |K|^2 Z / \lambda^4\), times a resolution cell of \((\pi/4) R^2 \theta_{az}\theta_{el}\,c\tau_c/2\).
Terrain and line of sight¶
Terrain height is procedural fractal noise (octaves, persistence and lacunarity are configurable) plus optional Gaussian peaks of 10 km standard deviation. The same function feeds the RHI profile, the 3D view and the line-of-sight test.
Line of sight marches along the straight ray from radar to target. Heights in a scenario are altitudes above the curved surface, so at ground distance \(d_1\) from the radar and \(d_2\) from the target the ray must clear
the Earth bulge of the 4/3-radius model (Skolnik 2008, §2.12). A masked target gets no SNR and cannot be detected; the event log records when it becomes masked and when it reappears.
Validity¶
- Propagation is straight-line with the standard 4/3 Earth; ducting and multipath lobing are not modelled.
- P.676 is used along a horizontal path at the given pressure and temperature; slant paths through the atmosphere are not integrated layer by layer.