After several months of development and detailed validation, TERA now provides a full-wave solver using the Method of Moments (MoM) to model terrain impact on antennas.
MoM is the method used to solve Maxwell's equations to calculate the radiated field from an antenna over real terrain. The real terrain uses a terrain profile constructed from Digital Elevation Models for a specific location. In the United States, this data comes from the USGS and is currently derived from the 1/3rd arc-second data giving a resolution of ~10m. International locations use the ASTER dataset of 1 arc-second, approximately 30m resolution.
MoM is the same method used in antenna modelling software like EZNEC or 4nec2, which are built on the Numerical Electromagnetics Code (NEC - the family is now at NEC-5). Applied to antenna modelling, NEC starts by segmenting wires/elements of the antenna into pieces a tenth of a wavelength or smaller, then solves for the current in each segment subject to the condition that the total E-field, tangential to a conducting surface is zero. Once calculated, the currents allow the radiated field of the antenna to be derived.
TERA applies the same technique to the ground. The terrain profile is segmented into small pieces, and instead of forcing the tangential E-field to zero, each segment carries an impedance boundary condition - the Leontovich condition, derived from the ground's electrical constants, relating the tangential field to the current induced on it. MoM solves for those induced terrain currents, and the scattered field they radiate combines with the antenna's direct field to give the pattern over real terrain. The antenna itself is treated as an illuminating source rather than being co-solved with the terrain.
MoM converges on the exact solution as the segments get smaller. The error introduced by chopping a continuous surface into discrete pieces falls towards zero as the pieces get smaller. In practice, you keep reducing the segment size until the result stops changing. TERA is converged at 10 segments per wavelength - the pattern is unchanged from λ/7.6 through λ/40.
Up until now, the Ham Community has used ray-tracing software like ARRL's HFTA to assess the impact of terrain on the far-field of an antenna. Ray-tracing uses a combination of Geometrical Optics (reflection) and the Uniform Theory of Diffraction (UTD) to examine the impact of terrain. UTD works by treating every terrain feature as an edge that bends the wave around it. Its accuracy depends on how closely the ground resembles the ideal wedges on which the theory was built. In essence, the feature is large relative to a wavelength, straight, and viewed from a sensible angle. When the terrain cooperates, it's fast and frequency independent. When it doesn't, for example with closely spaced features, rounded ridges, anything approaching a wavelength in size, the error is set by the terrain features themselves and no amount of extra computing improves it.
Frequently these errors stack up in terrains of particular interest to Hams, hill top locations with steep down slopes.
MoM makes none of these assumptions. It takes the terrain as it comes, chops it into small pieces, and solves for the current induced on each one of them. Interactions between features fall out of the solution rather than having to be added term by term. Where UTD's error comes from how well the terrain matches the theory, MoM's is set by how finely the terrain is segmented.
Fortunately this is a choice we can make. Make the pieces small enough and the answer stops changing. The penalty is in computer resources - memory and processing requirements. For example, double the frequency and you double the segment count, quadruple the memory and take roughly eight times longer to solve. With today's processing power and memory capacity, TERA solves a single bearing in a couple of seconds. A full 360-degree sweep runs as a background task as it can take many minutes.
None of this would matter if the results weren't right. The past several months have been heads down on validation, using two separate paths.
The first is checking the solver against problems that have an exact answer. A cylinder, a semicircular "bump" (known as a "boss" in the EM world) on a ground plane. The answer is known and published, so you can measure exactly how far off you are.
The second came from Dr Jim Breakall. A 1994 LLNL report by Gerald Burke, who co-authored the NEC codes at Lawrence Livermore. It has never been published, and I'm checking whether I can post it here. Burke worked the same problem with the same class of method as TERA. He covered the Cedar Valley terrain where Breakall made his field measurements. Burke's results are printed in that report as figures. TERA reproduces the pattern shapes across all 32 cases, and on the horizontal cases the base to summit ratios agree to a fraction of a dB.
TERA is live at K6TU.NET. There's a generous free tier, so run your own location and see what your terrain is doing.