Antennas on a levee: modelling real terrain

Every ground model on the workbench — Sommerfeld, reflection-coefficient, PEC — shares one assumption so basic it’s easy to forget it’s there: the ground is an infinite flat plane at the antenna’s feet. For a suburban backyard that’s fine. But plenty of the best antenna sites are good precisely because the ground is not flat — a hilltop, a bluff over the sea, a ridge. This example works one real site end to end and shows that no flat model, at any height, tells the truth about it — then does it properly with the faceted-terrain ground.

The site

A 20 ft (6.1 m) mast stands on a levee crest 10 ft (3 m) wide with ~20° slopes. One side drops 35 ft (10.7 m) to fresh water; the other drops 25 ft (7.6 m) to farmland. An inverted-V for 20 m through 10 m hangs from the mast.

The question every model must answer is: how high is this antenna? And the honest answer is: it depends which direction you ask. Straight up, it’s 6.1 m over soil. Toward the water at a low angle, the reflection happens off the water surface far below — the antenna is effectively 16.8 m high over water. Toward the land, 13.7 m over soil. One antenna, three heights, two grounds.

Geometry says which surface governs at each elevation angle — the specular reflection point walks outward from the mast as the angle drops:

elevation of departure	reflecting surface	effective model
above ~76°	the crest itself	6.1 m over soil
~30–76°	the slopes	transition (tilted facets)
below ~30°	the water / the plain	16.8 m over water / 13.7 m over soil

The band that matters for working distant stations — the lowest one — never touches the ground the mast stands on.

Two flat models, both wrong

Model the site flat at mast height (6.1 m over soil) — what the workbench does by default — and on 15 m the solver reports a broad lobe peaking 5.9 dBi at 36° elevation. Model it flat at the water-side effective height instead (16.8 m over water) and you get the textbook low antenna-over- water pattern: a fine 8.1 dBi lobe at 12°, then deep interference nulls at 25° and 60°.

The terrain model — same inverted-V, same mast — says the truth is neither:

elevation	terrain (water side)	flat 6.1 m/soil	flat 16.8 m/water
4°	0.9	−8.1	1.9
9°	6.2	−1.5	7.3
13°	7.1 (peak)	1.3	8.1
30°	−0.2	5.7	0.6
36°	−1.3	5.9 (peak)	≈6
75°	2.2	2.2	3.1

(15 m, dBi along the elevation cut toward the water.)

Read the two failure modes off the columns:

• The flat-at-mast-height model misses the entire DX story. At 9° — a workable one-hop angle on 15 m — it reports −1.5 dBi; the real site has 6.2 dBi there, nearly 8 dB more. Worse, its confident 36° “main lobe” points at a part of the sky where the real pattern is 8 dB below its own peak. Aim your expectations by this model and you’ll credit the wrong propagation for every contact.
• The flat-at-effective-height model gets the low angles nearly right (within ~1 dB below 15°) — that’s why the effective-height rule of thumb survives — but its multipath structure above ~20° is fiction: the ±10 dB swings at 25°/45°/60° assume the same water plane extends under the mast, and it doesn’t. The high-angle sky (short skip, NVIS-ish work) is governed by the crest at 6.1 m, which this model can’t see.
• Above ~76°, all three columns agree — exactly where the validity table said the crest governs. The terrain model contains both flat models, each in the band where it’s honest.

The levee’s asymmetry survives too: at 4° the water side carries ~1.8 dB more than the land side, and the first-lobe angles differ (water 18.5°→8.9°, land 22.9°→10.9° across 20→10 m) — none of which any single flat model can express.

What the terrain model actually does

The faceted terrain describes the surface around the site as a piecewise-linear height profile per azimuth sector, each facet carrying its own medium (εr, σ). It is deliberately a far-field model:

• The current solve stays flat. Soil and water can’t be wire-gridded — only conductors can — so the impedance/current solution runs over a flat Sommerfeld ground with the crest facet’s medium. That’s physically defensible because near-field ground interaction is crest-local, and it’s what keeps terrain solves exactly as fast as flat ones.
• Each far-field ray reflects off its own facet. Per direction, the model finds the facet the specular point lands on, tilts the incidence angle by the facet’s slope, applies that facet’s Fresnel coefficients, and adds the facet’s height offset to the reflected path phase — which is how the antenna “gets taller” toward the drops.
• What it doesn’t do: no diffraction over the crest edge, no surface roughness, no multiple bounces. It’s a specular model — trust it for lobe positions and the first-order asymmetry, not for field strength deep in a shadow.

It’s cross-checked against an independent implementation: NEC-2’s two-medium cliff (GD card) agrees with the equivalent single-cliff terrain to within a constant ~0.1 dB from 3° to 60° elevation. (If you try that comparison yourself, mind the trap: NEC-2 silently ignores GD under the normal RP 0 pattern request — the cliff only reaches the pattern in RP modes 2/3/5/6.) A degenerate single-flat-facet terrain reproduces the plain finite ground bit-for-bit, so switching the feature on costs nothing when the ground really is flat.

Driving it

In the simulator: ground plane → terrain, then pick the levee preset (crest width, slope, the two drops, water bearing), cliff (edge, drop, bearing, arc), or hillside (a bench on a slope — flat width, uphill slope, downhill slope; no bottom reference exists or is needed, since the slope itself is the reflector). The elevation cut’s bearing dial uses the same azimuth convention as the water bearing, so leaving both at 0° slices straight through the asymmetry; pin the pattern on a flat ground first and the ghost overlay shows exactly what the facets change. Both engine families run it — momwire natively, PyNEC as a hybrid (NEC solves the currents over the crest-medium Sommerfeld ground, the server applies the facet far field to those currents).

In Python, the same two presets plus arbitrary profiles:

from antennaknobs.engines.momwire import MomwireEngine
from antennaknobs.terrain import levee_terrain

terrain = levee_terrain(
    crest_width=3.0, slope_deg=20.0,
    drop_water=10.67, drop_land=7.62,
    water=(80.0, 0.005), land=(13.0, 0.005),
    water_azimuth=0.0,               # +x faces the water
)
eng = MomwireEngine(builder, ground=("terrain", terrain))

cliff_terrain(...) builds the single-drop case, hillside_terrain(...) the bench-on-a-slope, and the underlying Terrain(sectors=(Sector(..., facets=(Facet(...), ...)),)) dataclasses accept any piecewise profile per azimuth sector — a gully on one bearing, a rising hill on another — as long as each sector’s last facet extends to infinity and all sectors agree on the crest medium (it’s the impedance ground).

When to reach for it

Flat ground is still the right default — terrain adds information only when the site has real relief within a few wavelengths of the mast. The strongest signals that it’s worth switching on: the ground falls away in the directions you care about (the flat model is understating your low-angle gain), the drop-off differs by direction (no single flat model can be right), or land meets water (the media differ as much as the heights). And keep the model’s scope in mind: it sharpens where the lobes point; it does not model what happens behind a hill.