MASINDE MULIRO UNIVERSITY OF SCIENCE AND TECHNOLOGY

Department of Electrical & Communication Engineering

GROUND WAVE COMMUNICATION

Surface-Wave Propagation over the Earth

Course: ECE 523E — Antennas & Radiowave Communication
Level: 5^th Year, Electrical & Communication Engineering
Topic: Ground Wave Communication — Mechanisms, Ground Effects & Link Design

Learning Objectives

By the end of this lecture the student should be able to:

Explain the physical mechanism of ground-wave (surface-wave) propagation, including wave tilt and the role of ground currents.
Distinguish the ground wave from the space (LOS) wave and the sky wave, and identify the frequency bands in which each dominates.
Describe the composition of the ground wave near the surface: direct, ground-reflected and surface-wave components.
Quantify ground-wave attenuation using the Sommerfeld–Norton attenuation factor and ground constants (σ, ε_r).
Analyse the effects of frequency, ground conductivity/permittivity, and antenna polarisation and height on coverage.
Apply ground-wave field-strength relations to practical link-design problems (e.g. MF broadcast service planning).
Describe special ground-wave systems: LF/MF broadcasting, VLF earth–ionosphere waveguide links to submarines.

Fig. 1 — The ground wave is guided along the curved earth — the only natural mechanism that carries MF and LF signals reliably beyond the horizon.

Radio-Wave Propagation Modes — Recap

Fig. 2 — The three basic propagation modes: (a) ground wave, (b) space (line-of-sight) wave, (c) sky wave.

Mode	Band	Range
Ground wave	VLF, LF, MF (3 kHz – 3 MHz)	~50 km – 1000+ km (sea)
Sky wave	HF (3–30 MHz)	100 km – intercontinental (ionosphere)
Space (LOS) wave	VHF and above (> 30 MHz)	Line of sight only

At frequencies below ~2 MHz the ground wave is the only dependable mode — the ionosphere is too lossy/absorbing for reliable skywave at VLF/LF and antennas are too low for a space wave. This is why MW broadcasting (530–1700 kHz) works the way it does.

The ground wave is independent of ionospheric conditions — no fading, no diurnal collapse — but it is strongly dependent on the electrical properties of the terrain.

What is the Ground Wave?

Definition

A ground wave (or surface wave) is a radio wave that propagates in contact with the Earth's surface, guided by it. Its wavefronts remain perpendicular to the surface and continuously tilt forward, so energy is progressively redirected along the ground instead of escaping vertically.

Two complementary views

Diffraction view: the wave diffracts around the curved earth; for λ comparable to obstacle size, the wave "hugs" the surface (analogous to sound hugging a wall).
Sommerfeld surface-wave view: the finitely conducting ground carries induced currents that re-radiate; the resulting guided mode travels with its E-field tilted forward, with a small continuous power flow into the ground (which is the source of attenuation).

Key consequence: the ground wave decays approximately as 1/d² in field strength beyond the "numerical distance" — much faster than free space (1/d) — but still reaches hundreds of km at MF, and ~1000+ km at VLF over sea water.

Fig. 3 — Ground-wave propagation over a spherical earth: the wavefront tilts progressively so the energy follows the curvature of the surface.

The Wave-Tilt Mechanism

Fig. 4 — Sommerfeld surface wave over lossy ground: the E-field leans forward by the wave-tilt angle τ; induced ground currents re-radiate the wave along the surface.

Why the E-field tilts

Over a perfect conductor, the tangential E-field at the surface must vanish — E is purely vertical, and the wave slides along losslessly.
Over real (lossy) ground, a finite tangential component E_x exists: the resultant E tilts forward by the wave-tilt angle τ.
The Poynting vector S = E × H acquires a small downward component → continuous energy absorption by the ground → attenuation.

Wave tilt (low-loss approximation): tan τ ≈ 1/√(ε_r² + (60 λ σ)²) · (appropriate component ratio)
τ grows with λ and with poorer ground — low frequencies and good conductivity give the smallest tilt and the least loss.

Takeaway: vertical polarisation is essential. A horizontally polarised wave has its E-field parallel to a lossy ground and is shorted out within a wavelength or so. All ground-wave systems therefore use vertical antennas.

Composition of the Ground Wave Near the Surface

Three components at the receiver

Direct wave — travels in free space from TX to RX.
Ground-reflected wave — reflected at grazing angle ψ with coefficient R_v ≈ −1 near grazing (phase reversal!).
Surface wave — the Sommerfeld guided mode travelling along the interface.

Why the reflected wave nearly cancels

For small grazing angles the path difference Δ ≈ 2h₁h₂/d and the reflection phase is ~180°, so direct and reflected components largely cancel when h₁, h₂ are small compared with λ. The surface wave then dominates — it does not cancel because it exists only by virtue of the ground currents.

Practical consequence: raising antennas does not extend ground-wave range much. Ground-wave systems deliberately use low antennas (λ/4 monopole at ground level) rather than elevated arrays.

Fig. 5 — Flat-earth picture of the ground wave: direct ray, ground-reflected ray (image method, phase reversal at grazing) and the surface wave along the interface.

Electrical Constants of the Ground

Ground-wave behaviour is governed by the surface conductivity σ and relative permittivity ε_r. The ground enters the theory through the complex dielectric constant:

ε_c = ε_r − j·60·λ₀·σ (λ₀ in metres, σ in S/m)

Surface	σ (S/m)	ε_r	Ground-wave quality
Sea water	≈ 5	80	Excellent — transoceanic VLF/MF ranges
Fresh water	≈ 0.01	80	Fair
Good soil (clay/loam, wet)	0.03 – 0.01	15 – 30	Good
Average soil	≈ 0.01	15	Moderate — typical broadcast basis
Poor/rocky/sandy ground	≈ 0.001	5 – 10	Poor — severe attenuation
Urban/industrial areas	0.001 – 0.01	5	Poor, plus high man-made noise

Real-world planning uses conductivity maps (ITU-R / national regulator data): a coastal AM station reaches far over water paths but poorly inland over rocky terrain.

How the constants enter

At VLF/LF, 60λσ ≫ ε_r → conduction currents dominate; the ground behaves like a lossy conductor; sea water is superb, land is poor.
At MF, both terms matter; the 60λσ term still usually exceeds ε_r over land.
The numerical distance p = b·d of Sommerfeld theory is small for high σ and low f → slower attenuation.

Attenuation factor (Norton, flat earth):
F ≈ 1 for p ≪ 1; |F| ≈ 1/p for p ≫ 1 (field ∝ 1/d²)

Curves on the next slides are illustrative textbook curves generated with this standard transition behaviour.

Sommerfeld–Norton Ground-Wave Theory

The attenuation factor F

For a short vertical antenna over flat lossy ground, the ground-wave field is written as:

E_gw = E_fs · F(p), where E_fs = (300√P_kW·√G) / d_km mV/m
p = b·d = numerical distance

Norton's classical result for the attenuation function (vertical polarisation):

F = 1 − j·√(πp)·e^−p·erfc(j√p)

Limits worth memorising

p ≪ 1: F ≈ 1 → field follows free-space 1/d law.
p ≫ 1: |F| ≈ 1/(2p) → field ∝ 1/d², i.e. 12 dB more loss per distance decade than free space.

Numerical distance

p = b·d, b ∝ (1/λ) · f(ε_r, σ, λ) — smaller for low f and high σ

p ≈ 1 is reached within a few km on MF land, but only after hundreds of km over the sea → sea paths enjoy near-free-space behaviour much farther out.
Spherical-earth corrections (Bremmer, van der Pol) extend the flat-earth theory for ranges beyond ~50–100 km.

Standard prediction tools

ITU-R Recommendation P.368 — worldwide ground-wave field-strength curves (1 kW, vertical polarisation) as functions of distance, frequency and ground type.
FCC / ITU MF broadcast coverage methods based on these curves.

Note for the exam: all standard ground-wave curves are quoted for vertical polarisation, 1 kW radiated power — learn to rescale with 20·log(d) and 10·log(P).

Effect of Frequency on Ground-Wave Range

Fig. 6 — Field strength vs distance at three frequencies over average land. Beyond the transition point the ground wave falls off as 1/d² — much steeper than free space (dashed).

Reading the curves

All curves merge with the free-space line close in (p ≪ 1).
The breakaway point moves closer to the transmitter as frequency rises — higher frequencies are absorbed by the ground much sooner.
Rule of thumb over average land: usable ground-wave range scales roughly as 1/f. Halving the frequency roughly doubles the range.

At 0.3 MHz (LW): range ~ several hundred km
At 1 MHz (MW): range ~ 100 km
At 3 MHz: range ~ 20–30 km only

This is the physical reason the spectrum below 3 MHz is reserved for long-range broadcasting and maritime services, while short-range ground links at HF use elevated antennas and rely on the space wave.

Effect of Ground Conductivity

Reading the curves

At a fixed frequency (1 MHz shown), conductivity changes the range dramatically: sea water gives ~300 km, average land ~100 km, poor rocky ground ~20–30 km, for the same field-strength threshold.
The transition to the 1/d² region happens quickly over lossy ground; over sea water the wave behaves almost like free space for hundreds of kilometres.
Seasonal and weather effects: wet soil conducts better — coverage improves after rains and in wet seasons; dry frozen ground is lossy.

Directional planning example: a coastal MW transmitter radiating seaward reaches 3–5× farther over the water path than over land in the opposite direction — used to shape broadcast coverage.

A ground conductivity survey is part of the site-selection process for MF broadcasting stations.

Fig. 7 — Field strength vs distance at 1 MHz over four ground types. Higher conductivity dramatically extends the range before the 1/d² fall-off dominates.

Range vs Frequency & Service Allocation

Fig. 8 — Coverage range to a 0.3 mV/m threshold vs frequency, for sea and average-land paths, with the principal ground-wave service bands marked.

How the bands are used

Band	Frequency	Typical ground-wave use
VLF	3–30 kHz	Worldwide submarine/military messaging via earth–ionosphere waveguide
LF	30–300 kHz	Long-wave broadcasting (Europe), time signals (DCF77 77.5 kHz, WWVB 60 kHz), NDB beacons
MF	300 kHz–3 MHz	AM/MW broadcasting (530–1700 kHz), maritime NAVTEX 518 kHz, aeronautical NDB
HF (low end)	3–5 MHz	Short-range (~20 km) ground-wave fill in tropical/over-horizon gaps

Design rule: choose the lowest frequency the allocation and bandwidth allow, then maximise radiated power and ground conductivity (radial systems) — the range then follows from the curves.

Fresnel Reflection & the Brewster Angle

Why grazing launch is best

The ground-reflected component is controlled by the Fresnel coefficient R_v. At grazing incidence (ψ → 0) R_v ≈ −1: full cancellation of the direct wave at low antenna heights.
As ψ increases toward the Brewster angle, |R_v| dips sharply (the dip is deep for good dielectric ground) — the reflected wave nearly vanishes, so little energy is lost into the ground and low-angle radiation survives.

Brewster condition (lossy ground, low frequencies): tan ψ_B ≈ 1/√(ε_r² + (60λσ)²) — only a few degrees for typical ground

Engineering consequences

Vertically polarised waves launched at very low angles benefit from the Brewster dip — the ground becomes almost transparent at that angle.
Horizontal polarisation has no such benefit near grazing (R_h ≈ −1 for all small angles) — another reason ground-wave systems use vertical polarisation.

Fig. 9 — |R_v| vs grazing angle for three ground types at 1 MHz. The deep Brewster-angle minimum (marked by the dip) is what allows low-angle vertically polarised waves to travel with minimum ground loss.

Antennas for Ground-Wave Systems

Fig. 10 — (a) λ/4 vertical monopole on a radial ground system: the ground screen carries the return currents with low loss and the image antenna doubles the effective height. (b) The elevation pattern peaks along the horizon — the ideal ground-wave launcher.

Requirements

Vertical polarisation (E-field normal to ground).
Low-angle radiation — maximum field along the horizon, little energy wasted at high elevation angles.
Low base resistance & efficient ground return.

Practical antennas

λ/4 monopole over a ground plane of ~120 buried radials (broadcast standard); pattern max at horizon, null overhead.
Top-loaded / T- and L-antennas at VLF/LF where a full λ/4 is physically huge (25 km at 3 kHz!) — loading coils plus capacitive top hat.
Broadcast towers often radiate against an extensive radial field; ground-screen mesh under the tower base.

The image antenna theory of the monopole: a λ/4 monopole over perfect ground radiates like a λ/2 dipole with twice the radiation resistance — but only if the ground system is good enough to enforce the image.

Ground Wave vs Sky Wave: the MF Day/Night Coverage Pattern

Daytime

Only the ground wave is usable: the D-region absorbs the MF sky wave by day.
Coverage = clean, stable disk out to ~100 km (land) — precisely the ground-wave range from the curves.

Night-time

D-layer disappears → MF sky wave returns from the E-region → distant reception out to hundreds–thousands of km.
A skip zone opens between the ground-wave edge and the first sky-wave return.
Co-channel interference from distant skywave stations forces broadcasters to reduce power or use directional arrays after sunset.

The ground wave is the stable reference service; the night-time sky wave is a bonus (or an interference problem) — this asymmetry shapes the entire MF broadcast industry.

Fig. 11 — Schematic MF coverage: the ground-wave disk (blue) is present day and night; at night the sky wave (orange) arrives beyond a skip zone, extending — and complicating — coverage.

Special Case: VLF and the Earth–Ionosphere Waveguide

Fig. 12 — (a) VLF energy is trapped in the waveguide formed by the earth and the ionosphere, propagating with very low attenuation worldwide. (b) In sea water the VLF field decays with a skin depth of only ~2 m — submarines must trail an antenna just below the surface.

Why VLF reaches so far

At 3–30 kHz the wavelength (10–100 km) is comparable to the ionosphere height (~90 km), so the earth and ionosphere act as a parallel-plate waveguide.
Waveguide modes propagate with attenuation of only ~1–3 dB per 1000 km — signals circle the globe; worldwide coverage from a single ~1 MW transmitter.
Stable, penetration of seawater to tens of metres — the only practical way to reach submerged submarines.

Limitations

Enormous antennas (km-scale), huge transmitter powers (~1 MW), and bandwidth of only ~10–100 Hz → data rates of a few baud to ~100 bit/s.
Used for one-way broadcast of orders to submerged fleets; submarines trail long wire antennas near the surface to receive.

Worked Example — MF Ground-Wave Link Design

Problem. A 1 kW, 1 MHz AM transmitter with λ/4 monopole (G ≈ 3) serves average land (σ = 0.01 S/m, ε_r = 15). Find the field strength at 50 km and the ground-wave service range to a 0.3 mV/m threshold.

Step 1 — free-space field

E_fs = 104.8 + 10log(1) − 20log(50) = 70.8 dBµV/m

Step 2 — attenuation factor

Numerical-distance scale for this ground: d_c ≈ 18 km (from the σ/ε_r model). At 50 km, d/d_c = 2.8:

|F| = 1/√(1 + 2.8²) = 0.34 → −9.4 dB

Step 3 — ground-wave field

E ≈ 70.8 − 9.4 ≈ 61 dBµV/m ≈ 1.1 mV/m — strong signal

Step 4 — service range

Set E = 50 dBµV/m and solve: at 100 km, E_fs = 64.8 dBµV/m, |F| = −15.0 dB → E ≈ 49.8 dBµV/m ≈ 0.31 mV/m.

Ground-wave service range ≈ 100 km

Comparison cases

Same station over sea water: range ≈ 300 km to the same threshold.
Over poor rocky ground: range falls to ≈ 25–30 km.
Doubling frequency to 2 MHz (all else equal) roughly halves the range.

Class exercise: Estimate the range of a 500 W, 600 kHz transmitter over good soil (σ = 0.03 S/m). (Answer: roughly 250 km to 0.3 mV/m.)

Noise, Variability & Link Behaviour

What the ground wave does NOT suffer from

No ionospheric fading, no diurnal signal collapse, no skip-zone blackouts — field strength is remarkably stable hour-to-hour and season-to-season.

What it DOES suffer from

Atmospheric noise (worldwide thunderstorm activity) dominates below ~2 MHz — sets the real reception threshold, especially in the wet-season tropics (CCIR noise maps).
Man-made noise (power lines, vehicles, switching equipment) is severe in urban areas — often the limiting factor for MF reception in cities.
Ground conductivity variations: wet vs dry soil, frozen ground, terrain changes along the path — coverage varies with weather and season.
Two-ray fading close in: within a few km of the transmitter, the direct and reflected space-wave components interfere (phase reversal at grazing) producing distance-dependent field oscillations — fades at certain ranges even though average field rises.

Receiving considerations

Receiver location noise figure matters less than the external noise — sensitivity beyond atmospheric noise is wasted.
Ferrite-rod loops (directional, compact) are standard for portable MF receivers; the null can reject an interfering station.

Field-strength planning standards

Context	Typical planning threshold
MF broadcast (urban, good service)	2 – 10 mV/m
MF broadcast (rural, primary)	0.5 – 2 mV/m
NAVTEX / NDB aeronautical	50 – 100 µV/m
VLF submarine reception	µV/m over thousands of km

Exam hint: always compare the predicted field with the noise-limited threshold, not with receiver sensitivity, when assessing ground-wave link quality.

Applications & Representative Systems

System	Frequency	Ground-wave role
AM / MW broadcasting	530–1700 kHz	Primary day coverage disk ~100 km; night coverage complicated by sky wave
Long-wave broadcasting (ITU Region 1)	148–283 kHz	National coverage up to ~1000+ km, stable day and night
Maritime NAVTEX / GMDSS	518 kHz (plus 424 kHz)	Coastal warnings to ~200–400 km over sea paths
Aeronautical NDB beacons	190–1750 kHz	En-route and approach navigation to ~50–100 km
Time & frequency signals (DCF77, WWVB, MSF)	60–77.5 kHz	Continental coverage; indoor reception of time codes
Military VLF submarine broadcast	3–30 kHz	Worldwide one-way orders via earth–ionosphere waveguide
LF RFID, animal ID, key fobs	125–134 kHz	Short-range (<1 m) inductive/surface links
Mine / underground comms	LF/MF	Surface-to-underground through rock with large loops

Why ground wave remains essential in 2026

Complements satellite & HF: works underground, underwater (VLF), in urban canyons, and independent of ionospheric weather.
Simple, cheap receivers — no dish, no pointing: one tower serves an entire region.
Licensed MF bands still carry emergency and safety-of-life traffic (GMDSS, NDB).

Modern twist: researchers now use MF ground-wave "leakage" for passive radar and ionospheric tomography, and LF/MF signals are reference beacons for indoor positioning.

Summary & Key Takeaways

The ground wave is a surface-guided wave: wavefronts tilt forward continuously, induced ground currents re-radiate, and the wave follows the earth's curvature — no ionosphere needed.
It dominates at VLF/LF/MF (3 kHz – 3 MHz); usable range shrinks roughly as 1/f and grows with ground conductivity.
Near the surface the field = direct + reflected (≈ −1 at grazing, cancelling) + Sommerfeld surface wave, which alone survives at low antenna heights.
Field strength: E = E_fs·F(p); p ≪ 1 → 1/d (free-space-like); p ≫ 1 → 1/d². Standard curves: ITU-R P.368.
Vertical polarisation and low-angle radiation are mandatory; the Brewster-angle dip in R_v favours vertically polarised grazing waves.
Antennas: λ/4 monopole on a radial ground system (MF), top-loaded towers (VLF/LF); elevated arrays do not help.
MF coverage = stable ground-wave disk by day; night sky wave extends coverage beyond a skip zone but brings interference.
VLF exploits the earth–ionosphere waveguide for worldwide, seawater-penetrating links at baud-rate speeds.

Exam-style questions to revise

Explain wave tilt and why it forces vertical polarisation for ground-wave systems.
Show that the ground-wave field falls as 1/d² at large numerical distance, and derive the extra loss per decade relative to free space.
A 1 kW, 1 MHz transmitter gives 0.5 mV/m at 80 km over average land. Estimate the field at 160 km, all else equal. (Answer ≈ 0.12 mV/m — the 1/d² region.)
Why can an LW (200 kHz) broadcaster cover a whole country while an FM (100 MHz) station with the same power covers only ~100 km? Ground wave vs space wave.
Explain the day/night coverage pattern of an MF station using both ground-wave and sky-wave ideas.

Next lecture: Skywave communication — ionospheric refraction, MUF and hop geometry (the night-time companion of today's topic).

References & Further Reading

Balanis, C. A., Antenna Theory: Analysis and Design, 4th ed., Wiley, 2016 — Ch. 2–4 (ground-wave propagation, monopoles).
Collin, R. E., Antennas and Radiowave Propagation, McGraw-Hill, 1985 — Ch. 6 (surface-wave and ground-wave theory).
Jordan, E. C. & Balmain, K. G., Electromagnetic Waves and Radiating Systems, 2nd ed., Prentice-Hall, 1968.
Terman, F. E., Radio Engineers' Handbook, McGraw-Hill, 1943 — classic ground-wave curves.
Sunde, E. D., Earth Conduction Effects in Transmission Systems, Van Nostrand, 1949.
Wait, J. R., Electromagnetic Waves in Stratified Media, IEEE Press, 1996 — Sommerfeld/Norton theory.
ITU-R Recommendation P.368 — Ground-wave propagation curves for frequencies between 10 kHz and 30 MHz.
ITU-R P.1321 / P.341 — noise and field-strength definitions used in planning.

QUESTIONS &
DISCUSSION

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