B-X5 · Radio sounding

Radio Echoes from the Ionosphere

Why does a radio echo suggest a higher layer than the height where the wave actually turns? A pulse slows as it enters the plasma. Converting its round-trip delay into a height with the vacuum speed of light therefore places the apparent reflection above the actual turning point.

Send a radio pulse into an electron layer and follow its return or escape. Sweep the frequency, record the echo delays and compare the virtual height with the true turning height.

01 / Explore the path

Make the echo disappear. Then bring it back.

Frequency and direction decide whether a pulse turns or escapes. Start with a comparison, then change one setting.

Choose the radio pulse

Transmitted frequency

f/\mathrm{MHz}

6

Launch angle from vertical

\theta_0/\mathrm{deg}

0

In the source view, drag the gold handle to steer. The angle is measured from vertical.

Shape the electron layer

Peak electron density

N_m/(10^{12}\,\mathrm{m}^{-3})

1

Layer bottom height

z_b/\mathrm{km}

150

Layer half thickness

H/\mathrm{km}

100

Changing density or geometry clears the sweep. A different frequency or angle keeps your previous measurements.

Automatic preview · pulses shown in slow motion; no sweep is recorded.

Drag the scene to orbit. Select a label to look closer. Gold rings follow group travel time; their size and the antenna hardware are enlarged.

This is an ideal cold, unmagnetized, collisionless plasma with one flat parabolic density layer and fixed ions. Paths and narrow-band group delays follow geometrical optics. Density is illustrative. Earth curvature, polarization splitting, absorption, antenna response, irregularities, multiple layers and hops, finite pulse bandwidth and full-wave cutoff scattering are omitted. The data are simulated forward predictions, with no measured amplitudes or density-profile inversion. They cannot forecast a real radio link.

02 / Measure the delay

The echo is a clock. Is it also a ruler?

Keep the real turning point beside the height inferred from time. The plasma makes those two answers different.

Peak plasma frequency

\text{—}

True turning height

\text{—}

Round-trip delay

\text{—}

Virtual height or slant range

\text{—}

Ground landing distance

\text{—}

Record a vertical frequency sweep

Send 45 narrow-band test pulses and keep every return or missing echo. Click a recorded ionogram point to launch that frequency again.

The electron layer behind the echoes

The profile is the same one shown in the 3D cutaway. Gold marks the selected ray’s true turning height.

What the delay measures

For a vertical sounding, the vacuum light speed turns half the travel time into a virtual height. At an oblique angle that same quantity is a virtual slant range. The true turning height follows the plasma density and the conserved horizontal wave number.

h'=\frac{c\tau}{2}\quad(\theta_0=0),\qquad n^2(z_t)=\sin^2\theta_0

At the exact critical limit this ideal parabolic ray takes indefinitely long to turn. Near a cutoff, real finite-bandwidth pulses need a full wave calculation. This forward simulation does not infer an unknown density profile from field measurements.

Sources and reading scope

NOAA NCEI · Vertical Incidence Soundings
Read the short institutional introduction about virtual height and critical-frequency traces. No archived image is used as this simulation’s data.
UKSSDC · Basic ionosonde theory
Read the introductory density, frequency and group-delay discussion. Magnetic mode splitting is outside this model.
R. Fitzpatrick · Waves in unmagnetized plasmas
Read equations 9.27–9.35 for the cold-plasma dispersion and group speed. The parabolic-layer solution is derived for the stated profile.

Start with the essentials

Focus question: Why does a radio echo suggest a higher layer than the height where the wave actually turns?
One-sentence intuition: The group delay measures a virtual height; the turning point belongs to the density profile and the selected frequency.

Core mathematical model

The plasma changes the wave speed

\omega^2=c^2|\mathbf{k}|^2+\frac{N_e e^2}{\epsilon_0m_e},\qquad v_g=cn<c

This cold unmagnetized plasma law gives the group speed of a narrow-band pulse. The phase speed is different.

Horizontal symmetry fixes the ray

p=n\sin\theta=\sin\theta_0,\qquad n^2(z_t)=p^2

Angles are measured from vertical. Horizontal wave number stays fixed; the vertical component reaches zero at the turn.

Delay gives a virtual height

h'=\frac{c\tau}{2},\qquad \tau=\frac{2}{c}\int_0^{z_t}\frac{dz}{\sqrt{n^2(z)-p^2}}

The height definition applies to vertical soundings. For oblique paths half the light-speed delay is a virtual slant range.

An oblique wave can return at a higher frequency

f_m=\frac{1}{2\pi}\sqrt{\frac{N_m e^2}{\epsilon_0m_e}},\qquad f_{\mathrm{threshold}}=\frac{f_m}{\cos\theta_0}

This secant-law threshold assumes a flat, single layer. Its equality is an infinite-delay limit in the ideal parabolic ray model.

Common difficulties

Virtual height and a mirror

Typical misconceptionThe ionogram shows where a physical reflecting surface sits.

Better mental modelThe electron density changes continuously. A pulse bends and slows along its path; its travel time alone does not give the true turning height.

A cutoff and a working radio link

Typical misconceptionA returning path guarantees a usable signal at its landing point.

Better mental modelThis model calculates paths and delays. Absorption, antenna patterns, noise and a real receiver determine signal strength and practical availability.

Run the experiment

01
Start with a vertical echo
Select “A vertical echo” and press “Launch pulse”. Compare the true turning height with the virtual height.
What to observe: The pulse returns to the same sounder. The virtual height is larger because propagation slows inside the layer.
02
Record an ionogram
Press “Acquire vertical sweep”. Increase peak density and repeat. Export the CSV to inspect each simulated delay.
What to observe: The return limit moves upward with the square root of peak density. The trace bends to long delays near the limit.
03
Change only the direction
Compare the two 9 MHz presets. Open the turning-point view after the oblique launch.
What to observe: The vertical ray penetrates; the oblique ray turns and reaches a distant ground point. Its delay is labeled as slant range.