Radar Sounder Link Budget Design Tool

This tool is designed to build intuition about nadir-pointing ice-penetrating radar sounder instruments on novel platforms. Start from a preset below or enter custom system parameters to estimate the expected signal-to-noise ratio (SNR) for a radar sounder imaging the basal interface (bedrock topography or other sub-ice interface) across the Antarctic and Greenland ice sheets.

The most difficult part of building a radar sounder link budget is estimating what happens within the ice. Both attenuation within ice and reflectivity at the ice-bed interface can vary dramatically. This tool uses a statistical model of Required Surface SNR (RSSNR) to estimate the signal-to-noise ratio of a radar sounder across a wide range of possible instrument and platform configurations.

In short, RSSNR provides the expected difference between surface power return and basal power return, after correcting for geometric spreading. Once we have RSSNR, we can calculate the expected bed SNR using only properties of the instrument and its platform (aircraft, UAV, satellite, etc) plus the expected ice thickness.

This tool calculates SNR_surface using a standard radar sounder link budget and then applies the statistical model of RSSNR to estimate basal SNR according to:

SNR_bed  =  SNR_surface  +  Δspreading(d)  −  RSSNR

We treat the surface SNR as fixed (a loose approximation) and only the last two terms vary spatially, through ice thickness (d, derived from BedMachine) and the fitted RSSNR.

Note that these values carry a lot of uncertainty. This is intended as a general tool to build intuition about what systems perform best for what general use cases. Take care and verify local conditions before relying on it for specific predictions.

Detailed assumptions

Coherent Fresnel-zone summation. A 1/R² radar equation, assuming returns add coherently over the first Fresnel zone.
Azimuth gain is evaluated at the surface Fresnel zone, which is mildly conservative (especially at low altitudes).
RSSNR includes no estimate of frequency-dependence, which may bias results when the center frequency is far from the frequency of airborne radar sounders represented in OPR.
Pulse-compression gain cancels inside RSSNR — it applies to the surface and bed returns alike — so it is added back once here, for the bed.
The noise floor is sky-dominated at VHF. Antenna temperature defaults to the galactic background (ITU-R P.372) — ≈3700 K at 60 MHz — or 270 K, whichever is higher.
Clutter is not modelled. Where the ice is thin enough that the bed echo returns before the pulse ends, the tool charges the bed for the compressed surface return's sidelobe pedestal — but surface roughness scatter arrives over the same delays and is often larger. The overlap penalty is a lower bound on the interference, not the whole of it.
The model has real uncertainty ( cross-validated RMSE). The 20th-percentile layer and the posterior-predictive distributions both carry it; the median layer does not.

1 Start from a preset

2 Adjust the parameters fields marked auto are derived from the ones above them; type in one to override it

Platform

Altitude above surface m Ground velocity m/s

Power budget

Power available to payload W Power amplifier efficiency – Peak transmit power W

Pulse timing

Max ice thickness for PRI m Pulse length µs Pulse repetition interval µs

Center frequency MHz Bandwidth MHz Transmit antenna gain dBi Receive antenna gain dBi System losses dB Receiver noise figure dB Antenna noise temperature K Surface reflectivity dB

Processing

Azimuth integration distance m Radar equation Equation numbers from Haynes et al. (2018). Surface / bed overlap Receive weighting Relative permittivity of ice –

3 Results

Link budget

Expected basal SNR

Antarctica

Greenland

Outlines from the BedMachine mask. Gray fill marks areas below 0 dB predicted basal SNR.

Distributions

Histogram of basal SNR (area-normalised)

Fraction of ice-sheet area above a given basal SNR