Orbital Thermal Hotspot Detector

Orbit & Sensor

Orbital altitude 400 km

Footprint (GSD): 2.40 km/pixel

Surface (true, sub-pixel)

Vent / flow temperature 1150 K

Active hot-area radius 0.40 km

Planetary background temp 220 K

No thermal anomaly above noise floor

Sensor Readout — Hottest Pixel

Apparent T (T_app)

— K

Retrieval bias

— K

Radiant heat flux Q

— MW

Effusion rate est.

— m³/s

Sub-pixel hot fraction

— %

Sensor grid

—

How it works

An orbiting thermal-infrared sensor never resolves a lava flow directly — it reports one averaged radiance per pixel, and a pixel's footprint on the ground (its Ground Sample Distance, GSD) grows with altitude:

GSD ≈ altitude × IFOV   (IFOV = instrument's angular pixel size)

Each real surface emits thermal radiance following the Stefan–Boltzmann law, L = σT⁴. When a pixel's footprint contains both hot lava (fraction f, temperature T_hot) and cool background (fraction 1−f, temperature T_bg), the sensor measures the area-weighted radiance, not the area-weighted temperature — this is the classic "mixed pixel" or two-component thermal model used in real volcano-monitoring satellites (MODIS/MODVOLC, ASTER, Galileo NIMS on Io):

L_pixel = f·σT_hot⁴ + (1−f)·σT_bg⁴
T_app   = (L_pixel / σ)^(1/4)   ← what the sensor "sees"

Because temperature enters as a 4th power, even a small hot fraction dominates the radiance budget — but a single retrieved T_app is always a compromise between T_hot and T_bg, never the true vent temperature. That gap (T_hot − T_app) is the retrieval bias shown live: shrink the hot-area radius or fly higher (bigger GSD) and the bias grows, exactly as it does for real distant/small eruptions.

Observatories then work backward from the excess radiance to estimate how much lava is erupting, using the hot area's true (not pixel-diluted) radiant power and a simplified thermal-balance proxy for effusion rate (after Pieri & Baloga 1986; Crisp & Baloga 1990):

Q  = ε·σ·A_hot·(T_hot⁴ − T_bg⁴)          [W]  radiant heat flux
V̇  ≈ Q / [ρ·(cₚ·ΔT + c_L)]                [m³/s]  effusion-rate estimate

using representative basaltic-lava constants ε≈0.95 (emissivity), ρ=2600 kg/m³, cₚ=1150 J/kg·K, ΔT≈150 K (eruption to solidus), and latent heat of crystallisation c_L≈4×10⁵ J/kg.

Orbital altitude — sets the sensor's GSD; higher orbit = coarser pixels = more thermal dilution.
Vent/flow temperature & hot-area radius — the true (unobservable) state of the eruption.
Background temperature — the planetary body's ambient surface, e.g. ≈110 K on Io, ≈210 K on Mars, ≈730 K on Venus.

The 3D view shows the true continuous heat field on the surface and the coarser sensor pixel grid floating above it, each tile coloured by what the sensor actually retrieves.

Hottest / most radiant Cold background

orbiting sensor
400 km

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