Thermal IR Band 7: brightness temperature and hotspots

This is the foundational thermal-detection layer that every modern launch-detection and wildfire-detection system builds on, taught from the ground up. By the end of this week you'll have a working thermal hotspot detector that operates on real NOAA GOES-18 NetCDF files — the same public input and the same first-principles physics that any operator (LaunchDetect, NOAA HMS, NASA FIRMS, JMA) starts from before they layer their own discrimination, scoring, and gating logic on top.

Band 7 and the Planck function

GOES-R ABI Band 7 is centered at 3.9 µm. The level-1b (calibrated radiance) data product reports radiance in mW/m²/sr/cm⁻¹. To turn radiance into something physically meaningful, you invert the Planck function:

T_b = (h * c / (k * λ)) / log((2 * h * c² / (λ⁵ * L)) + 1)

where L is radiance, λ is the band center wavelength, and h, c, k are Planck's constant, the speed of light, and Boltzmann's constant. The output is a temperature in Kelvin — the temperature a perfect black body would need to emit the observed radiance. This is the brightness temperature, T_b.

For GOES Band 7, NOAA helpfully publishes the Planck constants in each NetCDF file:

import xarray as xr
import numpy as np

ds = xr.open_dataset('OR_ABI-L1b-RadM1-M6C07_G18_*.nc')
Rad = ds.Rad.values  # radiance, mW/m²/sr/cm⁻¹

# Constants from the NetCDF
fk1 = ds.planck_fk1.values
fk2 = ds.planck_fk2.values
bc1 = ds.planck_bc1.values
bc2 = ds.planck_bc2.values

Tb = (fk2 / np.log(fk1 / Rad + 1) - bc1) / bc2  # Kelvin

Typical brightness temperatures

• Open ocean: ~290 K (16°C effective) — Band 7 is sensitive to skin temperature, which differs from bulk SST.
• Land surfaces: 280–320 K depending on time of day, season, and surface type.
• Clouds: highly variable, often 220–270 K (cold) or 280–290 K (low warm clouds).
• Wildfires: 320–500 K in actively burning pixels.
• Rocket plumes: typically 340–400 K at GOES Band 7 spatial resolution. The actual plume temperature is 1,500–3,000 K, but the plume only fills a small fraction of the 2 km × 2 km pixel, so the area-weighted brightness temperature is much lower.

The threshold approach

The simplest detector: threshold the brightness temperature. If T_b > threshold, flag the pixel as a hotspot. Sensible thresholds:

• 320 K: aggressive — catches all plumes but also many false positives (wildfires, gas flares, industrial sources).
• 340 K: balanced — good plume recall, fewer false positives.
• 360 K: conservative — very few false positives, but misses smaller plumes (small launchers like Electron).

In a real production system, a static brightness-temperature threshold is almost never the whole story. Operational detectors combine spectral evidence (this week's signal) with spatial context, temporal context, and external priors — the exact combination is where each operator differentiates and is mostly out of scope for an open curriculum. The point of this week is the spectral baseline. The higher-order logic — what features you stack on top, in what order, with what gating — is what Track 4 and Track 5 prepare you to design.

Common false positives

The single biggest source of false positives is wildfires. Both produce hotspots in Band 7. The discriminators:

• Spatial coincidence — a thermal hotspot inside a known spaceport's geofence is almost certainly a launch; outside, it's almost certainly a fire.
• Temporal pattern — a launch plume appears for 1–3 minutes then disappears; a wildfire persists for hours.
• FIRMS overlap — NASA's FIRMS (Fire Information for Resource Management System) publishes confirmed fire hotspots in near-real-time. A Band 7 hotspot that overlaps a FIRMS detection is almost certainly a fire.

Other false positives: industrial gas flares (Iraqi/Saudi oil fields), reflective sun glint over water, and rarely volcanic eruptions.

The lab

You'll download several GOES-18 Band 7 frames spanning a known SpaceX Falcon 9 launch from Vandenberg, convert radiance to brightness temperature, threshold at 320 K, output the detected hotspot pixels with timestamps and lat/lon (via Week 15's georeferencing). The lab produces the same primary detection that drives a real launchdetect.com entry — without (yet) the parallax correction, clustering, or scoring layers.