How We Detect Contrails: The Science Behind ChemTracker
Every second, ChemTracker evaluates thousands of aircraft positions against real-time atmospheric data and applies the Schmidt-Appleman criterion to predict trail formation. Here is a full technical explanation of how that works — the criterion itself, our data sources, the Monte Carlo simulation layer, and the accuracy we achieve.
The Schmidt-Appleman Criterion: Background
The foundation of contrail prediction is thermodynamics. When a jet engine burns fuel, it produces a hot, moist exhaust plume. As this plume mixes with cold ambient air at cruising altitude, the mixture either crosses the water saturation curve — triggering condensation and ice crystal formation — or it does not.
Erich Schmidt formalized this in 1941, and Hermann Appleman extended it in 1953 into the model that became the standard in aviation meteorology. The Schmidt-Appleman criterion (SAC) defines a critical temperature G below which contrail formation is guaranteed, assuming the mixing trajectory crosses the saturation curve.
The Critical Temperature Formula
The critical temperature G is calculated as:
Where: cp = specific heat of air at constant pressure, p = ambient pressure, R_w = gas constant for water vapor, ε = ratio of molecular weights, EI_H₂O = water vapor emission index of the fuel, Q = lower heating value of fuel, η = overall propulsion efficiency.
If the ambient temperature at the aircraft's altitude is below G, and the mixing line crosses the saturation curve, a contrail will form. For typical commercial aviation (kerosene fuel, bypass ratio ~5–10), G falls between −44°C and −36°C at cruising altitudes, depending on ambient pressure.
Formation vs. Persistence
The SAC predicts formation. Persistence is a separate question governed by the ambient relative humidity with respect to ice (RHi).
Short-Lived Contrails (RHi < 100%)
If G is met (formation occurs) but ambient air is subsaturated with respect to ice, the newly formed ice crystals immediately begin to sublimate. The contrail appears as a brief bright line and disappears within seconds to a few minutes. This is the most common outcome over dry regions or at certain altitude layers.
Persistent Contrails (RHi > 100%)
When ambient air is supersaturated with respect to ice, the ice crystals in the contrail do not sublimate but instead grow by deposition of ambient moisture. The trail widens and persists, sometimes for hours, and can spread into cirrus- like cloud cover visible from the ground. This is the trail behaviour that generates the most public attention.
No Contrail (T > G)
If ambient temperature exceeds the critical threshold G — typically when aircraft fly in warmer or lower-altitude air — the exhaust and ambient air mixture never crosses the saturation curve. No condensation occurs and no visible trail forms, regardless of humidity.
ChemTracker reports all three cases to users and distinguishes between “forming but non-persistent” and “forming and persistent” trail predictions — because these have very different visual signatures and atmospheric significance.
Our Data Sources
Three data sources feed the detection pipeline:
ADS-B Flight Data
ADS-B (Automatic Dependent Surveillance–Broadcast) is a system where aircraft transmit their GPS position, altitude, speed, and identification every second. We receive this from a network of ground-based ADS-B receivers covering Europe and North America. Coverage over major air corridors exceeds 98% for aircraft above 10,000 feet. Position data updates every 5–15 seconds in our system.
Numerical Weather Prediction (NWP) Model Output
We ingest hourly outputs from global NWP models — specifically the variables we need at pressure levels from 150 to 400 hPa: temperature (T), specific humidity (q), and pressure (p). The horizontal resolution is approximately 0.25° (~28 km at mid-latitudes), and we interpolate between grid points to get estimates at the aircraft's exact longitude and latitude. Vertical interpolation gives us conditions at the aircraft's barometric altitude.
Aircraft and Engine Database
The SAC requires engine-specific parameters. We maintain a database of aircraft types linked to typical engine configurations, providing the fuel efficiency (η) and emission index values needed for accurate G calculations. For aircraft types not in our database, we use conservative typical-commercial-jet defaults that give a reliable estimate without overpredicting.
The Monte Carlo Layer
A single SAC calculation gives a binary answer: contrail expected or not. But atmospheric data has measurement and interpolation uncertainty. The temperature at a given altitude and location has an error range — typically ±1–2°C from NWP interpolation. Relative humidity at altitude has even higher uncertainty, sometimes ±15% RHi.
A binary answer derived from uncertain inputs is misleading. To address this, we run a Monte Carlo simulation for each aircraft: we draw 200 samples from the probability distributions of each uncertain input (T, RHi, η) and run the SAC for each sample. The fraction of samples that predict contrail formation becomes the trail probability score.
This produces results like “82% probability of trail formation” rather than just “trail forming: yes.” It is a more honest representation of what the data actually says, and it allows users to interpret borderline cases appropriately rather than treating a 51% prediction the same as a 99% prediction.
Threshold Bands in the App
- Red (>70%): High confidence trail formation. Conditions clearly meet the SAC threshold.
- Amber (30–70%): Borderline. Conditions are near the SAC threshold. Trail may or may not form depending on exact local conditions.
- Grey (<30%): Low probability. Conditions do not support trail formation with high confidence.
Accuracy
How accurate is the prediction? We have validated ChemTracker's output against satellite observations of contrail coverage and against user reports from the sky scanner (where users can confirm or deny whether a trail is visible on a given aircraft).
For red-flagged aircraft (probability >70%), trail formation is confirmed in approximately 85–90% of cases with good satellite coverage. For grey-flagged aircraft (<30%), absence of a visible trail is confirmed in approximately 88–92% of cases. The amber zone (30–70%) is genuinely uncertain and behaves as expected — with roughly 50% confirmation rate.
The primary limitation is NWP resolution. A 28 km horizontal grid means small-scale atmospheric features — particularly humidity pockets — are smoothed out. An aircraft can fly through a localized supersaturated layer that is not captured in the model output. This is an inherent limitation of the approach and explains most of the missed predictions. Real-time radiosonde assimilation and satellite humidity data would improve this; it is an active area of our development roadmap.
“The Schmidt-Appleman criterion is not a perfect predictor of every trail you will ever see. It is the best physical model we have, applied honestly with uncertainty quantification. That is what ChemTracker gives you.”
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