Contrail forecast

We use two different models to forecast contrails. The first, a machine learning (ML)-based model, predicts the probability of contrail formation. The ML contrail likely zone (CLZ) forecasting model is a deep neural network that takes weather features as inputs and predicts CLZs based on satellite contrail detections (Geraedts et al. 2023). The ML model's inputs consist primarily of HRES weather features. In particular, we use specific humidity, temperature, u component of wind, v component of wind, vertical velocity, relative vorticity, fraction of cloud cover, specific cloud ice water content, specific snow water content, and divergence. We use relative humidity calculated using specific humidity and temperature. We also use local solar time, day of year, latitude, and altitude of flight waypoints as input features. For our US forecast, we additionally use longitude as a feature. The model achieves state-of-the-art performance when evaluated against observational contrail data.

The second model, the Contrail Cirrus Prediction (CoCiP) model, predicts the energy forcing of the contrail, which is a measure of the climate impact of the contrail. Energy forcing is defined as

$$ EF [J] = \int_{0}^{t} RF'(t) \times L(t) \times W(t)dt $$

meaning the instantaneous radiative forcing of the contrail integrated over its lifetime (Teoh et al. 2020). We also normalize energy forcing by flight distance, leading to its units of \(J/m\).

CoCiP is a physics-based model that simulates contrail formation, evolution, and impact using atmospheric conditions, aircraft type, flight path, and other features (Schumann 2012; Schumann et al. 2012). We use 10 ensemble members from ECMWF's high-resolution forecast ensembles (HRES ENS) as inputs to CoCiP for advecting the flight waypoints where contrails have formed forward in time (Hersbach et al. 2020). The CoCiP model also uses cloud microphysics theory to determine which contrails persist, accounting for initial downdraft, fall, and sublimation. Given the simulated evolution of the contrail, CoCiP calculates energy forcing based on the contrail properties and the surrounding weather conditions.

In addition to CoCiP's estimate of energy forcing, we use a climatological estimate of energy forcing. The climatology is computed by averaging a year of CoCiP outputs, binned by time of day, season, and latitude.

The final energy forcing quantity is an average of the energy forcing from the CoCiP ensemble members with nonzero EF and the climatological average, which is always nonzero. By including climatology in the average, we always have an estimate of contrail impact, even when CoCiP does not predict the formation of a contrail using any of the weather ensemble members.

We combine these two forecasts using a product:

expected effective energy forcing \(=\) (probability of forming a contrail, ML model) \(\times\) (energy forcing of the contrail, CoCiP and climatology) \(\times\) (RF -> ERF conversion factor, 0.42)


Geraedts, Scott, Erica Brand, Thomas R. Dean, Sebastian Eastham, Carl Elkin, Zebediah Engberg, Ulrike Hager, et al. 2023. "A Scalable System to Measure Contrail Formation on a per-Flight Basis." arXiv []. arXiv.

Hersbach, Hans, Bill Bell, Paul Berrisford, Shoji Hirahara, András Horányi, Joaquín Muñoz-Sabater, Julien Nicolas, et al. 2020. "The ERA5 Global Reanalysis." Quarterly Journal of the Royal Meteorological Society 146 (730): 1999-2049.

Schumann, U. 2012. "A Contrail Cirrus Prediction Model." Geoscientific Model Development 5 (3): 543-80.

Schumann, U., B. Mayer, K. Graf, and H. Mannstein. 2012. "A Parametric Radiative Forcing Model for Contrail Cirrus." Journal of Applied Meteorology and Climatology 51 (7): 1391-1406.

Shapiro, Marc, Zeb Engberg, Roger Teoh, Marc Stettler, and Tom Dean. 2023. Pycontrails: Python Library for Modeling Aviation Climate Impacts.

Teoh, Roger, Ulrich Schumann, Arnab Majumdar, and Marc E. J. Stettler. 2020. "Mitigating the Climate Forcing of Aircraft Contrails by Small-Scale Diversions and Technology Adoption." Environmental Science & Technology 54 (5): 2941-50.