# Energy Forcing Interpretation#

The primary output of the CoCiP model is a prediction of the energy forcing (EF) caused by persistent contrail cirrus. In the trajectory CoCiP model, energy forcing predictions are measured in Joules (\(\text{J}\)) on a per-segment basis (here, a segment is defined by two consecutive waypoints). These can be normalized by the underlying segment length to arrive at a measure of contrail forcing per flight distance (\(\text{J} \; \text{m}^{-1}\)). In particular, this quantity is independent of the spacing of waypoints. In the gridded CoCiP model, energy forcing predictions are already normalized per flight distance. These two models can both be used to predict the forcing along a sequence of waypoints.

The following provides some ways to interpret energy forcing per flight distance (\(\text{J} \; \text{m}^{-1}\)) derived from CoCiP.

## Contextualizing with historic data#

Teoh et al. [to appear] analyzed CoCiP model predictions on 2019 global flight data. This dataset is comprised of approximately 6.6 billion waypoints. Of these, CoCiP predicts approximately 350 million generate persistent contrails. The percentiles of the normalized energy forcing predictions are given in the table below. Note that just over 35% of predicted persistent contrails have a net cooling effect.

Percentile |
EF per flight distance |
---|---|

\(1\) |
\(-6.39 \times 10^8\) |

\(5\) |
\(-1.95 \times 10^8\) |

\(10\) |
\(-6.93 \times 10^7\) |

\(15\) |
\(-2.45 \times 10^7\) |

\(20\) |
\(-7.78 \times 10^6\) |

\(25\) |
\(-2.69 \times 10^6\) |

\(30\) |
\(-1.47 \times 10^6\) |

\(35\) |
\(-2.74 \times 10^5\) |

\(40\) |
\(9.05 \times 10^5\) |

\(45\) |
\(6.31 \times 10^6\) |

\(50\) |
\(1.74 \times 10^7\) |

\(55\) |
\(3.72 \times 10^7\) |

\(60\) |
\(7.06 \times 10^7\) |

\(65\) |
\(1.23 \times 10^8\) |

\(70\) |
\(2.00 \times 10^8\) |

\(75\) |
\(3.07 \times 10^8\) |

\(80\) |
\(4.57 \times 10^8\) |

\(85\) |
\(6.72 \times 10^8\) |

\(90\) |
\(1.01 \times 10^9\) |

\(95\) |
\(1.63 \times 10^9\) |

\(99\) |
\(3.14 \times 10^9\) |

The data appearing in the table above is also plotted below. Focusing on the red region, waypoints above the 90th percentile contribute 56% of all positive energy forcing. Similarly, the waypoints above the 80th percentile contribute 82% of all positive energy forcing. Persistent contrails are rare (CoCiP predicts approximately 6% waypoints in the 2019 dataset generate persistent contrails); this analysis shows that the bulk of the climate impact is caused by only the most warming of these waypoints. Segments generating persistent contrails with EF per flight distance greater than \(5 \times 10^9\) or less than \(-5 \times 10^9\) are anomalous and not considered in this analysis.

Slicing perpendicular to the y-axis instead, regions for which the climate forcing of contrail formation is larger than \(10^9\) contribute 57% of all positive energy forcing according to CoCiP. Lowering this threshold picks up more contribution.

EF threshold |
Contribution to positive EF |
---|---|

\(1 \times 10^8\) |
\(97.3\%\) |

\(2 \times 10^8\) |
\(93.6\%\) |

\(3 \times 10^8\) |
\(89.3\%\) |

\(4 \times 10^8\) |
\(84.7\%\) |

\(5 \times 10^8\) |
\(79.9\%\) |

\(6 \times 10^8\) |
\(75.1\%\) |

\(7 \times 10^8\) |
\(70.4\%\) |

\(8 \times 10^8\) |
\(65.8\%\) |

\(9 \times 10^8\) |
\(61.2\%\) |

\(1 \times 10^9\) |
\(56.7\%\) |

Data from which these statistics were derived is available upon request.

## Comparison with GWP100-based CO2 emissions#

In Teoh et al. 2020 (lines 206-208), the authors derive a CO2 EF per fuel mass of \(4.70 \times 10^9 \; \text{J} \; \text{kg}^{-1}\) based on a 100 year time horizon (GWP100). Averaging over the mean fuel consumption of all aircrafts, this equates to a CO2 EF per flight distance of \(3.41 \times 10^7 \; \text{J} \; \text{m}^{-1}\). According to CoCiP, roughly half of all flight waypoints generating persistent contrails have an EF per flight distance greater than this value.

## Choosing the right EF Threshold#

When using the /grid/cocip endpoint for contrail avoidance via polygons, it is important to choose a reasonable EF threshold. This endpoint accepts a `threshold`

parameter to construct polygonal regions of high contrail impact (these polygons are level-sets of the EF per flight distance grid predicted by CoCiP). The API uses a default value of \(5 \times 10^8\). This particular value was chosen based on several factors.

In 2019, CoCiP predicts approximately 80% of contrail warming was caused by waypoints inside of these regions.

The contrail forcing of flights passing through these regions is at least 10 times as harmful as the CO2 impact of the same flights (based on GWP100). In other words, this threshold is conservative in the sense that CO2 emissions are given a higher weight than contrail impact.

With this particular threshold, polygon regions are still sufficiently sparse to be useful for contrail avoidance.