Differentiable CoCiP: exact sensitivities of contrail energy forcing with DIFFCOCIP v1.0

Abstract. Reducing contrail warming requires knowing how a flight's climate effect responds to changes in its trajectory, the weather and the contrail model's assumptions. The Contrail Cirrus Prediction model (CoCiP) computes this effect as energy forcing, EF, but its reference implementation does not provide these sensitivities. Finite differences could estimate them by perturbing one input at a time, but this is impractical for weather fields holding millions of values. We present diffcocip v1.0, a reimplementation that applies reverse-mode automatic differentiation to obtain all these sensitivities in a single backward pass. It reproduces the reference model's EF to the accumulated floating-point round-off and returns derivatives with respect to waypoint altitudes, gridded humidity and model parameters. Three applications assess the use and limits of these derivatives. In a four-season fleet campaign, altitude gradients guide the placement of candidate manoeuvre windows, and every candidate is then evaluated with the unmodified model. For about one third of reprofiled flights, the selected manoeuvre reduces EF despite a gradient prediction of an increase, showing why finite manoeuvres must still be checked against the full model. Humidity gradients identify the small part of a four-dimensional weather grid that influences one flight's EF, including positions reached by its drifting contrail after the aircraft has passed. Among six model parameters, EF proves most sensitive to the humidity-correction coefficient, whose effect is about 7 times larger than that of the next most influential parameter. The derivatives are exact within each smooth region of the implemented model, but do not capture discontinuous changes across the formation, persistence and termination thresholds. diffcocip also includes an optional smoothed formulation of these criteria to support gradient-based optimisation; the results reported here use the unmodified model throughout.