The aviation industry is anticipated to grow in the future, with high demand for air travel coming from emerging markets. Consequently, the climate impact attributable to aviation will grow, which is largely driven by non-CO₂ emissions and their associated effects. The role of propulsion systems is critical in reducing the aviation climate impact, as the various species relevant for climate impact are mostly produced during combustion. In this research, we present a novel reduced-order model for climate impact assessment of aircraft engines applicable during the preliminary engine cycle optimization stage. All information that is necessary to estimate the climate impact of combustion emissions is transparently built into the model, such as aircraft type, fleet characterization, route network and fuel type. First, a baseline emission inventory considering global coverage of short-medium range flights by A321neo-like aircraft operating on a Sustainable Aviation Fuel (SAF) in 2050 is generated. Second, the performance parameters of the inventory in terms of fuel burn and emissions are scaled on a one-at-a-time basis within predefined ranges to generate a wide array of inventories, corresponding to variation in cruise altitude. Third, the impact of each variation is analyzed using the climate assessment model OpenAirClim (version 0.16) for a fixed set of boundary conditions. The sensitivity of the climate metric ATR₁₀₀ for each species, i.e., CO₂, NO_x, H₂O and contrail-induced cloudiness, CiC, is analyzed with respect to the variation in the fuel burn, emissions and cruise altitude. This leads to closed-form analytical expressions describing the impact of each species as a function of engine performance parameters, namely the Climate Functions for Engine Design (CFED) version 1.0, which constitute the model. We find that CFED is able to reproduce relevant metric sensitivity trends due to emission and altitude variation across species with a mean error of 2.71%. Further, for a set of 100 randomly selected combinations of the variation in the fuel burn and emissions across all species and altitudes, the mean error of the CFED prediction relative to the full methodology was found to be within 0.25%. The CFED equations are suitable for integration in the engine cycle design framework as they effectively capture the climate sensitivity during conceptual phase, and are computationally inexpensive. They enable climate assessment of new engine designs and allow for engine cycle optimization to include the climate impact of engine emissions.