Assessment and correction of retrieval biases in ship tracks

Ship tracks serve as “natural laboratories” for investigating aerosol-cloud interactions, one of the largest sources of
uncertainty in climate change research. Observing ship tracks can help constrain the effect of anthropogenic aerosols on
cloud brightness and water content. The validity of these constraints relies, in part, on the accuracy of satellite retrieval
algorithms used to measure cloud properties. A known source of uncertainty in these algorithms is the representation of
the droplet size distribution. Standard operational retrievals (e.g. MODIS) assume a fixed effective variance (v_eff) for the
modified gamma distribution used to model cloud droplet dispersion. The introduction of aerosols into clouds produces not
only smaller droplets but also a narrower size distribution, contradicting this fixed assumption.

This study utilises a synthetic retrieval experiment to quantify the impact of this assumption. Top-of-atmosphere radiances
are forward-modelled for synthetic ship track scenes, ranging from clean to polluted regimes. These are then inverted using
standard retrieval logic, allowing us to compare retrieved products against a known “truth”, isolating the bias caused solely
by the fixed v_eff assumption.

Our results indicate that the fixed v_eff assumption causes a systemic overestimation of effective radius (r_𝑒) of 3.31% in the
polluted regime, while optical depth (𝜏) is virtually unaffected. Consequently, liquid water path (LWP) is robustly retrieved
with a small bias of 2.85%, which is expected due to the linear dependence of LWP on r_𝑒 and 𝜏. Cloud droplet number
concentration (N_𝑑 ), however, suffers from a much larger overestimation of 23.92% in polluted clouds. This large error
arises due to the sensitivity of N_𝑑  to the spectral width parameter 𝑘, which is a function of v_eff. This inflation of droplet
number in ship tracks may exaggerate cloud microphysical sensitivity to aerosols, potentially overstating the Twomey effect
in models constrained by observed N𝑑 and the efficacy of marine cloud brightening if monitored by satellite.

To address this, we introduce a physics-informed deep residual network (ResNet) correction model. This model does not
require prior knowledge of the true v_eff, and is trained on synthetic retrievals to map observable parameters to the underlying
bias. By leveraging the sensitivity of multi-angle scattering information implicit in the features, the network learns to
predict the v_eff and resulting correction factor. We demonstrate that the correction framework reduces the error in N_𝑑 in
our synthetic retrieval experiment to less than 1% while preserving the accuracy of LWP.