Advancements in fog prediction in weather and climate model guided by DNS

With the changing climate, the study of fog formation is essential and needs of the hour as the nature of fog has changed due to impact of complexity of natural and anthropogenic aerosols. The chemical and physical properties of cloud condensation nuclei (CCN) significantly influence fog formation and visibility, especially in regions like India. Ample water vapor, coupled with the microphysical and thermodynamic properties of CCN, plays a vital role in the occurrence and and sustenance of fog. Weather and Climate models often struggle to simulate fog droplets accurately due to the absence of aerosol indirect effects (AIE), a key factor contributing to uncertainties in aerosol-cloud interaction (ACI). The visibility calculation, which depends on the number of cloud droplets and liquid water content (LWC) in the atmosphere, is closely tied to aerosol dynamics. The conversion of aerosols into fog droplets (Nd) requires external nuclei for water vapor condensation, a process governed by condensation or diffusional growth. The condensation process is influenced by the solute effect (Raoult's effect) and the curvature effect (Kelvin effect) and may happen over a pre-existing Aitken aerosol particle. Droplet growth is determined by the size of CCN and a droplet will always try to maintain an equilibrium state and it happens if the equilibrium supersaturation is less than the amount of water vapor available in the atmosphere. The Köhler curve illustrates the interplay between the 'curvature effect' and the 'solute effect' in droplet behaviour, showing that droplets with higher solute concentrations exhibit lower critical supersaturation values, making them easier to activate into cloud droplets. Thus, hygroscopicity (κ), a key factor in CCN activation, relates to aerosol particle contributions to fog droplet formation. This is encapsulated in the κ-Köhler theory, which combines Kelvin's and Raoult's effects to describe the activation of deliquesced aerosols into cloud droplets. Hygroscopicity is linked with the water activity and thus the thermodynamics of solution governs the aerosols liquid water and hence, better understanding of hygroscopicity is essential in numerical model for the fog and visibility prediction. The evolution of the droplet size distribution (DSD) under varying aerosol-chemical conditions remains poorly understood. To reduce uncertainties in fog forecasting, the Eulerian-Lagrangian particle-based schemes in direct numerical simulation (DNS) are utilized to study the diffusional growth of droplets. Using observational data from the Winter Fog EXperiment (WiFEX) conducted at IGI airport, New Delhi, small-scale model simulations provide valuable insights into droplet activation processes. Additionally, a novel visibility parameterization has been proposed based on the small-scale model using WiFEX observed data, which incorporates both LWC and Nd. This advancement offers a pathway to more accurate fog and visibility forecasts in numerical weather prediction models.