The scientific community that includes meteorologists, physical scientists, engineers, medical doctors, biologists, and environmentalists has shown interest in a better understanding of fog for years because of its effects on, directly or indirectly, the daily life of human beings. The total economic losses associated with the impact of the presence of fog on aviation, marine and land transportation can be comparable to those of tornadoes or, in some cases, winter storms and hurricanes. The number of articles including the word ''fog'' in Journals of American Meteorological Society alone was found to be about 4700, indicating that there is substantial interest in this subject. In spite of this extensive body of work, our ability to accurately forecast/nowcast fog remains limited due to our incomplete understanding of the fog processes over various time and space scales. Fog processes involve droplet microphysics, aerosol chemistry, radiation, turbulence, large/small-scale dynamics, and surface conditions (e.g., partaining to the presence of ice, snow, liquid, plants, and various types of soil). This review paper summarizes past achievements related to the understanding of fog formation, development and decay, and in this respect, the analysis of observations and the development of forecasting models and remote sensing methods are discussed in detail. Finally, future perspectives for fog-related research are highlighted.

The objective of this work is to suggest a new warm-fog visibility parameterization scheme for numerical weather prediction (NWP) models. In situ observations collected during the Radiation and Aerosol Cloud Experiment, representing boundary layer low-level clouds, were used to develop a parameterization scheme between visibility and a combined parameter as a function of both droplet number concentration N d and liquid water content (LWC). The current NWP models usually use relationships between extinction coefficient and LWC. A newly developed parameterization scheme for visibility, Vis ϭ f (LWC, N d ), is applied to the NOAA Nonhydrostatic Mesoscale Model. In this model, the microphysics of fog was adapted from the 1D Parameterized Fog (PAFOG) model and then was used in the lower 1.5 km of the atmosphere. Simulations for testing the new parameterization scheme are performed in a 50-km innermost-nested simulation domain using a horizontal grid spacing of 1 km centered on Zurich Unique Airport in Switzerland. The simulations over a 10-h time period showed that visibility differences between old and new parameterization schemes can be more than 50%. It is concluded that accurate visibility estimates require skillful LWC as well as N d estimates from forecasts. Therefore, the current models can significantly over-/ underestimate Vis (with more than 50% uncertainty) depending on environmental conditions. Inclusion of N d as a prognostic (or parameterized) variable in parameterizations would significantly improve the operational forecast models.

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Complex topography significantly modifies radiation fluxes at the earth’s surface. As spatial resolutions of mesoscale weather forecast models increase, terrain effects on radiation fluxes induced by slope aspect, slope angle, sky view factor, and shadowing also gain importance. A radiation parameterization scheme is hence designed to better represent these topographic influences to improve weather forecasts. The grid- and subgrid-scale radiation parameterization scheme allows computation of radiation fluxes for each weather forecast model grid cell by considering arbitrarily fine resolved topography without degrading the model’s computational performance. The proposed scheme directly computes mean fluxes for each model grid cell based on flux computations at full spatial resolution of a digital elevation model covering the model domain. Thus the scheme does not require a problematic computation of averaged topographic properties such as aspect angles. Furthermore, the scheme has a nonlocal computation of sky view restriction and shadowing effects. Case studies with the Nonhydrostatic Mesoscale Model (NMM) at resolutions of 4 and 2 km, respectively, and the parameterization based on a 1-km resolved elevation model, showed that effects of this parameterization are significant and result in better temperature forecasts in complex terrain. Rms and mean error of 2-m temperature forecasts are generally improved by 0.5 to 1 K. At night, the consideration of restricted sky view leads to a temperature increase between 0.5 and 1.5 K along valleys. During clear-sky daytime, this warming is of the same magnitude for grid cells containing slopes exposed to the sun. Under overcast conditions, rms error is reduced by 0.2 to 0.5 K. In wintertime, shadows reduce temperatures in valleys by 0.5 to 3 K during daytime.

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Fog in complex terrain shows large temporal and spatial variations that can only be simulated with a three-dimensional model, but more modifications than simply increasing the resolution are needed. For a better representation of fog, we present a second-moment cloud water scheme with a parametrization of the Köhler theory which is combined with the mixed-phase Ferrier microphysics scheme. The more detailed PAFOG microphysics produce many differences to the first-moment Ferrier scheme and are responsible for the typically low liquid water content of fog. The inclusion of droplet sedimentation in the Ferrier scheme cannot reproduce the results obtained with PAFOG, as there is a large sensitivity to the sedimentation velocity. With explicitly predicted droplet number concentrations, sedimentation of cloud water can be modelled with variable fall speeds, which mainly affects the vertical distribution of cloud water and the end of the fog's life cycle. The complex topography of the Swiss Alps and their surroundings are used for model testing. As the focus is on the model's ability to forecast the spatial distribution of fog, cloud patterns derived from high-resolution MSG satellite data, rather than few point observations from ground stations, are used. In a five-day period of anticyclonic conditions, the satellite-observed fog patterns showed large day-to-day variations from almost no fog to large areas of fog. This variability was very well predicted in the three-dimensional fog forecast. Furthermore, the second-moment cloud water scheme shows a better agreement with the satellite observations than its firstmoment counterpart. For model initialization, the complex topography is actually a simplifying factor, as cold air flow and pooling dominate the more uncertain processes of evapotranspiration or errors in the soil moisture field.

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Abstract-A probabilistic fog forecast system was designed based on two high resolution numerical 1-D models called COBEL and PAFOG. The 1-D models are coupled to several 3-D numerical weather prediction models and thus are able to consider the effects of advection. To deal with the large uncertainty inherent to fog forecasts, a whole ensemble of 1-D runs is computed using the two different numerical models and a set of different initial conditions in combination with distinct boundary conditions. Initial conditions are obtained from variational data assimilation, which optimally combines observations with a first guess taken from operational 3-D models. The design of the ensemble scheme computes members that should fairly well represent the uncertainty of the current meteorological regime. Verification for an entire fog season reveals the importance of advection in complex terrain. The skill of 1-D fog forecasts is significantly improved if advection is considered. Thus the probabilistic forecast system has the potential to support the forecaster and therefore to provide more accurate fog forecasts.