Asymptotic Analysis of Equilibrium in Radiation Fog

Abstract

A vertical distribution formulation of liquid water content (LWC) for steady radiation fog was obtained and examined through the singular perturbation method. The asymptotic LWC distribution is a consequential balance among cooling, droplet gravitational settling, and turbulence in the liquid water budget of radiation fog. The cooling produces liquid water, which is depleted by turbulence near the surface. The influence of turbulence on the liquid water budget decreases with height and is more significant for shallow fogs than for deep fogs. The depth of the region of surface-induced turbulence can be characterized with a fog boundary layer (FBL). The behavior of the FBL bears some resemblance to the surface mixing layer in radiation fog. The characteristic depth of the FBL is thinner for weaker turbulence and stronger cooling, whereas if turbulence intensity increases or cooling rate decreases then the FBL will develop from the ground. The asymptotic formulation also reveals a critical turbulent exchange coefficient for radiation fog that defines the upper bound of turbulence intensity that a steady fog can withstand. The deeper a fog is, the stronger a turbulence intensity it can endure. The persistence condition for a steady fog can be parameterized by either the critical turbulent exchange coefficient or the characteristic depth of the FBL. If the turbulence intensity inside a fog is smaller than the turbulence threshold, the fog persists, whereas if the turbulence intensity exceeds the turbulence threshold or the characteristic depth of the FBL dominates the entire fog bank then the balance will be destroyed, leading to dissipation of the existing fog. The asymptotic formulation has a first-order approximation with respect to turbulence intensity. Verifications with numerical solutions and an observed fog event showed that it is more accurate for weak turbulence than for strong turbulence and that the computed LWC generally agrees with the observed LWC in magnitude.

Development and application of a method for the objective differentiation of fog life cycle phases

“…It usually forms near the surface under clear skies in stagnant air in association with anticyclonic conditions (Gultepe et al, 2007). However, the mechanisms of radiation fog formation, development and dissipation are very complex and have been extensively studied with a series of numerical simulations and comprehensive observational programs including in situ measurements (Meyer et al, 1986;Fitzjarrald and Lala, 1989;Fuzzi et al, 1992Fuzzi et al, , 1998Gultepe et al, 2007;Zhou and Ferrier, 2008;Liu et al, 2011;Dupont et al, 2012). Recently, field experiments have been conducted to investigate dynamic, thermodynamic, microphysical, and radiative processes in Beijing and Nanjing, China (Liu et al, 2011), in Canada (Gultepe et al, 2009), and in Paris, France (Haeffelin et al, 2010;Dupont et al, 2012).…”

Radiation in fog: quantification of the impact on fog liquid water based on ground-based remote sensing

“…Once the fog has formed, its evolution depends on the physical processes that impact the liquid water. A delicate balance between radiative cooling, turbulent mixing and droplet sedimentation has been found in observational and modelling studies of radiation fog (Brown and Roach, 1976;Zhou and Ferrier, 2008;Price et al, 2015). While radiative cooling produces liquid water by supersaturation, turbulent mixing usually is a loss mechanism for liquid water through the mixing of the fog with drier air or turbulent deposition of liquid water on the surface (Gultepe et al, 2007).…”

Characterization and Modeling of Fog in the Mexico Basin

“…Since fogs are formed primarily through dynamic and adiabatic processes in the boundary layer, their formation, dispersion and decay depend on the balance between condensation in the fog layer, evaporation processes and settling of droplets. Such a balance was noticed by Choularton et al (1981) during a radiation fog field study, and later theoretically confirmed by Zhou and Ferrier (2008). Like most hydrometeorological phenomena, fog occurrence strongly varies with geographical location (Croft et al, 1997), and its observation and recording methods are still very dependent on direct human presence and perception (Lee et al, 2010).…”

“…It is interesting to note that in all three simulations fog formation starts aloft (at a height of about 250 m for radiation and advection fogs, and about 800 m for frontal fog), then spreading up and downward to reach the ground after 30 to 60 minutes. Pagowski et al (2004) found a similar behavior while simulating a dense advection fog occurrence in Canada, whereas Zhou and Ferrier (2008) indicated that this is due to the existence of certain turbulence near the ground. As in the radiation fog case, the results for the spatial distribution, and formation and dissipation times were also quite well reproduced (Figs.…”