(From the book) Chapter 5: Radiation in Marine Fog

Introduction

Shortwave radiation is solar radiation, that is, radiation coming from the sun. When passing through the atmosphere, solar radiation will interact with clouds, aerosols found in the atmosphere, and the surface of the Earth. Longwave radiation, however, can be emitted by most objects depending on their emissivity and surface temperature. The net radiation is simply the sum of upwelling/downwelling longwave and shortwave radiation. The importance of longwave radiation is mainly in the formation and evolution of marine fog while the importance of solar radiation is in the dissipation of marine fog.

Longwave Radiation on Fog Formation

To be able to understand the effect of radiation on fog formation, we need to understand the longwave heating rate. The equation used in the book (from Barker 1977) determined the longwave heating rate by the vertical gradient of the longwave radiative flux:

$$H(z_r) = - \frac{1}{\rho C_p}\frac{\partial F_n}{\partial z} = - \frac{1}{\rho C_p}\frac{\partial (F_{UP}-F_{DN})}{\partial z}$$

where H is the heating rate in K/s at given height z_r, ρ is the density of air, Cp is the specific heat at constant pressure, and Fn , Fup, Fdn are the net, up and down radiative fluxes respectively.

Role of radiation in fog formation

Two types of fog can be formed over the sea surface:

• Radiation fog

Gaseous radiative cooling is when water vapor and carbon dioxide emit longwave radiation, especially in the form of infrared to the atmosphere causing it to cool down locally. This process is said to be necessary for fog formation in the time scale of a few hours. This process can occur on the sea surface under calm conditions and when warm air is advected over the cold sea surface.

• Advection fog

Advection fog can be caused by turbulent mixing. That is cold air being mixed down by wind shear stress over the sea surface. However, when the weather is calm and there is not a lot of turbulent mixing, it is believed that radiative cooling contributes mostly to the formation of advection fog.

When warm air moves to the cold sea surface, the temperature changes so that on a temperature profile, we can see an inversion. The warm, moist air will cool down and reach dew point temperature and the advection fog starts to form. Unlike land surfaces, sea surface temperature (SST) stays rather constant and does not go through diurnal cycles, so during the fog episode, the temperature of the sea surface will not necessarily play a role in forming and dissipating the fog. So, in a thermally stable boundary layer (weak wind conditions and so forth), radiative cooling contributes a lot to the formation of an advection fog whereas when the wind is strong and there is strong turbulence, the latter will dominate the process of fog formation.

Role of radiation on the evolution of marine fog

Once fog is formed, how it evolves strongly depends on the fog top radiative cooling. When the upper layer of fog cools down, it becomes less dense than the warm air above and will rise due to a difference in densities (buoyancy) which can destabilize the fog layer. Since it is hard to measure radiative cooling directly, its effect is analyzed through numerical modeling. Using a model, Brown and Roach (1976) examined the evolution of fog with and without fog droplets emitting radiation. They observed that when radiation was introduced, radiative cooling (LWC)was very strong at the top of the fog layer, where liquid water content was also higher than below. They also found that there was a lower amount of LWC and the height and depth of the fog layer were also reduced when the fog droplets were not emitting radiation.

Those observations indicated that top radiative cooling had a factor in the rise of the fog layer and its duration. So, the radiation emitted by the fog droplets depended on the microphysics properties of the fog droplet. Fog layer with higher LWC absorbed more longwave radiation and it was found that for the same LWC, smaller fog droplets in higher volume absorbed more longwave radiation than larger droplets, thus emitting longwave radiation more efficiently as well. As the top layer cools down, this will cause instability in the fog layer. As turbulence increases, TKE is generated and this can promote vertical growth.

Another way marine fog can be formed is by lowering of stratus cloud base. This happens due to turbulence in the cloud layer and this turbulence increases a lot with top radiative cooling. As the top layer of the cloud cools down, it will move down creating TKE. As it moves down, it can even reach below the cloud base level. As the cloud droplet evaporates in this layer, this increases moisture and decreases temperature and water vapor saturation can be reached. When the process continues, it is possible that the cloud layer lowers to the sea surface forming marine fog.

Role of radiation in dissipating marine fog

Dissipation of marine fog strongly depends on shortwave radiation. It is good to note that around 25% of solar radiation gets absorbed by fog and most of it gets reflected as fog and low-level marine stratus has an albedo of 0.6 to 0.7. As solar radiation gets absorbed by the upper layer of the cloud/fog, it warms up and causes the fog droplets to evaporate. As the top layer becomes warmer, this will generate turbulent mixing with the colder layer and the moisture level will decrease and eventually the fog layer will dissipate.