The overall depth of a fog layer is one of the important factors in determining the hazard that a fog event presents. With discrete observations and often coarse numerical grids, however, fog depth cannot always be accurately determined. To address this, I took lessons learned from earlier observational analysis in order to describe and model the growth/evolution of fog using simple analytical solutions.
The Growth of Fog
I ultimately show that the deepening of a fog layer is related to the relative moistening at the interface, divided by the slope of moisture above the fog layer. This is similar to a ladder placed against a wall. The length traveled along the ladder is the relative moistening, the horizontal base is the slope of the moisture profile, and the vertical axis is the growth in time. If placed at a shallow angle against a wall (steep profile), it takes many more steps to climb to the same height as if the ladder were more steeply angled (profile near saturation). Drying or moistening determines whether or not the fog layer deepens or erodes.
The Growth of Fog
I ultimately show that the deepening of a fog layer is related to the relative moistening at the interface, divided by the slope of moisture above the fog layer. This is similar to a ladder placed against a wall. The length traveled along the ladder is the relative moistening, the horizontal base is the slope of the moisture profile, and the vertical axis is the growth in time. If placed at a shallow angle against a wall (steep profile), it takes many more steps to climb to the same height as if the ladder were more steeply angled (profile near saturation). Drying or moistening determines whether or not the fog layer deepens or erodes.
Figure 1. (a) Sketch of the conditions in which fog exists. Given the hypothetical profile of qs near the interface, the profile of q must exist within the shaded regions, represented by the dashed line. (b) Growth illustrated as a ladder against a wall. The shallower (steeper) the ladder, the lesser (greater) the distance that can be travelled vertically.
We compare the estimates of fog growth to the observed evolution of the fog layer seen during the high-resolution campaign, as well as simple numerical simulations. The estimated evolution agrees very well with the observed/simulated evolution, suggesting that our simple model can be used to both estimated the growth of fog in time, as well as understand the impact of different processes on the growth of fog.
Figure 2. Observed fog height compared with the height estimated by the analytical formula. (a) High-resolution comparison using distributed temperature sensing (DTS)-estimated saturation (i.e., RH =99 % as the interface, left) and the camera-derived observations of fog depth. (b) Comparison against the fog depth observed along the Cabauw tower. Note, the camera is limited to a depth of 2.25 m, and the tower is restricted to discrete heights such that the observed fog depth is between the maximum height of observed fog, and the level above.
The Evolution of Fog
As radiation fog grows, it reaches a point of transition from shallow, optically thin fog to deep, optically thick fog. At this transition, the cooling shifts from the Earth's surface to the top of the cloud, resulting in a well-mixed fog layer with much larger turbulent motions. In Chapter 7 of my dissertation, I expand upon the growth equation to describe the lifecycle of fog from a simple conceptual/analytical perspective. I present equations that enable a priori estimation of a fog layer's evolution, including its rate of deepening during the two distinct stages of the fog lifecycle, as well as the time of transition between the two stages. Initial comparison with observations shows good agreement between the simple model and reality; however, this is ongoing work that needs further verification.
As radiation fog grows, it reaches a point of transition from shallow, optically thin fog to deep, optically thick fog. At this transition, the cooling shifts from the Earth's surface to the top of the cloud, resulting in a well-mixed fog layer with much larger turbulent motions. In Chapter 7 of my dissertation, I expand upon the growth equation to describe the lifecycle of fog from a simple conceptual/analytical perspective. I present equations that enable a priori estimation of a fog layer's evolution, including its rate of deepening during the two distinct stages of the fog lifecycle, as well as the time of transition between the two stages. Initial comparison with observations shows good agreement between the simple model and reality; however, this is ongoing work that needs further verification.
Further Reading
- Izett, J. G., B. J. H. van de Wiel (2020). Why Does Fog Deepen? An Analytical Perspective. Atmosphere 11(8). DOI: https://doi.org/10.3390/atmos11080865
- Izett, J. G. (2020). Fog from the Gound Up. Investigating the Conditions Under Which Fog Forms and Evolves Within the Nocturnal Boundary Layer. Defended: 1 September 2020. [Link]