Fog / Visibility calculations (modified Middle Wallop technique)

Fog point / Visibility

#### Dusk Vis : Mtrs

The original Middle Wallop technique was devised for forecasting air-mass visibility. It takes account of those factors known to affect overnight visibility reductions; air-mass dewpoint, minimum overnight temperature, maximum daytime visibility and surface wind speed.

The original supposition was that the visibility reductions, once the temperature has fallen to air-mass dewpoint, depend on the surface wind speed. A further supposition was that dusk visibility was generally 0.8 * daytime maximum visibility.

Original Middle Wallop Technique

Surface Wind (kts) Visibility
0-5 ⅓ Vismax
6-9 ½ Vismax
> 9 ¾ of Vismax

The technique was adapted by Matt Woods (Operational Meteorologist, Wattisham Met Office) to explicitly forecast the fog point - the technique is not site specific.

Extending the above technique downwards to the point at which fog develops (visibility < 1000 metres) will give the associated fog point temperature. This is particularly useful as even the latest high resolution NWP models have difficulty predicting fog formation in an accurate and timely manner. Other techniques such as Saunders construction are not viable due to the lack of balloon ascents and resultant tephigrams.

Selection of air-mass dew point at maximum visibility is crucial. It may be necessary to employ back trajectories in order to use a representative dew point for the overnight period.

Recent research conducted by the UK Met. Office facility at Cardington indicated an 85% success rate for the technique which included nights when a meteorologist would not consider a significant fog risk to exist due to strong gradient winds or an overnight frontal passage.

In order to develop a practical calculation tool we need to mathematically express the relationship between the fog point and the dew point as surface wind speed varies. This work was undertaken by Dan Harris, Deputy Chief Operational Meteorologist at the Met Office and can be expressed as follows:

$$T_{fog}=T_{dew}-\frac{ln \bigg(3*\frac{V_{max}}{n} \bigg)}{ln2}$$
where Vmax (max daytime visibility) is in metres and n is obtained from the following table:

Surface Wind (kts) n
0-5 9000
6-9 6000
> 9 4000