Ridge cloud, a thunderstorm warning and morning fog
A coastal town sits at sea level on the windward side of a ridge 900 m high, about 6 km inland. On a summer afternoon the air at the shore is at 24 °C with a dew point of 14 °C, and a steady onshore breeze carries it towards the ridge. Forecasters use a dry adiabatic lapse rate of 9.8 °C per km, and the dew point of unsaturated rising air falls by about 2 °C per km. The fire service has issued a dry-lightning warning for thunderstorms on the ridge that afternoon. A summit weather station records 17 °C at 15:00 and 0.0 mm of rain for the day, although the ridge is capped by a flat, uniform grey cloud layer that never develops vertically. Overnight the breeze drops, the sky clears, and the shore temperature falls to 10 °C by dawn; inland, in the valley behind the town, the minimum is 7 °C. The council asks whether the thunderstorm warning was justified and whether morning fog will affect the coastal road.
1. Estimate the height at which air lifted from the shore first becomes saturated, and use it to decide whether the ridge summit should lie inside cloud. Compare your prediction with the summit temperature record.
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The air starts 24 − 14 = 10 °C above its dew point. As the parcel rises, its temperature falls at 9.8 °C/km while its dew point falls at 2 °C/km, so the gap closes at 9.8 − 2 = 7.8 °C/km.
Lifting condensation level = 10 / 7.8 = 1.28 km, i.e. about 1300 m above the shore.
At the 900 m summit, the parcel would be at 24 − (9.8 × 0.9) = 15.2 °C with a dew point of 14 − (2 × 0.9) = 12.2 °C. It is still about 3 °C above its dew point, so on this simple upslope model the summit should be cloud-free.
The summit record disagrees on both counts: cloud is present, and the measured 17 °C is warmer than the 15.2 °C the model predicts. The observed lapse rate is (24 − 17)/0.9 = 7.8 °C/km, noticeably less than the dry adiabatic 9.8 °C/km. That means the air over the ridge is not a freely rising dry parcel from the shore: it has been mixed with other air, warmed, or the station sits in a sheltered spot. The model is a useful first estimate but it is not describing what actually happened.
2. The dry-lightning warning assumes thunderstorms will form. Judge how well the observations support that warning, and say what measurement would settle the question.
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A thunderstorm needs deep, moist convection: a parcel that is warmer than its surroundings once saturated, so it keeps accelerating upward, builds a cloud several kilometres deep, produces precipitation, and separates charge to give lightning.
The observations point the other way. The cloud is flat and uniform and shows no vertical development, which is characteristic of stratiform cloud formed by gentle lifting and mixing over the ridge, not of a cumulonimbus tower. Rainfall is 0.0 mm, so no precipitation-sized particles are falling out. The summit lapse rate of 7.8 °C/km is shallower than the dry adiabatic rate, indicating a stable layer in which a displaced parcel is pushed back rather than accelerated. The summit is also warmer than the adiabatic prediction, again consistent with mixing, not with a vigorously overturning updraught.
On the surface evidence the warning is not justified, and the risk of dry lightning on the ridge that afternoon is low. A surface dew point of 14 °C does not establish instability, because mixing and daytime heating of the boundary layer can lower the dew point considerably by afternoon.
The decisive evidence would be an upper-air sounding (radiosonde) measuring temperature and humidity to 5–10 km, which would show whether the lapse rate is steeper than the saturated adiabatic rate through a deep layer - the test for conditional instability - and whether a stable cap is present. Radar reflectivity and satellite cloud-top temperature would show whether any cell is actually growing and how cold its top is.
3. Will the coastal road be foggy by dawn? Use the dew point and the overnight minima to explain, and say what would have changed the outcome.
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Yes, fog is very likely on the coast. The near-surface air has a dew point of about 14 °C. Under clear skies and light winds, the ground radiates heat away efficiently and the air in contact with it cools until the temperature reaches the dew point - roughly 14 °C - at which point the air is saturated. Continued cooling condenses the excess vapour onto condensation nuclei, and the droplets stay suspended because the wind is too weak to mix them away: radiation fog, with visibility falling sharply on the coastal road.
The valley behind the town reaches 7 °C, a larger temperature fall because cold air drains into low ground, so the fog there should be deeper and denser and should clear later in the morning. The dew point itself stays close to 14 °C while condensation goes on, because the water leaving the vapour is only a small fraction of the total, which is why fog persists once formed rather than stopping instantly.
The outcome would have been different with a brisk wind, which mixes warmer air downwards and keeps the surface above 14 °C, giving dew or a shallow mist rather than fog; or with cloud overnight, which traps outgoing radiation and limits cooling. Once the sun rises, the surface warms and the fog thins from the ground up, usually clearing a few hours after sunrise over land but possibly persisting over the cooler sea.