Fog Formation at a Lakeside Station
At a lakeside town on a clear July day, a weather station 300 m from the shore records: 2:00 PM air temperature 28°C, dew point 18°C, wind 8 km/h; 4:00 AM air temperature 14°C, dew point 14°C, wind 2 km/h, fog; 10:00 AM air temperature 22°C, dew point 16°C, fog gone. The lake surface temperature is 22°C. Relative humidity at 2 PM is about 55%. One student says the fog formed because the lake added water vapor to the air. Another says it formed because the air cooled to its dew point. The sky was clear overnight, and the ground surface cooled rapidly.
1. Use the temperature and dew-point data to explain when and why fog formed, and identify which student's explanation is better supported.
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At 4:00 AM the air temperature equals the dew point, so relative humidity is 100% and condensation can occur. The clear sky allowed strong radiational cooling of the ground and the air just above it. The air temperature fell from 28°C to 14°C overnight, which is the cooling needed to reach saturation. The dew point also fell, but the essential condition is that temperature reached the dew point. The lake could add moisture and help raise the dew point, but the lake surface at 22°C was warmer than the 14°C air, so the lake was a heat source, not the main cooling agent. The second student's explanation is better supported. The lake may have supplied some vapor, but without cooling to saturation the fog would not have formed.
2. Explain why the fog disappeared by 10:00 AM even though the dew point rose from 14°C to 16°C.
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By 10:00 AM solar heating had raised the air temperature to 22°C while the dew point was 16°C. Because the temperature was above the dew point, relative humidity was below 100%, so the fog droplets evaporated. The dew point rose because evaporation from the lake and wet ground added water vapor, but the temperature rose more than the dew point. That increased the gap between temperature and dew point and made the air unsaturated. Gentle mixing with drier air aloft and the light wind also helped disperse the fog. Fog therefore disappeared even though the absolute moisture content increased, because warming dominated.
3. Predict what would happen to fog formation if the same overnight cooling occurred but the dew point were 8°C instead of 14°C. Justify using relative humidity reasoning.
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With a dew point of 8°C and a minimum temperature of 14°C, the air would not reach saturation. At 14°C the saturation vapor pressure is about 16 hPa, while at 8°C the vapor pressure is about 11 hPa. That gives a relative humidity near 70%, not 100%. The air would have to cool to 8°C for fog to form, but the observed cooling only reached 14°C. Fog would therefore be unlikely; at most there might be haze or some low cloud if other processes added moisture. This comparison shows that fog depends on the absolute moisture content as well as the amount of cooling, not on temperature change alone.