Reading a Fog Event, Three Rain Gauges, and a Fast Creek Rise
A school weather club logged a 14-hour period ending in valley fog:
| Time | T (°C) | Td (°C) | Pressure (hPa) |
|---|---|---|---|
| 3:00 p.m. | 26 | 14 | 1012 |
| 6:00 p.m. | 20 | 15 | 1010 |
| 9:00 p.m. | 15 | 13 | 1008 |
| 12:00 a.m. | 12 | 11 | 1006 |
| 4:30 a.m. | 9 | 9 | 1005 |
Fog was first visible at 4:30 a.m. and had thinned by 7:00 a.m. (11°C, dew point 10°C). The club's reference sheet gives saturation vapor pressure of 33.6 hPa at 26°C, 23.4 at 20°C, 17.0 at 15°C, 16.0 at 14°C, 14.0 at 12°C, 13.1 at 11°C, and 11.5 at 9°C.
Rain gauges for the same period read 28 mm in an open field, 12 mm under a maple, and 21 mm on the school roof. A nearby creek rose 0.8 m in 45 minutes; the previous week brought 60 mm of rain. One student says the falling pressure 'proves a hurricane,' and another says the creek rise means the storm was a 100-year event.
1. Compute relative humidity at 3:00 p.m. and at midnight, and explain both why the dew point fell so little while temperature dropped 17°C and why fog formed at 4:30 a.m.
Read the worked answer
Relative humidity is e ÷ e_s × 100, where e is the actual vapor pressure, obtained from the dew point. At 3:00 p.m., e = 16.0 hPa (the saturation value at Td = 14°C) and e_s = 33.6 hPa (at T = 26°C), so RH = 16.0 ÷ 33.6 ≈ 48%. At midnight, e = 13.1 hPa (Td = 11°C) and e_s = 14.0 hPa (T = 12°C), so RH ≈ 94%.
The dew point fell only from 14°C to 9°C over 13.5 hours while the temperature fell 17°C, because dew point tracks absolute moisture, not temperature. Clear skies allowed strong radiative cooling of the surface and the air above it, so temperature dropped quickly; the water vapor mixing ratio changed slowly, losing only a little moisture to dew deposited on cold surfaces, which lowers the dew point gradually. Once the temperature reached the dew point (9°C = 9°C), RH hit 100%, vapor condensed onto condensation nuclei, and a radiation fog formed in the valley, where cold, dense air collects. Fog thinned after 7:00 a.m. because solar heating raised the temperature above the dew point and evaporated the droplets.
2. Evaluate the three rain gauge readings and explain the creek's rapid rise. What evidence would you need before calling this a 100-year event?
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The open-field gauge (28 mm) is the most credible areal estimate: it is unobstructed and at standard height above ground. The maple gauge (12 mm) undercounts badly because the canopy intercepts rainfall and diverts much of it down the trunk, so it measures throughfall at one point, not the storm total. The roof gauge (21 mm) is affected by wind acceleration over the roof edge, splash, and its non-standard height, and roof-mounted gauges are known to undercatch in windy conditions. Use 28 mm, with a caveat that a single gauge is a point measurement.
The 0.8 m rise in 45 minutes indicates a fast, flashy hydrologic response. That is consistent with the 60 mm of rain the previous week, which would have raised soil moisture toward saturation and left little capacity for infiltration, so the new 28 mm became mostly overland flow. A small, steep, or paved catchment would amplify this.
A '100-year event' is a statistical statement: the rainfall or stage with a 1% chance of being equaled or exceeded in any year, estimated from a long record at that location. One storm at one gauge cannot establish it. You would need decades of quality-controlled gauge or stage data, a flood-frequency analysis with confidence intervals, and confirmation the gauge was not blocked, backwatered, or affected by a recent channel change.
3. Critique the hurricane claim using the pressure record, and describe what a hurricane signature would actually require.
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The record shows a fall from 1012 to 1005 hPa over 13.5 hours, about 0.5 hPa per hour and 7 hPa total. That is well within ordinary synoptic-scale behavior - a frontal passage or a developing low can produce 1–2 hPa per hour for a time - and the pressure was still falling gently at the end of the record. A hurricane produces a far deeper and faster fall (tens of hPa, often with a sharp eyewall drop), sustained strong winds, heavy convective rainfall, and a warm-core structure aloft. Nothing in the temperature or dew point record suggests a tropical cyclone: the dew point stayed near 9–15°C, indicating a relatively dry air mass, whereas tropical cyclones are characterized by very high moisture through a deep layer.
A second problem is that the club's barometer readings appear to be station pressure, not reduced to sea level. Station pressure depends on elevation, so the absolute values cannot be compared with map values without reduction.
The instructional move is to have students state what observation would distinguish the hypotheses - sustained wind speed and direction, radar or satellite imagery, 24-hour pressure tendency, and the dew point depression - and then check whether the club actually recorded them. It did not, which is itself the lesson about instrumentation planning.