Meteorology and Dispersion Questions and Answers

Answer: A

Geostrophic wind occurs when the pressure gradient force is balanced by the Coriolis force alone. The wind then blows parallel to the isobars, with no component across them. This is the situation in the free atmosphere above the friction layer, where the surface drag is negligible. Friction is absent, so the option adding a frictional force describes the lower, non-geostrophic boundary-layer wind, where the wind crosses the isobars at an angle. Centripetal force enters the gradient wind, where the isobars are curved, not the straight-isobar geostrophic case.

Answer: D

The scales of meteorology, from the smallest to the largest, are micro-, meso- and macro-scale. Micro-scale covers features of a few kilometres or less, such as turbulence, dust devils and local eddies. Meso-scale covers phenomena of tens to hundreds of kilometres, such as sea breezes, thunderstorms and mountain-valley winds. Macro-scale covers whole weather systems and global circulation, including cyclones, monsoons and jet streams. The order micro, meso, macro therefore starts from the least, and every other order places a scale out of sequence.

Answer: A

For a well mixed box with a conservative pollutant, the concentration approaches its final value exponentially with the flushing time equal to length divided by wind speed.\[ \tau = \frac{L}{u} \]\[ \tau = \frac{10^{4}\ \mathrm{m}}{5\ \mathrm{m/s}} \]\[ \tau = 2000\ \mathrm{s} \]After one time constant the concentration is \(1 - e^{-1} \approx 0.63\) of its final value, so 63% is reached in 2,000 s. The mixing height cancels out because it appears in both the box volume and the air flow. The values 5,000 s, 10,000 s and 1,000 s do not equal L/u.

Answer: B

Synoptic scale phenomena are the large weather systems such as cyclones, anticyclones and fronts, with horizontal scales of hundreds to a few thousand kilometres, and the keyed range is 200 to 40,000 km. The range 1 to 10 km belongs to local or microscale and convective features, and 10 to 100 km is mesoscale. A range of 10,000 to 100,000 km is not possible for weather systems, since the circumference of the Earth is only about 40,000 km.

Answer: D

The mixing height is the height at which the dry adiabatic line starting from the maximum surface temperature meets the ambient temperature profile. The ambient atmosphere is isothermal at 25 degrees Celsius and the surface warms to 35 degrees, a difference of 10 degrees. With an adiabatic lapse rate of 1 degree per 100 m:\[ h = \frac{35 - 25}{0.01} = 1000\ \mathrm{m} \]So the mixing height is 1 km. The values 1.5, 2.5 and 3.5 km would need temperature differences of 15, 25 and 35 degrees.

Answer: B

An atmosphere with an isothermal profile is slightly stable, option B. In an isothermal layer the temperature does not change with height, so the environmental lapse rate is zero, which is lower than the dry adiabatic rate of about 9.8 degrees per km, and a rising parcel of air becomes colder and denser than its surroundings and tends to sink back.

Option A, very stable, applies to an inversion, where the temperature rises with height. Options C and D, unstable and very unstable, apply when the environmental lapse rate exceeds the adiabatic rate. The isothermal case lies between the neutral and the inversion case.

Answer: A

In a box model of an urban air shed, a conservative pollutant emitted at a steady rate is mixed through a box of length L, width W and height H, with wind speed u. At steady state the concentration is \(C = \dfrac{Q}{u\,W\,H}\), where Q is the emission rate, so \(C \propto \dfrac{1}{H}\). The concentration falls in proportion to the mixing height. The options with \(H^{2}\), \(\sqrt{H}\) or \(H^{-3/2}\) do not follow from the mass balance.

Answer: C

Relative humidity is the ratio of the actual vapour content to the saturation vapour content at the air temperature. The actual mixing ratio is the saturation mixing ratio at the dew point, so \(RH = \dfrac{ws \text{ at } Td}{ws \text{ at } T}\), which is option C. Options A and B use the actual mixing ratio, w, which is not what the expression is given in, and option D inverts the ratio.

Answer: B

The sea breeze is a mesoscale phenomenon, with a horizontal extent of tens of kilometres. A cyclone is a synoptic scale system and eddies are of smaller scale, and the key does not give the tornado. So the answer is the sea breeze.

Answer: A

The key gives the exponent as \(\le 0.6\). The power law of wind with height, \(\dfrac{u_{1}}{u_{2}} = \left(\dfrac{z_{1}}{z_{2}}\right)^{p}\), has an exponent that depends on stability and roughness, and for heights of a few hundred metres it is well below 1. The exponent is not negative, and a value of 1 would make the wind speed increase in proportion to height, which does not happen. This explanation follows the official key.