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Growth by Collision and Coalescence Questions and Answers

31.

Assertion (A): The slope of the Marshall Palmer distribution changes with rainfall rate.
Reason (R): Heavier rain contains proportionally more large drops, which flattens the decay.

Answer: C

Correct answer: Both A and R are true, and R is the correct explanation of A

Both are true and the reason gives the mechanism. The slope parameter falls as the rainfall rate rises, so the exponential decays more gently and large drops are relatively more numerous. That is what allows a radar to infer a rainfall rate from reflectivity at all, since the two are related through the assumed spectrum.

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Answer: D

Correct answer: the sum of the sixth powers of the drop diameters

\[ Z = \sum D^6. \] The sixth power means a single 4 mm drop returns as much signal as 4,096 drops of 1 mm, so reflectivity is dominated by the largest drops present. Rainfall rate depends on a much lower power, which is why the relation between the two is empirical and varies with the type of rain.

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33.

Assertion (A): Radar reflectivity is dominated by the largest drops in the sample volume.
Reason (R): Reflectivity scales as the sixth power of drop diameter in the Rayleigh regime.

Answer: A

Both are true and the reason gives the scaling, and doubling a drop's diameter multiplies its contribution by sixty four. A handful of large drops can outweigh many thousands of small ones. Reflectivity and rain rate are related only statistically.

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34.

Consider the following statements about the Z-R relationship.
1. It links radar reflectivity to rainfall rate empirically.
2. Different coefficients suit convective and stratiform rain.
3. A single universal relationship applies to all rainfall types.

Answer: B

The first two are correct and reflect standard radar practice. The third is not so, because the drop size distribution differs systematically between rain types and no single fit serves them all. Operational radars switch coefficients by precipitation type.

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Answer: C

This geometric rate is then multiplied by the collection efficiency to give the actual kernel. Both factors grow with the collector size, which is the source of the accelerating growth. Area and fall speed both rise with the square of the radius.

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36.

If a collector drop's radius doubles, its geometric sweep-out rate in the Stokes regime increases by approximately

Answer: D

Cross sectional area rises with the square of the radius and Stokes fall speed with the square as well. The product therefore rises as the fourth power, which is why collection runs away once it begins. Reaching the threshold is the whole of the difficulty.

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37.

State whether the following is true or false.
Collection efficiency can exceed one for certain droplet pairs.

Answer: A

Wake capture behind a falling collector can draw in droplets from slightly outside the geometric cross section. The effect is modest but is well documented for particular size ratios. Wake capture is strongest at intermediate radius ratios.

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Answer: B

Small droplets almost always merge on contact, whereas large drops may bounce or separate again after temporary union. Grazing collisions between large drops are the least likely to end in a permanent merger. Grazing geometry and high impact energy both work against union.

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39.

Assertion (A): An electric field can raise the coalescence efficiency of colliding drops.
Reason (R): It helps drain the intervening air film that would otherwise keep the surfaces apart.

Answer: C

Both are true and the reason gives the mechanism, and charged drops behave similarly. This is one of the ways electrification inside a thunderstorm may feed back on its own microphysics. Laboratory work has confirmed the effect at realistic field strengths.

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Answer: D

The name refers to the mechanism rather than to the temperature at the ground. It is common in maritime tropical cumulus but occurs wherever a cloud remains entirely above freezing throughout. Tropical maritime cumulus are the archetypal case.

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