NATS 1780 A & B 6.0 Y (Winter 2015) – Assignment 3, Version 0.9

 

Due: No later than 11:00 pm on February 23, 2015 via Moodle

 

(Late Penalty: 5% per day – including weekends; 40% deduction after solutions are posted.)

 

Instructions:

· You are expected to provide answers for all questions. You are encouraged to show all of your work so that marks can be awarded for partially correct answers.

· Although you are encouraged to collaborate with your classmates, each of you is expected to submit a separate and distinct assignment.

 

 

 

 

1. Regarding precipitation. [40 marks]

 

a. What determines the terminal velocity of a hydrometeor? [2 marks]

b. How might each of the following effect terminal velocity:

i. Updrafts. [1 mark]

ii. Downdrafts. [1 mark]

iii. Buoyancy. [2 marks]

iv. Phase. [2 marks]

v. Shape. [2 marks]

c. Complete Table 1 by determining the terminal velocity of the hydrometeors based on their radii. Using this terminal velocity, and assuming a fall distance of 750 m, calculate the fall time and state whether the hydrometeor is cloud or rain. [12 marks]

d. Determine the volume of the 320 μm radius hydrometeor in m3. Assume it is spherical in shape, and comprised of pure water. [3 marks]

e. Suppose 1000 of these 320 μm hydrometeors accumulate over a period of 10 minutes.

i. Determine the total volume of accumulated water in m3. [2 marks]

ii. Determine the height of the water, h, in mm that occupies a rain gauge of diameter 5 cm. Use h = n V / π R2 to calculate the water height for a rain gauge of radius, R; here n represents the number of hydrometeors of volume, V (i.e., n V, your answer to 1(e)(i)). [4 marks]

iii. What assumption is implied regarding the hydrometeors in the rain-gauge height formula of 1(e)(ii)? [1 mark]

iv. Determine the corresponding hourly rain rate in mm/hr. [2 marks]

v. Based on the intensity determined in 1(e)(iv), classify this as stratiform or cumuliform precipitation. Justify your answer. [2 marks]

vi. How would the calculation of height in the rain gauge be affected if the precipitation type was snow versus rain? [2 marks]

vii. EMOS measures precipitation. Yet, it is stated that: “precip only works when temperature > 0”. Why do you think this is the case? [2 marks]

 

 

Radius (μm) Terminal Velocity (m/s) Fall Time Cloud or Rain 25       320

Table 1. Cloud versus rain classification on the basis of terminal-velocity derived fall times.

 

 

 

2. For stations above Mean Sea Level (MSL), the pressure at the point of observation (pOBS) can be corrected to its MSL equivalent pressure (pMSL) through use of the Hydrostatic Equation,[footnoteRef:0] namely: [0: ]

 

pMSL = pOBS + ρgzOBS. (Eq’n 1)

 

In this equation, zOBS is the height of the observation point relative to MSL, ρ is the density of air at the point of observation and g is the acceleration due to gravity.

a. Based on Figure 1 below, state the height (in m above MSL) of the EMOS meteorological observation station.

b. Assuming that ρ is 1.2041 kg/m3, g is 9.81 m/s2, and pOBS is the EMOS station air pressure in the above figure, calculate pMSL from the equation above (i.e., Eq’n 1). [Recall: 1 hPa ≡ 100 Pa and 1 Pa = 1 kg / (m s2). Note that 1.2041 kg/m3 is the value for the density of air at STP – namely at 20 °C and 1013.25 hPa.]

c. Compare and contrast the result of your calculation above (2(b)) with the EMOS-reported value for MSL air pressure in Figure 1.

d. Assuming that the reason for this difference is entirely due to density, calculate the density at EMOS using the Ideal Gas Law, namely:

 

ρ = pOBS / RTOBS (Eq’n 2)

 

Note that pOBS is the same EMOS station air pressure in the above figure, TOBS the EMOS air temperature from the above figure converted to K, and finally that R is a constant with the value 287 J/(kg K). [Note that the Joule, a unit of energy, is expressible as a (N m).]

e. Re-calculate pMSL from Eq’n 1 above using the improved value for density determined in 2(d).

f. Compare and contrast the result of your calculation above (2(e)) with the EMOS-reported value for MSL air pressure in the above figure.

g. Based on the comparisons (2(c) and 2(f)) state the significance of pressure and temperature-adjusted density in the calculation of pMSL.

 

 

Figure 1. EMOS observables captured at 14:45 UTC on January 24, 2015.

 

 

 

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