5.9 Preliminary Studies on Raindrop Size Distribution
5.9.1 Description of the Raindrop size Measurement and Distribution
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Fig. 5- 13a: Schematics diagram of configuration of distrometer with other accessories -RD-80 [Distrometer RD-80 Operating Instructions, Feb 2007]
Fig. 5-13b: Block diagram of the distrometer RD-80 [Distrometer RD-80 Operating Instruction, Feb, 2007]
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Fig. 5-14 below shows the distribution of the probability density function for the measured drop- sizes in Durban for six months (October 2008 – April, 2009). In this figure, the probability density function distribution for each month shows a negative exponential distribution. These distributions confirm the statement of Feingold et al. [1986] that says “the inherent assumption of drop-size distribution is that they are exponential” and also that of Joss and Gori [1978] that says
“drop size distribution tends to be exponential when the sampling time is sufficiently long”. This monthly probability distribution function can be said to be long-term.
0.000001 0.00001 0.0001 0.001 0.01 0.1 1 10
0 1 2 3 4 5
Raindrop diameter (mm)
October November December January February March April
13 pdff(Di),(mmm)
Fig. 5- 14: Probability density function for the measured drop-sizes in Durban
The rain events recorded in these six months are classified into drizzle, widespread, shower and thunderstorm rains for efficient propagation prediction and modeling. Though there are no defined ways of classifying these rain types, but various researchers such as Joss et al. [1968], Fang and Chen [1982], Ajayi and Adimula [1996], Tokay and Short [1996], etc. have classified the rain based on the climatic characteristics, drop diameter, and the rain rate recorded in their location (see Chapter 2).
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The 1-minute rain rates for all the rain events are then grouped into ten classes of rain and classified into the drizzle widespread, shower and thunderstorm. These rain types are classified based on the nature and the characteristics of rain, the drop diameters and the rain rates recorded in Durban. These rains are then categorized into the stratiform and convective rains using 10 mm/h rain rate as the boundary between the two categories of rain as used by Matricciani et al., [2000] and Konwar, et al., [2006]. Table 5-7 below shows the groups, descriptions of the rain types, and the mean rain rate values for each the rain rate group. Fig. 5-15 – 5-18 below shows the drop-size distributions that describe the measured rain drops spectra for the different rain types.
Table 5- 7: Groups and description of the rain types in Durban
From these figures (Fig. 5-15 – 5-18) the drizzle and widespread rains which have small mean rain rate values have larger numbers of smaller drop-size diameters. As the values of the rain rate increases, the number of the smaller drops diameters also decreases, especially with the shower and thunderstorm rains. To determine the suitable distribution for these rain types, quantitative analysis is done between the measured raindrop sizes and the distribution models. A measure of the error between the distributions and raindrop size measurement is conducted. Table 5-8 shows the root mean square percentage error between the lognormal, gamma, exponential distribution and the measured drop-size distribution
Rain rate, R (mm/h) groups
Mean rain rate (mm/h)
Description Types of rain Categories of rain
0.5
R 0.24 Extremely light rain
Drizzle
Stratiform rain
0.5 R 1 0.73
Light rain
1 R 3 1.71
3 R 5 3.84
5 R 10 6.90 Moderate rain Tropical widespread
10 R 20 13.70
Heavy rain Tropical shower
Convective rain
20 R 40 27.04
40 R 60 48.78 Very heavy rain
Tropical thunderstorm
60 R 100 68.15
Extreme rain
100
R 117.15
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0.01 1 100 10000 1000000
0 1 2 3 4 5 6
Raindrop diameter (mm)
Measured drop-size spectra Lognormal distribution Gamma distribution
Negative exponential distribution
13N(D),(mmm)
Mean rain rate, = 3.84 mm/h
Rm
Fig. 5- 15: Raindrop size distribution for drizzle rains
0.01 1 100 10000 1000000
0 1 2 3 4 5 6
Raindrop diameter (mm)
Measured drop-size spectra Lognormal distribution Gamma distribution
Negative exponential distribution
13N(D),(mmm)
Mean rain rate, = 6.90 mm/hRm
Fig. 5- 16: Raindrop size distribution for widespread rains
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0.1 1 10 100 1000 10000 100000
0 1 2 3 4 5 6
Raindrop diameter (mm)
Measured drop-size spectra Lognormal distribution Gamma distribution
Negative exponential distribution
13 N(D),(mmm)
Mean rain rate, = 27.04 mm/hRm
Fig. 5- 17: Raindrop size distribution for shower rains
1 10 100 1000 10000
0 1 2 3 4 5 6
Raindrop diameter (mm)
Measured drop spectra Lognormal distribution Gamma disribution
Negative exponential distribution
13 N(D),(mmm)
Mean rain rate, = 68.15 mm/hRm
Fig. 5- 18: Raindrop size distribution for thunderstorm rains
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Table 5- 8: The root mean square percentage error between the measured rain drop distribution and other distributions
Rain types Root mean square percentage error, rms (%) Lognormal
distribution
Gamma distribution
Negative exponential distribution
Drizzle 7.24 7.72 11.79
Widespread 6.06 6.89 23.41
Shower 3.71 5.66 43.96
Thunderstorm 63.31 13.23 201.87
From the above table (Table 5-8), the negative exponential distribution gives the highest percentage of error for all the rain types, therefore it is not suitable to predict the distribution for the rain types. The lognormal drop-size gives the lowest percentage error for drizzle, widespread, and shower rain types, and the gamma drop-size distribution gives the lowest percentage error for thunderstorm rains. Therefore the lognormal drop-size distribution can be employed to predict the drizzle, widespread, and shower rain types, while the gamma drop-size distribution is better suited for the thunderstorm rain types.
It should be noted that the measured raindrop-sizes are recorded for just six months in Durban, between October-April, which basically are the summer and autumn seasons. A longer period of the raindrop size measurements and 1-minute rain rates taken throughout the year may be required for accurate drop-size distribution models.