Empirical Conversion of Rainfall Rate Distribution for Various Integration Times in Malaysia

#A.F. Ismail1, W. Hashim2, K. Abdullah1 and N.A. Malik1 1Dept. of ECE, Kulliyyah of Engineering, International Islamic University Malaysia, Kuala Lumpur, Malaysia.

2MIMOS Berhad, Technology Park Malaysia, Bukit Jalil, Kuala Lumpur, Malaysia. 1af_ismail@iium.edu.my, 2wahidah.hashim@mimos.my, 1khaizuran@iium.edu.my and 1noreha@iium.edu.my

Abstract — The study of rainfall rate integration time is important to designers of satellite communication systems. In most part of the world, long-term rain statistics are typically available for integration time of very long durations; even perhaps of one hour or more. The method and appropriate conversion of rainfall rate distribution from variable integration times to the equivalent 1-minute are indeed vital. This is due to the fact that established prediction methods for estimating the rain induced attenuation on satellite-Earth links utilize the 1-minute rainfall rate data.

Keywords - rainfall rate; integration time; rain attenuation, prediction method.

I. INTRODUCTION

Rainfall intensity distribution is inhomogeneous in space and time. When considering satellite links of 10GHz and above, radiowave propagation in rainy condition is the major concern for telecommunication system engineers. Precipitation rate or rainfall intensity is defined as ‘a measure of the intensity of precipitation expressed by the increase in the height of water reaching the ground per unit time’ [1]. Precipitation rate is generally expressed in millimetres per hour and commonly presented in units of mm hr-1. There are several equipments that can be employed to obtained precipitation intensity measurements.

Comparison studies were conducted in the effort to evaluate the rainfall rates recorded using different precipitation measuring devices. It has been indicated in the literatures that collection techniques do play an important part in making accurate measurements of precipitation intensity. Different types of co-located equipment appeared to give different rainfall rates [2]. Corrective coefficients [3] [4] had also been proposed to relate between the measurements on different types of equipment.

The use of an integration time of 1-minute was selected and adopted by the ITU. This is as a compromise between experimental accuracy and the amount of available rainfall data. In many countries all over the world, long-term rain statistics are only available for long integration time of perhaps one hour or more. Since rainfall rate data at higher than 1-minute integration time are more readily available than 1-minute integration time data, technique to accurately convert

such rainfall rate distribution (i.e. with variable integration times) to the equivalent 1-minute is essential.

This is because most established rain induced attenuation prediction methods for satellite path (to name a few; the ITU-R model [5], the DAH model [6], the Crane models [7]) all utilize the 1-minute rainfall rate data for a specific range of time percentage. For instance, the ITU’s specific attenuation, γR is expressed as:

γR = k (R0.01)α (1)

Where k and α are the frequency-dependent coefficients and R0.01 is the location’s point rainfall rate for 0.01% of the year at 1 minute integration time

II. ESTABLISHED RELATIONSHIPS

The power law relationships had been exploited to approximate the association between the rainfall rate at 1-minute integration time and that obtained at other integration times. One method proposed by previous investigator [8] to convert rainfall data with finite integration time to equivalent 1-minute integration time was derived as the following:

R1(P)=aPbRτ(P) (2)

Consequently, based on 49 years of rainfall rate data measured in Barcelona, Spain, investigators [9] had suggested that such relationship can also be expressed as:

R1(P)=aRτ(P)b (3)

Where R1(P) and Rτ(P) are the rainfall rates exceeded with equal probability P for integration time of 1 minute and τ minutes respectively. The parameters of a and b for the conversions from τ-minute to 1-minute rainfall rate statistics are stated in the table below.

The research is being sponsored under Endowment Fund by IIUM Research and Innovation, International Islamic University Malaysia

2011 IEEE International RF and Microwave Conference (RFM 2011), 12th - 14th December 2011, Seremban, Malaysia

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Table 1: Values for a and b coefficients for Segal and Burgueno 1-minute conversion formula

III. DATA COLLECTED IN MALAYSIA

A. Set-up overview The Transmission Department of MEASAT Broadcast

Network Systems Sdn, Bhd. (MBNS) did carry out the Ku-band beacon signal attenuation and local rainfall intensity measurements drive. The campaign lasted for almost two years commencing from August 1996 and the measurements were recorded into databases. The hope back then was that findings based on the collected databases can lead to improvements in technology resulting in more reliable satellite transmission. It was of utmost important to explore such technology before initiating new service applications in the next/future MEASAT satellites.

A beacon signal attenuation and a rainfall intensity measurement systems were installed at the MEASAT’s All Asia Broadcast Centre Earth-station in Bukit Jalil Kuala Lumpur Malaysia. The satellite signal attenuation in dB during precipitation together with the rainfall intensity readings were simultaneously measured and recorded [10].

The rain gauge used was an optical sensor that measures precipitation rate and provides an analogue voltage equivalent to the measured precipitation intensity. The equipment employed the focusing and defocusing of an optical beam principle to estimate precipitation rate. It measured the precipitation rate by detecting the optical irregularities induced within the sample volume by precipitation particles falling through the beam of partially coherent infrared light. These irregularities are known as scintillation, and by detecting the intensity of scintillation, which are characteristics to precipitation; the actual rainfall rate was determined [11].

B. Measurements Analyses The measured event data were stored in monitoring files on

a daily basis when applicable. Each monitoring file contains data of detected precipitation intensities and calibrated signal levels. From each monitoring file database acquired from MBNS, time-series plots for every measured event can be produced by use of computer software. Table 2 below presents a summary description of the site related to this study

Table 2: Description of the experimental site

Location Latitude

Longitude Climate Dry Months

Duration

Kuala Lumpur

3°08’ N 101°32’ E Equatorial Nil 20 Months

Figure 1 and Figure 2 are two examples of time-series plots of rainfall intensity as attained from MBNS databases. Shown in the figures below are measurements of the rainfall intensity at 10 seconds sampling time. The measurement system sampled the point rainfall rate data from the optical rain sensor at 10-second time interval which was also the integration time. During precipitation events, (e.g. as shown in the figures below) the rain intensity were recorded at every 10-second interval; otherwise the data are stored at every 10-minute sampling.

Figure 1: Event measurement on 04/07/97

Figure 2: Event measurement on 20/07/97

τ (minute)

Segal’s Method Burgueno’s Method

a b a b

5 1.156 0 1.28 0.98

10 1.263 0 1.69 0.94

30 1.569 -0.015 1.32 1.06

60 1.759 -0.054 0.92 1.24

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IV. RESULTS AND ANALYSES Recent developments in weather measuring equipment

enable researchers to adopt an instantaneous or pre-selected integration time in computing the rainfall intensity. MBNS had acquired a ‘scintillation’ type rain gauge with programmable integration time facilities. Acquired databases contain measurements of rainfall rate that are mostly detected at 10-second interval (there are several occurrences where the time stamp is either 9 seconds or 11 seconds but the numbers are minor). As previously mentioned, the measurement system was assigned to take measurement at every 10-minute interval for each day. Whenever the system’s sensor detects precipitation, the systems automatically changed its measurement time interval to 10 seconds. In other words, all measurements during ‘non-rain’ conditions were recorded at interval time of 10 minutes.

Recorded measurements from MBNS rainfall databases at every 10-second interval enable the computations of the cumulative distributions of rainfall rates at 1, 5, 10, 30 and 60-minute integration time. Curves for rainfall rate cumulative distributions obtained with 10-second integration time and five others selected integration time are shown in figure below. From the figure, comparison can be made between the distributions of rainfall rates procured using various integration times.

There are reasonably good agreements for the percentage of the time exceedance greater than 0.01% among plotted statistics for 10 second, 1 minute and 5 minute. Plot drawn for computed 1-minute integration time exhibits very good agreement with the curve of measured rainfall rate at 10-second integration time at all time percentages.

Figure 3: Rainfall cumulative distributions with different integration time

Using the acquired information from above, suitability of the previously proposed conversion formulas was able to be examined. It can be observed from Fig. 4 that the 1-minute integration time statistics of rainfall rate estimated using Segal and Burgueno conversion formulas (for 10 minute and 30 minute) are higher than that of measured rainfall rate statistics at 1-minute integration time.

Figure 4: Comparison between 1-minute integration statistics with Segal

and Bergueno estimations

From the analysis of the rainfall rate data measured at Bukit Jalil over the period of twenty months, it was identified that the statistics of rainfall rate at 1-minute integration time can be related other integration time statistics using the power law relationship expressed as:

Po1(R)=αPτ(R)β (4)

In the above expression, the P01(R) and Pτ(R) are the probability exceeded with equal rainfall rates for integration time of 1 minute and τ minutes respectively. The parameter of α and β for the conversions from τ-minute to 1-minute rainfall rate statistics is provided in the Table 3.

Table 3: Values for α and β coefficients for the time conversion formula

τ (min) α β

5 0.8153 0.8671

10 0.8643 0.8557

30 0.7387 0.7235

60 0.7205 0.6794

V. CONCLUSION

In this paper, the rainfall rates statistics with 10-second integration time to that with different integration time has been presented. The results show that the 10-second rainfall rate statistics very much agrees with that of 1-minute rainfall rate statistics for all measurements higher than 0.01% of the time. There is also a reasonably good agreement between 1-minute rainfall rate statistics with that of 5-minute rainfall rate statistic

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within 0.05% to 1% of the time, but differ obviously at the percentage of time smaller than 0.01%.

Owing to the high rainfall rates encountered in Malaysia and tropical regions, the statistics of rainfall rates acquired is very dependent on the integration time employed. The integration time selected could determine the accuracy of some rain attenuation prediction models. From the figure above, we can observe that the value of rain intensity measured at 0.01% of the time decreases as the integration time increases.

REFERENCES

[1] Recommendation ITU-R PN.310-9, “Definition of Terms Relating to Propagation in Non-Ionised Media”, 1994.

[2] E. Brand, “A Comparative Study of Techniques for Measuring Rainfall Rate and Accumulation”, Proceedings AP2000 Millennium Conference on Antennas and Propagation, ESA Conference Proceedings SP-444, April 2000

[3] C.G. Migliora, M.S. Pontes, and L.S Mello, “Conversion of Rainrate Statistics with Various Integration Times to Equivalent One-Minute Distributions”, IEEE CCECE 2003 Canadian Conference on Electrical and Computer Engineering, vol. 1, pp. 35 - 37, 2003

[4] L.D. Emiliani, L. Luini and C. Capsoni, “Analysis and Parameterization of Methodologies for the Conversion of Rain-Rate Cumulative Distributions from Various Integration Times to One Minute”, IEEE Antennas and Propagation Magazine, vol. 51, pp. 70 – 84, 2009

[5] Recommendation ITU-R P.618-6. “Propagation Data and Prediction Methods Required for the Design of Earth-Space Telecommunication Systems” 1999

[6] A. Dissanayake, J. Allnutt, and F. Haidara, “A Prediction Model that Combines Rain Attenuation and Other Propagation Impairments Along Earth-Satellite Paths”, IEEE Transactions on Antennas and Propagation, AP-45, pp. 1546-1558, 1997

[7] R. Crane, “Modeling Attenuation by Rain in Tropical Region”, International Journal of Satellite Communication, vol. 8, pp. 197-210, 1990

[8] B. Segal, “The Influence Of Rain gauge Integration Time on Measured Rainfall-Intensity Distribution Functions”, Journal of atmospheric and Oceanic Technology, pp. 662-671, 1986

[9] A. Burgueno, M. Puigcerver, and E. Vilar, “Influence of Rain gauge Integration Time on Rain Rate Statistics Used in Microwave Communications”, Annales des Telecommunications - Annals of Telecommunications, vol. 43, pp.522-527, 1988

[10] A. Ismail and P. Watson, “Characteristics of Fading and Fade Countermeasures on Satellite-Earth Link Operating in an Equatorial Climate with Reference to Broadcast Applications”, IEE Proc. Microwave Antenna Propagation, vol 147, no 5, pp. 369-373, 2000

[11] TWI System Inc., “User Manual”, 1996

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