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Performance analysis of 60-min to 1-min integration time rain rate conversion models in Malaysia
Accepted Manuscript Performance analysis of 60-min to 1-min integration time rain rate conversion models in Malaysia Yun-Yann Ng, Mandeep Singh Jit Singh, Vinesh Thiruchelvam PII:
S1364-6826(17)30167-0
DOI:
10.1016/j.jastp.2017.10.004
Reference:
ATP 4707
To appear in:
Journal of Atmospheric and Solar-Terrestrial Physics
Received Date: 19 March 2017 Revised Date:
6 October 2017
Accepted Date: 9 October 2017
Please cite this article as: Ng, Y.-Y., Singh, M.S.J., Thiruchelvam, V., Performance analysis of 60-min to 1-min integration time rain rate conversion models in Malaysia, Journal of Atmospheric and SolarTerrestrial Physics (2017), doi: 10.1016/j.jastp.2017.10.004. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT PERFORMANCE ANALYSIS OF 60-MIN TO 1-MIN INTEGRATION TIME RAIN RATE CONVERSION MODELS IN MALAYSIA Yun-Yann Ng1*, Mandeep Singh Jit Singh1, Vinesh Thiruchelvam2 1 Universiti Kebangsaan Malaysia, Faculty of Engineering and Built Environment, Department of Electrical, Electronic and System Engineering, Selangor, Malaysia. 2 Asia Pacific University of Technology & Innovation, Faculty of Computing, Engineering & Technology, Malaysia. *Corresponding author email: [email protected]
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ABSTRACT Utilizing the frequency band above 10 GHz is in focus nowadays as a result of the fast expansion of radio communication systems in Malaysia. However, rain fade is the critical factor in attenuation of signal propagation for frequencies above 10 GHz. Malaysia is located in a tropical and equatorial region with high rain intensity throughout the year, and this study will review rain distribution and evaluate the performance of 60-minute to 1-minute integration time rain rate conversion methods for Malaysia. Several conversion methods such as Segal, Chebil & Rahman, Burgeono, Emiliani, Lavergnat and Gole (LG), Simplified Moupfouma, Joo et al, fourth order polynomial fit and logarithmic model have been chosen to evaluate the performance to predict 1-minute rain rate for 10 sites in Malaysia. After the completion of this research, the results show that Chebil & Rahman model, Lavergnat & Gole model, Fourth order polynomial fit and Logarithmic model have shown the best performances in 60-minute to 1-minute rain rate conversion over 10 sites. In conclusion, it is proven that there is no single model which can claim to perform the best across 10 sites. By averaging RMSE and SC-RMSE over 10 sites, Chebil and Rahman model is the best method. Keywords: 1-min Integration Time Rain Rate; Conversion Models; Tropical Region; Rain Rate distribution.
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1. INTRODUCTION Rapid development of technology for wireless communication above 10 GHz, is important to resolve the crowding of the currently used frequency bands. This is particularly important in developing countries such as Malaysia. Telecommunication system engineers seek for Ku-band (12/14 GHz) because of its advantages of wider spectrum availability, higher data transfer and smaller antenna size (Owolawi et al., 2009). However, rain fade is the most critical factor of signal degradation when analysing satellite communication links at frequencies above 10 GHz. Rain affects the transmission of an electromagnetic signal by increasing the system noise temperature, attenuating the signal and changing in polarization. These three mechanisms cause degradation in the signal quality received. When the frequency increases, the signal strength deteriorates and rain drops affect the signal propagation (Ooi et al., 2013). According to International Telecommunication Union (ITU-R P837-6, 2012), 1-minute rain rate statistics are required to estimate the rain influenced fade effect on the propagation rate. 1-minute integration times ensures that the peaks of rain event are sufficiently experimented and the use of longer integration times would result in an averaging effect (as the rain rate would be the average of accumulation over a longer time interval), causing high intensity rain rate value to appear low (Emiliani et al., 2008). Yet long term basis of 1-minute integrated rainfall data is insufficient in Malaysia. As a result, an effective conversion method for rain rate is necessary to predict a precise 1-minute rain rate distribution (Mandeep et al., 2008). Malaysia is a tropical country where precipitation occurs throughout the year, particularly during monsoon seasons. There were several local studies conducted to understand conversion process of rain rate distribution
from higher integration times into 1-minute in Malaysia. From the studies done by J.S. Mandeep, et al. (2008), Segal method is the best conversion models when applied to Southeast Asia and Kuching (Mandeep et al., 2008). Chebil & Rahman applied Segal's method to convert 60-minute and 1-minute rain rate in Malaysia and published conversion method by modified Segal model in year 1999 (Chebil and Rahman, 1999). Selamat et al. (2014) did comparison among 5 existing conversion methods for converting 60-minute to 1-minute on 5 sites of East Malaysia and the result shows Segal method gave the best performance among 5 methods: Segal, Burgueno et al, Emiliani et al, Chebil and Rahman, ITU-R P.837-6 Annex 3 (Selamat et al. 2014). Here we present the analysis of 1-minute and 60minute rain rate statistics observed from a 4-year (year 2010 – 2013) measurement at 10 locations from Peninsular of Malaysia and East Malaysia. There are 9 rain rate conversion models selected to convert 60-minute to 1-minute integrated time. The performance analysis over the conversion models and rain rate models are evaluated in this paper. The study is important to understand the performance of existing models and to look for the suitable models to be used in the selected areas in Malaysia. 2. OVERVIEW OF CONVERSION METHODS FOR RAIN RATE DISTRIBUTION The conversion methods can be categorized into 3 groups: physical, analytical and empirical method. Most of the researchers tend to use the empirical method extensively to convert from higher integrated time to lower equivalent due to its simplicity and experiment dependent (Emiliani et al., 2009). The proposed conversion methods used in this paper are Segal method
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(1986), Chebil and Rahman method (1999), Burgueno et ACCEPTED al. method (1988), Joo et al. method (2002), Lavergnat and Gole method (1998), Emiliani and Luini method (2008), simplified Moupfouma (1995), fourth order polynomial fit (2016) and logarithmic model (1994).
butions of rain rate 1-, 10-, 20-, 30-, 60-minutes integraMANUSCRIPT
tion time (Joo et al., 2002). P1(P) = aPτ10[b exp(-t/24.28)] (P) (6) where P1 and Pτ are the possibility of a specified amount of rain rate at 1-minute and τ-minute, respectively. The sampling interval (minute) for the rain gauge was expressed as t, and a and b are indicated as regression coefficients.
2.1 EMPIRICAL METHOD Empirical method provides simple methodical laws to express the correlation between equiprobable rain rate values. This method is easy to use and experiment dependent (Emiliani et al., 2009). Example: Segal model (1986), Chebil & Rahman model (1999), Burgueno et al. model (1988), Joo et al. model (2002), Emiliani and Luini model (2008) fourth order polynomial fit (2016) and lognormal method (1994).
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2.1.5 Emiliani et al. Method (2008) Emiliani et al. is an extension of ITU-R P.837-5 and the method was published at year 2008. New set of coefficient values was used based on an extended database of three types of Köppen climatic region when developing power law conversion method (Emiliani et al., 2008).
2.1.1 Segal Method (1986) A rain rate conversion factor was proposed by Segal based on the data analysis from 45 stations in Canada up to 10-year rainfall data. A specialized database of high resolution rainfall records prepared at the Communications Research Centre was used for developed this model (Segal, 1986). The proposed method by Segal (1986) expressed as equation (1) and (2): (1) R1(P) = ρτ(P)Rτ(P) mm/h With conversion factor, pτ(P) stated as per power law ρτ(P) = aPb (2) R1 (P) and Rτ (P) are the rain rate with a sampling interval of 1 and τ min, correspondingly, which contain a percentage of time, P. The conversion variables were be symbolized as a and b.
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2.1.6 Fourth Order Polynomial Fit (2016) The new proposed model by Shrestha et al (2016) was based on the data analysis from rainfall distribution data from KMA (2004-2013) over 9 regions of the South Korea. R1(P) = ae(a-b)[Rτ(P)] 4 + be(b-a) [Rτ(P)] 3 + c[Rτ(P)] 2 +d[Rτ(P)] mm/h (7) R1 (P) and Rτ (P) are the rain rate with a sampling interval of 1 and τ min, respectively, which contain a percentage of time, P. a, b, c and d are regression coefficients that are obtained though statistical analysis of rainfall date with curve fitting technique.
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2.1.2 Chebil And Rahman Method (1999) This conversion method was modified conversion factor of Segal methods and recommended approximating the rain rate conversion factor from 60 minute to 1minute integration time for 82 locations in Malaysia (Chebil and Rahman, 1999). Conversion factor from 60minute to 1-minute rainfall rate were expressed as (3) and (4): ρ60 (P) = R1 (P) / R60 (P) (3) where ρ60 (P) is represented as a mixed Power – Exponential Law. ρ60 (P) = aPb + ce(dP) (4) where the percentage of time is expressed as P. The rain 1-minute rain rate and 60-minute rain rate integration time to the percentage of time is designated as R1 (P) and R60 (P), respectively. The regression variables are represented as a, b, c, and d.
2.1.7 Logarithmic model (1994) The empirical equation for Logarithmic model (Lee et al., 1994) is given as below: log[R1(P)] = a log[Rτ(P)] mm/h (8) Where a is the regression co-efficient derived from statistical analysis of rainfall rate. 2.2 PHYSICAL METHOD The physical method uses the conversion of statistics which is constructed on the physical processes elaborated in the rain formation and development and in the evolution of a rain event in time. The physical modelling of the rainfall process is usually mathematically complex and principally particular to the meteorology’s field, for weather forecasting activities (Emiliani et al., 2009).
2.2.1 Lavergnat and Gole model (1998) LG model was developed based on 2-year data collection in Paris by using a disdrometre that analyzed fine rain temporal structure rather that its intensity characteristic (Lavergnant and Gole, 1998). A conversion factor to scale both the rain and the probability were represented as shown in equation (9) and (10) respectively: mm/h (9) R1 = RT / h α (10) P(R1)1 = hαP(RT)T Where h is conversion factor, h = 1/T and α is the coefficient which is determined empirically. Only one parameter is needed for conversion between integration times.
2.1.3 Burgueno et al. method (1988) This method was developed from data analysis of 49year of rain rate measurement at Barcelona in Spain (Burgueno et al, 1988). The principle of direct power law fit was applied in the equation as shown below. R1(P) = aRτb (P) mm/h (5) R1 (P) and Rτ (P) are the rain rate with 1-minute and τminute sampling interval, respectively, which contain a percentage of time, P. a and b represent the conversion variables. 2.1.4 Joo et al. method (2002) Joo method was developed according to 2-year of rain events in Korea (July 1998 to May 2000) with the distri-
2.3 ANALYTICAL METHOD
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2.3.1 Simplified Moupfouma and Martin (1995) This analytical method was developed based on the rain rate measurement in Chilbolton, UK for integration times ranging from 1-minute to 60-minute (Moupfouma and Martin, 1995). The formulation of this method is shown below: P( R)1 = (a1 / aT) R (br-b1) e (ur-u1)RP(R )T (11) The conversion of cumulative distributions requires the knowledge of 6 coefficients corresponding to a, b and u for both the 1-minute and T-minute rain rate cumulative distribution functions on top of P( R)T.
Latitude (oN) 3.16 1.48 5.98 6.22 6.66 4.58 3.71 5.33 3.83 5.39
Longitude (oE) 101.69 110.34 116.17 102.26 100.32 101.12 101.74 103.14 103.29 100.40
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Table 1 The location selected for the research study. Station ID Location 3116003 Main Office of JPS Malaysia at Wilayah Persekutuan 1403001 Kuching Airport At Sungai Sarawak Basin 5961001 Kiansam At Sabah 6122064 Stor JPS. Kota Bharu At Kelantan 6603002 Padang Besar At Titi Keretapi Perlis 4511111 Politeknik Ungku Omar 3717101 Bukit Fraser, Selangor 5331048 Setor JPS Kuala Terengganu 3833002 Pejabat JPS Pahang 5303053 Komplek Prai Pulau Pinang
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3. DATA COLLECTION For this study, rainfall data source is from DID (Department of Irrigation and Drainage) Malaysia which has huge hydrology network station all over Malaysia. DID delivers rainfall data in 1-minute or longer time interval depending on the station ability. Stations using automatic logger provide 1-minute rainfall with inadequate recoding span, meanwhile other stations provide longer interval data with manual check gauge. The rainfall data is collected in millimetre every minute for 4-year (2010-2013), starting from 1st January 2010 to 31st December 2013. 8 sites at Peninsular Malaysia, 1 site at Sarawak and 1 site of Sabah are selected for this study and shown in Table 1. The map of the selected locations is reflected in Fig- 1.
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The analytical method assumes thatACCEPTED the rain rate cumulative distribution functions can be denoted by a given function of which the general shape remains constant, nonetheless the parameters of which differ subject to the integration time (Emiliani et al., 2009).
Fig- 1 The map of locations selected for the research study. The rain intensities are measured using automatic rainfall gauges of 0.5mm per tip at 1-minute. The rain rate cumulative distribution from 1-minute and 60minute integration times engendered from the rain gauge data. The data availability is 98.2% for all sites from year 2010-2013. Rain gauge calculates the time of occurrence of a tip, however it does not recorded the precipitation rate at that particular moment. DID's rainfall data is recorded in a comma separated value (.csv) file with columns of date, time and rain amount (mm). The 1-minute rain rate is calculated by using for-
mula (12): 1-minute Rain rate (R1-min) = Rain amount in t-minute x (60-minute / t-minute) (12) The cumulative statistics for rain rate are usually presented as the exceedance probability (abscissa) versus the rain rate (ordinate). The rain rate cumulative distribution by calculating P(R ε ro) the probability of the rain rate intensity R(mm/hr) exceeds a threshold value of r (mm/hr) for a time period, T. (13) Pr =P(R≥r0) = N0 / NT where No is the number of rain rate value larger than ro
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and NT the total number of rainfall rate inACCEPTED a time period, T.
Malaysia is located MANUSCRIPT
in equatorial and tropical area which having high rainfall throughout the year. It is important to understand the rainfall amount over a year for every site in this study. Table 2 is the summary of rainfall amount from year 2010 to 2013.
4. RESULTS AND DISCUSSION 4.1 Distribution of Rain Rate
Table 2 Rainfall (in mm) from year 2010 – 2013 for over 4-year. Sites Rainfall amount (mm) 2011
2012
2013
Average
Wilayah Persekutuan
2330
2517
2969
3322
2784
Kuching, Sarawak
4303
4263
3681
3934
4045
Kiansam, Sabah
4597
3151
2218
3044
3252
Kota Bharu, Kelantan
2205
2902
2772
2001
2470
Padang Besar, Perlis
1881
1445
1626
1212
1541
Politeknik Ungku Omar Ipoh
2885
2196
2257
2123
2365
Bukit Fraser, Selangor
1948
2283
2586
2020
2209
Setor JPS Kuala Terengganu
1737
2587
2575
2248
2287
Pejabat JPS Pahang
1952
1832
2726
1289
1950
Komplek Prai Pulau Pinang
1422
1908
1618
2239
1796
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2010
the straits of Malacca during April to September. Along the east coast of Peninsular Malaysia, the northeast coast of Sabah and Western Sarawak experience heavy rain spells for the period of the northeast monsoon season. In contrast, inland regions and regions that sheltered by mountain ranges are fairly exempted from its influence. In general, November, December and January are the months with maximum rainfall over the study areas, whereas June and July are the driest months in the most districts. Fig- 2 shows the monthly rainfall amount for 10 sites over 4-year (2010-2013).
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From Table 2, Kuching and Kiansam which located in East Malaysia experience the highest annual rainfall amount and average rainy days throughout a year. Nevertheless Padang Besar and Prai which located at the north of Peninsular Malaysia have the lowest annual rainfall amount and average rainy days over a year. The rainfall distribution pattern is determined by monsoon seasons. There are 2 monsoon seasons occurred in Malaysia, e.g. northeast and southwest monsoon seasons. Northeast monsoon blows from South China Sea during October to March and southwest monsoon blows from
Fig- 2 Monthly rainfall amount summary. Yearly rain rate statistics for numerous percentages of time are needed in the areas of interest when designing satellite link systems. The average rainy days per year,
annual rainfall amount, 1-min R0.01% and 60min R0.01% rain rate over 4-year for 10 sites is shown in Table 3.
Table 3
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Summary of average rainy days per year, ACCEPTED annual rainfall amount, 1-min R0.01% and 60min R0.01% rain rate over 4-year for 10 MANUSCRIPT sites. Sites Average rainy days per Annual rainfall amount 1-min R0.01% 60 min R0.01% year (mm) (mm/h) (mm/h) Wilayah Persekutuan 179 2784 143 70 Kuching 246 4045 140 70 Kiansam 194 3252 140 72 Kota Bharu 168 2470 120 57 Padang Besar 156 1541 120 62 Ipoh 180 2365 136 64 Bukit Fraser 223 2209 124 56 Kuala Terengganu 171 2287 128 58 Pahang 149 1950 128 52 Prai 163 1796 122 48 observed that the higher of very heavy rainfall event occurred at Wilayah Persekutuan. Bukit Fraser, Kota Bharu and Padang Besar Perlis were having the higher light rain rate events if compare with Wilayah Persekutuan, Kuching Sarawak and Kiansam Sabah. The summary of rainfall event of 4 rain rate categories is shown in Table 4.
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1-minute rain rate at 0.01% of time is between 120mm/h – 143mm/h and 60-minute rain rate at 0.01% of time is between 52mm/h – 70mm/h among 10 sites. From Table 3, it is shown that the sites which have higher rainfall amount gave higher 1-minute rain rate at 0.01% of time. From the rain rate distribution during observation period, the highest rain rate at 0.01% of time 143mm/h was occurred at Wilayah Persekutuan. It is
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Table 4 The summary of rainfall event of 4 rain rate categories. Sites Light 1-10 mm/h Moderate mm/h Wilayah Persekutuan 2994 261 Kuching 3758 365 Kiansam 2901 266 Kota Bharu 5240 228 Padang Besar 5497 139 Ipoh 4443 233 Bukit Fraser 7840 209 Kuala Terengganu 5621 234 Pahang 4825 203 Prai 1860 174
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4.2 Rain Rate Conversion Methods Comparison Nine conversion methods are selected to convert 60-minute rain rate to 1-minute rain rate and compare with 1-minute rain rate measured at 10 sites. The performance of the selected conversion models was evaluated by using mean prediction error, root mean square error (RMSE) and spread corrected root mean square error (SC-RMSE). Mean prediction error is used for finding the best fitting line which see how close the predicted rain rate and measured rain rate. The equation is shown below: Prediction error, εp = Rp – Rm (14) Mean Prediction Error = (15)
11-30
Heavy 31-60 mm/h
59 80 57 74 23 50 32 26 25 14
Mean Square Error (RMSE) is typically used between values predicted by a model and the values actually observed from the environment that is being exhibited. The formula is shown in equation (16). RMSE =
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Very Heavy >60mm/h 9 2 7 2 5 4 0 2 14 2
(16)
SC-RMSE is used to give an idea of error in excess of expected variance due to temporal deviation. The formula is shown in equation (17). SC-RMSE =
(17)
4.3 60-minute to 1-minute rain rate conversion study 60-minute integration time rainfall rate from 10 sites was converted to 1-minute integration time rainfall rate by using 9 existing conversion models. 1-minute rain rate estimated by the selected conversion models was compared with 1-minute rain rate measured. Fig-s 3 - 12 show the comparison of 1-minute rain rate measured and 1-minute rain rate predicted at Wilayah Persekutuan, Kuching, Kiansam, Kota Bharu, Padang Besar, Ipoh, Bukit Fraser, Kuala Terengganu, Pahang and Prai. Fig- 3
where Rp and Rm are the predicted and measured rain rate estimates for 0.001%
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closely from 1% to 0.1% of the time, however Chebil & MANUSCRIPT
Rahman model followed closely from 0.1% to 0.01% of time. From Fig- 6 and Fig- 7, Chebil & Rahman model followed closely from 1% to 0.01% of time at Kota Bharu and Padang Besar Perlis. From Fig-s 8 - 10, fourth order polynomial fit model predicted well from 1% to 0.01% at Ipoh, Bukit Fraser and Kuala Terengganu respectively. Based on Fig-s 11 - 12, Logarithmic model performed well from 1% to 0.01% of time at Pahang and Prai respectively.
Wilayah Persekutuan 1.00% 100
150
200
250
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and Fig- 4 shows Comparison of 1-minute rain rate ACCEPTED measured and 1-minute rain rate predicted at Wilayah Persekutuan and Kuching respectively. All models overestimated 1-minute rain rate from 1% to 0.10% of time, however Lavergnat and Gole model started to perform well from 0.10% to 0.01% of time. The rain rate at 0.01% of time for Wilayah Persekutuan and Kuching is approximately 140 mm/h, therefore the graph pattern is similar. Comparison of 1-minute rain rate measured and 1-minute rain rate predicted at Kiansam is shown in Fig- 5. Lavergnat & Gole model and Joo model followed
Rain Rate (mm/h)
R (1min) Segal R (1min) Joo R (1min) Emiliani
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R (1min) measured R (1min) Chebil& Rahman R (1 min) Moupfouma R (1min) Logarithmic
R (1min) Burgueno R (1min) Lavergnat & Gole R (1min) 4th Order Polynomial fit
Fig- 3 Comparison of 1-minute rain rate measured and 1-minute rain rate predicted at Wilayah Persekutuan
Kuching
1.00%
100
150
200
250
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50
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Percentage of time (%)
0
0.10%
0.01% Rain Rate (mm/h) R (1min) measured R (1min) Chebil& Rahman R (1 min) Moupfouma R (1min) Logarithmic
R (1min) Segal R (1min) Joo R (1 min) Emiliani
R (1min) Burgueno R (1min) Lavergnat & Gole R (1min) 4th Order Polynomial fit
Fig- 4 Comparison of 1-minute rain rate measured and 1-minute rain rate predicted at Kuching
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1.00%
Percentage of time (%)
0
50
100
150
200
250
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0.10%
0.01% Rain Rate (mm/h) R (1min) Segal R (1min) Joo R (1 min) Emiliani
R (1min) Burgueno R (1min) Lavergnat & Gole R (1min) 4th Order Polynomial fit
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R (1min) measured R (1min) Chebil& Rahman R (1 min) Moupfouma R (1 min) logarithmic
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Fig- 5 Comparison of 1-minute rain rate measured and 1-minute rain rate predicted at Kiansam Kota Bharu
1.00% 50
0.10%
0.01%
100
150
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Percentage of time (%)
0
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R (1min) measured R (1min) Chebil& Rahman R (1 min) Moupfouma R (1 min) logarithmic
200
250
Rain Rate (m m /h)
R (1min) Segal R (1min) Joo R (1 min) Emiliani
R (1min) Burgueno R (1min) Lavergnat & Gole R (1min) 4th Order Polynomial fit
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Fig- 6 Comparison of 1-minute rain rate measured and 1-minute rain rate predicted at Kota Bharu
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100
150
200
250
0.10%
0.01% Rain Rate (mm /h) R (1min) Segal R (1min) Joo R (1min) Emiliani
R (1min) Burgueno R (1min) Lavergnat & Gole R (1min) 4th Order Polynomial fit
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R (1min) measured R (1min) Chebil& Rahman R (1 min) Moupfouma R (1 min) logarithmic
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Ipoh
1.00% 50
0.10%
100
150
200
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0.01%
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Fig- 7 Comparison of 1-minute rain rate measured and 1-minute rain rate predicted at Padang Besar, Perlis
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Rain Rate, mm/h
R (1min) Segal R (1min) Joo R (1min) Emiliani
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R (1min) measured R (1min) Chebil& Rahman R (1 min) Moupfouma R (1 min) logarithmic
Fig-8 Comparison of 1-minute rain rate measured and 1-minute rain rate predicted at Ipoh
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R (1min) Burgueno R (1min) Lavergnat & Gole R (1min) 4th Order Polynomial fit
ACCEPTED MANUSCRIPT Bukit Fraser
1.00% 50
100
150
200
250
0.10%
0.01% Rain Rate (mm/h) R (1min) Segal R (1min) Joo R (1min) Emiliani
R (1min) Burgueno R (1min) Lavergnat & Gole R (1min) 4th Order Polynomial fit
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R (1min) measured R (1min) Chebil& Rahman R (1 min) Moupfouma R (1 min) logarithmic
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Fig- 9 Comparison of 1-minute rain rate measured and 1-minute rain rate predicted at Bukit Fraser
Kuala Terengganu
1.00% 50
100
0.10%
150
200
250
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Percentage of time (%)
0
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0.01%
Rain Rate (mm/h)
R (1min) Segal R (1min) Joo R (1min) Emiliani
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R (1min) measured R (1min) Chebil& Rahman R (1 min) Moupfouma R (1 min) logarithmic
R (1min) Burgueno R (1min) Lavergnat & Gole R (1min) 4th Order Polynomial fit
Fig- 10 Comparison of 1-minute rain rate measured and 1-minute rain rate predicted at Kuala Terengganu
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ACCEPTED MANUSCRIPT Pahang
1.00% 50
100
150
200
250
0.10%
0.01%
Rain Rate, mm/h R (1min) Segal R (1min) Joo R (1min) Emiliani
R (1min) Burgueno R (1min) Lavergnat & Gole R (1min) 4th Order Polynomial fit
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R (1min) measured R (1min) Chebil& Rahman R (1 min) Moupfouma R (1 min) logarithmic
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Fig- 11 Comparison of 1-minute rain rate measured and 1-minute rain rate predicted at Pahang Prai
1.00% 50
100
0.10%
150
200
250
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Percentage of time (%)
0
0.01%
Rain Rate (mm/h)
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R (1min) measured R (1min) Chebil& Rahman R (1 min) Moupfouma R (1 min) logarithmic
R (1min) Segal R (1min) Joo R (1min) Emiliani
R (1min) Burgueno R (1min) Lavergnat & Gole R (1min) 4th Order Polynomial fit
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Fig- 12 Comparison of 1-minute rain rate measured and 1-minute rain rate predicted at Prai Tables 5 - 7 show the comparison statistics for the conversion models selected for predicted over 10 sites. Table 5 shows the mean prediction error comparison for the conversion models for 10 sites. RMSE is another method to test the best prediction model. RMSE
comparison for conversion models for 10 sites is shown in Table 6. In additional, SC-RMSE was calculated for 10 sites and compared SC-RMSE reading among those models. The result is shown in Table 7.
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Table 5 ACCEPTED MANUSCRIPT Mean prediction error comparison for the conversion models for 10 sites Lavergna t & Gole (mm/h)
Moupfouma (mm/h)
Emiliani (mm/h)
4th Order Polynomial fit (mm/h)
Logarithmic (mm/h)
6.315
5.546
35.275
17.046
11.015
9.828
26.866
19.676
12.939
9.196
8.409
37.854
19.269
14.063
12.268
Kiansam, Sabah
15.290
16.304
2.324
2.675
3.751
24.013
12.192
6.883
4.670
Kota Bharu, Kelantan
12.616
14.541
2.428
3.998
4.562
17.652
5.631
3.007
3.184
Padang Besar, Perlis
12.846
12.942
3.060
3.110
3.661
16.495
8.702
4.950
5.533
15.581
21.200
6.911
8.919
9.378
23.275
6.736
4.404
6.118
Bukit Fraser, Selangor
11.539
15.570
5.284
6.011
6.391
16.509
3.240
1.702
2.912
Setor JPS Kuala Terengganu
10.314
16.211
3.475
5.840
6.685
Pejabat JPS Pahang
14.276
15.558
3.894
4.528
4.739
16.779
13.489
6.958
Wilayah Persekutuan
24.471
Kuching, Sarawak
Politeknik Ungku Ipoh
Komplek Pinang
Prai
Omar
Pulau
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Burgueno (mm/h)
15.671
5.478
3.226
4.120
20.030
5.597
2.654
2.303
4.192
4.269
2.929
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Segal (mm/h )
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Joo (mm/h )
18.016
Chebil & RahRahman (mm/h) 10.334
Model
5.502
5.420
18.842
Table 6 RMSE comparison for the conversion models for 10 sites Segal (mm/h )
Burgueno (mm/h)
Wilayah Persekutuan
29.644
Kuching, Sarawak
Lavergna t & Gole (mm/h)
Moupfouma (mm/h)
Emiliani (mm/h)
4th Order Polynomial fit (mm/h)
Logarithmic (mm/h)
7.123
6.480
43.588
26.703
12.669
13.167
13.916
10.604
10.036
42.689
24.512
14.462
13.475
3.174
3.509
4.477
32.968
18.580
8.206
7.600
3.090
4.982
5.810
21.946
8.911
4.451
3.614
3.900
4.087
4.708
25.943
15.207
7.959
7.380
Joo (mm/h )
22.694
Chebil & RahRahman (mm/h) 10.987
29.710
23.479
Kiansam, Sabah
22.036
23.115
Kota Bharu, Kelantan
16.359
19.475
Padang Besar, Perlis
19.619
17.999
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Model
18.721
25.845
8.176
9.217
9.769
27.509
12.475
5.449
6.416
Bukit Fraser, Selangor
13.421
21.698
5.669
7.940
8.688
18.612
4.923
2.126
4.258
Setor JPS Kuala Terengganu
13.679
22.682
4.310
7.679
8.600
19.585
7.636
3.703
4.872
Pejabat JPS Pahang
17.475
21.177
4.446
5.481
6.172
24.296
9.863
4.096
3.048
Komplek Prai Pulau Pinang
18.161
16.525
7.963
6.717
6.696
20.789
6.161
4.832
3.664
Average RMSE over 10 sites
19.882
21.469
6.563
6.734
7.144
27.793
13.497
6.795
6.749
Politeknik Ipoh
Ungku
Omar
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Table 7 ACCEPTED MANUSCRIPT SC-RMSE comparison for the conversion models for 10 sites Lavergna t & Gole (mm/h)
Moupfouma (mm/h)
Emiliani (mm/h)
4th Order Polynomial fit (mm/h)
Logarithmic (mm/h)
4.470
4.006
27.370
20.852
7.861
8.827
19.027
14.535
9.346
6.573
6.213
26.791
15.700
11.208
8.711
Kiansam, Sabah
15.879
16.387
2.168
2.307
2.772
22.634
14.140
5.079
6.141
Kota Bharu, Kelantan
10.644
13.052
1.980
3.144
3.724
13.832
7.024
3.293
2.258
Padang Besar, Perlis
14.963
12.515
2.502
2.691
3.042
20.332
13.028
6.364
4.927
Politeknik Ungku Omar Ipoh
11.610
16.116
5.054
6.991
7.182
17.005
11.155
3.424
4.610
Bukit Fraser, Selangor
8.302
15.119
3.827
5.253
5.907
11.683
3.736
1.344
3.113
Setor JPS Kuala Terengganu
9.083
15.868
2.712
5.058
5.558
Pejabat JPS Pahang
10.918
14.416
2.767
3.408
4.031
Komplek Prai Pulau Pinang
14.027
8.038
4.927
4.684
4.737
Average SC-RMSE over 10 sites
13.289
14.048
4.287
4.458
4.717
Wilayah Persekutuan
18.435
Kuching, Sarawak
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Burgueno (mm/h)
12.385
5.322
2.300
3.012
15.117
8.504
3.154
2.020
16.721
4.546
3.024
2.318
18.387
10.401
4.705
4.594
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Segal (mm/h )
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Joo (mm/h )
14.429
Chebil & RahRahman (mm/h) 7.585
Model
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From performance criteria indication, Chebil and Rahman model is the best fit for Perlis, Kota Bharu and Kiansam. Fourth order polynomial fit model shows a good result for Prai, Kuala Terengganu and Bukit Fraser. Lavergnat and Gole model performs well on Wilayah Persekutuan and Kuching. Logarithmic model gives lowest mean prediction error, RMSE and SC-RMSE at Pahang and Prai. Chebil & Rahman model performed well because the regression coefficients of the model are based on thunderstorm activities, whereas rainfall which drops in higher prediction errors is not considered (Emiliani et al. 2008). Lavergnat-Gole model is a good performance model because it was developed as an application of stochastic process for the time intervals between raindrops, and has reliable theoretical background (Ito and Hosoyo, 2002). Fourth order polynomial fit considered that the rain pattern is observed to be noticeable through exponential functions (Shrestha et al., 2016). Logarithmic model predicted well in Pahang and Prai sites because the experimental 1-minute rainfall rate distribution at both sites are following logarithmic scale. Burgueno and Moupfouma performed bad at these 10 sites based on mean prediction error, RMSE and SCRMSE. The coefficient suggested by Burgueno model limits the prediction accuracy of the model. Simplified Moupfouma model gives large RMSE value because this model was developed based on the rain rate measurement in Chilbolton UK for integration times ranging from 20-second to 60-minute. Segal model was generated by using data analysis from 45 stations in Canada up to 10-year rainfall data which are in temperate climates instead of tropical climates. Joo model was developed according to 2-year of rain events in Korea (July 1998 to May 2000) as Korean climate is temperate climate.
5. CONCLUSIONS 4-year rainfall data at 10 sites of Malaysia have been used in the rain rate distribution observation and integration time conversion model performance evaluation. Performance evaluation result shows that there is no single model which provides a good fit and outperforms at the same time and over 10 sites. By averaging RMSE and SC-RMSE over 10 sites, Chebil and Rahman model is the best method. The study is useful pertaining to the design of wireless link and telecommunications system design such as High Speed Broadband implementation. It is important to revisit the existing models as a result of climate condition change due to effect of global warning.
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REFERENCES Owolawi, P.A., Afullo, T.J. and Malinga, S.B.. Effect of Rainfall on Millimeter Wavelength Radio in Gough and Marion Islands. PIERS online, 2009; 5: 328-35. Ooi, W.C., and Mandeep, J.S. Empirical Methods for Converting Rainfall Rate Distribution from Several Higher Integration Times into a- 1-minute Integration Time in Malaysia. Geofizika 2013; 30: 143-54. Emiliani L. D., Luini L., and Capsoni, C.. Extension of ITU-R Method for conversion of rain rate statistics from various integration times to one minute. Electron. Lett., 2008; 44: 43-4. Emiliani L. D., Luini L., and Capsoni, C. 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, 2009;51: 3.
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ogy, 1998; 37: 805-18. ACCEPTED MANUSCRIPT
ITU-R Recommendation ITU-R P.837-6, 2012.
Moupfouma, F., and Martin, L. Modelling of the Rainfall Rate Cumulative Distribution for the Design of Satellite and Terrestrial Communication Systems. International Journal of Satellite Communications, 1995; 13: 105-15.
Mandeep, J.S., and Hassan, S.I.S. 60- to 1-Min RainfallRate Conversion: Comparison of Existing Prediction Methods with Data Obtained in the Southeast Asia Region. J. Appl. Meteorol. Climatol., 2008; 47: 925-30.
Mandeep, J.S., Tanaka, K., and Lida, M. Conversion of 60-, 30-, 10-, and 5-Minute Rain rates to 1-Minute Rates in Tropical Rain Rate Measurement. ETRI Journal, 2007; 29: 542-4.
Chebil, J., and Rahman, T.A. Rain rate statistical conversion for the prediction of rain attenuation in Malaysia. Electronics Letter, 1999; 35: 1019-21.
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Selamat, S., Mohd Marzuki, A.S., Md Azlan, A.T., Naemat, A., and Khalil, K. 60-min to 1-min Rainfall Rate Conversion Using East Malaysia Data. IEEE Applied Electromagnetics Asia Pacific Conference 2014; p 115-8.
Ito, C and Hosoya, Y. The Thunderstorm Ratio as A Regional Climatic Parameter: It effects on differentintegration –time rain rate conversion, rain attenuation, site diversity and rain depolarization. Proceedings of URSI GA02; 2002.
Segal, B. The Influence of Rain Gauge Integration Time on Measured Rainfall Intensity Distribution Functions. J. of Atmospheric Oceanic Tech, 1986; 3: 662-71.
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Luis D., Emiliani, Lorenzo Luini and Carlo Capsoni. Analysis and Parameterization of Methodologies for the Conversion of Rain-Rate Cumulative Distribution from Various Integration Times to One-minute. IEEE Antennas and Propagation Magazine, 2009; 51: 3.
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Burgueno, A., Puigcerver, M., and Vilar, E. Influence of Rain Gauge Integration Time on the Rain Rate Statistics used in Microwave Communications. Ann. Telecom, 1988; 10: 522-7.
Lee J.H. et al.. Conversion of rain rate distribution for various integration time. IEEE Trans Microw Theory Tech, 1994; 4: 2099-106. Shrestha S., Park J.J., and Choi D.Y. Rain Rate Modeling of 1-min from Various Integration Times in South Korea. Springer Plus, 2016; 5 (433)
Joo, H.L., Yang, S.K., Jong, H.K., and Yong, S.C. Empirical Conversion Process of Rain Rate Distribution for Various Integration Time. Proc. URSI Commission F Wave Propagation and Remote Sensing Maastricht, 2002; 1450-4.
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Lavergnat, J. and Gole, P. A Stochastic Raindrop Time Distribution Model. AMS Journal of Applied Meteorol-
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Shrestha S., and Choi D.Y. Study of 1-min Rain Rate Integration Statistic in South Korea. Journal of Atmospheric and Solar-Terrestrial Physics, 2017; 155: 1-11
ACCEPTED MANUSCRIPT
Dear editor and reviewers, This paper objective is to study the performance of several conversion methods in Malaysia. I add the average RMSE and SC-RMSE and add one row into the table to show which method gives low average RMSE and SCRMSE over 10 sites. I revise the conclusion with concluded Chebil and Rahman model is the best model according to average RMSE and SC-RMSE value.
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I have invited English experts to correct and give the advice to my English writing. I hope it helps this manuscript quality is getting improve. Many thanks for editor and reviewers to spend time reading this manuscript and giving the valuable inputs. It’s really helpful to give me have idea how to improve the works. I wish you all the best.
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Best Regards, Yun Yann
S1364-6826(17)30167-0
DOI:
10.1016/j.jastp.2017.10.004
Reference:
ATP 4707
To appear in:
Journal of Atmospheric and Solar-Terrestrial Physics
Received Date: 19 March 2017 Revised Date:
6 October 2017
Accepted Date: 9 October 2017
Please cite this article as: Ng, Y.-Y., Singh, M.S.J., Thiruchelvam, V., Performance analysis of 60-min to 1-min integration time rain rate conversion models in Malaysia, Journal of Atmospheric and SolarTerrestrial Physics (2017), doi: 10.1016/j.jastp.2017.10.004. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT PERFORMANCE ANALYSIS OF 60-MIN TO 1-MIN INTEGRATION TIME RAIN RATE CONVERSION MODELS IN MALAYSIA Yun-Yann Ng1*, Mandeep Singh Jit Singh1, Vinesh Thiruchelvam2 1 Universiti Kebangsaan Malaysia, Faculty of Engineering and Built Environment, Department of Electrical, Electronic and System Engineering, Selangor, Malaysia. 2 Asia Pacific University of Technology & Innovation, Faculty of Computing, Engineering & Technology, Malaysia. *Corresponding author email: [email protected]
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ABSTRACT Utilizing the frequency band above 10 GHz is in focus nowadays as a result of the fast expansion of radio communication systems in Malaysia. However, rain fade is the critical factor in attenuation of signal propagation for frequencies above 10 GHz. Malaysia is located in a tropical and equatorial region with high rain intensity throughout the year, and this study will review rain distribution and evaluate the performance of 60-minute to 1-minute integration time rain rate conversion methods for Malaysia. Several conversion methods such as Segal, Chebil & Rahman, Burgeono, Emiliani, Lavergnat and Gole (LG), Simplified Moupfouma, Joo et al, fourth order polynomial fit and logarithmic model have been chosen to evaluate the performance to predict 1-minute rain rate for 10 sites in Malaysia. After the completion of this research, the results show that Chebil & Rahman model, Lavergnat & Gole model, Fourth order polynomial fit and Logarithmic model have shown the best performances in 60-minute to 1-minute rain rate conversion over 10 sites. In conclusion, it is proven that there is no single model which can claim to perform the best across 10 sites. By averaging RMSE and SC-RMSE over 10 sites, Chebil and Rahman model is the best method. Keywords: 1-min Integration Time Rain Rate; Conversion Models; Tropical Region; Rain Rate distribution.
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1. INTRODUCTION Rapid development of technology for wireless communication above 10 GHz, is important to resolve the crowding of the currently used frequency bands. This is particularly important in developing countries such as Malaysia. Telecommunication system engineers seek for Ku-band (12/14 GHz) because of its advantages of wider spectrum availability, higher data transfer and smaller antenna size (Owolawi et al., 2009). However, rain fade is the most critical factor of signal degradation when analysing satellite communication links at frequencies above 10 GHz. Rain affects the transmission of an electromagnetic signal by increasing the system noise temperature, attenuating the signal and changing in polarization. These three mechanisms cause degradation in the signal quality received. When the frequency increases, the signal strength deteriorates and rain drops affect the signal propagation (Ooi et al., 2013). According to International Telecommunication Union (ITU-R P837-6, 2012), 1-minute rain rate statistics are required to estimate the rain influenced fade effect on the propagation rate. 1-minute integration times ensures that the peaks of rain event are sufficiently experimented and the use of longer integration times would result in an averaging effect (as the rain rate would be the average of accumulation over a longer time interval), causing high intensity rain rate value to appear low (Emiliani et al., 2008). Yet long term basis of 1-minute integrated rainfall data is insufficient in Malaysia. As a result, an effective conversion method for rain rate is necessary to predict a precise 1-minute rain rate distribution (Mandeep et al., 2008). Malaysia is a tropical country where precipitation occurs throughout the year, particularly during monsoon seasons. There were several local studies conducted to understand conversion process of rain rate distribution
from higher integration times into 1-minute in Malaysia. From the studies done by J.S. Mandeep, et al. (2008), Segal method is the best conversion models when applied to Southeast Asia and Kuching (Mandeep et al., 2008). Chebil & Rahman applied Segal's method to convert 60-minute and 1-minute rain rate in Malaysia and published conversion method by modified Segal model in year 1999 (Chebil and Rahman, 1999). Selamat et al. (2014) did comparison among 5 existing conversion methods for converting 60-minute to 1-minute on 5 sites of East Malaysia and the result shows Segal method gave the best performance among 5 methods: Segal, Burgueno et al, Emiliani et al, Chebil and Rahman, ITU-R P.837-6 Annex 3 (Selamat et al. 2014). Here we present the analysis of 1-minute and 60minute rain rate statistics observed from a 4-year (year 2010 – 2013) measurement at 10 locations from Peninsular of Malaysia and East Malaysia. There are 9 rain rate conversion models selected to convert 60-minute to 1-minute integrated time. The performance analysis over the conversion models and rain rate models are evaluated in this paper. The study is important to understand the performance of existing models and to look for the suitable models to be used in the selected areas in Malaysia. 2. OVERVIEW OF CONVERSION METHODS FOR RAIN RATE DISTRIBUTION The conversion methods can be categorized into 3 groups: physical, analytical and empirical method. Most of the researchers tend to use the empirical method extensively to convert from higher integrated time to lower equivalent due to its simplicity and experiment dependent (Emiliani et al., 2009). The proposed conversion methods used in this paper are Segal method
1
(1986), Chebil and Rahman method (1999), Burgueno et ACCEPTED al. method (1988), Joo et al. method (2002), Lavergnat and Gole method (1998), Emiliani and Luini method (2008), simplified Moupfouma (1995), fourth order polynomial fit (2016) and logarithmic model (1994).
butions of rain rate 1-, 10-, 20-, 30-, 60-minutes integraMANUSCRIPT
tion time (Joo et al., 2002). P1(P) = aPτ10[b exp(-t/24.28)] (P) (6) where P1 and Pτ are the possibility of a specified amount of rain rate at 1-minute and τ-minute, respectively. The sampling interval (minute) for the rain gauge was expressed as t, and a and b are indicated as regression coefficients.
2.1 EMPIRICAL METHOD Empirical method provides simple methodical laws to express the correlation between equiprobable rain rate values. This method is easy to use and experiment dependent (Emiliani et al., 2009). Example: Segal model (1986), Chebil & Rahman model (1999), Burgueno et al. model (1988), Joo et al. model (2002), Emiliani and Luini model (2008) fourth order polynomial fit (2016) and lognormal method (1994).
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2.1.5 Emiliani et al. Method (2008) Emiliani et al. is an extension of ITU-R P.837-5 and the method was published at year 2008. New set of coefficient values was used based on an extended database of three types of Köppen climatic region when developing power law conversion method (Emiliani et al., 2008).
2.1.1 Segal Method (1986) A rain rate conversion factor was proposed by Segal based on the data analysis from 45 stations in Canada up to 10-year rainfall data. A specialized database of high resolution rainfall records prepared at the Communications Research Centre was used for developed this model (Segal, 1986). The proposed method by Segal (1986) expressed as equation (1) and (2): (1) R1(P) = ρτ(P)Rτ(P) mm/h With conversion factor, pτ(P) stated as per power law ρτ(P) = aPb (2) R1 (P) and Rτ (P) are the rain rate with a sampling interval of 1 and τ min, correspondingly, which contain a percentage of time, P. The conversion variables were be symbolized as a and b.
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2.1.6 Fourth Order Polynomial Fit (2016) The new proposed model by Shrestha et al (2016) was based on the data analysis from rainfall distribution data from KMA (2004-2013) over 9 regions of the South Korea. R1(P) = ae(a-b)[Rτ(P)] 4 + be(b-a) [Rτ(P)] 3 + c[Rτ(P)] 2 +d[Rτ(P)] mm/h (7) R1 (P) and Rτ (P) are the rain rate with a sampling interval of 1 and τ min, respectively, which contain a percentage of time, P. a, b, c and d are regression coefficients that are obtained though statistical analysis of rainfall date with curve fitting technique.
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2.1.2 Chebil And Rahman Method (1999) This conversion method was modified conversion factor of Segal methods and recommended approximating the rain rate conversion factor from 60 minute to 1minute integration time for 82 locations in Malaysia (Chebil and Rahman, 1999). Conversion factor from 60minute to 1-minute rainfall rate were expressed as (3) and (4): ρ60 (P) = R1 (P) / R60 (P) (3) where ρ60 (P) is represented as a mixed Power – Exponential Law. ρ60 (P) = aPb + ce(dP) (4) where the percentage of time is expressed as P. The rain 1-minute rain rate and 60-minute rain rate integration time to the percentage of time is designated as R1 (P) and R60 (P), respectively. The regression variables are represented as a, b, c, and d.
2.1.7 Logarithmic model (1994) The empirical equation for Logarithmic model (Lee et al., 1994) is given as below: log[R1(P)] = a log[Rτ(P)] mm/h (8) Where a is the regression co-efficient derived from statistical analysis of rainfall rate. 2.2 PHYSICAL METHOD The physical method uses the conversion of statistics which is constructed on the physical processes elaborated in the rain formation and development and in the evolution of a rain event in time. The physical modelling of the rainfall process is usually mathematically complex and principally particular to the meteorology’s field, for weather forecasting activities (Emiliani et al., 2009).
2.2.1 Lavergnat and Gole model (1998) LG model was developed based on 2-year data collection in Paris by using a disdrometre that analyzed fine rain temporal structure rather that its intensity characteristic (Lavergnant and Gole, 1998). A conversion factor to scale both the rain and the probability were represented as shown in equation (9) and (10) respectively: mm/h (9) R1 = RT / h α (10) P(R1)1 = hαP(RT)T Where h is conversion factor, h = 1/T and α is the coefficient which is determined empirically. Only one parameter is needed for conversion between integration times.
2.1.3 Burgueno et al. method (1988) This method was developed from data analysis of 49year of rain rate measurement at Barcelona in Spain (Burgueno et al, 1988). The principle of direct power law fit was applied in the equation as shown below. R1(P) = aRτb (P) mm/h (5) R1 (P) and Rτ (P) are the rain rate with 1-minute and τminute sampling interval, respectively, which contain a percentage of time, P. a and b represent the conversion variables. 2.1.4 Joo et al. method (2002) Joo method was developed according to 2-year of rain events in Korea (July 1998 to May 2000) with the distri-
2.3 ANALYTICAL METHOD
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2.3.1 Simplified Moupfouma and Martin (1995) This analytical method was developed based on the rain rate measurement in Chilbolton, UK for integration times ranging from 1-minute to 60-minute (Moupfouma and Martin, 1995). The formulation of this method is shown below: P( R)1 = (a1 / aT) R (br-b1) e (ur-u1)RP(R )T (11) The conversion of cumulative distributions requires the knowledge of 6 coefficients corresponding to a, b and u for both the 1-minute and T-minute rain rate cumulative distribution functions on top of P( R)T.
Latitude (oN) 3.16 1.48 5.98 6.22 6.66 4.58 3.71 5.33 3.83 5.39
Longitude (oE) 101.69 110.34 116.17 102.26 100.32 101.12 101.74 103.14 103.29 100.40
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Table 1 The location selected for the research study. Station ID Location 3116003 Main Office of JPS Malaysia at Wilayah Persekutuan 1403001 Kuching Airport At Sungai Sarawak Basin 5961001 Kiansam At Sabah 6122064 Stor JPS. Kota Bharu At Kelantan 6603002 Padang Besar At Titi Keretapi Perlis 4511111 Politeknik Ungku Omar 3717101 Bukit Fraser, Selangor 5331048 Setor JPS Kuala Terengganu 3833002 Pejabat JPS Pahang 5303053 Komplek Prai Pulau Pinang
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3. DATA COLLECTION For this study, rainfall data source is from DID (Department of Irrigation and Drainage) Malaysia which has huge hydrology network station all over Malaysia. DID delivers rainfall data in 1-minute or longer time interval depending on the station ability. Stations using automatic logger provide 1-minute rainfall with inadequate recoding span, meanwhile other stations provide longer interval data with manual check gauge. The rainfall data is collected in millimetre every minute for 4-year (2010-2013), starting from 1st January 2010 to 31st December 2013. 8 sites at Peninsular Malaysia, 1 site at Sarawak and 1 site of Sabah are selected for this study and shown in Table 1. The map of the selected locations is reflected in Fig- 1.
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The analytical method assumes thatACCEPTED the rain rate cumulative distribution functions can be denoted by a given function of which the general shape remains constant, nonetheless the parameters of which differ subject to the integration time (Emiliani et al., 2009).
Fig- 1 The map of locations selected for the research study. The rain intensities are measured using automatic rainfall gauges of 0.5mm per tip at 1-minute. The rain rate cumulative distribution from 1-minute and 60minute integration times engendered from the rain gauge data. The data availability is 98.2% for all sites from year 2010-2013. Rain gauge calculates the time of occurrence of a tip, however it does not recorded the precipitation rate at that particular moment. DID's rainfall data is recorded in a comma separated value (.csv) file with columns of date, time and rain amount (mm). The 1-minute rain rate is calculated by using for-
mula (12): 1-minute Rain rate (R1-min) = Rain amount in t-minute x (60-minute / t-minute) (12) The cumulative statistics for rain rate are usually presented as the exceedance probability (abscissa) versus the rain rate (ordinate). The rain rate cumulative distribution by calculating P(R ε ro) the probability of the rain rate intensity R(mm/hr) exceeds a threshold value of r (mm/hr) for a time period, T. (13) Pr =P(R≥r0) = N0 / NT where No is the number of rain rate value larger than ro
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Malaysia is located MANUSCRIPT
in equatorial and tropical area which having high rainfall throughout the year. It is important to understand the rainfall amount over a year for every site in this study. Table 2 is the summary of rainfall amount from year 2010 to 2013.
4. RESULTS AND DISCUSSION 4.1 Distribution of Rain Rate
Table 2 Rainfall (in mm) from year 2010 – 2013 for over 4-year. Sites Rainfall amount (mm) 2011
2012
2013
Average
Wilayah Persekutuan
2330
2517
2969
3322
2784
Kuching, Sarawak
4303
4263
3681
3934
4045
Kiansam, Sabah
4597
3151
2218
3044
3252
Kota Bharu, Kelantan
2205
2902
2772
2001
2470
Padang Besar, Perlis
1881
1445
1626
1212
1541
Politeknik Ungku Omar Ipoh
2885
2196
2257
2123
2365
Bukit Fraser, Selangor
1948
2283
2586
2020
2209
Setor JPS Kuala Terengganu
1737
2587
2575
2248
2287
Pejabat JPS Pahang
1952
1832
2726
1289
1950
Komplek Prai Pulau Pinang
1422
1908
1618
2239
1796
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2010
the straits of Malacca during April to September. Along the east coast of Peninsular Malaysia, the northeast coast of Sabah and Western Sarawak experience heavy rain spells for the period of the northeast monsoon season. In contrast, inland regions and regions that sheltered by mountain ranges are fairly exempted from its influence. In general, November, December and January are the months with maximum rainfall over the study areas, whereas June and July are the driest months in the most districts. Fig- 2 shows the monthly rainfall amount for 10 sites over 4-year (2010-2013).
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From Table 2, Kuching and Kiansam which located in East Malaysia experience the highest annual rainfall amount and average rainy days throughout a year. Nevertheless Padang Besar and Prai which located at the north of Peninsular Malaysia have the lowest annual rainfall amount and average rainy days over a year. The rainfall distribution pattern is determined by monsoon seasons. There are 2 monsoon seasons occurred in Malaysia, e.g. northeast and southwest monsoon seasons. Northeast monsoon blows from South China Sea during October to March and southwest monsoon blows from
Fig- 2 Monthly rainfall amount summary. Yearly rain rate statistics for numerous percentages of time are needed in the areas of interest when designing satellite link systems. The average rainy days per year,
annual rainfall amount, 1-min R0.01% and 60min R0.01% rain rate over 4-year for 10 sites is shown in Table 3.
Table 3
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Summary of average rainy days per year, ACCEPTED annual rainfall amount, 1-min R0.01% and 60min R0.01% rain rate over 4-year for 10 MANUSCRIPT sites. Sites Average rainy days per Annual rainfall amount 1-min R0.01% 60 min R0.01% year (mm) (mm/h) (mm/h) Wilayah Persekutuan 179 2784 143 70 Kuching 246 4045 140 70 Kiansam 194 3252 140 72 Kota Bharu 168 2470 120 57 Padang Besar 156 1541 120 62 Ipoh 180 2365 136 64 Bukit Fraser 223 2209 124 56 Kuala Terengganu 171 2287 128 58 Pahang 149 1950 128 52 Prai 163 1796 122 48 observed that the higher of very heavy rainfall event occurred at Wilayah Persekutuan. Bukit Fraser, Kota Bharu and Padang Besar Perlis were having the higher light rain rate events if compare with Wilayah Persekutuan, Kuching Sarawak and Kiansam Sabah. The summary of rainfall event of 4 rain rate categories is shown in Table 4.
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1-minute rain rate at 0.01% of time is between 120mm/h – 143mm/h and 60-minute rain rate at 0.01% of time is between 52mm/h – 70mm/h among 10 sites. From Table 3, it is shown that the sites which have higher rainfall amount gave higher 1-minute rain rate at 0.01% of time. From the rain rate distribution during observation period, the highest rain rate at 0.01% of time 143mm/h was occurred at Wilayah Persekutuan. It is
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Table 4 The summary of rainfall event of 4 rain rate categories. Sites Light 1-10 mm/h Moderate mm/h Wilayah Persekutuan 2994 261 Kuching 3758 365 Kiansam 2901 266 Kota Bharu 5240 228 Padang Besar 5497 139 Ipoh 4443 233 Bukit Fraser 7840 209 Kuala Terengganu 5621 234 Pahang 4825 203 Prai 1860 174
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4.2 Rain Rate Conversion Methods Comparison Nine conversion methods are selected to convert 60-minute rain rate to 1-minute rain rate and compare with 1-minute rain rate measured at 10 sites. The performance of the selected conversion models was evaluated by using mean prediction error, root mean square error (RMSE) and spread corrected root mean square error (SC-RMSE). Mean prediction error is used for finding the best fitting line which see how close the predicted rain rate and measured rain rate. The equation is shown below: Prediction error, εp = Rp – Rm (14) Mean Prediction Error = (15)
11-30
Heavy 31-60 mm/h
59 80 57 74 23 50 32 26 25 14
Mean Square Error (RMSE) is typically used between values predicted by a model and the values actually observed from the environment that is being exhibited. The formula is shown in equation (16). RMSE =
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Very Heavy >60mm/h 9 2 7 2 5 4 0 2 14 2
(16)
SC-RMSE is used to give an idea of error in excess of expected variance due to temporal deviation. The formula is shown in equation (17). SC-RMSE =
(17)
4.3 60-minute to 1-minute rain rate conversion study 60-minute integration time rainfall rate from 10 sites was converted to 1-minute integration time rainfall rate by using 9 existing conversion models. 1-minute rain rate estimated by the selected conversion models was compared with 1-minute rain rate measured. Fig-s 3 - 12 show the comparison of 1-minute rain rate measured and 1-minute rain rate predicted at Wilayah Persekutuan, Kuching, Kiansam, Kota Bharu, Padang Besar, Ipoh, Bukit Fraser, Kuala Terengganu, Pahang and Prai. Fig- 3
where Rp and Rm are the predicted and measured rain rate estimates for 0.001%
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closely from 1% to 0.1% of the time, however Chebil & MANUSCRIPT
Rahman model followed closely from 0.1% to 0.01% of time. From Fig- 6 and Fig- 7, Chebil & Rahman model followed closely from 1% to 0.01% of time at Kota Bharu and Padang Besar Perlis. From Fig-s 8 - 10, fourth order polynomial fit model predicted well from 1% to 0.01% at Ipoh, Bukit Fraser and Kuala Terengganu respectively. Based on Fig-s 11 - 12, Logarithmic model performed well from 1% to 0.01% of time at Pahang and Prai respectively.
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and Fig- 4 shows Comparison of 1-minute rain rate ACCEPTED measured and 1-minute rain rate predicted at Wilayah Persekutuan and Kuching respectively. All models overestimated 1-minute rain rate from 1% to 0.10% of time, however Lavergnat and Gole model started to perform well from 0.10% to 0.01% of time. The rain rate at 0.01% of time for Wilayah Persekutuan and Kuching is approximately 140 mm/h, therefore the graph pattern is similar. Comparison of 1-minute rain rate measured and 1-minute rain rate predicted at Kiansam is shown in Fig- 5. Lavergnat & Gole model and Joo model followed
Rain Rate (mm/h)
R (1min) Segal R (1min) Joo R (1min) Emiliani
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R (1min) measured R (1min) Chebil& Rahman R (1 min) Moupfouma R (1min) Logarithmic
R (1min) Burgueno R (1min) Lavergnat & Gole R (1min) 4th Order Polynomial fit
Fig- 3 Comparison of 1-minute rain rate measured and 1-minute rain rate predicted at Wilayah Persekutuan
Kuching
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0.01% Rain Rate (mm/h) R (1min) measured R (1min) Chebil& Rahman R (1 min) Moupfouma R (1min) Logarithmic
R (1min) Segal R (1min) Joo R (1 min) Emiliani
R (1min) Burgueno R (1min) Lavergnat & Gole R (1min) 4th Order Polynomial fit
Fig- 4 Comparison of 1-minute rain rate measured and 1-minute rain rate predicted at Kuching
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0.10%
0.01% Rain Rate (mm/h) R (1min) Segal R (1min) Joo R (1 min) Emiliani
R (1min) Burgueno R (1min) Lavergnat & Gole R (1min) 4th Order Polynomial fit
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R (1min) measured R (1min) Chebil& Rahman R (1 min) Moupfouma R (1 min) logarithmic
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Fig- 5 Comparison of 1-minute rain rate measured and 1-minute rain rate predicted at Kiansam Kota Bharu
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Rain Rate (m m /h)
R (1min) Segal R (1min) Joo R (1 min) Emiliani
R (1min) Burgueno R (1min) Lavergnat & Gole R (1min) 4th Order Polynomial fit
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Fig- 6 Comparison of 1-minute rain rate measured and 1-minute rain rate predicted at Kota Bharu
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0.01% Rain Rate (mm /h) R (1min) Segal R (1min) Joo R (1min) Emiliani
R (1min) Burgueno R (1min) Lavergnat & Gole R (1min) 4th Order Polynomial fit
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R (1min) measured R (1min) Chebil& Rahman R (1 min) Moupfouma R (1 min) logarithmic
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Fig- 7 Comparison of 1-minute rain rate measured and 1-minute rain rate predicted at Padang Besar, Perlis
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R (1min) Segal R (1min) Joo R (1min) Emiliani
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R (1min) measured R (1min) Chebil& Rahman R (1 min) Moupfouma R (1 min) logarithmic
Fig-8 Comparison of 1-minute rain rate measured and 1-minute rain rate predicted at Ipoh
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R (1min) Burgueno R (1min) Lavergnat & Gole R (1min) 4th Order Polynomial fit
ACCEPTED MANUSCRIPT Bukit Fraser
1.00% 50
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0.10%
0.01% Rain Rate (mm/h) R (1min) Segal R (1min) Joo R (1min) Emiliani
R (1min) Burgueno R (1min) Lavergnat & Gole R (1min) 4th Order Polynomial fit
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Fig- 9 Comparison of 1-minute rain rate measured and 1-minute rain rate predicted at Bukit Fraser
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R (1min) Burgueno R (1min) Lavergnat & Gole R (1min) 4th Order Polynomial fit
Fig- 10 Comparison of 1-minute rain rate measured and 1-minute rain rate predicted at Kuala Terengganu
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1.00% 50
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0.10%
0.01%
Rain Rate, mm/h R (1min) Segal R (1min) Joo R (1min) Emiliani
R (1min) Burgueno R (1min) Lavergnat & Gole R (1min) 4th Order Polynomial fit
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Fig- 11 Comparison of 1-minute rain rate measured and 1-minute rain rate predicted at Pahang Prai
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Rain Rate (mm/h)
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R (1min) Burgueno R (1min) Lavergnat & Gole R (1min) 4th Order Polynomial fit
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Fig- 12 Comparison of 1-minute rain rate measured and 1-minute rain rate predicted at Prai Tables 5 - 7 show the comparison statistics for the conversion models selected for predicted over 10 sites. Table 5 shows the mean prediction error comparison for the conversion models for 10 sites. RMSE is another method to test the best prediction model. RMSE
comparison for conversion models for 10 sites is shown in Table 6. In additional, SC-RMSE was calculated for 10 sites and compared SC-RMSE reading among those models. The result is shown in Table 7.
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Table 5 ACCEPTED MANUSCRIPT Mean prediction error comparison for the conversion models for 10 sites Lavergna t & Gole (mm/h)
Moupfouma (mm/h)
Emiliani (mm/h)
4th Order Polynomial fit (mm/h)
Logarithmic (mm/h)
6.315
5.546
35.275
17.046
11.015
9.828
26.866
19.676
12.939
9.196
8.409
37.854
19.269
14.063
12.268
Kiansam, Sabah
15.290
16.304
2.324
2.675
3.751
24.013
12.192
6.883
4.670
Kota Bharu, Kelantan
12.616
14.541
2.428
3.998
4.562
17.652
5.631
3.007
3.184
Padang Besar, Perlis
12.846
12.942
3.060
3.110
3.661
16.495
8.702
4.950
5.533
15.581
21.200
6.911
8.919
9.378
23.275
6.736
4.404
6.118
Bukit Fraser, Selangor
11.539
15.570
5.284
6.011
6.391
16.509
3.240
1.702
2.912
Setor JPS Kuala Terengganu
10.314
16.211
3.475
5.840
6.685
Pejabat JPS Pahang
14.276
15.558
3.894
4.528
4.739
16.779
13.489
6.958
Wilayah Persekutuan
24.471
Kuching, Sarawak
Politeknik Ungku Ipoh
Komplek Pinang
Prai
Omar
Pulau
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Burgueno (mm/h)
15.671
5.478
3.226
4.120
20.030
5.597
2.654
2.303
4.192
4.269
2.929
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Joo (mm/h )
18.016
Chebil & RahRahman (mm/h) 10.334
Model
5.502
5.420
18.842
Table 6 RMSE comparison for the conversion models for 10 sites Segal (mm/h )
Burgueno (mm/h)
Wilayah Persekutuan
29.644
Kuching, Sarawak
Lavergna t & Gole (mm/h)
Moupfouma (mm/h)
Emiliani (mm/h)
4th Order Polynomial fit (mm/h)
Logarithmic (mm/h)
7.123
6.480
43.588
26.703
12.669
13.167
13.916
10.604
10.036
42.689
24.512
14.462
13.475
3.174
3.509
4.477
32.968
18.580
8.206
7.600
3.090
4.982
5.810
21.946
8.911
4.451
3.614
3.900
4.087
4.708
25.943
15.207
7.959
7.380
Joo (mm/h )
22.694
Chebil & RahRahman (mm/h) 10.987
29.710
23.479
Kiansam, Sabah
22.036
23.115
Kota Bharu, Kelantan
16.359
19.475
Padang Besar, Perlis
19.619
17.999
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18.721
25.845
8.176
9.217
9.769
27.509
12.475
5.449
6.416
Bukit Fraser, Selangor
13.421
21.698
5.669
7.940
8.688
18.612
4.923
2.126
4.258
Setor JPS Kuala Terengganu
13.679
22.682
4.310
7.679
8.600
19.585
7.636
3.703
4.872
Pejabat JPS Pahang
17.475
21.177
4.446
5.481
6.172
24.296
9.863
4.096
3.048
Komplek Prai Pulau Pinang
18.161
16.525
7.963
6.717
6.696
20.789
6.161
4.832
3.664
Average RMSE over 10 sites
19.882
21.469
6.563
6.734
7.144
27.793
13.497
6.795
6.749
Politeknik Ipoh
Ungku
Omar
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Table 7 ACCEPTED MANUSCRIPT SC-RMSE comparison for the conversion models for 10 sites Lavergna t & Gole (mm/h)
Moupfouma (mm/h)
Emiliani (mm/h)
4th Order Polynomial fit (mm/h)
Logarithmic (mm/h)
4.470
4.006
27.370
20.852
7.861
8.827
19.027
14.535
9.346
6.573
6.213
26.791
15.700
11.208
8.711
Kiansam, Sabah
15.879
16.387
2.168
2.307
2.772
22.634
14.140
5.079
6.141
Kota Bharu, Kelantan
10.644
13.052
1.980
3.144
3.724
13.832
7.024
3.293
2.258
Padang Besar, Perlis
14.963
12.515
2.502
2.691
3.042
20.332
13.028
6.364
4.927
Politeknik Ungku Omar Ipoh
11.610
16.116
5.054
6.991
7.182
17.005
11.155
3.424
4.610
Bukit Fraser, Selangor
8.302
15.119
3.827
5.253
5.907
11.683
3.736
1.344
3.113
Setor JPS Kuala Terengganu
9.083
15.868
2.712
5.058
5.558
Pejabat JPS Pahang
10.918
14.416
2.767
3.408
4.031
Komplek Prai Pulau Pinang
14.027
8.038
4.927
4.684
4.737
Average SC-RMSE over 10 sites
13.289
14.048
4.287
4.458
4.717
Wilayah Persekutuan
18.435
Kuching, Sarawak
SC
Burgueno (mm/h)
12.385
5.322
2.300
3.012
15.117
8.504
3.154
2.020
16.721
4.546
3.024
2.318
18.387
10.401
4.705
4.594
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Segal (mm/h )
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Joo (mm/h )
14.429
Chebil & RahRahman (mm/h) 7.585
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From performance criteria indication, Chebil and Rahman model is the best fit for Perlis, Kota Bharu and Kiansam. Fourth order polynomial fit model shows a good result for Prai, Kuala Terengganu and Bukit Fraser. Lavergnat and Gole model performs well on Wilayah Persekutuan and Kuching. Logarithmic model gives lowest mean prediction error, RMSE and SC-RMSE at Pahang and Prai. Chebil & Rahman model performed well because the regression coefficients of the model are based on thunderstorm activities, whereas rainfall which drops in higher prediction errors is not considered (Emiliani et al. 2008). Lavergnat-Gole model is a good performance model because it was developed as an application of stochastic process for the time intervals between raindrops, and has reliable theoretical background (Ito and Hosoyo, 2002). Fourth order polynomial fit considered that the rain pattern is observed to be noticeable through exponential functions (Shrestha et al., 2016). Logarithmic model predicted well in Pahang and Prai sites because the experimental 1-minute rainfall rate distribution at both sites are following logarithmic scale. Burgueno and Moupfouma performed bad at these 10 sites based on mean prediction error, RMSE and SCRMSE. The coefficient suggested by Burgueno model limits the prediction accuracy of the model. Simplified Moupfouma model gives large RMSE value because this model was developed based on the rain rate measurement in Chilbolton UK for integration times ranging from 20-second to 60-minute. Segal model was generated by using data analysis from 45 stations in Canada up to 10-year rainfall data which are in temperate climates instead of tropical climates. Joo model was developed according to 2-year of rain events in Korea (July 1998 to May 2000) as Korean climate is temperate climate.
5. CONCLUSIONS 4-year rainfall data at 10 sites of Malaysia have been used in the rain rate distribution observation and integration time conversion model performance evaluation. Performance evaluation result shows that there is no single model which provides a good fit and outperforms at the same time and over 10 sites. By averaging RMSE and SC-RMSE over 10 sites, Chebil and Rahman model is the best method. The study is useful pertaining to the design of wireless link and telecommunications system design such as High Speed Broadband implementation. It is important to revisit the existing models as a result of climate condition change due to effect of global warning.
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REFERENCES Owolawi, P.A., Afullo, T.J. and Malinga, S.B.. Effect of Rainfall on Millimeter Wavelength Radio in Gough and Marion Islands. PIERS online, 2009; 5: 328-35. Ooi, W.C., and Mandeep, J.S. Empirical Methods for Converting Rainfall Rate Distribution from Several Higher Integration Times into a- 1-minute Integration Time in Malaysia. Geofizika 2013; 30: 143-54. Emiliani L. D., Luini L., and Capsoni, C.. Extension of ITU-R Method for conversion of rain rate statistics from various integration times to one minute. Electron. Lett., 2008; 44: 43-4. Emiliani L. D., Luini L., and Capsoni, C. 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, 2009;51: 3.
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ogy, 1998; 37: 805-18. ACCEPTED MANUSCRIPT
ITU-R Recommendation ITU-R P.837-6, 2012.
Moupfouma, F., and Martin, L. Modelling of the Rainfall Rate Cumulative Distribution for the Design of Satellite and Terrestrial Communication Systems. International Journal of Satellite Communications, 1995; 13: 105-15.
Mandeep, J.S., and Hassan, S.I.S. 60- to 1-Min RainfallRate Conversion: Comparison of Existing Prediction Methods with Data Obtained in the Southeast Asia Region. J. Appl. Meteorol. Climatol., 2008; 47: 925-30.
Mandeep, J.S., Tanaka, K., and Lida, M. Conversion of 60-, 30-, 10-, and 5-Minute Rain rates to 1-Minute Rates in Tropical Rain Rate Measurement. ETRI Journal, 2007; 29: 542-4.
Chebil, J., and Rahman, T.A. Rain rate statistical conversion for the prediction of rain attenuation in Malaysia. Electronics Letter, 1999; 35: 1019-21.
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Selamat, S., Mohd Marzuki, A.S., Md Azlan, A.T., Naemat, A., and Khalil, K. 60-min to 1-min Rainfall Rate Conversion Using East Malaysia Data. IEEE Applied Electromagnetics Asia Pacific Conference 2014; p 115-8.
Ito, C and Hosoya, Y. The Thunderstorm Ratio as A Regional Climatic Parameter: It effects on differentintegration –time rain rate conversion, rain attenuation, site diversity and rain depolarization. Proceedings of URSI GA02; 2002.
Segal, B. The Influence of Rain Gauge Integration Time on Measured Rainfall Intensity Distribution Functions. J. of Atmospheric Oceanic Tech, 1986; 3: 662-71.
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Luis D., Emiliani, Lorenzo Luini and Carlo Capsoni. Analysis and Parameterization of Methodologies for the Conversion of Rain-Rate Cumulative Distribution from Various Integration Times to One-minute. IEEE Antennas and Propagation Magazine, 2009; 51: 3.
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Burgueno, A., Puigcerver, M., and Vilar, E. Influence of Rain Gauge Integration Time on the Rain Rate Statistics used in Microwave Communications. Ann. Telecom, 1988; 10: 522-7.
Lee J.H. et al.. Conversion of rain rate distribution for various integration time. IEEE Trans Microw Theory Tech, 1994; 4: 2099-106. Shrestha S., Park J.J., and Choi D.Y. Rain Rate Modeling of 1-min from Various Integration Times in South Korea. Springer Plus, 2016; 5 (433)
Joo, H.L., Yang, S.K., Jong, H.K., and Yong, S.C. Empirical Conversion Process of Rain Rate Distribution for Various Integration Time. Proc. URSI Commission F Wave Propagation and Remote Sensing Maastricht, 2002; 1450-4.
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Lavergnat, J. and Gole, P. A Stochastic Raindrop Time Distribution Model. AMS Journal of Applied Meteorol-
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Shrestha S., and Choi D.Y. Study of 1-min Rain Rate Integration Statistic in South Korea. Journal of Atmospheric and Solar-Terrestrial Physics, 2017; 155: 1-11
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Dear editor and reviewers, This paper objective is to study the performance of several conversion methods in Malaysia. I add the average RMSE and SC-RMSE and add one row into the table to show which method gives low average RMSE and SCRMSE over 10 sites. I revise the conclusion with concluded Chebil and Rahman model is the best model according to average RMSE and SC-RMSE value.
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I have invited English experts to correct and give the advice to my English writing. I hope it helps this manuscript quality is getting improve. Many thanks for editor and reviewers to spend time reading this manuscript and giving the valuable inputs. It’s really helpful to give me have idea how to improve the works. I wish you all the best.
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Best Regards, Yun Yann