Conversion of 5-min and 10-min to 1-min Average ...

Conversion of 5-min and 10-min to 1-min Average Rainfall Rate using East Malaysia data Surati Selamat, Azah Syafiah Mohd Marzuki, Azlinda Tee Md Azlan Tee, Amran Naemat, Khaidir Khalil TM R&D Sdn Bhd Cyberjaya, Malaysia

Abstract— Malaysia is well known for its wet tropical climate and monsoon seasons which bring rainfall almost throughout the year. Therefore, designing wireless communication links above 10 GHz for Malaysian weather involves study of rainfall rate and its integration time. The knowledge of local 1-min rainfall rate statistic is the key input for the estimation of signal attenuation due to rain. Due to limitation of 1-min rain rate data availability, the conversion model is necessary to translate higher integration time rainfall rate to the required 1-min rainfall statistic. In this paper, rainfall data from six locations in the East Malaysia is acquired from a local hydrological agency and processed to a meaningful 1-min, 5-min and 10-min rainfall rate statistics. Then, four conversion models are used to convert from 5-min and 10min rainfall rate to 1-min rainfall rate. From the conversion error analysis, it is found that the Emiliani et al conversion method performed the best for this study. Keywords—rainfall rate conversion, 5-min to 1-min, 10-min to 1-min

I.

Introduction

The effect of rain to microwave system operating at frequency above 10 GHz is more critical for countries located in tropical and equatorial region. Being a wet tropical country with two monsoon seasons, precipitation is high in most part of Malaysia. International Telecommunication Union - Radio (ITU-R) in [1], once mapped Malaysia in the P-region which the rainfall intensity exceeded 145mm/hr for 0.01% of the average year; i.e. R0.01 = 145m/hr. Rainfall distribution, in particular R0.01 is essential for estimating rain attenuation using ITU-R model. The method to convert rainfall distribution of higher integration time to 1-min rainfall distribution has been studied since 1980s. This is because local rainfall data is more accessible nowadays and the rain attenuation estimation based on measured rainfall data is more accurate. ITU-R has accepted 1-minute (1-min) rain rate for estimating rain attenuation [2]. However, the availability of 1-min rain rate statistic in most part of the world is still limited, including Malaysia. Therefore, several studies have been done locally and regionally to find the most suitable method to convert higher integration time rainfall data to 1-min rain rate statistics.

In Malaysian context, Chebil and Rahman in [3] has revised Segal's model to describe the relationship between hourly and 1-min rain rate statistic. Chebil and Rahman in [4] also come out with 1-min rain rate prediction using mean annual rainfall data. In reference [5] and [6], Chebil and Rahman method and other three established conversion models were used to convert from 60-, 30-, 10- and 5-min to 1-min rain rate. The studies found that Segal method gave the best transformation. Then, Mandeep and Chun in [7] applied six conversion methods to discover that Segal again gave the best estimation. For this paper, six sites in Malaysia; three in Sabah and three in Sarawak are selected based on the station capability to provide 1-min rainfall data for approximately 5 years span. This hydrological data obtained from Drainage and Irrigation Department Malaysia is processed to produce 1-min, 5-min and 10-min rainfall rate statistic. Later in the section, four conversion methods are briefly introduced and they are applied to the 5-min and 10-min rain rate distribution to get back the 1-min rain rate. In the results and discussion, the converted 1-min rain rate is then compared to original 1-min rain rate. The conversion error is also analyzed. The conclusion of this study is presented in the last section. II.

Conversion Models

Integration time of rainfall data, τ is the time intervals between the recorded rainfall data. Higher τ rainfall data is more common in hydrological and meteorological purposes, but it hides the high rain rate values. A. Segal method A representative equal probability based method has been suggested by Segal in 1986 [8]. Segal method applies power law to the conversion factor, ρτ (P) such as in (1) and (2).

ρτ ( p) = R1 (P ) Rτ (P)

(1)

ρτ ( p ) = aP b

(2)

R1 (P) and Rτ (P ) are the rainfall rates exceeded with

equal probability, P for integration time of 1-min and τ min respectively. a and b are the regression coefficients proposed by Segal based on 10 years rainfall data collected at 47 stations in Canada.

B. Burgueno et al method Burgueno et al in [9] suggested conversion method based on 49 years rainfall rate data measured in Barcelona, Spain. The 1-min rainfall rate is determined by using (3). R1 (P ) = aRτ b (P )

(3)

R1 (P ) and Rτ (P ) are the rainfall rates exceeded with

equal probability, P for integration time of 1-min and τ min respectively. a and b are the conversion variables. C. ITU-R P.837-5 Recommendation ITU-R recommended similar conversion formula such as Burgueno et al method, however with a new set of coefficients. The coefficients are obtained through regressions made to a database of 14 sites in Korea, China, and Brazil for 5-min, 10-min, and 30-min. D. Emiliani et al method An extension of ITU-R P.837-5 has been proposed by Emiliani et al in [10]. The study further derived a new set of global coefficients for the power law conversion method. The coefficient values are obtained using an extended database including 18 sites from three types of Köppen climatic region. Table I summarizes the coefficients used in this study. TABLE I. τ

Segal

COEFFICIENT VALUES FOR 5-MIN AND 10-MIN Burgueno et al

ITU-R P.837-5

Emiliani et al

a

b

a

b

a

b

a

b

5

1.156

0

1.28

0.98

0.986

1.038

0.924

1.044

10

1.263

0

1.69

0.94

0.919

1.088

0.829

1.097

TABLE II.

SITE'S PROFILE

Station No

Station Name

State

Latitude

Longitude

6064001

Dalas

Sabah

06 02 00

116 28 00

5961001

Kiansam

Sabah

05 59 05

116 10 40

4278004

Kuhara

Sabah

04 16 05

117 53 17

3130003

Bintulu JPS Stapang

Sarawak

113 02 20

Miri Airport

Sarawak

003 10 20 002 23 55 004 19 50

2321001 4339005

Sarawak

112 08 05 113 59 15

Data availability for all sites at Sabah is 100% when averaged over 5 years. Meanwhile Sarawak's site has 98.2% data availability for Dalas, 94.13% for Kiansam and 91.15% for Kuhara. B. Raw Data Processing DID's rainfall recorded data comes in a comma separated value (.csv) file with columns of date, time and rain amount (mm). For this study, the interval between recorded data is 1 minute i.e. Integration time, τ=1-min. For full 5 years rainfall data, the size of the row involved is approximately 2.62 million. This amount of data cannot be analyzed by common spreadsheet. Therefore, scripts are developed using Microsoft SQL server. The first script loads the raw data into table in Microsoft SQL server database. Then, another script checks any error and redundancy, before the rain rate (mm/hr) calculation based on (4) is made. Rain Rate = Rain Amount in τ-min x (60-min/τ-min)

III.

Research Method

A. Local Rainfall Data This conversion study requires long term local rainfall data that can be provided by local government agencies such as Drainage and Irrigation Department Malaysia (DID) or Malaysia Meteorological Department (MMD). For this paper, the rainfall data is acquired from DID because the fee is more cost efficient. DID has hydrological stations all over Malaysia that may provide rainfall data in the interval of 1-min or longer, depending on the station's capability. New stations has automatic logger that may provide 1-min rainfall, but with limited recording span. The raw data is collected for a period of 5 years, starting 1st January 2009 until 31st December 2013. According to ITU-R, an appropriate measurement period for rainfall statistics is between 3 to 7 years [4]. Six sites at Sabah and Sarawak have been chosen for this study, because of future implementation of the second phase of High Speed Broadband (HSBB 2) in the East Malaysia. Telekom Malaysia Bhd (TM) is dedicated to provide broadband services to urban and rural areas as part of Malaysian Communications and Multimedia Commission's initiative. Table II list the stations under experiment and its location. All these sites are able to provide 1-minute rainfall data, thus comparisons between conversion methods can be tested.

(4)

C. Frequency Distribution Rows of rain rate only become useful for this study if the frequency distribution is constructed. The script calculates an appropriate number of class range, K using Sturges’ formula such as in (5). n is the number of observation of raining events. K = 1 + 3.3log10(n)

(5)

Then, the suitable class interval, I or “width” of each class is determined by applying (6). ahigh is the highest rain rate and alow is the lowest rain rate in the list. I = (ahigh - alow ) / K

(6)

Using K and I value, the lower limit, ai and the upper limit, bi for each class is determined. Then, the frequency of occurrence for each class range, F is tabulated starting from the lowest rain rate class to the highest rain rate class. The probability of exceedence Fr is evaluated for each class using (7). mi is the total frequency of occurrence when x exceeds ai. ݉ (7) ‫ܨ‬௥ ൌ ‫ܨ‬ሺ‫ ݔ‬൐ ܽ௜ ሻ ൌ ௜ൗ݊ The exceedence probability forms the foundation of rainfall rate statistics. The rainfall rate statistics for 1-min, 5min, and 10-min are plotted in Fig. 1, Fig. 2 and Fig. 3 for all the sites chosen. Note that the R0.01 is reduced when the integration time is increased.

120

Segal

Miri_Airport

Burgueno et. al

ITU-R P.837-5

Emiliani et. al

15

Stapang

Percentage of error (%)

1-min rainfall rate (mm/hr)

100

Kuhara

80

Kiansam 60

Bintulu Dalas

40

0 -5 -10

Miri

Stapang Kuhara

Kiasam

Bintulu

Dalas

Bintulu

Dalas

Bintulu

Dalas

Location

(a) at P = 0.01% 0.1

1

20

% of time of five years the rainfall rate is exceeded

Percentage of error (%)

Fig. 1. 1-minutes measured rainfall rate statistics. 120

Miri_Airport Stapang

100

5-min rainfall rate (mm/hr)

5

20

0 0.01

Kuhara 80

Kiansam

15 10 5 0 -5 -10 -15 -20

Bintulu

60

Miri

Stapang Kuhara

Kiasam

Location

Dalas 40

(b) at P = 0.1%

20

0.01

0.1

1

% of time of five years the rainfall rate is exceeded

Fig. 2. 5-min rainrate statistics translated from 1-min measured rainfall Miri_Airport

100

10 5 0

Stapang Kuhara

Kiasam

(c) at P = 1% Fig. 4. 5-min to 1-min conversion error percentage for (a) P = 0.01%, (b) P = 0.1% and (c) P = 1%

Dalas 40

20

0.1

1

% of time of five years the rainfall rate is exceeded

Fig. 3. 10-min rainrate statistics translated from 1-min measured rainfall.

Results and Discussion

Four conversion methods such as in Section II were applied to the rain rate statistic of 5-min and 10-min for all the sites to get the predicted 1-min rainfall rate of equal probability. The predicted 1-min and the measured 1-min rainfall rate are then compared by calculating the error using (8). Rp is the predicted rainfall rate using the conversion methods and Rm is the measured rainfall rate at a specific probability. %error = 100*(Rp-Rm)/Rm

15

Location

Bintulu

IV.

20

Miri

Kiansam

0 0.01

25

-10

Kuhara

60

30

-5

Stapang 80

Percentage of error (%)

35

0

10-min rainfall rate (mm/hr)

10

(8)

Fig. 4 shows the error percentage of 5-min to 1-min conversion for the six study sites. At P = 0.01%, each method over-estimated the rainfall rate for all sites; except an underestimation for Kuhara. All the methods gave an error below 11% for all sites; which Emiliani et al method gave the smallest error except for Kuhara. Kuhara is an exception for most of the cases all the way through the analysis, because the available data was less than 92%. At P = 0.1%, all methods over-estimated for most of the sites except Emiliani et al method under-estimated for Stapang, Kiasam and Bintulu. At this probability, it is found that Emiliani et al method or ITU-R P.837-5 method gave the smallest error. At P = 1%, the trend was more steady. Emiliani et al method gave the smallest error, while ITU-R P.837-5 came second. For 5-min rainfall rate, Emiliani et al method performed the best conversion for most of the sites and for most of the probability.

⎛1 MAPE = ⎜ ⎝n

∑

TABLE III.

(a) at P = 0.01% 25

Percentage of error (%)

20 15

-10 -15 -20 -25

Miri

Stapang

Kuhara

Kiasam

Bintulu

Dalas

Location

(b) at P = 0.1%

Burrgueno e al et

ITU-R P.837-5

Emiliani et al

Miri

14.21

199.82

14.08

6.40

Stapang Kuhara Kiasam Bintulu Dalas

8.78 8.89 7.53 10.03 13.75

144.40 100.60 144.14 166.02 200.45

7.98 8.00 5.47 9.13 11.93

6.32 10.44 3.69 4.92 5.43

Con nclusion

In this paper, four methodss (Segal, Burgueno et al, ITU-R P.837-5 and Emiliani et al) weere used to convert local 5-min and 10-min rainfall statistics to t 1-min rainfall statistics. This study suggests that Emilianni et al method is the best conversion method for 10-minn and 5-min of East Malaysia data.

55

Acknowleedgement

45

Percentage of error (%)

MEAN ABSOLUTE PERCENT ERROR

Segal

V.

0 -5

(9)

Site

10 5

Rp − Rm R ⎞ ⎟ *100 Rm ⎠

Acknowledgement goes too technical leaders and project members of G-Fiwi2 for the oppportunity to run this study.

35 25 15

Referrences

5 -5

[1]

-15 -25

Miri

Stapang

Kuhara

Kiasam

Bintulu

Dalas

Location

(c) at P = 1% Fig. 5. 10-min to 1-min conversion error percentage foor (a) P = 0.01%, (b) P = 0.1% and (c) P = 1%

For 10-min to 1-min conversion, the perccentage of error is depicted in Fig. 6. At P = 0.01%, Emiliiani et al method showed the smallest error except at Kiasam m. However at P = 0.1%, Segal method gave the smallest error e for Stapang, Kuhara and Bintulu. For the remainder sittes, Emiliani et al gave the best error. Whereas at P = 1%, Em miliani et al offered the smallest error for Miri, Bintulu and Dalass. For Stapang and Kiasam, ITU-R P.387-5 showed the best perccentage error. Based on Fig. 5 and Fig. 6, it is observeed that Emiliani et al method had shown the smallest error for most of the analysis. In order to verify the analysis, thhe Mean Absolute Percent Error (MAPE) is calculated by using (9). Table III summarizes the MAPE for each site. Segal and Burgueno are less suitable metthod for this study because the coefficient values are based onn rainfall data in a region that have different climate from Malaaysia. On the other hand, Emiliani et al method has considered three climate zones, including seven tropical countries suuch as Singapore, Thailand and Philippines.

ITU-R, “Recommendation IT TU-R P.837-1: Characteristics of precipitation for propagation moddelling,” 1994. [2] ITU-R, “Recommendation ITU U-R P.530-15: Propagation data and prediction methods required forr the design of terrestrial line-of-sight systems,” 2013. Rain rate statistical conversion for the [3] J. Chebil and T. A. Rahman, “R prediction of rain attenuation in Malaysia,” Electron. Lett., vol. 35, no. 12, pp. 1019–1021, 1999. Development of 1 min rain rate contour [4] J. Chebil and T. A. Rahman, “D maps for microwave applicationns in Malaysian Peninsula,” Electron. Lett., vol. 35, no. 20, pp. 1772–17774, 1999. [5] J. S. Mandeep and S. I. S. Hassan, “60- to 1-Min Rainfall-Rate Conversion: Comparison of Exxisting Prediction Methods with Data Obtained in the Southeast Asia Region,” J. Appl. Meteorol. Climatol., vol. 47, no. 3, pp. 925–930, Mar. 2008. [6] J. S. Mandeep, K. Tanaka, and M. Iida, “Conversion of 60-, 30-, 10-, and 5-Minute Rain Rates to 1-Minute Rates in Tropical Rain Rate Measurement,” ETRI, vol. 29, noo. 4, pp. 542–544, 2007. [7] O. W. Chun and J. S. Mandeeep, “Empirical methods for converting rainfall rate distribution from several higher integration times into a 1minute integration time in Malayysia,” Geofizika, vol. 30, 2013. [8] B. Segal, “The Influence of Raaingage Integration Time on Measured Rainfall-Intensity Distribution Functions,” F J. Atmos. Ocean. Technol., vol. 3, pp. 662–671, 1986. a E. Vilar, “Influence of rain gauge [9] A. Burgueño, M. Puigcerver, and integration time on the rain rate statistics used in microwave communications,” Ann. Des Téléécommunications, vol. 43, no. 9–10, pp. 522–527, 1988. [10] L. D. Emiliani, L. Luini, and C. Capsoni, “Extension of ITU-R Method for conversion of rain rate statistiics from various integration times to one minute,” Electron. Lett., vol. 44, no. 8, pp. 43–44, 2008.