J. lnf. Commun. Converg. Eng. 14(3): 153-162, Sep. 2016 Regular paper

Proposed One-Minute Rain Rate Conversion Method for Microwave Applications in Korea

Sujan Shrestha and Dong-You Choi*, Member, KIICE Department of Information and Communications Engineering, Chosun University, Gwangju 61452, Korea

Abstract Microwave and millimeter waves are considered suitable frequency ranges for diverse applications. The prediction of rain attenuation required the 1-min rainfall rate distribution, particularly for data obtained locally from experimental measurement campaigns over a given location. Rainfall rate data acquired from Korea Meteorological Administration (KMA) for nine major sites are analyzed to investigate the statistical stability of the cumulative distribution of rainfall rate, as obtained from a 10-year measurement. In this study, we use the following rain rate conversion techniques: Segal, Burgueno et al., Chebil and Rahman, exponential, and proposed global coefficient methods. The performance of the proposed technique is tested against that of the existing rain rate conversion techniques. The nine sites considered for the average 1-min rain rate derivation are Gwangju, Daegu, Daejeon, Busan, Seogwipo, Seoul, Ulsan, Incheon, and Chuncheon. In this paper, we propose a conversion technique for a suitable estimation of the 1-min rainfall rate distribution.

Index Terms: 1-Minute rain rate, Microwave communication, Rain rate model

I. INTRODUCTION application to the prediction of experimental local data remains challenging [2]. Efforts to localize rain attenuation The advancement of technologies in the fields of satellite models however depend on the knowledge of the rainfall communications, multimedia applications, the Internet, and rate and the experimental data for the chosen location. The mobile communications has increased the demand for a high data further enhance the development of the local rain data transmission rate. Consequently, in the field of data attenuation model. In this paper, the experimental result of transmission technology, the emphasis has shifted to high- rainfall rate statistics of certain selected locations of Korea frequency microwave bands. However, the problem of rain is described. According to climatologists, recently, major is significant for operation frequencies of more than 10 GHz. cities in Korea have experienced unusually heavy rainfall, A reduction in the transmitted signal amplitude because of which might be attributed to urban heat island phenomena an atmospheric mechanism such as the absorption and [3]. A comprehensive effort for the characterization of scattering of radio waves results in rain attenuation [1]. the 1-min rainfall rate has been made by International Further, a communication system designer faces a problem Telecommunication Union Radiocommunication Study in the prediction of the effects of rain on radar and the Group 3 (ITU-R, formerly the CCIR). Moreover, to convert remote sensing of a location on or above the Earth’s surface. a relatively high integration time’s rainfall data to the Although numerous rain attenuation models exist, their equivalent 1-min distribution, various procedures have been ______

Received 05 July 2016, Revised 06 July 2016, Accepted 02 August 2016 *Corresponding Author Dong-You Choi (E-mail: [email protected], Tel: +82-62-203-7060) Department of Information and Communications Engineering, Chosun University, 309, Pilmun-daero, Dong-gu, Gwangju 61452, Korea.

Open Access http://dx.doi.org/10.6109/jicce.2016.14.3.153 print ISSN: 2234-8255 online ISSN: 2234-8883 This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by- nc/3.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Copyright ⓒ The Korea Institute of Information and Communication Engineering

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enforced considering the relevant physical, analytical, and RSC) method is used for the conversion of the rainfall rate empirical models [4]. Because of the experimental statistics from a long integration time to a 1-min integration dependence and for simplicity, in this study, empirical time. This method is based on the simulated movement of models are selected as an appropriate method for rain cells over a virtual rain gauge, during the given determining the distribution of the rainfall rate at the 1-min integration time T, whose translation velocity depends on integration time. Further, in this paper, we emphasize on the both the type of precipitation and the observation period. difference between the measured rainfall rate statistics and The rainfall conversion is obtained using a virtual rain the ITU-R P.837-6 [5] model along with the applicable gauge according to the local mean yearly wind velocity, empirical nature methods. which is extracted from the ERA-40 database. The The rest of the paper is organized as follows: Section II prediction approach is based on the annual rainfall amount presents a brief overview of the predicted point rainfall rate. of the convective type and the stratiform type along with the The experimental setup is described in Section III. Section probability of 6-hr rainy periods. Depending on the type of IV highlights the performed regression analyses for the precipitation, rain structures appear to move mostly because applicable empirical methods. Similarly, Section V details of the wind speed (convective rain) or because of the time the performance evaluation of the proposed technique. evolution (stratiform rain) [14]. The theoretical concept of Finally, Section VI draws some useful conclusions. this model is explained using a physical model-based methodology in [15] and in an update of Recommendation ITU-R P.837-5, Annex 3 [5]. EXCELL RSC is globally II. REVIEW OF SELECT 1-MIN RAIN RATE applicable and has strong physical soundness for CONVERSION MODELS measurements with an arbitrary integration time, T. The effectiveness of the EXCELL RSC model was tested using Several studies have been conducted to measure the effect various error analyses against other global models in [16], of this natural phenomenon on the radio propagation path where the EXCELL RSC model was found to be suitable for above 10 GHz, using the various rain attenuation statistical the estimation of the 1-min rainfall rate. models either globally or locally. Further, a considerable Several researchers around the globe have proposed amount of research work has been carried out in this area regional rainfall rate models. These rainfall rate models over the years locally [3, 6-10]. Interestingly, the have been developed from empirical equations using the experimental duration of the rainfall rate data is relatively results of field measurements collected over a long period of low, and more research needs to be carried out to ensure a time [12]. Similarly, the mathematical theory based on the reliable signal transmission. Furthermore, the rainfall rate principles for de-integrating a T-min experimental research carried out in the neighboring country Japan [11] probability distribution (pd) into the corresponding 1-min pd relies on the thunderstorm ratio and the regional climatic is presented in [17]. However, there is a need for more parameters of only one location of Korea as Daejeon. efficient propagation planning, based on the use of the Because of the variations in the performed experiment, this number and the duration of rain events along with the model has not been analyzed, but the exponential nature of fraction of the rain time. The experimental system used by rain rate variation has been studied. Rainfall rate models are Korea Meteorological Administration (KMA) provides the classified into global and localized rainfall rate models [12]. experimental record only for the 1-min rainfall amount as Global rainfall rate models depend on climatic parameters discussed later in this paper. Despite the numerous models and geographical locations. In this study, we consider the proposed thus far, empirical techniques have been selected proposed global coefficient values as listed in [13], which due to its simplicity as they are all based on conversion extend global coefficients value’s application to rain rate coefficients determined by means of measured data and their conversion methods in temperate, tropical, and cold climates, simple formulation, which allows one to extend their along with the ITU-R P.837-6 [5] method. ITU-R P.837-6 applicability to more than one climatic regions. Empirical contains the software that implements the conversion of rain conversion techniques provide analytical laws expressing rate statistics with different integration times, adopted by the relationship between equiprobable rain rate values with Study Group 3 in Recommendation P.837-6, Annex 3. Of the available 1-min and T-min integrated distributions [4]. the two operational modes as recommended in the software, In this study, we test the applicability of the following Mode A is chosen for inputting data for various times and empirical conversion methods: the Segal method [18], percentage rain rate values. Similarly, the latitude and which provides a systematic approach for obtaining a longitude information of the sites along with various source specified number of rain zones in countries such as Canada integration times, such as 5 min, 10 min, 20 min, 30 min, that have sufficiently large databases of short integration and 60 min, are provided as additional input parameters. time data; the method proposed by Burgueno et al. [19] with The EXCELL Rainfall Statistics Conversion (EXCELL data from Barcelona, which emphasizes the power law

http://dx.doi.org/10.6109/jicce.2016.14.3.153 154 Proposed One-Minute Rain Rate Conversion Method for Microwave Applications in Korea

relationship that exists between equiprobable rain rates of two integration times; the Chebil and Rahman method [20] with data of Malaysia, which uses an empirical formula that combines the Segal method and the power law; the method proposed by Lee et al. [10] using the Electronics and Telecommunications Research Institute (ETRI) rainfall rate data measured through an optical rain gauge (ORG), which is a conversion model with zero interception for the logarithmic scale that shows an efficient measure for the Fig. 1. Tipping bucket rain gauge [27]. estimated 1-min rainfall rate data; and the conversion method that employed an exponential function for equal rain rate in

[11, 21, 22], which determined the probability distribution Table 1. Characteristics of study locations [27] function of the M distribution. In this research, an exponential function is studied for equal time percentage Station Latitude (°N) Longitude (°E) ranges. Further, polynomial fit is considered the most Gwangju 35°9'23.7" 126°51'28.45" preferred method to characterize the 1-min rainfall rate [23], Daegu 35°52'23" 128°36'4.35" which emphasizes that the conversion technique is Daejeon 36°21'4.55" 127°23'4.37" dependable and consistent to be used for the Malaysian Busan 35°10'49.86" 129°04'32.31" tropical climate. Furthermore, model application against the Seogwipo 33°15'14.97" 126°33'35.85" measured statistical data at 0.01% time exceedance results Seoul 37°33'36" 126°59'24" in good agreement. In addition, polynomial fit gives a better Ulsan 35°32'18.5" 129°18'40.89" Incheon 37°27'14.4" 126°43'55.2" statistical result for the conversion of the rain rate from a 5- Chuncheon 37°52'54.24" 127°43'49.17" min to a 1-min integration time equivalent for South Africa and the surrounding islands. The suitable coefficients are proposed for this method in [24, 25]. The empirical methods Table 2. Specifications of tipping bucket rain gauge [5] selected in this study have been proposed at different moments in time as recommended by ITU-R P.311-15 [26] Rain gauge equipment Description for rainfall statistics conversion. Sensor type Tipping bucket Switch Form A reed, mercury-wetted Size 200 mm in diameter III. EXPERIMENTAL PROCEDURE Resolution 0.5 mm Sensitivity 0.1 mm per tip In order to measure the 1-min rainfall amount, several Accuracy Less than 5% experimental systems have been developed by KMA since Operating temperature −40°C to +50°C 2004. The system for collecting and storing rainfall data at 1-min intervals was installed in 93 different locations, out of which nine major sites that are characterized as big is mounted on a particular axis of rotation to shift the center metropolis are considered. The latitude and longitude like a seesaw. This bucket is in contact with the Reed switch information of these sites is listed in Table 1. on the rotation axis, which is operated by an electrical These major cities lie in a temperate climatic region pulse generated by the tipping phenomenon. Finally, the whose experimental 1-min rainfall rate data for a decade are signal generated through the Reed switch is recorded on a analyzed. Korea has a temperate climate with four distinct recording device that records the post-processing of the time seasons. Winters are usually long, cold, and dry. Summers stamp of each tip, which provides the measurement of the 1- are very short, hot, and humid. Spring and autumn are min rainfall amount. The heater is installed inside the sewer pleasant but also short in duration. The country has for measurement under snowfall. Further, Table 2 presents sufficient rainfall; rarely does it have less than 75 cm of the specifications of the rain gauge. rainfall in any given year or more than 100 cm [27]. The The tipping bucket has an unstably balanced twin bucket maximum rainfall is noted from May to September of each with a sensitivity of 0.1 mm per tip, which triggers an year. The measurement setup includes a tipping bucket rain electronic impulse that is stored in the data logger, which gauge, as shown in Fig. 1. scans the data at an interval of 1 min. The availability of the KMA uses a conducting vessel size of 0.5 mm to improve gauge is about 99.2%. The 0.8% unavailability is due to the shortcomings of the gutter. Once the collected water is system maintenance. Fig. 2 shows the overall operation of more than 0.5 mm, it eventually fills the bucket. The bucket the experimental system used for the rainfall data logging

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Fig. 2. Experimental system used for measuring the 1-min rain rate [27].

parts where the accumulated rainfall amount is first collected in a data logger and then stored in the data storage devices. The calculated 1-min rain rate from the experimental 1- min rainfall amount obtained from the KMA database at 0.01% of the time lies between 60 to 90 mm/hr for all the considered regions. The Ulsan region shows greater rain rate variability because this region lies near the coastal area and the average rainfall accumulation is higher in this belt. At a time percentage higher than 0.1%, the 1-min rainfall amount values are extremely low and tend to be negligible. Analyses of these cumulative statistics indicate that the rainfall process is mostly of the convective type and shows the saturation limit in the rain mechanism. The rain rate at a Fig. 3. Mean rainfall rate distribution at various integration times of nine regions [27]. higher time integration of 5 min, 10 min, 20 min, 30 min, and 60 min are used as the input parameter for the software recommended by ITU-R P.837-6 [5]. The value of the 1-min rain rate distribution at 0.01% of the time lies between 80 and 90 mm/hr for most of the prime locations in Korea. The rainfall rate at 0.01% of the time is preferred in communication system design and to precisely predict rain attenuation. ITU-R P.618-12 [28] emphasized the use of the 1-min integration time of the rainfall rate at this prominent integration time for the prediction of rain attenuation. The importance of the 1-min rain rate has been further studied for satellite and terrestrial rain attenuation predictions [29, 30, 33]. Furthermore, the mean rainfall rate distribution generated for the nine regions is shown in Fig. 3. The 1-min rainfall rate distribution, which is obtained after averaging over these sites, is used for further analyses with the application of six empirical conversion methods along with the second- order and third-order polynomial fits. The conversion from the 10-min and the 20-min curves to the 1-min curve shows a slightly higher rain rate at a lower time percentage when P ≤ 0.05%, which might be due to the higher rainfall Fig. 4. 1-Min average rainfall rate distribution for various integration times for nine main regions [5]. distribution obtained in the Ulsan region. Similarly, Fig. 4 indicates the mean 1-min rain rate distribution along with the average 1-min rain rate generated after averaging over However, as integration times increase, the probability of several integration times, namely 5 min, 10 min, 20 min, 30 overestimation also increases. Further, Fig. 5 presents the min, and 60 min, to the 1-min conversion time from ITU-R overall distribution of the 1-min rain rate over nine regions. P.837-6 [5]. This indicates that ITU-R P.837-6 [5] shows a These graphs clearly depict that the 1-min rain rate at 0.01% fair estimation of the 1-min rainfall rate at a lower time of the time lies between 60 mm/hr and 90 mm/hr for most of conversion, particularly 5 min to 1 min. the major cities in Korea.

http://dx.doi.org/10.6109/jicce.2016.14.3.153 156 Segal Burgueno et al. Chebil and Rahman Logarithmic Exponential Global Coefficients Second Order Polynomial Fit Third Order Polynomial Fit T-min. to 1-min. a b a b a b c d a a b a b a b c a b c d 5-min. to 1-min. 1.03 -0.005367 1.36 0.948 1.134 -0.005801 -0.1138 27.41 1.018 34.54 0.01094 0.924 1.044 -0.005601 1.98 -32.49 -0.0001114 0.02288 -0.3016 24.45 10-min. to 1-min. 1.322 0.02072 5.872 0.6095 1.309 0.01953 -0.001517 129.5 1.016 52.41 0.005388 0.829 1.097 -0.008213 2.44 -47.31 -0.00007127 0.01392 0.4615 5.387 20-min. to 1-min. 1.464 0.03245 3.061 0.7583 12.79 0.0003768 -11.67 0.001617 1.016 38.93 0.009036 0.736 1.169 -0.006129 1.863 -19.97 0.0003082 -0.08317 7.852 -165 30-min. to 1-min. 1.201 0.005379 1.836 0.8889 -0.3521 0.7067 1.143 4.676 1.031 34.95 0.01124 0.583 1.265 -0.005853 1.944 -24.28 0.000204 -0.0546 5.613 -110.8 60-min. to 1-min. 0.9994 -0.02069 0.971 1.054 -1170 1.054 1.246 435.1 1.046 29.93 0.01438 0.509 1.394 -0.004187 1.893 -24.77 0.00000471 -0.005229 1.966 -26.4

Proposed One-Minute Rain Rate Conversion Method for Microwave Applications in Korea

Chebil and Rahman [20] introduced an experimental technique for estimating the precipitation rate conversion element by using the conversion process from 60-min to 1- min integration time as follows:

ρ60(P) = R1(P)/R60(P), (3)

where R60(P) denotes the precipitation rate for the 60-min integration time. ρ60(P) is expressed as a mixed power- b (dP) exponential law; ρ60(P) = aP + ce with regression variables represented by a, b, c, and d obtained from a statistical analysis of rainfall data. The suitability of this method has been further tested for other lower integration time intervals. (iv) Logarithmic model [10]:

Fig. 5. 1-Min rainfall rate distribution of nine regions [27]. log[R1(P)] = a log[Rτ(P)], (4)

where a denotes the regression variable derived from a IV. REGRESSION ANALYSIS OF RAINFALL statistical analysis of the rainfall rate. RATE (v) Exponential model:

A regression analysis was performed to match the data to R (P) = a exp(b *R (P)), (5) the known mean distribution using six applicable empirical 1 τ conversion methods along with the second-order and third- where a and b represent the regression coefficients obtained order polynomial fits. The regression models summarize a from a statistical analysis of the rainfall rate. large amount of data with a minimum modeling error [2]. Regression analysis is a statistical method to estimate the (vi) Proposed approach: values of dependent variables that correspond to certain values of new independent variables once the magnitude of In this study, we statistically evaluate the different degree of the influence of independent variables on the dependent polynomial fits as follows: variables is measured, thereby determining the regression Second-order polynomial fit: plane or line with respect to the independent variables. The 2 expressions used in the equal probability method R1(P) = a[Rτ(P)] + b[Rτ(P)] + c. (6) representing R1(P) and Rτ(P) for the 1-min and τ-min integration times with an equal probability of time Third-order polynomial fit: percentage, P, respectively, are given as follows: R (P) = a[R (P)]3 + b[R (P)]2 + c[R (P)] + d. (7) (i) Segal method [18]: 1 τ τ τ

The suitability of the proposed techniques has been R (P) = ρ (P) R (P), (1) 1 τ τ further analyzed in [31, 32]. The obtained regression

coefficient values applicable for different conversion where conversion factor ρ (P) = aPb, and the parameters a τ techniques against the mean 1-min rain rate distribution are and b denote the regression coefficients that are derived tabulated in Table 3. from a statistical analysis of rainfall data. These coefficients are used for obtaining the mean 1-min (ii) Burgueno et al.’s method [19]: rain rate distribution from the 5-min, 10-min, 20-min, 30- min, and 60-min integration times. Furthermore, the b R1(P) = aRτ (P), (2) coefficient of determination is calculated for the applicable empirical nature of methods. The coefficient of where a and b represent the conversion variables obtained determination, R2, describes the proportion of the variance from a statistical analysis of rainfall data. in the measured data explained by the model. The proportion of variability in a dataset is accounted for by this (iii) Chebil and Rahman’s method [20]: statistical model [35]. R2 provide a measure of the accuracy of

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Table 3. Estimated parameter values obtained from a statistical program [34]

Second-order Third-order τ-min integration times Burgueno et al. [19] Exponential polynomial fit polynomial fit 5-min to 1-min 0.965 0.931 0.976 0.980 10-min to 1-min 0.931 0.882 0.957 0.974 20-min to 1-min 0.935 0.873 0.944 0.971 30-min to 1-min 0.917 0.905 0.943 0.962 60-min to 1-min 0.864 0.821 0.927 0.949

Table 4. Coefficient of determination R2 as obtained from a statistical program [34]

Burgueno Log- Global Second-order Segal Chebil and Rahman [20] Exponential Third-order polynomial fit et al. [19] arithmic coefficients polynomial fit

a b a b a b c d a a b a b a b c a b c d 5- to 1-min 1.03 -0.005367 1.36 0.948 1.134 -0.005801 -0.1138 27.41 1.018 34.54 0.01094 0.924 1.044 -0.005601 1.98 -32.49 -0.0001114 0.02288 -0.3016 24.45 10- to 1-min 1.322 0.02072 5.872 0.6095 1.309 0.01953 -0.001517 129.5 1.016 52.41 0.005388 0.829 1.097 -0.008213 2.44 -47.31 -0.00007127 0.01392 0.4615 5.387 20- to 1-min 1.464 0.03245 3.061 0.7583 12.79 0.0003768 -11.67 0.001617 1.016 38.93 0.009036 0.736 1.169 -0.006129 1.863 -19.97 0.0003082 -0.08317 7.852 -165 30- to 1-min 1.201 0.005379 1.836 0.8889 -0.3521 0.7067 1.143 4.676 1.031 34.95 0.01124 0.583 1.265 -0.005853 1.944 -24.28 0.000204 -0.0546 5.613 -110.8 60- to 1-min 0.9994 -0.02069 0.971 1.054 -1170 1.054 1.246 435.1 1.046 29.93 0.01438 0.509 1.394 -0.004187 1.893 -24.77 0.00000471 -0.005229 1.966 -26.4

future predictions which ranges from 0 to 1, with higher values indicating lower error variance. The values of R2 are obtained through a statistical analysis whose results are calculated after averaging over the nine mentioned sites, as listed in Table 4. As summarized in Table 4, the polynomial models of the second-order and third order has a relatively high correlation with the rainfall rate over the various integration times. Within these models, the proposed polynomial technique of the third order exhibits greater correlation values, which show its effectiveness in the estimation of the 1-min rainfall rate. Comparatively, the exponential model and the logarithmic model show a lower value of R2. This confirms that the error variance increases when we apply the exponential and Burgueno et al.’s models for the prediction of the 1-min rainfall rate. Because of the dependability on the statistical analyses, the coefficient of determination values for the Segal, Chebil and Rahman, logarithmic, and Fig. 6. 1-Min rainfall rate compared with 5-min integration rainfall rate global coefficients are not listed in Table 4. data [34].

V. PERFORMANCE EVALUATION OF Figs. 6 and 7, this method tends to overestimate for higher PROPOSED TECHNIQUE time integration of 20 min, 30 min, and 60 min to 1 min, as shown in Figs. 8–10. The relative error percentage deviations The mean 1-min rainfall rates estimated using the along with other statistical analyses are calculated for the applicable models from the relatively high integration times proposed conversion technique. such as 5 min, 10 min, 20 min, 30 min, and 60 min to the 1- In order to determine the adequacy of the proposed min time interval are shown in Figs. 6–10, respectively. technique, the mean, standard deviation (STD), and root These plots indicate the suitability of the empirical method mean square (RMS) values of the absolute percentage to characterize the 1-min rainfall rate. Although the ITU-R relative error ε(P) are calculated, where they are compared P.837-6 method shows a fair estimation from lower to the performance of the ITU-R [5] and other conversion integration times of 5 min and 10 min to 1 min, as shown in models. The RMS error values of 0 indicate a perfect fit.

http://dx.doi.org/10.6109/jicce.2016.14.3.153 158 Proposed One-Minute Rain Rate Conversion Method for Microwave Applications in Korea

Fig. 7. 1-Min rainfall rate compared with 10-min integration rainfall rate Fig. 9. 1-Min rainfall rate compared with 30-min integration rainfall rate data [34]. data [34].

Fig. 8. 1-Min rainfall rate compared with 20-min integration rainfall rate Fig. 10. 1-Min rainfall rate compared with 60-min integration rainfall rate data [34]. data [34].

The relative error percentages, ε(P), error values have Seogwipo, Seoul, Ulsan, Incheon, and Chuncheon sites with been weighted over the probability levels of 0.001%, an evaluation of the average rain rate values weighted over 0.002%, 0.003%, 0.005%, 0.01%, 0.02%, 0.03%, 0.05%, several probability levels. The error matrices are calculated and 0.1% of the time, as recommended in ITU-R P.311-15 by following the approaches presented in [31, 32]. [26]. The 1-min rainfall amount values beyond 0.1% are The error variables thus obtained between the experimental very few and tend to be smaller as the percentage of time result and the estimated 1-min cumulative distributions are reaches 1%. Hence, following the recommendation from presented in Tables 5 and 6. ITU-R P.311-15 [26], in this paper, we present the As noted from Table 5, the ITU-R P. 837-6 and global approaches to determine the goodness of fit for 10 years of coefficient methods generate higher error probabilities observations at the Gwangju, Daegu, Daejeon, Busan, because of the increased RMS values. The error probabilities

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Table 5. Error obtained after testing over the interval (0.001% to 0.1%) [34]

5 to 1 min 10 to 1 min 20 to 1 min 30 to 1 min 60 to 1 min Methods Error ε SD RMSE Error ε SD RMSE Error ε SD RMSE Error ε SD RMSE Error ε SD RMSE (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) ITU-R P.837-6 0.05 0.04 4.36 0.14 0.05 10.22 0.44 0.03 36.43 0.72 0.06 63.60 1.16 0.09 102.76 Segal 0.00 0.04 4.27 0.02 0.25 20.61 0.01 0.09 8.55 0.00 0.06 5.34 0.00 0.04 3.78 Burgueno et al. 0.01 0.04 3.77 0.03 0.15 10.61 0.01 0.08 6.20 0.01 0.06 4.49 0.01 0.04 3.89 [19] Chebil and 0.00 0.04 4.33 0.02 0.25 20.73 0.00 0.11 10.42 0.00 0.06 5.68 0.00 0.04 3.54 Rahman [20] Logarithmic 0.00 0.04 4.23 0.01 0.28 23.07 0.00 0.12 11.23 0.00 0.06 6.29 0.00 0.04 3.90 Exponential 0.02 0.10 7.32 0.05 0.21 14.64 0.02 0.11 7.68 0.02 0.10 6.62 0.02 0.08 6.07 Global 0.03 0.04 5.91 0.18 0.26 39.52 0.42 0.24 51.00 0.58 0.20 61.38 1.18 0.22 113.09 coefficients Second-order 0.00 0.02 1.79 0.00 0.03 1.85 0.01 0.06 5.64 0.00 0.04 3.78 0.00 0.04 3.49 polynomial fit Third-order 0.00 0.01 1.15 0.00 0.01 0.81 0.00 0.05 3.10 0.00 0.04 2.98 0.00 0.04 3.49 polynomial fit

Table 6. Error obtained over 0.01% of the time [34] 5 to 1 min 10 to 1 min 20 to 1 min 30 to 1 min 60 to 1 min Methods Error ε (%) RMSE (%) Error ε (%) RMSE (%) Error ε (%) RMSE (%) Error ε (%) RMSE (%) Error ε (%) RMSE (%)

ITU-R P.837-6 0.04 3.52 0.13 10.39 0.44 34.69 0.72 56.94 1.17 93.20 Segal -0.04 3.40 -0.07 5.72 -0.13 9.98 -0.09 6.79 -0.06 4.63 Burgueno et al. -0.04 2.84 -0.04 2.92 -0.10 7.76 -0.07 5.86 -0.06 4.39 [19] Chebil and -0.04 3.41 -0.07 5.74 -0.13 10.62 -0.09 6.79 -0.04 3.33 Rahman [20] Logarithmic -0.05 3.59 -0.09 7.24 -0.14 11.07 -0.09 7.15 -0.06 4.65 Exponential -0.06 4.93 -0.05 4.02 -0.13 10.03 -0.10 8.03 -0.08 6.58 Global coefficients -0.01 1.16 0.06 4.73 0.20 15.62 0.40 31.87 1.01 80.43 Second-order -0.01 0.46 0.01 0.51 -0.07 5.31 -0.05 3.81 -0.04 3.13 polynomial fit Third-order -0.02 1.87 -0.02 1.42 -0.02 1.81 -0.02 1.67 -0.04 3.12 polynomial fit

will be higher for higher integration times, which are To further elaborate the accuracy of the proposed justified by the increasing RMS values of 4.36%, 10.22%, technique at 0.01% of the time, several tests are carried out, 36.43%, 63.60%, and 102.76% for the conversion of 5-min, whose results are tabulated in Table 6. As shown in Table 6, 10-min, 20-min, 30-min, and 60-min data to the 1-min data, although the ITU-R P.837-6 and global coefficient respectively. approaches exhibit a fairly good accuracy with a relatively In contrast, the polynomial fits of the second-order and small error of about 0.04% and 0.01% at a low time third-order show low error probabilities. In particular, the integration of 5-min to 1-min conversion time, respectively, third-order polynomial exhibits low error probabilities the error probabilities increase from a higher time because of the relatively low RMS errors of 1.15%, 0.81%, conversion to 1-min as justified from the increase in the 3.10%, 2.98%, and 3.49% for the 5-min, 10-min, 20-min, RMS error. In contrast, polynomial fits of the second-order 30-min, and 60-min times to the 1-min integration time, and third-order show a lower marginal change in the relative respectively. Similar trends of statistical values are obtained error percentages and RMS values than the other empirical with the application of the second-order polynomial fit. formulas. The error probabilities still remain higher for Although the application of the Segal, Burgueno et al., other models such as the Segal, Burgueno et al., Chebil and Chebil and Rahman, logarithmic, and exponential formulas Rahman, logarithmic, and exponential methods, which are show a fair goodness of fit, the error probabilities remain justified by the increasing error values, as listed in Table 6. high because of the relatively high RMS error values. Hence, we can confirm that the proposed technique exhibits

http://dx.doi.org/10.6109/jicce.2016.14.3.153 160 Proposed One-Minute Rain Rate Conversion Method for Microwave Applications in Korea

stable and relatively low RMS values of prediction and can cumulative distributions from various integration times to one be effectively used for the 1-min rain rate prediction for minute,” IEEE Antennas and Propagation Magazine, vol. 51, no. 3, Korea. pp. 70-84, 2009. [ 5 ] Characteristics of precipitation for propagation modelling, Recommendation ITU-R P.837-6, 2012. VI. CONCLUSIONS [ 6 ] D. Y. Choi, “Rain attenuation prediction model by using the 1-hour rain rate without 1-minute rain rate conversion,” International The scope of work in this study is limited to the CDF Journal of Computer Science and Network Security, vol. 6, no. 3A, analysis of the rainfall rate using the measured rainfall pp. 130-133, 2006. distribution as received from KMA for a 10-year period [ 7 ] M. W. Jung, I. T. Han, M. Y. Choi, J. H. Lee, and J. K. Pack, (2004–2013) over nine regions of Korea. The analysis of the “Empirical prediction models of 1-min rain rate distribution for 1-decade rainfall data has given an appropriate indication various integration time,” Journal of the Korean Institute of for the study of rainfall behavior over these regions. As Electromagnetic Engineering and Science, vol. 8, no. 2, pp. 84-89, observed, empirical formulations are simple yet powerful 2008. tools for the conversion of rainfall statistics among the [ 8 ] Y. H. Park, J. H. Lee, N. Jambaljav, and J. K. Pack, “Empirical available models. The performance of the proposed study on the rain drop-size model for rain attenuation calculations,” polynomial fits is considered to be the best for the in Proceedings of the URSI General Assembly, Maastricht, The conversion of the rain rate from various integration times to Netherlands, 2002. their 1-min equivalent because of the relatively low average [ 9 ] J. H. Lee, Y. S. Kim, J. H. Kim, and Y. S. Choi, “Empirical error evaluation, which confirms the overall best-performing conversion process of rain rate distribution for various integration regression fit. In particular, the ITU-R P.837-6 and global time,” in Proceedings of 2000 Asia-Pacific Microwave Conference, coefficient approaches are unable to provide a reliable Sydney, Australia, pp. 1593-1597, 2000. estimation against the experimental result of the 1-min rain [10] J. H. Lee, Y. S. Choi, J. K. Pack, and E. H. Ha, “Conversion of rain rate. Through the evaluation of different error matrices, it rate distribution for various integration time,” IEEE Transactions hasbeen shown that the proposed technique adequately trails on Microwave Theory and Techniques, vol. 42, no. 11, pp. 2099- the nature of the 1-min rainfall rate. Overall, in this paper, 2106, 1994. we emphasize a suitable technique that can best describe the [11] C. Ito and Y. Hosoya, “Proposal of a global conversion method for 1-min rainfall characteristics of Korea. different integration time rain rates by using M distribution and regional climatic parameters,” Electronics and Communications in Japan (Part I: Communications), vol. 89, no. 4, pp. 1-9, 2006. ACKNOWLEDGMENTS [12] P. A. Owolawi, “Rainfall rate probability density evaluation and mapping for the estimation of rain attenuation in South Africa and This research was supported by Basic Science Research surrounding islands,” Progress In Electromagnetics Research, vol. Program through the National Research Foundation of 112, pp. 155-181, 2011. Korea (NRF) funded by the Ministry of Education (NRF- [13] L. D. Emiliani, L. Luini, and C. Capsoni, “Extension of ITU-R 2014R1A1A2053645). 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received his Bachelors in Electronic and Communication Engineering from Tribhuvan University, Nepal, in 2010. He is currently pursuing his Masters in Information and Communication Engineering from Chosun University. He has worked as an engineer in companies such as Huawei and in broadcasting firms. His research interests include rain attenuation, microwave and satellite communication, antenna design, and wave propagation.

received his B.S., M.S., and Ph.D. degrees from the Department of Electronic Engineering of Chosun University, Gwangju, Korea, in 1999, 2001, and 2004, respectively. Since 2006, he has been a researcher and has been teaching as a full professor. His research interests include rain attenuation, antenna design, wave propagation, and microwave and satellite communication. He is a member of IEEE, IEICE, JCN, KEES, IEEK, KICS, and ASK.

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