Rain Integration Time and Percentage Probability of Rain in Indian Subcontinent

for Satellite Communications Aravind Kilaru I, Nicholas Avlonitis2, Sarat K Kotamraju3 and Ifiok Otung4

I Researcher, Department of ECE, K L University, Guntur, INDIA aravind@kilaru.in*

2 Research Engineer, Cardiff, UK nick.avlonitis@gmail.com

3 Professor, Department of ECE, K L University, Guntur, INDIA kksarat@kluniversity.in

4Professor of Satellite Communications, University of South Wales, UK ifiok.otung@southwales.ac.uk

Abstract-The study of rain statistics, including average and extreme conditions, plays a significant role in predicting link availability and in calculating required tradeoff margins for the designing of a ground to space RF link. In this paper the cumulative distribution of average rainfall measured for 15 years is used in order to obtain probabilities of exceedance of rainfall rates using cumulative time statistics and empirical models for the Indian subcontinent. The results are compared with the rain rates extracted from the ITU-R model for the locations under study. The calculated rainfall rates suggest significant variances in the climatic features such as probability of heavy rain and number of rainy days in a year. The analysis shows that the ITU-R model underestimates the rainfall intensity rates by 32.6%, 26.2% and 40.7%, 19% at higher and lower percentage of time when compared with measured rain rate data from Indian Metrological department. It is shown that the discrepancy between the empirical model and ITU-R model at higher percentage of time results in a 15 to 5 dB difference in predicted signal attenuation depending on the region, percentage of time and frequency. Adaptive Power Control is proposed as a means to improve the link availability during period of higher intensity rainfall.

Keywords- rain integration time; rain rate; attenuation; probability of rain; satellite link attenuation; Adaptive Power Control

I. Introduction

The continuous investment in satellite communications has ensured remotest areas are connected via satellite. However, the high link availability and feasibility of dish size can be improved further in order to maximise link availability in any climatically conditions up to the last mile. Adaptive Power Control (APC) in satellite communication concept is been around for many years. APC can be employed in order to optimise the power utilisation [13]. With the existing infrastructure it is possible to implement APC and achieve maximum link availability with smaller dish

size without reducing the capacity of the link. More specifically, additional margins introduced by rain attenuation can be compensated by APC.

For designing a link to establishing satellite link, it's important to understand the climatical effects on the signal power which is directly related to intensity of rainfall for the link availability. ITU-R recommends the use of 1 minute rainfall while designing the link. ITU-R also recommends the utilization of local measurements where available in order to optimize the link design.

In this study five locations Madurai (9.50�78.100E), Chennai (13.04�80.17°E), Vijayawada (16.51°N80.62°E), Ahmedabad (23.03�72.58°E), and Guwahati (26.18�91.73°E) in the Indian region are chosen on the bases of their climatic features. These locations can be categorized on the bases of normal, average, heavy rainfall rates in according to difference in thunderstorm ratio, as defined in [12], so that a variety of rain intensity levels are considered in this study [11].

In Section II of this paper the analysis of the dataset is presented. In India, the monsoon period is between the months June to September whereas the rest of the year most of the heavy rainfall is due to cyclones in the ocean and sea. In tropical climates like India we can observe great variability of rainfall from year to year [11], which effects the signal attenuation and therefore the link availability.

In the following sections Rain Integration Time and Percentage Probability of Rain in an average year along with the attenuation induced by rain is analyzed in order to present the case for the use of APc. The obtained 1 min rainfall data is compared with Rice and Holmberg Model (RHB Model) [12], Moupfouma and Martin Model (MM Model) [9], & International Telecommunications union (ITU-R) rain rates [3] with the percentage probability of heaviest rain in a year. The analysis continuous by converting the rainfall rates in predicted signal attenuation levels

(dB) [2]. The conclusion helps reinforce the case for the use of APC by revisiting the important points of the results.

II. Dataset

To ensure better accuracy of the comparison a period longer than a sunspot cycle is considered. A

*Corresponding Author, aravind@kilaru.in

rainfall dataset of a 15-year-period obtained from the Indian Meteorological Department (lMD) is used for the analysis. The IMD data includes the number of rainy days in a year and heaviest and lowest rainfall measured in 24hrs [11].

Madurai (Lat. 9.50"N Long. 78.100E) the collected annual rainfall for the 15 years is in between 490.3 to 1364.4mm/year with an average of 812.68 mm/year for 15 years. From the data the possibility of rain in an average year is 40.4 days with the heaviest rain possible is 3.4% of the 40.4 days. The heaviest rainfall recorded for 24 hrs is 178 mm in 15 years with an average of 81.13mm possible in 40.4 days.

Chennai (Lat. 13.04°N Long. 80.17°E) the collected annual rainfall for the 15 years is in between 1357.86 to 2573.4 mm/year with an average of 918.4 mm/year for 15 years. From the data the possibility of rain in an average year is 52.4 days with the heaviest rain possible is 3.6% of the 52.4 days. The heaviest recorded 24 hrs rainfall is 282.8 mm in 15 years with an average of 136.43mm possible in 52.4 days.

Vijayawada (Lat. 16.51°N Long. 80.62°E) the collected annual rainfall for the 15 years is in between 736.1 to 1354.87 mm/year with an average of 736.1 mm/year for 15 years. From the data the possibility of rain in an average year is 49.73 days with the heaviest rain possible is 3.3% of the 49.73 days. The heaviest recorded 24 hrs rainfall is 154 mm in 15 years with an average of 96.14 mm possible in 49.73 days.

Ahmedabad (Lat. 23.03°N Long. 72.58°E) the collected annual rainfall for the 15 years is in between 382 to 1293.5 nun/year with an average of 786.66mm/year. From the data the possibility of rain in an average year is 33.9 days with the heaviest rain possible of 2.9% of the 33.9 days. The heaviest recorded 24 hrs rainfall is 325.9 mm in 15 years with an average of 135.63mm possible in 33.9 days.

Guwahati (Lat. 26.18°N Long. 91. 73°E) the collected annual rainfall for the 15 years is in between 1213.1 to 2075 mm/year with an average of 1709.433 mm/year. From the data the possibility of rain in an average year is 94.6 days with the heaviest rain possible is 11.78% of the 94.6 days. The heaviest recorded in 24 hrs rainfall is 141mm in 15 years with an average of 10 1.44mm possible in 94.6 days.

Table II shows that the heaviest possible percentage of rain (Pw) in a year is <4% for four locations and 11.7% for Guwahati. Therefore excess resources are utilized during 1-Pw% of time in order to maintain the link during extreme rain conditions. As Guwahati is located in mountain range its percentage probability of heaviest rain (%P w) is higher than other locations. On the other hand, from Table III the intensity of rain rate is shown to be similar to other locations.

Table III shows that CR Model, RHB Model have smallest average error rate at lower percentage of time (mm/hr), whereas RHB Model and MM Model have smaller error rate at higher percentage of time (mm/min). Table IV suggest, ITU-R model underestimates the rain intensity at higher (mm/min) and lower (mm/hr) percentage of time when compared with CR, RHB and MM Models.

Analysis of the data produces the results shown in Tables I and II. In the last column of Table II the percentage probability of heaviest rain during rainy days (%P w) is presented as an indication of extreme conditions [3].

TABLE 1. RAINFALL DATA FROM INDIAN METEOROLOGICAL DEPARTMENT (lMD)

Location Average 24 Urs recorded rainfall in 15 annual years (mm)

Lat& Lon Rainfall for 15 years Heaviest Lowest Average (mm/year)

9.50oN78.IOoE 812.68 178 27 81.13

13.04°N80.l7°E 1357.86 282.8 31.9 136.43

16.51°N80.62°E 1058.3 154 50 96.14

23.03°N72.58°E 786.66 325.9 49 135.63

26. I 8°N91.73°E 1709.433 141 68.2 101.44

T ABLE II. PERCENTAGE PROBABILITY OF HEAVIEST POSSIBLE RAIN DURING RAINY DAYS IN AN

A VERAGE YEAR.

Location Number of rainy days in a Percentage year for 15 years (days) probability

of heaviest Lat& Lon Highest Lowest Average rain during

rainy days (%P,,)

9.50oN78.IOoE 55 12 40.4 3.4

I 3.04°N80.I7°E 71 II 52.4 3.6

16.51°N80.62°E 59 34 49.73 3.3

23.03°N72.58°E 39 17 33.9 2.9

26. I 8°N91.73°E 108 82 94.6 11.7

TABLE Ill. COMPARISON OF RAIN RATES

Lat eH RHB ! lTU-R ! RUB MM I I

& Model Model i i Model Model

Lon mmlhr mmlmin 9.50oN 90.09 70 85.13 194.28 224 206 78.IOoE 13.04°N 104.94 89 78.23 186.98 241 240 80.17°E 16.51oN 97.44 79 60.43 167.66 233 223 80.62°E 23.03°N 89.22 70 56.61 163.54 223 204 72.58°E 26.I8°N 112.38 112 77.36 184.71 266 257 91.73°E

Next, rainfall is converted to rainfall rates using 4 different models as shown in Table III. The rainfall rates are in good agreement with the rainfall rates reported elsewhere (e.g. Table 2 of [10]). It is evident from the results that the ITU-R model underestimates the rainfall intensity rate in most cases by a big margin.

TABLE IV.

ITU-R

mmlmin

194.28 18.98 167.66 163.54 184.71

Comparison of error between different models with ITU-R

RHB MM CH RHB ITU-R Model Model Model Model

% difference compared to ITU-R model mmlhr

15.3% 6.0% 5.8% -17.7% 85.13 28.8% 28.4% 34.1% 13.7% 78.23 38.9% 33.0% 61.2% 30.7% 60.43 36.3% 24.7% 57.6% 23.6% 56.61 44.0% 39.1% 45.2% 44.7% 77.36

The Comparison of % of error in intensity of rainfall between different models with ITU-R is presented in Table IV. As mentioned in [8], precipitation measuring systems have long integration time and tend to fail to record short term peaks during higher intensity rainfall [8].

III. Methodology

The monthly cumulative rainfall for 15 years from Indian Metrological department (lMD) was categorized into Number of observed days, Number of rainy days recorded and 24 hrs highest rainfalls measured in a year [11]. Monthly cumulative rainfall data from IMD is converted into rain rate using Rice

Holmberg model (RHB Model) [12], Moupfouma & Martin model (MM Model) [9], Chebil and Rahman Model (CH Model) [1] and compared with ITU-R P.837-6 [3]. The data is presented Table III. The predicted attenuation is obtained using ITU-R P.618-10 [2] and is presented in Fig. 1 to 5. [4] [5] [6] [7]

IV. Results

Each of the graphs in Figs. 1 to 5 corresponds to the results obtained for each of the regions considered. The graphs show the rain attenuation levels against percentage of time the value is exceeded for different frequencies (11, 20, 30 GHz). The 3 different curves for each frequency correspond to the rainfall rates (nun/min) of the 3 different models considered (lTU-R, RHB , MM) as presented in Table III.

According to Figure 1, the rain attenuation levels predicted by the ITU-R model (194.2 nun/min), the RHB model (224 nun/min) and the MM model (206 nun/min) differ by 1 dB at 0.001% of time for the llGHz frequency. The difference drops to 0.5 dB when the percentage of time considered is 0.01%. The equivalent values for 20 and 30 GHz are 5.5 dB and lO.6 dB for 0.001% of time, respectively. The difference is 4.7 and 9 dB for 20 GHz and 30 GHz, respectively, for the 0.01 % of time.

Considering only the 30 GHz frequency, the different models differ by 10 dB, 20 dB, 25 dB, 25 dB, 30 dB for Madurai, Chennai, Vijayawada, Ahmedabad, and Guwahati, respectively, for a time exceedance of 0.001% of time. The corresponding values are 9 dB, 17 dB, 21 dB, 20 dB, 24 dB for 0.01% of time. Evidently, these values correspond to the gains that can be achieved by employing APC.

% of TIME Vs ATTENUATION Vs FREQUENCY Vs RAIN RATE (mm/min) 160

140

120

ill 100 � c .'2 8 10 :::J C OJ

� 60

40

20

Percentage of time

Fig I. Percentage of Time Vs Rain Attenuation Vs Frequency Vs Rain rate for the location Madurai (9.50oN 78.100E).

CD TI

� 100 o

� :::J C Q)

�

40

% of TlME Vs ATTENUATION Vs FREQUENCY Vs RAIN RATE (mm/min)

20[:::::: �::::::::=:'"

Percentage of time

Fig 2. Percentage of Time Vs Rain Attenuation Vs Frequency Vs Rain rate for the location Chennai (13.04°N 80.1 TE).

CD TI

� 100 o

� :::J C Q)

� 60

40

20

% of TIME Vs ATTENUATION Vs FREQUENCY Vs RAIN RATE (mm/min)

Percentage of time

Fig 3. Percentage of Time Vs Rain Attenuation Vs Frequency Vs Rain rate for the location Vijayawada (16.51°N 80.62°E).

% of TIME Vs ATTENUATION Vs FREQUENCY Vs RAIN RATE (mm/min)

140

120 m u

� 100 .Q iii ::::J 80 c Q)

� 60

40

20

Percentage of time

Fig 4. Percentage of Time Vs Rain Attenuation Vs Frequency Vs Rain rate for the location Ahmedabad (23.03°N 72.58°E).

% of TIME Vs ATTENUATION Vs FREQUENCY Vs RAIN RATE (mm/min)

Percentage of time

Fig 5. Percentage of Time Vs Rain Attenuation Vs Frequency Vs Rain rate for the location Guwahati (26.18°N 91. 73°E).

V. Conclusion

In conclusion, the difference in rain attenuation levels predicted by the standard ITU-R model and empirical models based on actual measurements has been presented. The results show that due to the climatic features of the considered regions in the Indian sub­continent rainfall rates are underestimated by the ITU-R model during heavy rainfall. For the 11, 20 to 30 GHz region, attenuation increases with percentage of time approximately in the range of 1, 5 to IOdB to achieve high link availability during periods of heavy rain. The location Guwahati has higher %P w but attenuation increases similar to other locations. The results show that rain attenuation variability plays a major role in designing the satellite link which detennines the dish size. Consequently, by varying the transmitted power during %P w it is possible to achieve high link availability by implementing APC while maintaining a small antenna aperture.

ACKNOWLEDGMENT

The authors are also highly thankful to the Sahena Begum at University of South Wales, UK and the management of K L University for supporting and encouraging this work. The authors especially thank the support given from Department of Science and Technology (DST), Government of India through the funded project with F. No: SRlS4/AS-82/2011 and SRiFTP/ETA-079/2009. They also thank their Parents, Professors and friends who constantly extended their support during the tenure of this work.

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