"رسم منحنيات تكرار الشذة المطرية وتقذير معادلة الشذة لمذينة الناصرية العراق " مذرس مساعذ أحمذ عودة دخيل جامعة ري قار

"Drawing Curves of The Rainfall Intensity Duration Frequency (IDF) and Assessment equation Intensity Rainfall for Nasiriyah City, Iraq" Assistant Lecture Ahmed Awda Dakheel Abstract Thi Qar University The rainfall Intensity-Duration-Frequency (IDF) relationship is one of the most commonly used tools in water resources engineering, either for planning, designing and operating of water resource projects. The purpose of this research is to get curves frequency the intensity of rain duration for Nasiriyah city, Iraq, and finding empirical equations the curves. Where are collected data of the rain 36 years ago from 1980 to 2015. Used Indian Meteorological Department (IMD) empirical reduction formula and methods of distribution: Gumbel and Log Pearson Type III during short periods (10, 20, 30, 60,120,180, 360, 720 and1440) minute with a specified return period (2, 5, 10, 25, 50 and 100) years. The results obtained showed that intensity of rainfall decreases with increase in storm duration and rainfall of any given duration will have a larger intensity if its return period is large. The chi-square goodness of fit test was used to determine the best fit methods of distribution (Easy fit software 5.6) and conclude that the Log Pearson type III was the best method. "رسم منحنيات تكرار الشذة المطرية وتقذير معادلة الشذة لمذينة الناصرية العراق " مذرس مساعذ أحمذ عودة دخيل جامعة ري قار 63 الخالصة حعخبز انعالقت ب انشذة ان طز ت وحكزار اسخذايت انشذة ه احذي اكثز االدواث ان سخع هت ف ه ذست يصادر ان ا سىاء ف انخخط ظ وانخص ى او ف حشغ م يصادر ان ا. انغزض ي هذا انبحث هى ا جاد ي ح اث حكزار شذة االسخذايت ان طز ت ن ذ ت ان اصز ت انعزاق وا جاد يعادالث ان ح اث. ح ث ج عج انب ا اث ان طز ت 36 س ت يضج ي 1989 ان 5915. اسخخذيج ان عادنت انخجز بت نقسى االرصاد انجى ت انه ذ ت (IMD) وطزق انخىس ع: كايبم وب زس نىغارحى ان ىع III خالل يذد قص زة 19( )1449 759 369 189 159 69 39 59 دق قت وفخزاث رجىع 5(

199( 59 55 19 5 س ت. ان خائج اظهزث ا انشذة ان طز ت حخ اقص باسد اد يذة انعاصفت ان طز ت وكذنك ب ا هطىل االيطار عط كثافت يطز ت خالل فخزاث رجىع كب زة. كذنك حى ا جاد افضم طز قت حىس ع باسخخذاو طز قت انكا حزب ع ف بز ايج (5.6 (Easy fit software واسخ خج ا طز قت ب زس نىغارحى ان ىع III ه االفضم. Keywords: IDF curves, daily rainfall, goodness of fit test, return period, Nasiriyah city. 1. Introduction Statistics and evaluation of extreme rainfall data are important in water resources planning and management for design purposes in construction of sewerage and storm systems, determination of the required discharge capacity of channels, and capacity of pumping stations. So they are important in order to prevent flooding, thereby reducing the loss of life and property, insurance of water damage and evaluation of hazardous weather. Assessment of rainfall Intensity-Duration-Frequency (IDF) relationship is a primary basic input for the design of the storm water drainage system for cities (Chawathe, 1977). The IDF curves allow the engineer to design safe and economical flood control measures. Studies on the rainfall IDF relationship have received much attention in past few decades. Matin et al. (1984), developed the IDF curve for North- East cities Bangladesh and also observed that the rainfall data in this city follow Gumbel s distribution. Al-Dokhayel (1986), estimated the rainfall depth duration frequency relationships for Qasim city in Saudi Arabia at various return periods, using two methods distributions (Gumbel and the LPT III). Koutsoyiannis et al. (1998), cited that IDF relationship is a mathematical relationship between the rainfall intensity, the duration and the return period, the IDF-curves allow for the estimation of the return period of an observed rainfall event or conversely of the rainfall amount corresponding to a given return period for different aggregation times. Chowdhury et al. (2007), developed the short duration rainfall IDF curve for Sylhet with return period of 2, 5, 10, 20, 50 and 100 years. Marta bara et al. (2009), elaborated the evaluation of IDF curves of extreme rainfall by simple scaling theory to the IDF characteristics of short duration rainfall in Slovakia. Khaled et al. (2011), applied L-moments and generalized least squares regression methods 64

for estimation of design rainfall depths and development of IDF relationships. Al Hassoun (2011), developed an empirical formula to estimate the rainfall intensity in Riyadh city and find that there was not much difference in the results of rainfall analysis of IDF curves between Gumbel and LPT III methods. Ayad Hussain, (2014), derived IDF empirical formula that used at Karbala city and compared different statistical distributions and conclude that the Log Pearson type III was the best method of other methods. The study objective to collect rainfall data for Nasiriyah city to get IDF curves and derive empirical equation of IDF for various return period where used two different statistical distributions, investigate probability distribution function for the maximum daily rainfall data by Chi-square test using Easy fit software 5.6.These curves and equations are useful in the design of urban drainage works, e.g. storm sewers, culverts and other hydraulic structures. 2. Description of Study Area The study area is Nasiriyah, a city in southeastern Iraq on the Euphrates river, which is capital of Thi Qar. Its position is between latitude 39 39-35 90 N, longitude 45 90-47 00 E(Al ziady, 2017). Figure 1: Location map of Nasiriyah city, Iraq. 65

3. Collected Data To draw IDF curve and estimate the formula for intensity duration frequency relationship for Nasiriyah city, the available data are acquired from Republic of Iraq, Ministry of Transportation, Iraqi Meteorological Organization and Seismology, (Unpublished data( includes 24 hour rainfall data basis from 1980-2015 for Nasiriyah city were considered as presented in Table 1. Table (1) Maximum Daily Rainfall Recorded in Nasiriyah City During 1980-2015 (Iraqi Meteorological Organization and Seismology). NO year Maximum daily Rainfall during year in 'mm' NO year Maximum daily Rainfall during year in 'mm' 1 1980 29.3 19 1998 51.5 2 1981 20.6 20 1999 36.1 3 1982 26.2 21 2000 47.8 4 1983 18.0 22 2001 17.0 5 1984 30.9 23 2002 85.9 6 1985 17.2 24 2003 M* 7 1986 39.1 25 2004 21.0 8 1987 12.0 26 2005 27.0 9 1988 M* 27 2006 28.3 10 1989 11.6 28 2007 73.8 11 1990 14.8 29 2008 10.8 12 1991 48.3 30 2009 12.1 13 1992 21.9 31 2010 10.8 14 1993 10.7 32 2011 10.4 15 1994 22.8 33 2012 31.4 16 1995 27.3 34 2013 50.9 17 1996 44.9 35 2014 33.4 18 1997 22.0 36 2015 18.0 M*: Missing data. 4. Estimation of Short Duration Rainfall The rainfall data consists of the maximum daily rainfall values from 1980 to 2015. From maximum daily rainfall corresponding values of 0.166 hr, 0.33 hr, 0.5 hr,1 hr, 2 hr, 3 hr,6 hr,12 hr and 24 hr, rainfall values can be obtained 66

using Indian Meteorological Department(IMD) empirical reduction formula (Ramaseshan,1996) which is; P (t ) =P (24 ) (t 24) ^(1/3) (1) Where; P (t) is the required rainfall depth in mm at t-hr duration, P (24) is the daily rainfall in mm and t is the duration of rainfall for which the rainfall depth is required in hr. Table 2 explains derived shorter duration rainfalls from maximum daily rainfall during year. Table (2) The required precipitation P (t) depth for the duration t-hour in mm. Year 0.166 hr. 0.33 hr. 0.5 hr. 1 hr. 2hr. 3hr. 6hr. 12hr. 24hr. 1980 5.675 7.12 8.166 10.265 12.904 14.751 18.543 23.309 29.3 1981 3.990 5.006 5.741 7.217 9.072 10.371 13.037 16.388 20.6 1982 5.075 6.367 7.302 9.179 11.539 13.191 16.581 20.843 26.2 1983 3.486 4.374 5.017 6.306 7.927 9.062 11.391 14.319 18 1984 5.985 7.509 8.612 10.826 13.609 15.557 19.555 24.582 30.9 1985 3.331 4.179 4.794 6.026 7.575 8.659 10.885 13.683 17.2 1986 7.574 9.502 10.898 13.699 17.22 19.685 24.745 31.105 39.1 1987 2.324 2.916 3.344 4.204 5.285 6.041 7.594 9.546 12 1988 M* M M M M M M M M 1989 2.247 2.819 3.233 4.064 5.108 5.84 7.341 9.228 11.6 1990 2.866 3.596 4.125 5.185 6.518 7.451 9.366 11.773 14.8 1991 9.356 11.737 13.462 16.923 21.272 24.317 30.568 38.424 48.3 1992 4.242 5.322 6.104 7.673 9.645 11.026 13.86 17.422 21.9 1993 2.072 2.6 2.982 3.748 4.712 5.387 6.771 8.512 10.7 1994 4.416 5.54 6.355 7.988 10.041 11.479 14.429 18.138 22.8 1995 5.288 6.634 7.609 9.565 12.023 13.744 17.277 21.718 27.3 1996 8.697 10.911 12.515 15.731 19.775 22.606 28.416 35.719 44.9 1997 4.261 5.346 6.132 7.708 9.689 11.076 13.923 17.501 22 1998 9.976 12.515 14.354 18.044 22.681 25.929 32.593 40.97 51.5 1999 6.993 8.772 10.062 12.648 15.899 18.175 22.846 28.718 36.1 2000 9.259 11.616 13.323 16.747 21.052 24.066 30.251 38.026 47.8 2001 3.293 4.131 4.738 5.956 7.487 8.559 10.758 13.524 17 2002 16.64 20.875 23.943 30.097 37.832 43.248 54.364 68.336 85.9 2003 M* M M M M M M M M 2004 4.068 5.103 5.853 7.357 9.248 10.573 13.29 16.706 21 2005 5.230 6.561 7.525 9.46 11.891 13.593 17.087 21.479 27 2006 5.482 6.877 7.888 9.915 12.463 14.248 17.91 22.513 28.3 2007 14.296 17.934 20.57 25.857 32.503 37.156 46.706 58.71 73.8 67

2008 2.092 2.624 3.01 3.784 4.756 5.437 6.835 8.591 10.8 2009 2.343 2.94 3.372 4.239 5.329 6.092 7.657 9.625 12.1 2010 2.092 2.624 3.01 3.784 4.756 5.437 6.835 8.591 10.8 2011 2.014 2.527 2.898 3.643 4.58 5.236 6.581 8.273 10.4 2012 6.082 7.63 8.752 11.001 13.829 15.809 19.872 24.979 31.4 2013 9.86 12.369 14.187 17.833 22.417 25.627 32.213 40.492 50.9 2014 6.47 8.116 9.309 11.702 14.71 16.816 21.138 26.57 33.4 2015 3.486 4.374 5.017 6.306 7.927 9.062 11.391 14.319 18 M*: Missing data. 5. Frequency Distribution Methods The first step in the construction of IDF curves is fitting some theoretical frequency distribution to the extreme rainfall amounts for a number of fixed durations. A logical step to proceed then is to describe the change of the parameters of the distribution with duration by a functional relation. From the fitted relationships the rainfall intensity for any duration and return period can be derived (Nguyen et al., 1998). In this study, annual maximum values for all the available durations have been statistically analyzed using two different distributions, namely: Gumbel distribution and Log Pearson III distribution. 5.1 Gumbel Theory of Distribution Gumbel distribution methodology was selected to perform the flood probability analysis. The Gumbel distribution is the most widely used distribution for IDF analysis owing to its suitability for modeling maximum. It is relatively simple and uses only extreme events (maximum values or peak rainfalls). The Gumbel distribution calculates the 2, 5, 10, 25, 50 and 100 years return intervals for each duration period and requires several calculations. Frequency precipitation P T (in mm) for each duration with a specified return period Tr (in year) is given by (Borga, 2005): P T = P ave + K T S (2) Where K T is Gumbel frequency factor given by:, * ( )+- (3) 68

And P ave is the average of the maximum precipitation corresponding to a specific duration. In utilizing Gumbel s distribution the arithmetic average in EQ. (2) is used: (4) Where; n is the number of events or years of record and the standard deviation S is calculated by: 2 (P Pave ) S (5) n 1 Where; P Maximum precipitation depth corresponding to a specific duration. Then the rainfall intensity I T (mm/h) for return period T r is obtained from: Where; T d is duration in hours. (6) Table (3) The values of standard deviation (S) and the average of precipitation (Pave). Duration S P ave 0.166 hr. 3.553 5.445 0.33 hr. 4.457 6.83 0.5 hr. 5.112 7.834 1 hr. 6.426 9.848 2 hr. 8.078 12.379 3 hr. 9.234 14.152 6 hr. 11.608 17.789 12 hr. 14.591 22.361 24 hr. 18.342 28.108 69

Table (4) The values of Gumbel frequency factor in order to a specified return period. Tr years K T 2-0.164 5 0.719 10 1.305 25 2.044 50 2.592 100 3.137 Table (5) Computed precipitation (P T ) in (mm) and intensity (I T ) in (mm/h) (Gumbel distribution). Tr t min 2 5 10 25 50 100 PT IT PT IT PT IT PT IT PT IT PT IT 10 4.862 30.389 7.999 49.998 10.082 63.012 12.707 79.423 14.654 91.593 16.591 103.697 20 6.099 18.484 10.035 30.411 12.647 38.327 15.942 48.309 18.384 55.711 20.814 63.073 30 6.996 13.992 11.51 23.021 14.506 29.013 18.285 36.57 21.086 42.173 23.873 47.746 60 8.794 8.794 14.469 14.469 18.235 18.235 22.984 22.984 26.506 26.506 30.008 30.008 120 11.054 5.527 18.188 9.094 22.921 11.461 28.891 14.445 33.318 16.659 37.721 18.86 180 12.637 4.212 20.791 6.93 26.203 8.734 33.028 11.009 38.088 12.696 43.121 14.374 360 15.885 2.647 26.135 4.355 32.938 5.489 41.516 6.919 47.878 7.979 54.204 9.034 720 19.968 1.664 32.852 2.737 41.403 3.45 52.187 4.348 60.183 5.015 68.136 5.678 1440 25.1 1.045 41.296 1.72 52.045 2.168 65.6 2.733 75.651 3.152 85.648 3.568 70

Figure 2: IDF curves by Gumbel distribution at Nasiriyah City. 5.2 Log Pearson Type III Distribution (LPT III). The LPT III distribution model is used to calculate the rainfall intensity at different rainfall durations and return periods to form the historical IDF curves for each station. LPT III distribution involves logarithms of the measured values. The mean and the standard deviation are determined using the logarithmically transformed data. In the same manner as with Gumbel method, the frequency precipitation is obtained using LPT III method. The simplified expression for this latter distribution is given as follows: P (t) *=log P (t) (7) P T * = P ave * + K T S* (8) (9) 2 (P * Pave*) S* (10) n 1 71

Where; P T *, P ave * and S* are as defined previously in Section 5.1 but based on the logarithmically transformed P (t) values; i.e. P (t) * of Eq. (7). K T is the Pearson frequency factor which depends on return period (Tr) and skewness coefficient (Cs). The skewness coefficient Cs is required to compute the frequency factor for this distribution. The skewness coefficient is computed by Eq.(11) (Chow, 1988): (11) K T values can be obtained from tables in many hydrology references; for example (reference Chow, 1988). By knowing the skewness coefficient and the recurrence interval, the frequency factor, K T for the LPT III distribution can be extracted. The antilog of the solution in Eq. (8) will provide the estimated extreme value for the given return period. Table 6 shows the computed frequency precipitation P T * values and intensities (I T ) for nine different durations and six return periods using LPT III methodology. Figure 3: IDF curves by Log Pearson III distribution at Nasiriyah City. 72

Table (6) Computed precipitation (PT) in (mm) and intensity (IT) in (mm/h) (Log Pearson III distribution) Tr t min 2 5 10 25 50 100 PT IT PT IT PT IT PT IT PT IT PT IT 10 4.673 29.211 7.641 47.761 10.010 62.562 13.468 84.180 16.392 102.45 6 19.634 6 122.71 6 20 5.835 17.682 9.538 28.905 12.533 37.979 16.831 51.004 20.510 62.152 24.596 74.534 30 6.692 13.385 10.940 21.881 14.375 28.750 19.305 38.610 23.524 47.049 28.211 56.423 60 8.413 8.413 13.752 13.752 18.069 18.069 24.267 24.267 29.570 29.570 35.461 35.461 120 10.575 5.287 17.287 8.643 22.714 11.357 30.504 15.252 37.171 18.585 44.576 22.288 180 12.089 4.029 19.762 6.587 25.966 8.655 34.871 11.623 42.492 14.164 50.957 16.985 360 15.196 2.532 24.842 4.14 32.640 5.440 43.834 7.305 53.414 8.902 64.055 10.675 720 19.102 1.591 31.227 2.602 41.029 3.419 55.100 4.591 67.142 5.595 80.518 6.709 1440 24.013 1 39.253 1.635 51.574 2.148 69.261 2.885 84.398 3.516 101.21 1 4.217 6. Gneralized IDF Formula The IDF formulas are the empirical equations representing a relationship among maximum rainfall intensity (as dependent variable) and other parameters of interest such as rainfall duration and frequency (as independent variables). There are several commonly used functions found in the literature of hydrology applications (Chow, 1988). In this research Bernard equation was used to estimate equation rainfall intensity (Rathnam, 2000) which is: (12) Where I T intensity in mm/hr, Tr return period in years, d duration in hours and c, m, e are regional coefficients. 73

6.1 Find constants a and e In order to find the constants (a) and (e) of EQ. (12), A log-log graph was plotted between the duration and rainfall intensity for each return period to find the constant (e) by nonlinear regression analysis. From graphs the average value of exponents for all recurrence intervals equations was used to establish (e) coefficient. To obtain the values of (c) and (m) derived values of (a) are plotted on log-log scale against corresponding recurrence intervals (Gringorten, 1963) the resulting shown in Table (7). Table (7). The parameters values used in deriving formulas. Parameter Gumbel Log Pearson III c 8.283 7.565 m 0.301 0.350 e 0.674 0.674 Equation 7. Goodness of Fit Test The aim of the test is to decide how good is a fit between the observed frequency of occurrence in a sample and the expected frequencies obtained from the hypothesised distributions. A goodness of fit test between observed and expected frequencies is based on the chi-square quantity, which is expressed as; (13) Where; X 2 is a random variable whose sampling distribution is approximated very closely by the chi-square distribution. The symbols O i and E i represent the observed and expected frequencies respectively, for the i-th class interval in the histogram. The symbol k represents the number of class intervals. If the observed frequencies are close to the corresponding expected frequencies, the X 2 value will be small, indicating a good fit; otherwise, it is a poor fit. A good fit leads to the acceptance of null hypothesis, whereas a poor fit leads to its rejection. The critical region will, therefore, fall in the right tail of the chisquare distribution. For a level of significance equal to α, the critical value is 74

found from readily available chi-square tables and X 2 > constitutes the critical region (Al-Shaikh, 1985). The software (Easy Fit 5.6) was used to conduct the tests of goodness of fit by using chi-square quantity (see reference 18). Figure (4) shows the values of chi-square test for evaluating the goodness of fit according to different probability distributions for 0.16 hr, 0.33 hr, 0.5 hr, 1hr, 2hr, 3hr, 6hr, 12hr and 24hr durations. Figure 4: Goodness of fitting results by chi-square Test. 8. Results and Discussion The purpose of this study was to get IDF curves and derive an empirical formula to estimate the rainfall intensity at Nasiriyah city in Iraq. Data collected maximum daily rainfall and estimation of short duration rainfall for 36 years and each duration (10, 20, 30, 60, 120, 180, 360, 720, 1440) min. There is no much difference in rainfall amount in the recorded years; this might be because that Nasiriyah city has flat topography where variations of precipitation is not large and maximum daily rainfall amount recur every ten year. Rainfall estimates in mm and their intensities in mm/hr for various return periods and different durations were analysed using the two techniques: (Gumbel and LPT III). The results are listed in Tables 5 and 6. According to the IDF curves, rainfall estimates are increasing with increase in the return period and the rainfall intensities decrease with rainfall duration in all return periods. Rainfall intensities rise in parallel with the rainfall return periods. The results obtained from the two methods have good consistency. 75

Figure 2 and 3 show results of the IDF curves obtained by Gumbel and LPT III methods for Nasiriyah city. It was shown that there were small differences between the results obtained from the two methods, where Gumbel method gives slightly higher results than the results obtained by Log Pearson III method. The resulted two equations for Gumbel, LPT III, the parameters and the average values obtained by analyzing the IDF data by applying the procedures described on section (6) shows in Table (7). Also, goodness of fit tests were used to choose the best statistical distribution among those techniques. It was found that the chi-square values obtained by Easy fit software 5.6 for the two methods all the data fit the distributions at the level of significance of α =0.05, which yields X critical < 7.814. The study showed that the LPT III given best estimation with smallest X 2 for all durations. The final plotted curve on normal scale for Log Pearson III distribution as shown on Figure (5). Figure 5: Intensity - Frequency - Duration Curves of Nasiriyah City (on normal scale). 76

9. Conclusions 1- This research presented equation intensity rain for Nasiriyah city, which is possible to be useful in finding the optimal design of the gutter and find the inlet locations on the roads. 2- This equation will make a good guide to estimate the rainfall intensity for any specific return period at different durations. 3- Maximum intensity occur at return period 100 years with duration of 10 minute. 4- Minimum intensity occur at return period 2 years with duration of 24 hours. 5- The goodness of fit test by chi-square showed the Log Pearson type III was the best distribution compared with Gumble distribution. 10. References 1- Chawathe, S.D., Shinde, U.R., Fadanvis, S.S. and Goel, V.V. Rainfall Analysis for the Design of Storm Sewers in Bombay, The Institution of Engineers, India. Journal EN, 58, 14-20.1977. 2- Matin M. A. and Ahmed S. M. U. Rainfall Intensity Duration Frequency Relationship for the N-E Region of Bangladesh. Journal of Water Resource Research. 5(1).1984. 3- Al-Dokhayel, A.A. Regional rainfall frequency analysis for Qasim, B.S. Project, Civil Engineering Department, King Saud University, Saudi Arabia. April,1986. 4- Koutsoyiannis, D., Kozonis, D. and Manetas, A. A mathematical framework for studying rainfall intensity duration frequency relationships Journal Hydrological 206, 118 135.1998. 5- Chowdhury R., Alam J. B., Das P. and Alam M. A. Short Duration Rainfall Estimation of Sylhet: IMD and USWB Method. Journal of Indian Water Works Association. pp. 285-292.2007. 6- Marta bara, silviakohnova, Ladislvagaal, Jan szolgay and Kamilahlavcova, estimation of IDF curves of extreme rainfall by simple scaling in Slovakia. Contribution to Geophysics and Geodesy. Volume 39/3, pp.187-206. 2009. 77

7- Al Hassoun, S.A. Developing an empirical formulae to estimate rainfall intensity in Riyadh region. Journal of King Saud University Engineering Sciences, Saudi Arabia. 2011. 8- Khaled H, Ataur R, Janice G. and George K. Design rainfall estimation for short storm durations using L-Moments and generalized least squares regression-application to Australian Data. International Journal of Water Resources and Arid Envi-ronments. 1(3):210-218. 2011 9- Ayad Kadhum Hussein. Deriving Rainfall Intensity-Duration- Frequency Relationships for Kerbala City. ALMuthana Journal for Engineering sciences, 3(1): 25-37. 2014. 10- Al ziady, H., Land of Civilization Dhi Qar province, Geography, University of Thi Qar, College of Arts, Iraq. 2017. 11- Ramaseshan, S., Urban Hydrology in Different Climatic Conditions, Lecture notes of the International Course on Urban Drainage in Developing Countries", Regional Engineering College, Warangal, India.1996. 12- Nguyen, V.T.V., Nguyen, T.D. and Wang, H. Regional estimation of short duration rainfall extremes. Water Sci. Technol. 37 (11), 15 19. 1998. 13- Borga, M., Vezzani, C. and Fontana, G.D. A Regional Rainfall Depth Duration Frequency Equations for an Alpine Region, Department of Land and AgroForest Environments, University of Padova, Legnaro 35020, Natural Hazards, vol. 36, pp. 221 235, Italy. 2005. 14- Chow, V.T., Maidment, D.R. and Mays, L.W. Applied Hydrology, McGraw-Hill Company, 1988. 15- Rathnam, E.V, Jayakumar, K.V and Cunnane,C., Runoff Computation in a Data Scarce Environment for Urban Storm water Management a Case Study, Ireland, 2000. 16- Gringorten I.I.. A Plotting Rule for Extreme Probability Paper. J. Geophys. Res. 68(3): 813-814. 1963. 17- Al-Shaikh, A.A. Rainfall frequency studies for Saudi Arabia. M.S.Thesis, Civil Engineering Department, King Saud University, Saudi Arabia. 1985. 18- http://www.mathwave.com/downloads.html. 78