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

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1 "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 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 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( ) دق قت وفخزاث رجىع 5(

2 199( 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

3 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 N, longitude E(Al ziady, 2017). Figure 1: Location map of Nasiriyah city, Iraq. 65

4 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 for Nasiriyah city were considered as presented in Table 1. Table (1) Maximum Daily Rainfall Recorded in Nasiriyah City During (Iraqi Meteorological Organization and Seismology). NO year Maximum daily Rainfall during year in 'mm' NO year Maximum daily Rainfall during year in 'mm' M* M* M*: Missing data. 4. Estimation of Short Duration Rainfall The rainfall data consists of the maximum daily rainfall values from 1980 to From maximum daily rainfall corresponding values of 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

5 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 hr hr. 0.5 hr. 1 hr. 2hr. 3hr. 6hr. 12hr. 24hr M* M M M M M M M M M* M M M M M M M M

6 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

7 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 hr hr hr hr hr hr hr hr hr

8 Table (4) The values of Gumbel frequency factor in order to a specified return period. Tr years K T Table (5) Computed precipitation (P T ) in (mm) and intensity (I T ) in (mm/h) (Gumbel distribution). Tr t min PT IT PT IT PT IT PT IT PT IT PT IT

9 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

10 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

11 Table (6) Computed precipitation (PT) in (mm) and intensity (IT) in (mm/h) (Log Pearson III distribution) Tr t min PT IT PT IT PT IT PT IT PT IT PT IT 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

12 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 m e 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

13 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

14 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 < 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

15 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, 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) Al-Dokhayel, A.A. Regional rainfall frequency analysis for Qasim, B.S. Project, Civil Engineering Department, King Saud University, Saudi Arabia. April, Koutsoyiannis, D., Kozonis, D. and Manetas, A. A mathematical framework for studying rainfall intensity duration frequency relationships Journal Hydrological 206, 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 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

16 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 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): Ayad Kadhum Hussein. Deriving Rainfall Intensity-Duration- Frequency Relationships for Kerbala City. ALMuthana Journal for Engineering sciences, 3(1): Al ziady, H., Land of Civilization Dhi Qar province, Geography, University of Thi Qar, College of Arts, Iraq 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 Nguyen, V.T.V., Nguyen, T.D. and Wang, H. Regional estimation of short duration rainfall extremes. Water Sci. Technol. 37 (11), 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 , Italy Chow, V.T., Maidment, D.R. and Mays, L.W. Applied Hydrology, McGraw-Hill Company, 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, Gringorten I.I.. A Plotting Rule for Extreme Probability Paper. J. Geophys. Res. 68(3): Al-Shaikh, A.A. Rainfall frequency studies for Saudi Arabia. M.S.Thesis, Civil Engineering Department, King Saud University, Saudi Arabia