Generation of Rainfall Intensity-Duration-Frequency Relationship for North-Western Region in Bangladesh

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1 IOSR Joural of Evirometal Sciece, Toxicology ad Food Techology (IOSR-JESTFT) e-issn: ,p- ISSN: Volume 9, Issue 9 Ver. I (Sep. 2015), PP Geeratio of Raifall Itesity-Duratio-Frequecy Relatioship for North-Wester Regio i Bagladesh Mushi Md. Rasel 1, Md. Mazharul Islam 2 1 (Lecturer, Departmet of Civil Egieerig, Ahsaullah Uiversity of Sciece & Techology (AUST), Bagladesh) 2 (GRA, Departmet of Civil Egieerig, Ahsaullah Uiversity of Sciece & Techology (AUST), Bagladesh) Abstract: The objective of this research is to geerate Raifall IDF relatioship for North-Wester regio of Bagladesh. Two commo frequecy aalysis techiques Gumbel ad Log Pearso Type III (LPTIII) distributio were used to develop IDF relatioship from raifall data of this regio. Yearly maximum raifall data for last 41 years ( ) from Bagladesh Meteorological Departmet (BMD) was used i this study. Idia Meteorological Departmet (IMD) empirical reductio formula was used to estimate short duratio raifall itesity from yearly maximum raifall data. Results obtaied usig Gumbel method are slightly higher tha LPT III distributio method. Chi-square goodess of fit test was used to determie the best fit probability distributio. The parameters of the IDF equatios ad coefficiet of correlatio for differet retur periods (2, 5, 10, 25, 50 ad 100 years) were calculated by usig oliear multiple regressio method. The results obtaied preseted that i all the cases the correlatio coefficiet is very high represetig goodess of fit of the formulae to estimate IDF curves i the regio of iterest. It was foud that itesity of raifall decreases with icrease i raifall duratio. Further, a raifall of ay give duratio will have a larger itesity if its retur period is large. Keyword:Raifall Itesity, Raifall Duratio, Raifall Frequecy, Gumbel s Extreme Value Distributio Method, Log Pearso Type III I. Itroductio Raifall itesity-duratio-frequecy (IDF) curves are graphical exemplificatios of the amout of water that falls withi a give period of time i catchmet areas [1]. The raifall Itesity- Duratio-Frequecy (IDF) relatioship i oe of the most importat tools i water resource egieerig to assess the risk ad vulerability of water resource structure as well as for plaig, desig ad operatio.the establishmet of such relatioship was doe as early as 1932[1, 2]. Sice the, may sets of relatioships have bee costructed for several parts of the globe. However, such relatioships have ot bee accurately costructed i may developig coutries [4]. IDF relatioship is a mathematical relatioship betwee the raifall itesity I, the duratio d, ad the retur period T [4, 3]. Ideed IDF curves allow the estimatio of the retur period of a observed raifall evet or coversely of the raifall amout correspodig to a give retur period for differet aggregatio times. Further studies were performed o raifall aalysis ad regioalizatio of IDF curves for differet regios [5]. I Bagladesh water loggig ad flood is a commo problem durig Mosoo period because of iadequate draiage system. I order to solve this problem ew draiage desig is eeded where raifall data of differet duratio is eeded. But due to istrumetal limitatio these data were ot available. I the preset study, aual maximum raifall series is cosidered for Raifall Frequecy Aalysis (RFA). Raifall i a regio ca be characterized if the itesity, duratio ad frequecy of the diverse storms occurrig at that place are kow [6, 7, ad 8]. The frequecy-data for raifalls of various duratios, so obtaied, ca be represeted by IDF curves, which give a plot of raifall itesity versus raifall duratio ad recurrece iterval. I recet studies, various authors attempted to relate IDF relatioship to the syoptic meteorological coditios i the area of hydrometric statios [1, 9].The IDF curve for North-East regio of Bagladesh was developed ad observed that the raifall data i this regio follow Gumbel s Extreme Value Distributio [10]. The short duratio raifall IDF curve was developed for Sylhet with retur period of 2, 5,10,20,50, ad 100 years [11].The accuracy of IDF was improved curves by usig log ad short duratio separatio techique [12]. L-momets ad geeralized least squares regressio method was applied for estimatio of desig raifall depths ad developmet of IDF relatioships [13]. Pearso Type-III distributio was applied for modellig of short duratio raifall ad developmet of IDF relatioships for sylhet city i Bagladesh [14]. DOI: / Page

2 Geeratio of Raifall Itesity-Duratio-Frequecy Relatioship for North-Wester Regio Atomic Eergy Regulatory Board (AERB) guidelies described that the Order Statistics Approach (OSA) is the most appropriate method for determiatio of parameters of Gumbel ad Frechetdistributios [15]. I probability theory, extreme value distributios amely Gumbel, Frechet ad Weibull are geerally cosidered for frequecy aalysis of meteorological variables. I this preset study Gumbel s Extreme Value Distributio method is used to develop IDF curves ad equatios. I this cotext, a attempt has bee made to estimate the raifall for differet retur periods for differet duratios of such as 10-mi, 20-mi, 30-mi, 60-mi, 120-mi, 180-mi, 360-mi, 720-mi, 1440-mi adoptig Gumbel ad LPTIII distributios for developmet of IDF relatioships for North-Wester regio of Bagladesh. Model performace idicators (MPIs) such as correlatio coefficiet (R) is used to aalyze the performace of the developed IDF relatioships by Gumbelad LPTIII distributios for estimatio of raifall itesity for the statios uder study. II. Data Collectio Ad Methodology For this study 24 hr daily raifall data from year 1974 to 2014 was collected from Bagladesh Meteorological Departmet (BMD) for North-Wester regio. From the daily data maximum yearly raifall data was used i the aalysis. I North-Wester regio there are seve BMD statios (Bogra, Ishurdi, Diajpur, Ragpur, Rajshahi, Sydpur, Chuadaga) which were take ito cosideratio to develop IDF curve for this regio of Bagladesh. 2.1Estimatio of Short Duratio Raifall Idia Meteorological Departmet (IMD) use a empirical reductio formula equatio (1) for estimatio of various duratio like 1-hr, 2-hr, 3-hr, 5-hr, 8-hr raifall values from aual maximum values. This formula was used to estimate the short duratio raifall from daily raifall data i Sylhet city ad foud that this formula give the best estimatio of short duratio raifall [11]. I this study this empirical formula equatio (1) was used to estimate short duratio raifall of sevestatios of North-Wester regio of Bagladesh. P t = P 24 3 t (1) Where, P t is the required raifall depth i mm at t-hr duratio, P 24 is the daily raifall i mm ad t is the duratio of raifall for which the raifall depth is required i hr. 2.2Gumbel Theory of Distributio The Gumbel method calculates the 2, 5, 10, 25, 50 ad 100 year retur itervals for each duratio period ad requires several calculatios. Frequecy precipitatio P T (i mm) for each duratio with a specified retur period T (i year) is give by the followig equatio: P T = P ave + KS.. (2) Where K is Gumbel frequecy factor give by: K=- 6 T [ l[l[ ]]]..... (3) π T 1 Where P ave is the average of the maximum precipitatio correspodig to a specific duratio. I utilizig Gumbel s distributio, the arithmetic average i equatio (2) is used: P ave = 1 Pi i=1.. (4) Where Pi is the idividual extreme value of raifall ad is the umber of evets or years of record. The stadard deviatio is calculated by equatio (5) computed usig the followig relatio: (Pi Pave) 2 ] 1/2... (5) S=[ 1 1 i=1 Where S is the stadard deviatio of P data. The frequecy factor (K), which is a fuctio of the retur period ad sample size, whe multiplied by the stadard deviatio gives the departure of a desired retur period raifall from the average. The the raifall itesity, I T (i mm/hr) for retur period T is obtaied from: I T = Pt..... (6) Td Where T d is duratio i hours. The frequecy of the raifall is usually defied by referece to the aual maximum series, which cosists of the largest values observed i each year. A alterative data format for raifall frequecy studies is that based DOI: / Page

3 Geeratio of Raifall Itesity-Duratio-Frequecy Relatioship for North-Wester Regio o the peak-over threshold cocept, which cosists of all precipitatio amouts above certai thresholds selected for differet duratios. Due to its simpler structure, the aual-maximum-series method is more popular i practice [16]. 2.3 Log Pearso type III The LPT III probability model is used to calculate the raifall itesity at differet raifall duratios ad retur periods to form the historical IDF curves for each statio. LPT III distributio ivolves logarithms of the measured values. The mea ad the stadard deviatio are determied usig the logarithmically trasformed data. I the same maer as with Gumbel method, the frequecy precipitatio is obtaied usig LPT III method. The simplified expressio for this distributio is give as follows: P* log(pi).. (7) PT* Pave * KTS * (8) 1 Pave* P*.... (9) i 1 1/ (10) i1 1 S* ( P* Pave*) 1 Where P T *, Pave*, S* are desired raifall peak value for a specific frequecy, average of maximum precipitatio correspodig to a specific duratio, stadard deviatio of P* value respectively. K T is the Pearso frequecy factor which depeds o retur period (T) ad skewess coefficiet (Cs). The skewess coefficiet, Cs, is required to compute the frequecy factor for this distributio. The skewess coefficiet is computed by equatio (11) [2&17] C S ( Pi * Pave*) i1 3 ( 1)( 2)(S*) 3...(11) K T values ca be obtaied from tables i may hydrology refereces; for example referece [2]. By kowig the skewess coefficiet ad the recurrece iterval, the frequecy factor, K T for the LPT III distributio ca be extracted. The atilog of the solutio i equatio (7) will provide the estimated extreme value for the give retur period. 2.4 Derivatio of IDF equatio To derive a equatio for calculatig the raifall itesity (I) for the regios of iterest, there are some required steps for establishig a equatio to suit the calculatio of raifall itesity for a certai recurrece iterval ad specific raifall period which depeds maily o the results obtaied from the IDF curves. Two approaches were tried to estimate the equatio parameters. By applyig the logarithmic coversio, where it is possible to covert the equatio ito a liear equatio, thus to calculate all the parameters related to the equatio. The followig steps are followed: 1. Covert the origial equatio i the form of power-law relatio as follows: I CT T m r e d (12) By applyig the logarithmic fuctio to get logi = log K e log T d..... (13) Where K=CTr m.... (14) Ad e represets the slope of the straight lie. DOI: / Page

4 Geeratio of Raifall Itesity-Duratio-Frequecy Relatioship for North-Wester Regio 2. Calculate the atural logarithm for (K) value foud from Gumbel method or from LPTIII method as well as the atural logarithmic for raifall period T d. 3. Plot the values of (log I) o the y-axis ad the value of (log T d ) o the x axis for all the recurrece itervals for the two methods. 4. From the graphs (or mathematically) fid the value of (e) for all recurrece itervals. The it was foud out the average value of e value, e ave, by usig the followig equatio: e eave (15) Where represets recurrece itervals (years) value oted as Tr. 5. From the graph, it was foud logk values for each recurrece iterval where logk represets the Y-itercept values as per Gumbel method or LPTIII method. The covert equatio (14) ito a liear equatio by applyig the atural logarithm to become: logk= logc + m logtr.... (16) 6. Plot the values of logk o the y-axis ad the values of logtr o the x-axis to fid out the values of parameters c ad m as per Gumberl method or LPTIII where m represets the slope of the straight lie ad c represets the (ati log) for the y itercept. I aother approach Estimatio of the equatio parameters by usig oliear regressio aalysis: Usig the Solver fuctio of the ubiquitous spreadsheet program Microsoft Excel, which employs a iterative least squares fittig routie to produce the optimal goodess of fit betwee data ad fuctio. The R 2 value calculated is desiged to give the user a estimate of goodess of fit of the fuctio to the data. 2.5 Goodess of fit test The purpose of this test is to decide how good is a fit betwee the observed frequecy of occurrece i a sample ad the expected frequecies obtaied from the hypothesized distributios. A goodess of fit test betwee observed ad expected frequecies is based o the chi-square quatity, which is expressed as, k 2 2 (Oi E i) / Ei i1... (17) 2 where is a radom variable whose samplig distributio is approximated very closely by the chi-square distributio. The symbols O i ad E i represet the observed ad expected frequecies, respectively, for the i-th class iterval i the histogram. The symbol k represets the umber of class itervals. If the observed 2 frequecies are close to the correspodig expected frequecies, the value will be small, idicatig a good fit; otherwise, it is a poor fit. A good fit leads to the acceptace of ull hypothesis, whereas a poor fit leads to its rejectio. The critical regio will, therefore, fall i the right tail of the chi-square distributio. For a level of 2 sigificace equal to a, the critical value is foud from readily available chi-square tables ad > costitutes the critical regio [19]. III. ResultAd Discussio Fig 1-2 show results of the IDF curves obtaied by Gumbel ad LPT III methods for North- Wester regio. It was show that there were small differeces betwee the results obtaied from the two methods, where Gumbel method gives slightly higher results tha the results obtaied by Log Pearso Type III. This is show also from parameters of the derived equatio for calculatig the raifall itesity usig the two methods. DOI: / Page

5 Itesity (mm/hr) Geeratio of Raifall Itesity-Duratio-Frequecy Relatioship for North-Wester Regio years 5 years 10 years Duratio 25 (mi) years 50 years 100 years Figure 1: IDF curve by Gumbel method at North-Wester regio Parameters of the selected IDF formula were adjusted by the method of miimum squares, where the goodess of fit is judged by the correlatio coefficiet. The results obtaied showed that i all the cases the correlatio coefficiet is very high, ad rages betwee ad 0.987, except few cases where itrages betwee ad whe usig LPT III at 50 ad 100 years. This idicates the goodess of fit of the formulae to estimate IDF curves i the regio of iterest. For each regio the results are give as the mea value of the poits results. Table 1 shows the parameters values obtaied by aalyzig the IDF data usig the two methods ad those are used i derivig formulae for the two regios. Figure 2: IDF curve by LPTIII method at North-Wester Regio DOI: / Page

6 Geeratio of Raifall Itesity-Duratio-Frequecy Relatioship for North-Wester Regio Figure 3: IDF curve by average at North-Wester Regio Table 1: IDF parameters values used i derivig formula Regio Parameter Gumbel Method Log Pearso Type III c North- Wester m e Also, goodess-of-fit tests were used to choose the best statistical distributio amog those techiques. Results of the chi-square goodess of fit test o aual series of raifall are show i Table 2. As it is see most of the data fit the distributios at the level of sigificace of =0.05, which yields <3.84. Oly the data for 10, 20, 30 mi do ot give good fit usig Gumbel method distributio. Also the data for 10, 20 mi usig LPTIII method do ot give good fit. cal Regio North- Wester Table 2: Results of chi-square goodess of fit test o aual maximum raifall Duratio (mi) Distributio Gumbel LPTIII IV. Coclusios Sice Bagladesh has differet climatic coditios from regio to regio, a relatioshipof R-IDF for each regio has to be obtaied to estimate raifall itesities for differet duratios ad retur periods ragig betwee 2 ad 100 years. It was foud that Gumbel method gave some larger raifall itesity estimates compared to LPT III distributio. I geeral, the results obtaied usig the two approaches are very close at most of the retur periods ad have the sametred.the results obtaied from that work are cosistet with the results from previous studies doe i some parts of the study area. The parameters of the desig raifall itesity for a give period of recurrece iterval were estimated for this regio. The results showed that i all the cases data fitted the formula with a correlatio coefficiet greater tha This idicates the goodess of fit of the formulae to estimate IDF curves i the regio of iterest for duratios varyig from 10 to 1440 mi ad retur periods from 2 to 100 years. The Chi-square test was used o oe had to examie the combiatios or cotigecy of the observed ad theoretical frequecies, ad o the other had, to decide about the type of distributio which the available data set follows. The results of the chi-square test of goodess of fit showed that i all the duratios the ull hypothesis that the extreme raifall series have the Gumbel distributio is acceptable at the 5% level of sigificace. Oly few cases i which the fittig was ot good obtaied by usig the LPT III distributio. Although the Chi-square values are appreciably below the critical regio usig Gumbel distributio ad few values are higher tha the critical regio usig LPT III distributio, it is difficult to say that oe distributio is superior to the other. Further studies are recommeded wheever there will be more data to verify the results obtaied or update the IDF curves. DOI: / Page

7 Geeratio of Raifall Itesity-Duratio-Frequecy Relatioship for North-Wester Regio Ackowledgemet Authors are grateful to the Bagladesh Meteorological Departmet (BMD) for providig the ecessary meteorological data. Refereces [1]. Dupot, B.S., Alle, D.L.,Establishmet of Itesity Duratio Frequecy Curves for Precipitatio i the Mosoo Area of Vietam. Ketucky Trasportatio Ceter, College of Egieer, Uiversity of Ketucky i corporatio with US Departmet of Trasportatio, 2006 [2]. Chow, V.T., Hadbook of Applied Hydrology. McGraw-Hill Book, [3]. Koutsoyiais, D., O the appropriateess of the Gumbel distributio for modellig extreme raifall, i: Proceedigs of the ESF LESC Exploratory Workshop, Hydrological Risk: recet advaces i peak river flow modellig, predictio ad real-time forecastig, Assessmet of the impacts of lad-use ad climate chages, Europea Sciece Foudatio, Natioal Research Coucil of Italy, Uiversity of Bologa, Bologa, October 2003.Koutsoyiais, D., Kozois, D., Maetas, A., A mathematical framework for studyig raifall itesity-duratio- frequecy relatioships. J. Hydrol. 206, [4]. Iloa, V., Fraces, F Raifall aalysis ad regioalizatio computig itesity-duratio-frequecy curves, UiversidadPolitecica de Valecia - Departameto de IgeieriaHidraulicaMedioAmbiete - APDO Valecia - Spai. [5]. Burlado P ad Rosso R. Scalig ad multi-scalig models of depth-duratio-frequecy curves for storm precipitatio. Joural of Hydrology. 1996; 187(1&2): [6]. Koutsoyiais D, Kozois D ad Maetas A. A mathematical framework for studyig raifall itesity- duratio-frequecy relatioships. Joural of Hydrology. 1998; 206(1&2): [7]. Bougadis J ad Adamowski K. Scalig model of a raifall itesity-duratio-frequecy relatioship. Hydrological Process. 2006; 20(17): [8]. Mohymot1,B.,Demaree1,G.R.,Faka2,D.N.2004.Establishmet of IDF-curves for precipitatio i the tropical area of Cetral Africa-compariso of techiques ad results, Departmet of Meteorological Research ad Developmet, Royal Meteorological Istitute of Belgium, Riglaa 3, B-1180 Brussels, Belgium. [9]. Mati M. A. ad Ahmed S. M. U Raifall Itesity Duratio Frequecy Relatioship for the N-E Regio of Bagladesh. Joural of Water Resource Research. 5(1). [10]. Chowdhury R., Alam J. B., Das P. ad Alam M. A Short Duratio Raifall Estimatio of Sylhet: IMD ad USWB Method. Joural of Idia Water Works Associatio. pp [11]. Kim T, Shi J, Kim K ad Heo J. Improvig accuracy of IDF curves usig log- ad short duratio separatio ad multi-objective geetic algorithm. World Evirometal ad Water Resources Cogress. 2008, [12]. Khaled H, Ataur R, Jaice G ad George K. Desig raifall estimatio for short storm duratios usig L-Momets ad geeralized least squares regressio-applicatio to Australia Data. Iteratioal Joural of Water Resources ad Arid Eviromets. 2011; 1(3): [13]. Rashid MM, Faruque SB ad Alam JB. Modellig of short duratio raifall itesity duratio Frequecy (SDRIDF) equatio for Sylhet City i Bagladesh. ARPN Joural of Sciece ad Techology. 2012; 2(2): [14]. Atomic Eergy Regulatory Board (AERB), Extreme values of meteorological parameters (Guide No. NF/SG/S-3), [15]. Borga, M., Vezzai, C., Fotaa, G.D A Regioal Raifall Depth Duratio Frequecy Equatios for a Alpie Regio, Departmet of Lad ad AgroForest Eviromets, Uiversity of Padova, Legaro 35020, Italy, Natural Hazards, vol. 36, pp [16]. Burke, C.B., Burke, T.T., Storm Draiage Maual. Idiaa LTAP. [17]. M. M. Rashid, S.B. Faruque J. B. Alam, Modelig of Short Duratio Raifall Itesity Duratio Frequecy (SDRIDF) Equatio for Sylhet City i Bagladesh, ARPN Joural of Sciece ad Techology, Vol 2, No. 2 [18]. Al-Shaikh, A.A. Raifall frequecy studies for Saudi Arabia, M.S.Thesis, Civil Egieerig Departmet, Kig Saud Uiversity, Riaydh (K.S.A), DOI: / Page

GENERATION OF RAINFALL INTENSITY-DURATION-FREQUENCY RELATIONSHIP FOR CENTRAL REGION IN BANGLADESH

Proceedigs of the 3 rd Iteratioal Coferece o Civil Egieerig for Sustaiable Developmet (ICCESD 206), 2~4 February 206, KUET, Khula, Bagladesh (ISBN: 978-984-34-0265-3) GENERATION OF RAINFALL INTENSITY-DURATION-FREQUENCY