Temporal Distribution of 24-hour Maximum Rainfall

Transcription

1 International Journal of Engineering Science Invention ISSN (Online): ISSN (Print): Volume 6 Issue 7 July 2017 PP Temporal Distribution of 24-hour Maximum Rainfall * Omer Leven Asikoglu (Ege University Department of Civil Engineering Bornova Izmir TURKEY) Abstract: Rainfall measurements are an important input to hyrological moeling or esign of ater structures. For example hile average flos an hence average rainfalls are effective in planning a hyroelectric poer plant minimum rainfall for rought analysis stuies an maximum precipitation for floo analysis stuies are important. Rainfall measurements can be conventionally measure ith evices calle pluviometers an pluviographs. The main ifference beteen the to evices is that the pluviometer measures rainfall at certain intervals (generally every 24 hours) hile the pluviograph continuously recors the amount of the rainfall. With this feature pluviographs are of great avantage in achieving the temporal istribution of rainfall an thus etermining the rainfall amount in certain stanar urations (5min 10min 1h 18h 24h). In this stuy an empirical approach as investigate in orer to etermine the temporal istribution of 24-hour rainfall. By etermination of the temporal istribution of rainfall the rainfall epth of a stanar uration can be calculate using the ata of a pluviometric station (ith a 24-hour rainfall recor). Keyors: Temporal istribution of rainfall pluviograph recors I. INTRODUCTION In cases here the project flo of ater structures such as floo control erosion an rainage systems are estimate using synthetic methos maximum rainfall of certain urations are use as a basic hyrological input. In Unite States the Natural Resources Conservation Service has continue orking on the evelopment of empirical formulas to improve the Soil Conservation Service (SCS) metho for preicting storm runoff from esign storm events. The SCS metho (1973) presents the 24-hr Type I IA II an IIA rainfall time istributions for runoff preictions. Technical Release 55 (TR-55) presents rainfall istribution maps for the Unite States. [1 2 3]. Guo an Hargain [3] analyze a 57-year hourly rainfall ata recore in Denver Colorao an compare the results ith the SCS 24-hr rainfall curves. It is conclue that these SCS 24-hr Type I an II curves are not the statistically average rather they represent the orst time istribution to form a sever storm. The measurement netork of pluviometric stations is much bigger than that of pluviographic stations. The main reason for this is that pluviometer is a more economical tool. Genovez [4] an Mello et al. [5] state that the time istribution of a esign storm shoul be obtaine from ata observe in the area of stuy or from regional ata. Back [6] etermine the time istribution pattern of heavy rain events in Urussanga Santa Catarina State Brazil. Rain events ere classifie into four types accoring to the uration quartile in hich the greatest amount of precipitation occurre. It is foun that type I rain events are more frequent folloe by type II an these occur preominantly uring the summer hile type III an IV rain events are istribute throughout the year. Ghassabi et al. [7] fitte a three-parametric logistic function to the rainfall ata in orer to compute the temporal rainfall istribution. They examine the spatial variation of the parameters of this istribution. Asikoglu [8] evelope to functional approaches for the time istribution of annual extreme rainfall of stanar urations. The three-point metho an polynomial approach foun to represent the time istribution of rainfall successfully. In this stuy the temporal istribution curves of maximum rainfall are successfully represente ith a logarithmic relationship. Annual maximum rainfall observations of 14 stanar urations (5min 10min 1h 18h 24h) of 31 stations in the Aegean region of Turkey are use in obtaining these curves. A generalize relationship is constructe to represent the stuy area. By etermining the temporal istribution of rainfall it may be possible to shift from maximum 24-hour (or aily) rainfall to the maximum rainfall of another uration. It also allos the calculation of rainfall epths of stanar urations at stations ithout any pluviograph equipment. II. METHODS The efinition of temporal istribution of precipitation is of great importance in terms of the establishment of synthetic unit hyrograph moels. Besies by using the temporal istribution of rainfall it is possible to calculate project rainfall of ifferent uration from certain perio of precipitation [ ] In orer to obtain the temporal istribution of the 24-hour rainfall the largest rainfall amounts of every uration (= 5min 10min 1h 18h 24h) for each year is consiere. Then the averages of these maximum values are calculate for each uration an these values are ivie by the average of the 24-hour maximums. 6 Page

2 X / X (1) 24 When the variation of these values obtaine for each station (i=1 2 k) over time is analyze graphically it is observe that this change is perfectly efine by the logarithmic equation. a b.ln( ) (2) i i i From here the i ratios ere etermine for all the stations an the averages (or the regional values the ratios are calculate as in Eq. (3). k i 1 r (3) k i ) of In the equation k is the number of stations in the region. Finally a logarithmic equation is aopte to the series of the averages an a regional logarithmic curve ( a r b r. ln( ) ) as etermine. The performance of this generalize logarithmic relationship hich efines the rainfall rates (or the temporal istribution) of the hole region is measure by the correlation coefficients. III. DATA an STUDY AREA The stuy area covers nearly one-eighth of Turkey. The region has a Meiterranean climate ith annual mean rainfall ranging from 450 to 1200mm yr -1. This ork examines annual maximum rainfalls of 14 stanar urations of 34 rain gauge stations from the Aegean region of Turkey. The ata ere obtaine from the State Meteorological Works (DMI). Figure 1 isplays the locations of the stations an Table 1 shos geographical characteristics an annual maximum 24-hour rainfall of the stations. r Figure 1. The locations of rain gauging stations IV. RESULTS The temporal istribution of 24-hour rainfall as obtaine for all pluviographic rainfall stations ith the rates ( =X /X 24 ) on the vertical axis an stanar rainfall urations () on the horizontal axis. It has been foun that logarithmic equations are the most appropriate representations of temporal istribution curves in each station. A regional logarithmic temporal istribution curve as obtaine at this stage to represent the entire region. For this the average of the ratios of all stations as calculate for 14 ifferent rainfall urations. Then a generalize logarithmic equation as fitte to these averages ln( ) (4) Figure 2 isplays the generalize temporal istribution curve of maximum 24-hour rainfall. The ratios of 34 rain gauging stations; the averages of the ratios an the estimations r ˆ obtaine accoring to the Eq. 4 r are given in Table 2. 7 Page

3 Table 1: The geographical characteristics an annual maximum 24-hour rainfall of the stations Station N X24 (mm) Latitue (N) Longitue (E) Altitue (m) 1 Acıpayam Afyonkarahisar Akhisar Ayın Ayvalık Bergama Borum Bolvain Bornova Çeşme Demirci Denizli Dikili Dinar Eremit Fethiye Geiz Güney İzmir Köyceğiz Kuşaası Kütahya Manisa Marmaris Milas Muğla Nazilli Öemiş Salihli Selçuk Sultanhisar Tavşanlı Uşak Yatağan r (min) Figure 2: Average ratios an temporal istribution curve of 24-hour maximum r 8 Page

4 Table 2. The ratios of rain gauging stations the averages r an the estimations ˆ r of the ratios Station R 1 Acıpayam Afyonkarahisar Akhisar Ayın Ayvalık Bergama Borum Bolvain Bornova Çeşme Demirci Denizli Dikili Dinar Eremit Fethiye Geiz Güney İzmir Köyceğiz Kuşaası Kütahya Manisa Marmaris Milas Muğla Nazilli Öemiş Salihli Selçuk Sultanhisar Tavşanlı Uşak Yatağan r ˆ r The last column (R) in Table 2 shos the correlation coefficients calculate beteen the ratios of each station an the generalize temporal istribution curve. The correlation coefficient (R=0992) at the bottom of the table is calculate beteen the average (or regional) ratios an the generalize temporal istribution curve. V. DISCUSSION Almost all meteorological stations ith or ithout pluvyograph equipments have 24-hour or aily total rainfall recors. There is no possibility to irectly calculate the rainfall epth for any stanar rainfall uration especially at stations ithout pluviograph equipment. In this stuy it is aime to fin an approximate solution to this problem. In this stuy the ata of 34 rain gauging stations ith measurements of stanar rainfall urations (5min 10min 1h 18h 24h) are evaluate. The X / X 24 ratios for each station ere calculate an the average values of these ratios are obtaine for the region. Then a logarithmic curve is fitte to these r r averages to obtain a generalize temporal istribution curve for all stations. When Figure 2 is examine it is seen that the generalize temporal istribution curve successfully represents the regional average ratios. The correlation coefficient at the bottom of Table 2 (R=0992) also r confirms this suitability mathematically. When the generalize temporal istribution curve is evaluate on the station-by-station basis the R correlation coefficients for each station in Table 2 sho that this generalize curve successfully represents the ratios of each station. In summary the generalize curve obtaine for the stuie area is sufficiently safe to represent the temporal istribution of maximum 24-hour precipitation. REFERENCES [1] U. S. Soil Conservation Service A Metho for Estimating Volume an Rate of Runoff in Small Watershes SC-TP-149 (Department of Agriculture 1973). [2] U. S. Soil Conservation Service A Metho for Estimating Volume an Rate of Runoff for Urban Watershes SC-TP-55 (Department of Agriculture 1986). [3] J.C. Guo K. Hargain Conservative Design Rainfall Distribution. Journal of Hyrologic Engineering 14(5) [4] A.M. Genovez Vazões máximas. In: Paiva J. B. D.; Paiva E. M. C. D. (E.). Hirologia aplicaa á gestão e pequenas bacias hirográficas. (Porto Alegre: ABRH 2003) r 9 Page

5 [5] C.R. Mello A.M. Silva J.M. Lima D.F. Ferreira M.S. Oliveira Moelos matemáticos para preição a chuva e projetos para regiões o Estao e Minas Gerais. Revista Brasileira e Engenharia Agrícola e Ambiental 7(1) [6] A.J. Back Time istribution of heavy rainfall events in Urussanga Santa Catarina State Brazil Acta Scientiarum 33 (4) [7] Z. Ghassabi G. Alikamali A-H. Meshkatee S. Hajam N. Javaheri Time istribution of heavy rainfall events in southest of Iran Journal of Atmospheric an Solar-Terrestrial Physics [8] O. L. Asikoglu Regional Frequency Analysis of Maximum Rainfall in the Aegean Region of Turkey MSc Thesis Ege University Grauate School of Natural an Applie Sciences (1997) Omer Leven Asikoglu Temporal Distribution of 24-hour Maximum Rainfall International Journal of Engineering an Science Invention (IJESI) 6.7 (2017): Page