International Journal of Civil Engineering and Technology (IJCIET) Volume 8, Issue, June, pp., Article ID: IJCIET_8 Available online at http://www.ia aeme.com/ijciet/issues.asp?jtype=ijciet&vtyp pe=8&itype= ISSN Print: 9-8 and ISSN Online: 9- IAEME Publication Scopus Indexed DEVELOPMENT OF MAXIMUM AVERAGE RAINFALL INTENSITY RELATIONSHIPS WITH HOUR AVERAGE RAINFALL INTENSITY S. Aruna Jyothy Assistant Professor Department of Civil Engineering, S.V.U College of Engineering, Tirupati, A.P, India D. Srinivasa Murthy Assistant Professor, Department of Civil Engineering, Sree Vidyanikethan Engineering College, A. Rangampet, Andhra Pradesh, India P. Mallikarjuna Professor, Department of Civil Engineering, S.V.U College of Engineering, Tirupati, A.P, India ABSTRACT Hourly rainfall data at Ananthapur, Arogyavaram and Kurnool raingauge stations located in Rayalaseema region and Kakinada, Machilipatnam and Nellore located in Coastal region of Andhra Pradesh state and, Hyderabad, Nizamabad and Ramagundam raingauge stations of Telangana state have been used in the present study for developing relationships between one to seven hour maximum average rainfall intensities with that of hour average rainfall intensities. A fairly good correlation has been observed between one to seven hour maximum average rainfall intensity with corresponding hour average rainfall intensity at the raingauge stations. The intensity-duration relationships of the form have also been developed to estimate the average rainfall intensity of any duration with reasonable degree of accuracy with the help of hour average rainfall intensity for use in the design of drainage systems and hydraulic structures. These relationships may also be adopted to obtain the rainfall intensities at the nearby meteorologically homogeneous non-recording raingauge stations. Key words: Regional rainfall intensity, maximum average rainfall intensities for one to seven hour durations, hour average rainfall intensity. Cite this Article: S. Aruna Jyothy, D. Srinivasa Murthy and P. Mallikarjuna. Development of Maximumm Average Rainfall Intensity Relationshipss with Hour Average Rainfall Intensity. International Journal of Civil Engineering and Technology, 8(),, pp.. http://www.iaeme.com/ijci IET/issues.asp?JType=IJCIET&VType=8&ITy ype= http://www.iaeme.com/ijciet/index.asp editor@iaeme.com
S. Aruna Jyothy, D. Srinivasa Murthy and P. Mallikarjuna. INTRODUCTION Hydrologic phenomena, such as rainfall, are highly erratic and random. These processes are not fully understood due to complexity of the hydrologic cycle. Rainfall, a physical process, that transports water from the atmosphere to the Earth s surface is one of the key climatic variables which affects both spatial and temporal patterns of water variability and is characterized in terms of its frequency, duration and intensity, with intensity being most relevant to the less frequent but more damaging flood events. Intensity relationships of extreme rainfalls are used in the storm water drainage systems and flood estimation of small watersheds. Graphical intensity-duration relationships have been prepared for some locations in United States using recorded rainfall and, rainfall intensity-duration equations for various frequencies have been developed for some cities (Chow 9, Wenzel 98). Ferreri and Ferro (99) by using Sicilian and Sardinian short-duration rainfall data, proposed power relationship between the regional mean value of the ratio (h t /h )=(t/) s where h t = rainfall in time t, h = hourly rainfall, t=duration in minutes and s=exponent equal to.8 for Sicily and. for Sardinia. Froehlich (99) describes a graphical method for obtaining parameters for several forms of rainfall - intensity equations for durations of one hour or less for any location in the United States using available rainfall maps. Froehlich (99) developed rainfall intensity-duration equations for long duration rainfall i.e. for durations from to days using data from available isopluvial maps prepared by the National Weather Service (NWS) for four geographical regions which are useful for developing precipitation patterns used in the hydrologic design of structures that control storm runoff and flooding. Ferro and Bangarello (99) made a comparison among the regional rainfall depth-duration relationships of four regions of South Italy and the results showed that the short-duration rainfall is dependent on geographical factors. Gerold and Watkins () developed IDF estimates for the state of Michigan using regional frequency analysis and results indicated that the short-duration estimates are consistent with historical observations. Guo () updated the rainfall Intensity Duration Frequency (IDF) relationships for Chicago to represent the recent climate conditions. Using these IDF relationships, the impact of heavy rainfall events on the design and performance of urban drainage systems was quantified. Froehlich et al. () developed a practical method for rainfall-intensity equations for short durations (one hour or less) for some locations in the United States. They also developed design storm hyetographs using intensity-duration expression by distributing rainfall about the time of peak intensity. Updated rainfall intensity-duration-frequency (IDF) relationships for Andhra Pradesh, India were developed by Dourte et al. () and these relationships showed a significant change in rainfall characteristics compared to earlier relationships. In the design of storm water drainage systems and hydraulic structures, the knowledge of short-duration rainfall is necessary. In the present analysis, an attempt has been made to develop the rainfall- intensity relationships between maximum average rainfall intensities of different durations and hour average rainfall intensities in the regions of Andhra Pradesh and Telangana states. Hourly rainfall data at Ananthapur, Arogyavaram, and Kurnool located in the drought prone area of Rayalaseema region and Kakinada, Machilipatnam and Nellore located in Coastal region of Andhra Pradesh state and, Hyderabad, Nizamabad and Ramagundam raingauge stations of Telangana state have been used in the present study for regional rainfall intensity analysis. http://www.iaeme.com/ijciet/index.asp editor@iaeme.com
Development of Maximum Average Rainfall Intensity Relationships with Hour Average Rainfall Intensity. MATERIALS AND METHODS The location map of raingauge stations selected for the study is presented in Fig. and their brief description is presented in Table. Hourly rainfall data were collected for the period 99 to 8 ( years) at the raingauge stations from India Meteorological Department (IMD), Pune. Maximum average rainfall intensity for different durations (h, h, h, h, h, h and h) and corresponding hour intensity were calculated for different regions and used in the analysis. Regression analysis was carried out for the development of empirical relationships. Figure Location of raingauge stations Table Brief description of raingauge stations Region Rayalaseema Region (Andhra Pradesh State) Coastal Region (Andhra Pradesh State) Telangana State Raingauge station Latitude ( N) Longitude ( E) Altitude (m) Mean annual rainfall (mm) Ananthapur ' 9' 8 Arogyavaram ' 8 ' 9 Kurnool ' 8 9' 8 Kakinada ' 8 ' Machilipatnam 9' 8 ' 99 Nellore ' 9 9' 8 98 Hyderabad ' 8 8' 8 Nizamabad 8 ' 8 ' 8 8 Ramagundam 8 ' 9 8' http://www.iaeme.com/ijciet/index.asp editor@iaeme.com
S. Aruna Jyothy, D. Srinivasa Murthy and P. Mallikarjuna. RESULTS AND DISCUSSION The typical variation of maximum average rainfall intensity of hour to hour durations with hour average rainfall intensity is shown in Figs. to. Hour Maximum Average Rainfall Intensity,i (mm/h) Hour Maximum Average Rainfall Intensity, i (mm/h) 8 8 8 Hour Maximum Average Rainfall Intensity, i (mm/h) Hour Maximum Average Rainfall Intensity, i (mm/h) 8 8 Hour Maximum Average Rainfall Intensity i (mm/h) 8 Hour Maximum Average Rainfall Intensity, i (mm/h) 8 Figure Typical variation of maximum average rainfall intensity (mm/h) of one to seven hour durations with hour average rainfall intensity (mm/h) (Raingauge Station: Ananthapur, Region : Rayalaseema, State : Andhra Pradesh http://www.iaeme.com/ijciet/index.asp editor@iaeme.com
Development of Maximum Average Rainfall Intensity Relationships with Hour Average Rainfall Intensity Hour Maximum Average Rainfall Intensity,i (mm/h) Hour Maximum Average 8 8 9 8 9 Hour Maximum Average Hour Maximum Average 8 9 8 9 Hour Maximum Average Rainfall Intensity,i (mm/h) 8 9 Figure Typical variation of maximum average rainfall intensity (mm/h) of one to seven hour durations with hour average rainfall intensity (mm/h) (Raingauge Station: Machilipatnam, Region : Coastal State : Andhra Pradesh) http://www.iaeme.com/ijciet/index.asp editor@iaeme.com
S. Aruna Jyothy, D. Srinivasa Murthy and P. Mallikarjuna Hour Maximum Average Hour Maximum Average Rainfall Intensity,i (mm/h) 8 Hour Maximum Average Rainfall Intensity,i (mm/h) Hour Maximum Averge Rainfall Intensity,i (mm/h) 8 9 Intensity (mm/h) 8 8 8 Hour Maximum Hour Maximum Average Rainfall Intensity,i (mm/h) Hour Maximum Average Rainfall Intensity,i (mm/h) Hour Maximum Average Rainfall Intensity,i (mm/h) 8 8 8 9 8 8 8 http://www.iaeme.com/ijciet/index.asp 8 editor@iaeme.com
Development of Maximum Average Rainfall Intensity Relationships with Hour Average Rainfall Intensity Hour Maximum Average Rainfall Intensity,i (mm/h) 8 8 Figure Typical variation of maximum average rainfall intensity (mm/h) of one to seven hour durations with hour average rainfall intensity (mm/h) (Raingauge Station: Ramagundam, State : Telangana) From Figs. to, it may be observed that a fairly good correlation exists between one to seven hour maximum average rainfall intensity with corresponding hour average rainfall intensity. A relationship of the form i t = a i b, where i t = maximum average intensity of duration t, i = corresponding hour average intensity and a and b are empirical constants is fitted and presented in Tables to. From the values presented in Table, higher intensities at Arogayarvam at smaller durations may be observed compared to Anantapur and Kurnool. However, at longer rainfall durations the intensities at these stations are slightly more. Similarly from Table higher intensities at Kakinada with smaller durations than at Nellore and Machilipatnam and more or less similar intensities for longer rainfall durations. From Table higher intensities at smaller durations may be observed at Nizamabad and Hyderabad compared to Ramagundam. Variations of empirical coefficient (a) and exponent (b) of the relations with rainfall duration at the regions are shown in Fig. and the equations relating these coefficients with rainfall duration are presented in Table. These relations may be used to estimate the intensities at smaller durations. Regression analysis has also been carried out to develop a relationship in the form where n is an empirical exponent. Values of n for different raingauge stations and regions are presented in Table. It may be observed from Table that the variations in n value is not very significant for the raingauge stations in Rayalaseema and Telangana regions, whereas a significant change may be observed in the coastal region of Andhra Pradesh. This may be due to large spatial rainfall variability with in the coastal region where rainfalls are mostly of cyclonic nature. http://www.iaeme.com/ijciet/index.asp 9 editor@iaeme.com
S. Aruna Jyothy, D. Srinivasa Murthy and P. Mallikarjuna Table Relationships between maximum average rainfall intensity of to hour duration and the corresponding hour average rainfall intensity in Rayalaseema Region of Andhra Pradesh State Raingauge Station Duration, t (h) Relationship Correlation Coefficient, R i =.89 i.9. i =. i..99 i =. i.8.9 i =.8 i.88.8 Ananthapur i =. i.9.8 i =. i.98.89 i =. i..9 i =. i.9.8 i =. i.8.88 Arogyavaram i = 8. i.8.8 i =.9 i..8 i =. i.8.8 i =. i.88.8 i =.9 i.8.8 i =. i..888 i =. i.9.99 i =.9 i.9.9 Kurnool i =. i.8.889 i =. i.8.9 i =.98 i.8.9 i =.8 i.8.9 http://www.iaeme.com/ijciet/index.asp editor@iaeme.com
Development of Maximum Average Rainfall Intensity Relationships with Hour Average Rainfall Intensity Table Relationships between maximum average rainfall intensity of to hour duration and the corresponding hour average rainfall intensity in Coastal Andhra Pradesh Raingauge Station Duration, t (h) Relationship Correlation Coefficient, R Kakinada Machilipatnam Nellore i =.8 i.. i =. i.. i = 8.8 i..8 i =.99 i.. i =. i.8. i =.8 i.8.9 i =.89 i.9.8 i =. i.8. i =. i.8. i =.8 i.8.8 i =. i.8.8. i =. i.88 i =.8 i.8.8 i =. i.89.89 i =.8 i.9.8 i =.8 i..9 i = 9. i.8.88 i =.9 i..8 i =.9 i.8.89 i =.8 i.8.9 i =. i.8.9 http://www.iaeme.com/ijciet/index.asp editor@iaeme.com
S. Aruna Jyothy, D. Srinivasa Murthy and P. Mallikarjuna Table Relationships between maximum average rainfall intensity of to hour duration and the corresponding hour average rainfall intensity in Telangana State Raingauge Station Duration, t (h) Relationship Correlation Coefficient, R i = 9. i.88.98 i =.8 i..9 i = 8. i.8.9 Hyderabad i =. i.8.99 i =.8 i.8.9 i =.88 i.89.98 i =. i.8.88 i =.89 i.9.8 i =. i..89 i = 9. i..8 Nizamabad i =. i..8 i =.9 i..89 i =.9 i..89 i =. i..9 i =.98 i..9 i =. i.8.8 i = 8.9 i.88.9 Ramagundam i =.9 i.9.9 i =. i.9.9 i =.9 i.9.9 i =.8 i.9.98 http://www.iaeme.com/ijciet/index.asp editor@iaeme.com
Development of Maximum Average Rainfall Intensity Relationships with Hour Average Rainfall Intensity. Coefficient (a) 8 Exponent (b).8... 8 Duration (hours) Duration (hours) (a) Raingauge Station : Ananthapur (Rayalaseema region of Andhra Pradesh) Coefficient (a) 8 Duration (hours) Exponent (b).8... 8 Duration (hours) (b) Raingauge Station : Machilipatnam (Coastal Andhra Pradesh). Coefficient (a) 8 Exponent (b).8... 8 Duration (hours) Duration (hours) (c) Raingauge Station : Ramagundam (Telangana State) Figure Variations of a and b in rainfall-intensity relationship at typical raingauge stations http://www.iaeme.com/ijciet/index.asp editor@iaeme.com
S. Aruna Jyothy, D. Srinivasa Murthy and P. Mallikarjuna Table Equations relating coefficient (a) and exponent (b) with rainfall duration (t) Region Rayalaseema Region (Andhra Pradesh State) Coastal Region (Andhra Pradesh State) Telangana State Raingauge Station Equation For a For b Ananthapur a =. t -. b=. t. Arogyavaram a =.8 t -. b=. t.99 Kurnool a =. -.9 b=.9 t.8 Kakinada a = 9. t -. b=. t. Machilipatnam a =. t -. b=.8 t. Nellore a = 8.8 t -. b=. t. Hyderabad a =. t -.9 b=.8 t -. Nizamabad a =. t -.88 b=. t. Ramagundam a =. t -. b=. t.9 Table Regression constant (n) of Intensity-duration- relationships Raingauge Station / Region n (Exponent) Ananthapur.89 Arogyavaram.898 Kurnool.88 Rayalaseema Region.89 Kakinada.8 Machilipatnam. Nellore. Coastal Region. Hyderabad.89 Nizamabad.88 Ramagundam.89 Telangana Region.888. CONCLUSIONS Maximum average rainfall intensity relationships for Rayalaseema, Coastal and Telangana regions for different durations with hour average rainfall intensity have been developed. A fairly good correlation exists between maximum average rainfall intensities of one to seven durations with corresponding hour average rainfall intensity. Intensity-duration relationships of the form have also been developed at the raingauge stations of these regions. The rainfall- intensity relationships developed may be used to estimate the rainfall intensities of smaller durations for the design of storm water drainage systems for obtaining peak rates of runoff at the watersheds of the regions. The relationships proposed may be adopted to obtain the rainfall intensities at the nearby meteorologically homogeneous non-recording stations in the planning and design of urban drainage system and hydraulic structures of nearby watersheds. http://www.iaeme.com/ijciet/index.asp editor@iaeme.com
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