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The change in rainfall pattern and intensity is becoming a great concern for hydrologic engineers and planners. Many parts of the world are experiencing extreme rainfall events such as experienced on 26
^{th} July 2005 in Mumbai, India. For the appropriate design and planning of urban drainage system in an area, Intensity Duration Frequency (IDF) curves for given rainfall conditions are required. The aim of the present study is to derive the IDF curves for the rainfall in the Mumbai city, Maharashtra, India. Observed rainfall data from 1901 pertaining to Colaba and from 1951 of the Santacruz rain gauge stations in Mumbai are used in the present study to derive the IDF curves. Initially, the proposed IDF curves are derived using an empirical equation (Kothyari and Garde), by using probability distribution for annual maximum rainfall and then IDF curves are derived by modifying the equation. IDF curves developed by the modified equation gives good results in the changing hydrologic conditions and are compatible even with the extreme rainfall of 26
^{th} July 2005 in Mumbai.

In many parts of the world, flooding is probably the most severe hazard among the natural hazards occurring due to change in rainfall pattern. Development of rainfall Intensity-Duration-Frequency (IDF) relationship is a primary basic input for the design of the storm water drainage system for cities [

While designing the new drainage system, proper information having IDF relationship reflecting recent hydrologic changes has to be used as design criteria [

The aim of the present study is to develop the IDF rainfall curves for the Mumbai city using longer length of observed rainfall data. Initially, the proposed IDF curves are modeled using the empirical relationship developed by Kothyari and Garde [^{th} July 2005 in the Mumbai region.

Mumbai (lat. 18.50˚N, long. 72.52˚E), (^{th} July 2005, Mumbai city experienced extreme rainfall event with highest rainfall intensity of 190.3 mm/hr and total rainfall of 944.2 mm in 24 hours period coinciding with highest tide level. There was severe loss of lives and huge economic losses [^{th} July 2005, Municipal Corporation of Greater Mumbai (MCGM) has installed total 60 automatic weather stations all over the city which records rainfall as well as other weather data at an interval of 15 minutes. Thus, considering the importance of the city and vulnerability to flooding, for proper designing of the drainage system, knowledge of proper rainfall intensity for different return periods is necessary.

Before 26^{th} July 2005 floods, there were only two rain gauge stations in Mumbai. The observed daily rainfall data for a period of 108 years (1901 to 2008) from Colaba rain gauge station, and 58 years (1951 to 2008) from the Santacruz rain gauge station were used [

and Garde [

The statistical analysis of daily as well as hourly rainfall data was carried out using Gumbel distribution [^{th} July 2005, IMD at Santacruz rain gauge station recorded 944 mm of total rainfall in 24 hours time (

The maximum intensity of rainfall recorded was 190.3 mm/hr during 14.30 to 15.30. The Colaba rain gauge station which is within 23 km apart recorded only 74 mm of total rainfall on the same day [^{th} July 2005.

In this study, annual maximum daily method [

・ Find out year wise annual maximum daily rainfall series.

・ Rank (m) the rainfall totals.

・ Find out return periods (T).

where N is the number of years data.

・ Plot the graph of rainfall depth v/s return period on semi log paper.

・ Find out the equation of regression line to find out precipitation depth.

where, P = maximum daily precipitation.

Find out rainfall intensity for different return periods and different durations by using formulas as described below.

Kothyari and Garde [

where,

In the above equation, the value of R (mean annual rainfall) is taken as constant as 24 hr rainfall and 2-year return period to find out the rainfall intensities for the shorter time durations with respect to different return periods (T). IDF curves with the above equation have been developed by analyzing the rainfall data of an annual daily maximum series [^{th} July 2005 rainfall. The IDF curves derived by using the Equation (3) as given by Kothyari and Garde [^{th} July 2005 (

Thus, IDF curves established by equation given by Kothyari and Garde are not compatible with the rainfall on 26th July 2005 in Mumbai with an intensity of about 190 mm/hr as well as today’s changing hydrological conditions and extremities of the rainfall event.

In this method, the rainfall frequency analysis of the maximum rainfall depth corresponding to hourly storm

Geographical region | Zone | Value of C |
---|---|---|

Northern India | 1 | 8.0 |

Central India | 2 | 7.7 |

Western India | 3 | 8.3 |

Eastern India | 4 | 9.1 |

Southern India | 5 | 7.1 |

durations (1969-2008) were determined for each year of data for both the rain gauge stations, and then the results were ranked in descending order with the highest intensity taking the value of one in the rank. Probability function was used to fit the data. Rainfall frequency analysis for different return periods was done by using the extreme value Gumbel Type I distribution [_{T} (in mm) for each duration having the specified return period T (year) is given by Equation (4) [

where,

For the Gumbel distribution, the value of K is given in the Equation (5) as below [

For the rain gauge stations, statistical analyses were carried out with mean and standard deviations and value of K of annual maximum depths having various durations were derived. The IDF relationships obtained by an annual maximum method for the Colaba rain gauge station is shown in

As per the derived IDF rainfall curves, rainfall intensity for the 100-year return period is 124.86 mm/hr for the Colaba rain gauge station and 160.11 mm/hr and 132.72 mm/hr respectively with and without considering 26^{th} July 2005 rainfall for the Santacruz rain gauge station.

In the present study, it was aimed to develop the IDF curves for the rainfall in the Mumbai city in changing hydrologic conditions. The IDF curves developed by using the Equation (3) as given by Kothyari and Garde [^{th} July 2005 (

In the changing climatic conditions, to avoid urban flooding and to take appropriate care, proper knowledge of rainfall intensity should be available for the proper and efficient design of the storm water drainage system. As discussed above, to obtain better results, the Equation (3) was modified and the new equation is obtained as:

In the above equation, the value of an R will vary with the return period (T) to derive the rainfall intensity for smaller durations. The IDF curves developed by using the above Equation (6), for the Colaba rain gauge station (^{th} July 2005 for the Santacruz rain gauge station are shown in

From the modeled IDF curves by the above new equation, it had been observed that for 100-year return period, the rainfall intensity at the Colaba is 164.56 mm/hr and at the Santacruz rain gauge station with considering and excluding the rainfall of 26^{th} July 2005 is 176.37 mm/hr and 160.35 mm/hr respectively, which shows the better results as compared with the past rainfall records for a Mumbai city. As per IDF curves modeled by the probability distribution for annual maximum rainfall, the rainfall intensity [^{th} July 2005 rainfall is 160.11 mm/hr and 132.72 mm/hr respectively. Thus, comparing the results obtained from the equation given by Kothyari and Garde, the

new modified equation and an annual maximum rainfall method, IDF curves established by using the new modified equation shows better results in the changing hydrologic conditions as observed on 26^{th} July 2005 in Mumbai. Also, from the rainfall analysis, it was observed that the intensities for all frequencies and durations of storms are generally lower for Colaba as compared to those at Santacruz.

Due to change in global mean temperature and hydrological changes, the higher frequency of rainfall may occur in the future as observed in the last few years in many parts of the world. Mumbai being the coastal city, surrounded by sea and creek, is vulnerable to flooding due to many reasons such as high intensity of rainfall, high tides, loss of drainage capacity due to design faults, development of reclaimed areas and improper knowledge and adoption of intensity of rainfall in designing the drainage system. For the design of appropriate drainage system, IDF curves are to be considered. The IDF relationships developed in the present study can be used effectively in designing the new drainage system and in modifying or replacing the old ones. As observed, the IDF curves derived by modifying the Kothyari and Garde’s equation shows good results in the changing hydrologic conditions as reported on 26^{th} July 2005 in Mumbai. Alternatively, the IDF relationship developed for Santacruz rain gauge station may be used for the entire city, since it is located centrally and also being expressing the higher intensities of rainfall, the design would be safer to avoid flooding in the future.

The authors are grateful to the Municipal Corporation of Greater Mumbai and also grateful to India Meteorological Department for providing the rainfall data of Santacruz and Colaba rain gauge stations, Mumbai, India for this study.

P. E. Zope,Eldho T. I.,V. Jothiprakash, (2016) Development of Rainfall Intensity Duration Frequency Curves for Mumbai City, India. Journal of Water Resource and Protection,08,756-765. doi: 10.4236/jwarp.2016.87061