This work involves the revision of the Rainfall Intensity Duration Frequency (IDF) Curves for the city of Kumasi. Annual Maximum Rainfall depths of various durations over twenty-two years were obtained from the Ghana Meteorological Services. The data set was then subjected to frequency analysis to determine the distribution of which best characterize the data set. The annual maximum series were found to be drawn from the Gumbel distribution whose parameters were computed by fitting the statistics to the data. The Chi-square test and the Kolmogorov-Smirnov test prove the appropriateness of the fitting. Since the data available was only 22 years, IDF values for return periods higher than 22 years were obtained using frequency factors. The IDF estimates resulting from this work have been compared with the existing IDF curves prepared by J.B Danquah. The results show that for shorter durations (12 min and 24 min), the new IDF Curves give higher intensities for the same return period; the percentage increase ranges between 2% and 25%, whiles for longer durations (42min, 1 hr, 2hr, 3hr, 6hr, 12hr and 24 hr), the new IDF Curves give lower intensities for the same return period with the percentage decrease ranging between 3% and 49% when compared with the existing J.B Danquah IDF Curves. This might be as a result of low precipitation trends for shorter durations and high precipitation trends for longer durations in 1970s and before. These therefore call for the revision and updating of the existing IDF Curves for all the major cities and towns in Ghana to take into account the effect of climate change
Revision of the Rainfall Intensity Duration Frequency Curves for the City of ...theijes
This work involves the revision of the Rainfall Intensity Duration Frequency (IDF) Curves for the city of Kumasi. Annual Maximum Rainfall depths of various durations over twenty-two years were obtained from the Ghana Meteorological Services. The data set was then subjected to frequency analysis to determine the distribution of which best characterize the data set. The annual maximum series were found to be drawn from the Gumbel distribution whose parameters were computed by fitting the statistics to the data. The Chi-square test and the Kolmogorov-Smirnov test prove the appropriateness of the fitting. Since the data available was only 22 years, IDF values for return periods higher than 22 years were obtained using frequency factors. The IDF estimates resulting from this work have been compared with the existing IDF curves prepared by J.B Danquah. The results show that for shorter durations (12 min and 24 min), the new IDF Curves give higher intensities for the same return period; the percentage increase ranges between 2% and 25%, whiles for longer durations (42min, 1 hr, 2hr, 3hr, 6hr, 12hr and 24 hr), the new IDF Curves give lower intensities for the same return period with the percentage decrease ranging between 3% and 49% when compared with the existing J.B Danquah IDF Curves. This might be as a result of low precipitation trends for shorter durations and high precipitation trends for longer durations in 1970s and before. These therefore call for the revision and updating of the existing IDF Curves for all the major cities and towns in Ghana to take into account the effect of climate change
A rainfall-runoff model for Chew and Kinder Reservoirs, Peak District; utilising the Flood Studies Report to find whether the dams at Chew and Kinder could withstand a 1-in-10,000 year storm (UK recommended safety limit)
Grade: 91%
Runoff is one of the most significant hydrological variables used in most of the water resources applications. Physiographically the area is characterized by undulating topography with plains and valleys. The Soil Conservation Service Curve Numbers also known as hydrologic soil group method were used in this study. This method is adaptable and suitable approach for quick runoff estimation and is approximately easy to use with minimum data and it gives good result. From the study yearly rainfall and runoff were estimated easily. The study area covers an area of 466.02 km2, having maximum length of 36.5 km. The maximum and minimum elevation of the basin is 569 m and 341 m above MSL, respectively.
A study confined to the lower tapi basin in Gujarat, India to find out the primary causes for 2006 floods in Surat city. The study involves collection of topographical data from the local geological survey organization, rainfall data from meteorological department of india and the application of HEC-HMS software from US Army corps of engineers to identify the primary cause of the runoff.
Revision of the Rainfall Intensity Duration Frequency Curves for the City of ...theijes
This work involves the revision of the Rainfall Intensity Duration Frequency (IDF) Curves for the city of Kumasi. Annual Maximum Rainfall depths of various durations over twenty-two years were obtained from the Ghana Meteorological Services. The data set was then subjected to frequency analysis to determine the distribution of which best characterize the data set. The annual maximum series were found to be drawn from the Gumbel distribution whose parameters were computed by fitting the statistics to the data. The Chi-square test and the Kolmogorov-Smirnov test prove the appropriateness of the fitting. Since the data available was only 22 years, IDF values for return periods higher than 22 years were obtained using frequency factors. The IDF estimates resulting from this work have been compared with the existing IDF curves prepared by J.B Danquah. The results show that for shorter durations (12 min and 24 min), the new IDF Curves give higher intensities for the same return period; the percentage increase ranges between 2% and 25%, whiles for longer durations (42min, 1 hr, 2hr, 3hr, 6hr, 12hr and 24 hr), the new IDF Curves give lower intensities for the same return period with the percentage decrease ranging between 3% and 49% when compared with the existing J.B Danquah IDF Curves. This might be as a result of low precipitation trends for shorter durations and high precipitation trends for longer durations in 1970s and before. These therefore call for the revision and updating of the existing IDF Curves for all the major cities and towns in Ghana to take into account the effect of climate change
A rainfall-runoff model for Chew and Kinder Reservoirs, Peak District; utilising the Flood Studies Report to find whether the dams at Chew and Kinder could withstand a 1-in-10,000 year storm (UK recommended safety limit)
Grade: 91%
Runoff is one of the most significant hydrological variables used in most of the water resources applications. Physiographically the area is characterized by undulating topography with plains and valleys. The Soil Conservation Service Curve Numbers also known as hydrologic soil group method were used in this study. This method is adaptable and suitable approach for quick runoff estimation and is approximately easy to use with minimum data and it gives good result. From the study yearly rainfall and runoff were estimated easily. The study area covers an area of 466.02 km2, having maximum length of 36.5 km. The maximum and minimum elevation of the basin is 569 m and 341 m above MSL, respectively.
A study confined to the lower tapi basin in Gujarat, India to find out the primary causes for 2006 floods in Surat city. The study involves collection of topographical data from the local geological survey organization, rainfall data from meteorological department of india and the application of HEC-HMS software from US Army corps of engineers to identify the primary cause of the runoff.
Flood frequency analysis of river kosi, uttarakhand, india using statistical ...eSAT Journals
Abstract In the present study, flood frequency analysis has been applied for river Kosi in Uttarakhand. The river Kosi is an important tributary of Ganga river system, which arising from Koshimool near Kausani, Almora district flows on the western side of the study area and to meet at Ramganga River. The annual flood series analysis has been carried out to estimate the flood quantiles at different return period at Kosi barrage site of river Kosi. The statistical approach provided a significant advantage of estimation of flood at any sites in the homogenous region with very less or no data. In the at –site analysis of annual flood series the Normal, Log normal, Pearson type III, Log Pearson type III, Gumbel and Log Gumbel distribution were applied using method of moments . From the analysis of different goodness of fit tests, it has been found that the Log Gumbel distribution with method of moment as parameters estimation found to be the best-fit distribution for Kosi River and other sites in the region. It is recommended that the regional parameters for Kosi Basin may be used only for primary estimation of flood and should be reviewed when more regional data available. Keywords: Flood Frequency Analysis, River Kosi, Annual Peak Flood discharge, Return Period, Goodness of fit Test.
Intensity-Duration-Frequency Curves and RegionalisationAM Publications
Storm sewers make up a large percentage of drainage system in an urban setup. The design of these
components are based on rainfall intensities of a specific design period for that location. These can be derived from
intensity-duration-frequency (IDF) relationship. These IDF relationships are derived from historical rainfall, using
an extreme value distribution for maximum rainfall intensity. In the present study the IDF curves and parameter
regionalisation were studied for various kinds of basins. These equation parameters can be then used to understand
the spatial variation of rainfall intensity in the study area. The parameter contour maps subsequently generated using
various interpolation method are then used for plotting IDF curves for any ungauged station in the basin.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
Hydrological Application of Remote – Sensing and GIS for Handling of Excess R...IDES Editor
A GIS based hydrological analysis has been carried
out to explore the possibility of diverting storm runoff
generated from the upper catchment safely through a canal
system constructed at the foothill to avoid flooding at
downstream. The study area consisted of Kalapahar-Udyachal
hills (5.38 km sq) in the Kahilipara- Odalbakra area, situated
in the city of Guwahati, Assam. The Digital Elevation Model
(DEM) of the study area was developed from the Survey of
India(SOI) toposheet (1972) using Arcgis software. Watershed
delineation and derivation of required topographic parameters
for for calculating the peak discharge from different
watersheds were done with the help of the generated DEM.
Based on the hydrological analysis, means of safe diversion
of runoff water from hillocks was found out and canal
design of varying geometry capable of handling the peak
discharge suggested.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
A study on comparision of runoff estimated by Empirical formulae with Measure...Ahmed Ali S D
MAIN PUPOSE OF THIS PPT PRESENTATION IS TO SELECT SIUTABLE DISCHARGE FORMULA FOR A RIVER BASIN TO ESTIMATE RUNOFF ONLY BY USING PRECIPITATION DATA ONLY. IF WE KNOW RAINFALL DATA WE EASILY ESTIMATE FUTURE RUNOFF ALSO.
These slides - based on the webinar featuring David Monahan, research director for security and risk management at leading IT analyst firm Enterprise Management Associates (EMA), and David Cramer, vice president of product management for Data Center Automation and Cloud at BMC - cover how to set a strategy to protect your organization.
Attend this webinar to:
• Understand the risks of the misalignment between security and operations
• Learn what tools and technology are available to help bridge the gap between security and operations
• Build your game plan to help your organization bridge the gap
Flood frequency analysis of river kosi, uttarakhand, india using statistical ...eSAT Journals
Abstract In the present study, flood frequency analysis has been applied for river Kosi in Uttarakhand. The river Kosi is an important tributary of Ganga river system, which arising from Koshimool near Kausani, Almora district flows on the western side of the study area and to meet at Ramganga River. The annual flood series analysis has been carried out to estimate the flood quantiles at different return period at Kosi barrage site of river Kosi. The statistical approach provided a significant advantage of estimation of flood at any sites in the homogenous region with very less or no data. In the at –site analysis of annual flood series the Normal, Log normal, Pearson type III, Log Pearson type III, Gumbel and Log Gumbel distribution were applied using method of moments . From the analysis of different goodness of fit tests, it has been found that the Log Gumbel distribution with method of moment as parameters estimation found to be the best-fit distribution for Kosi River and other sites in the region. It is recommended that the regional parameters for Kosi Basin may be used only for primary estimation of flood and should be reviewed when more regional data available. Keywords: Flood Frequency Analysis, River Kosi, Annual Peak Flood discharge, Return Period, Goodness of fit Test.
Intensity-Duration-Frequency Curves and RegionalisationAM Publications
Storm sewers make up a large percentage of drainage system in an urban setup. The design of these
components are based on rainfall intensities of a specific design period for that location. These can be derived from
intensity-duration-frequency (IDF) relationship. These IDF relationships are derived from historical rainfall, using
an extreme value distribution for maximum rainfall intensity. In the present study the IDF curves and parameter
regionalisation were studied for various kinds of basins. These equation parameters can be then used to understand
the spatial variation of rainfall intensity in the study area. The parameter contour maps subsequently generated using
various interpolation method are then used for plotting IDF curves for any ungauged station in the basin.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
Hydrological Application of Remote – Sensing and GIS for Handling of Excess R...IDES Editor
A GIS based hydrological analysis has been carried
out to explore the possibility of diverting storm runoff
generated from the upper catchment safely through a canal
system constructed at the foothill to avoid flooding at
downstream. The study area consisted of Kalapahar-Udyachal
hills (5.38 km sq) in the Kahilipara- Odalbakra area, situated
in the city of Guwahati, Assam. The Digital Elevation Model
(DEM) of the study area was developed from the Survey of
India(SOI) toposheet (1972) using Arcgis software. Watershed
delineation and derivation of required topographic parameters
for for calculating the peak discharge from different
watersheds were done with the help of the generated DEM.
Based on the hydrological analysis, means of safe diversion
of runoff water from hillocks was found out and canal
design of varying geometry capable of handling the peak
discharge suggested.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
A study on comparision of runoff estimated by Empirical formulae with Measure...Ahmed Ali S D
MAIN PUPOSE OF THIS PPT PRESENTATION IS TO SELECT SIUTABLE DISCHARGE FORMULA FOR A RIVER BASIN TO ESTIMATE RUNOFF ONLY BY USING PRECIPITATION DATA ONLY. IF WE KNOW RAINFALL DATA WE EASILY ESTIMATE FUTURE RUNOFF ALSO.
These slides - based on the webinar featuring David Monahan, research director for security and risk management at leading IT analyst firm Enterprise Management Associates (EMA), and David Cramer, vice president of product management for Data Center Automation and Cloud at BMC - cover how to set a strategy to protect your organization.
Attend this webinar to:
• Understand the risks of the misalignment between security and operations
• Learn what tools and technology are available to help bridge the gap between security and operations
• Build your game plan to help your organization bridge the gap
In its research study, "Network Management Megatrends 2016: Hybrid Cloud, Network Analytics and the Internet of Things," leading IT analyst firm Enterprise Management Associates (EMA) surveyed 150 enterprise network management decision-makes on a wide range of topics that are affecting their daily operations. This research explores the Internet of Things, hybrid cloud networking and advanced network analytics. It also explores emerging requirements for network management tools and identifies best practices for network operations success.
T-Shaped People: Time to Get in Shape for Your Testing FutureTechWell
Today, agile testers are being asked to do a lot more than just testing. The notion of “T-shaped people,” who combine technical skills with collaborative capabilities, was created by Tim Brown in the 1990s to describe the new breed of worker. Mary Thorn believes that anyone—including testers—can contribute more to the business than their standard role traditionally dictates. The tester’s critical view and skeptical thinking can be used earlier in the development process. This role can stretch to include other aspects that intrigue them and keep them interested. Mary has testers who write product documentation, serve as ScrumMasters, build infrastructure to support rapid releases, take ownership for security and compliance to standards, present the development process to customers, visit customer sites to research how people are using the product, write social media content, devise internal communication strategies, do agile coaching, create personas, and use their natural skills and abilities where they are best suited to help move the business forward. Mary explores many ways testers can “Get into Shape” for future testing.
With the drive for continuous integration and delivery, the implications and approaches for designing more testable software are receiving substantial discussion and debate. What does testability really mean in practice? How do you take the idea of testability—how easy it is to test software—and put it into action through the different dimensions of designing and testing a real world product? Nir Szilagyi recognizes that the challenges of difficult-to-test software can transform a testing cycle from a small automation and exploratory effort to a long struggle of test preparation, execution, and debugging. He says testability starts with software design, goes through implementation, and encompasses building modular software, abstraction, simplicity, clear data interface, separation of business logic into self-sustained entities, and more. On the technical side of testability, Nir explores ways quality engineers and leaders can influence testability from early development through deployment. From his experiences he shares real-life testability examples which touch on the human process of building software including the relationship between testers and developers.
நல்ல போர்ச்சேவகன் என்னும் இத்தியானம் நாம் எவ்வாறு கிறிஸ்துவுக்கு நல்ல போர்ச்சேவகராய் இருந்து சத்துருவை எதிர்த்து போராட வேண்டும் என்பதை பற்றி தியானிக்கிறது. மேலும் அறிய www.jesussoldierindia.wordpress.com
The International Journal of Engineering and Science (The IJES)theijes
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
A Holistic Approach for Determining the Characteristic Flow on Kangsabati Cat...ijceronline
Kangsabati river rises from the Chotanagpur plateau in the state of West Bengal, India and passes through the districts of Purulia, Bankura and Paschim Medinipur in West Bengal before joining into river Rupnarayan. It is life of these three districts of West Bengal situated in the western part of the state. The river has ephemeral characteristics i.e. it has low flow in the year round and have a high peak on a certain time basis. In the Kangasabati catchment hydrological study gives an evident that during the period every two years there is a chance of drought condition and consecutively after that there is a high flow year. In our study period from 1991 to 2010 there are six low streamflow year i.e. in that year there is less rainfall than the average rainfall on that area. The year 1991, 2002 and 2009 are the drought prone year and above that in 2010 the severe drought condition was seen and this is the lowest rainfall year among the last 20 years and the rainfall on this year is only 766 mm which is in an about 38% less rainfall than the average rainfall of the catchment. And the highest flood peak in the last twenty year is noted on 19th Aug 2007 as 377107.8 Mm3
Fitting Probability Distribution Functions To Discharge Variability Of Kaduna...IJMER
International Journal of Modern Engineering Research (IJMER) is Peer reviewed, online Journal. It serves as an international archival forum of scholarly research related to engineering and science education.
International Journal of Computational Engineering Research(IJCER)ijceronline
International Journal of Computational Engineering Research(IJCER) is an intentional online Journal in English monthly publishing journal. This Journal publish original research work that contributes significantly to further the scientific knowledge in engineering and Technology.
Modelling of Short Duration Isopluvial Map For Raichur District Karnataka Moh...Mohammed Badiuddin Parvez
Everyoneacknowledges that it rains, runoff is generated for a design point of view we should know how much and how often it rains on our project location.Estimation of rainfall intensity is commonly required for the design of hydraulic and water resources engineering control structures. The present study aimed the Estimation of rainfall intensityin Raichur District using twenty five Rain gauge Station with 19 years of rainfall data (1998 to 2016). Log Normal Distribution, techniques are used to derived the rainfall intensity values of 2,5,10,15,30,60,120,720,1440 minutes of rainfall duration with different return period. The short duration IDF using daily rainfall data are presented, which is input for water resources projects. Isopluvial maps were developed for 25years, 50years, 75years and 100years return period
GENERATION OF IDF CURVES IN ARID AND SEMI-ARID AREAS: CASE STUDY HURGHADA, EGYPTIAEME Publication
Intensity-Duration-Frequency (IDF) curves are commonly used in water resources projects and hydrological analyses. One of the most important requirements for creating IDF curves is the actual distribution of rainfall intensity during the period of rainfall, but usually short-duration rainfall records are rare in arid regions while daily rainfall data are available. Hydrologists can generate short-duration rainfall data from daily rainfall data through using the Natural Resources Conservation Service (NRCS) standard synthetic rainfall distributions. The main purpose of this paper is to show the procedure to be followed in developing the IDF curves using the daily rainfall data recorded at the Hurghada weather station. Frequency analysis of the observed rainfall records was performed using HyfranPlus software. The gamma distribution is the most widely accepted probability distribution in this research.
Delineation of Mahanadi River Basin by Using GIS and ArcSWATinventionjournals
Precipitation is the significant segment of hydrologic cycle and this essential wellspring of overflow. In hydrological models precipitation as information, release is mimicked at the outlet of a watershed. Exactness of release re-enactment relies on drainage zone of the watershed. Therefore in the present work Mahanadi river basin lying within Odisha (drainage area approximately 65000 sq. km.) has been delineated in to five subbasins based on the five CWC operated discharge sites in Odisha. In the present work Arc-Swat has been used to delineate the watershed with the help of the (digital elevation model) DEM. At last as indicated by area of release locales, the aggregate study range was isolated into five sub-basins in particular Kesinga, Kantamal, Salebhata, Sundergarh and Tikarpada. It was observed that number of sub-watersheds into which the study area is being depicted relies on number of outlets and density of drainage. For a specific number of outlets, the thick is the density of drainage the more is the quantity of sub-watershed and the other way around.
Similar to Revision of the Rainfall Intensity Duration Frequency Curves for the City of Kumasi-Ghana Journal of Engineering and Science (20)
Harnessing WebAssembly for Real-time Stateless Streaming PipelinesChristina Lin
Traditionally, dealing with real-time data pipelines has involved significant overhead, even for straightforward tasks like data transformation or masking. However, in this talk, we’ll venture into the dynamic realm of WebAssembly (WASM) and discover how it can revolutionize the creation of stateless streaming pipelines within a Kafka (Redpanda) broker. These pipelines are adept at managing low-latency, high-data-volume scenarios.
Industrial Training at Shahjalal Fertilizer Company Limited (SFCL)MdTanvirMahtab2
This presentation is about the working procedure of Shahjalal Fertilizer Company Limited (SFCL). A Govt. owned Company of Bangladesh Chemical Industries Corporation under Ministry of Industries.
An Approach to Detecting Writing Styles Based on Clustering Techniquesambekarshweta25
An Approach to Detecting Writing Styles Based on Clustering Techniques
Authors:
-Devkinandan Jagtap
-Shweta Ambekar
-Harshit Singh
-Nakul Sharma (Assistant Professor)
Institution:
VIIT Pune, India
Abstract:
This paper proposes a system to differentiate between human-generated and AI-generated texts using stylometric analysis. The system analyzes text files and classifies writing styles by employing various clustering algorithms, such as k-means, k-means++, hierarchical, and DBSCAN. The effectiveness of these algorithms is measured using silhouette scores. The system successfully identifies distinct writing styles within documents, demonstrating its potential for plagiarism detection.
Introduction:
Stylometry, the study of linguistic and structural features in texts, is used for tasks like plagiarism detection, genre separation, and author verification. This paper leverages stylometric analysis to identify different writing styles and improve plagiarism detection methods.
Methodology:
The system includes data collection, preprocessing, feature extraction, dimensional reduction, machine learning models for clustering, and performance comparison using silhouette scores. Feature extraction focuses on lexical features, vocabulary richness, and readability scores. The study uses a small dataset of texts from various authors and employs algorithms like k-means, k-means++, hierarchical clustering, and DBSCAN for clustering.
Results:
Experiments show that the system effectively identifies writing styles, with silhouette scores indicating reasonable to strong clustering when k=2. As the number of clusters increases, the silhouette scores decrease, indicating a drop in accuracy. K-means and k-means++ perform similarly, while hierarchical clustering is less optimized.
Conclusion and Future Work:
The system works well for distinguishing writing styles with two clusters but becomes less accurate as the number of clusters increases. Future research could focus on adding more parameters and optimizing the methodology to improve accuracy with higher cluster values. This system can enhance existing plagiarism detection tools, especially in academic settings.
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Understanding Inductive Bias in Machine LearningSUTEJAS
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Using recycled concrete aggregates (RCA) for pavements is crucial to achieving sustainability. Implementing RCA for new pavement can minimize carbon footprint, conserve natural resources, reduce harmful emissions, and lower life cycle costs. Compared to natural aggregate (NA), RCA pavement has fewer comprehensive studies and sustainability assessments.
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Revision of the Rainfall Intensity Duration Frequency Curves for the City of Kumasi-Ghana Journal of Engineering and Science
1. The International Journal Of Engineering And Science (IJES)
|| Volume || 6 || Issue || 1 || Pages || PP 51-56|| 2017 ||
ISSN (e): 2319 – 1813 ISSN (p): 2319 – 1805
www.theijes.com The IJES Page 51
Revision of the Rainfall Intensity Duration Frequency Curves for
the City of Kumasi-Ghana Journal of
Engineering and Science
Sulemana Abubakari1*
, Kwabena Antwi Kusi2
, and Dong Xiaohua1
1*
College of Hydraulic and Environmental Engineering, China Three Gorges University, No. 8, Daxue Road,
Yichang, Hubei, China.
2
Sunyani Technical University, P.O.Box SN 206, Sunyani-Brong Ahafo Region, Ghana.
--------------------------------------------------------ABSTRACT-----------------------------------------------------------
This work involves the revision of the Rainfall Intensity Duration Frequency (IDF) Curves for the city of Kumasi.
Annual Maximum Rainfall depths of various durations over twenty-two years were obtained from the Ghana
Meteorological Services. The data set was then subjected to frequency analysis to determine the distribution of
which best characterize the data set. The annual maximum series were found to be drawn from the Gumbel
distribution whose parameters were computed by fitting the statistics to the data. The Chi-square test and the
Kolmogorov-Smirnov test prove the appropriateness of the fitting. Since the data available was only 22 years,
IDF values for return periods higher than 22 years were obtained using frequency factors. The IDF estimates
resulting from this work have been compared with the existing IDF curves prepared by J.B Danquah. The results
show that for shorter durations (12 min and 24 min), the new IDF Curves give higher intensities for the same
return period; the percentage increase ranges between 2% and 25%, whiles for longer durations (42min, 1 hr,
2hr, 3hr, 6hr, 12hr and 24 hr), the new IDF Curves give lower intensities for the same return period with the
percentage decrease ranging between 3% and 49% when compared with the existing J.B Danquah IDF Curves.
This might be as a result of low precipitation trends for shorter durations and high precipitation trends for longer
durations in 1970s and before. These therefore call for the revision and updating of the existing IDF Curves for
all the major cities and towns in Ghana to take into account the effect of climate change.
Keywords: IDF Curves, Gumbel Distribution, Annual Maximum Series, Climate Change, Rainfall Intensity
---------------------------------------------------------------------------------------------------------------------------------------
Date of Submission: 18 January 2017 Date of Accepted: 05 February 2017
--------------------------------------------------------------------------------------------------------------------------------------
I. INTRODUCTION
The design of any civil engineering infrastructure requires a comprehensive understanding of the intended
purpose of the structure and the physical environment in which it would operate. In the management of storm
water in a municipality, the dimensions of various components of the infrastructure system are based on the return
period of heavy rainfall events. This information is often expressed as Intensity-Duration-Frequency (IDF) curves
obtained from a statistical study of extreme events. The IDF curves are empirical relationships that relate the
rainfall intensity, the duration and the return period in a given catchment area.
The establishment of such relationships was done as early as 1932 by Chow [1] and Dupont and Allen [2]. Since
then, a lot of these curves have been developed in many parts of the world. Example Chen [3] developed a simple
method to obtain a generalised rainfall IDF formula for any location in the United States using three isopluvial
maps of the U.S Weather Bureau. Yu et al. [4] also developed regional IDF relations for non-recording sites based
on scaling theory using the hypothesis of piecewise simple scaling combined with the Gumbel distribution. In
Africa, Mohymont et al. [5] assessed IDF-curves for precipitation for three stations in Central Africa and proposed
more physically based models for the IDF-curves, Oyebande [6] established IDF curves for Nigeria, similarly,
Dankwa [7] developed IDF curves for various towns and cities in Ghana.
The normal balance of the earth’s hydrological cycle has been altered due to the changes in temperature and
precipitation patterns. Projections from climate models suggest that the probability of occurrence of intense
rainfall in future will increase due to the increase in green house gas emissions [8]. The design standards at present
are based on historical climate information. Under a changing climate, it has become a priority for municipalities
to search for appropriate procedures in the planning and management of water resources infrastructure to deal with
changing climatic conditions [9].
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Rainfall intensity is an important parameter for the determination of peak flow at a point in a catchment, which is
used for the design of drainage structures. The IDF curves developed by Dankwa [7] is what is used in Ghana for
the design of drainage structures in various cities. These IDF curves were developed based on the rainfall data
available at that time. One of the main assumptions in the creation of these curves was that the rainfall data was
stationary. That is, climatic trends and variability have negligible effects on the curves. But as has been proved in
recent history, climatic variability and trends do exist and their effects on precipitation have not been negligible.
Climate change has lead to droughts and floods around the world, and long term trends in rainfall, both increases
and decreases, have been seen in different parts of the world including Ghana. There is therefore a possibility that
the rainfall intensities used by Dankwa [7] for the development of the IDF curves might have changed. The IDF
curves developed by Dankwa [7] have not been revised or updated, however, drainage engineers in Ghana still
rely on these curves for their designs. This might lead to over-design or under-design due to the changes in
climatic conditions that might have occurred after 1974. Over-designing leads to economic losses as bigger
structures are designed whereas under-designing leads to drains of inadequate capacity leading to increased
incidents of flooding. In both cases economic losses are incurred.
To reduce economic losses due to over design or under design of drainage structures that might occur using IDF
curves developed by Dankwa [7], there is therefore the need for its revision. The main objective of this project
therefore is to develop IDF curves for Kumasi based on additional available rainfall information and verify the
validity of the existing IDF curves developed by Dankwa [7]. It is hoped that this research work will catapult
further research works into revision and updating of the existing IDF Curves for all the major cities and towns in
Ghana to take into account the effect of climate change.
II. MATERIALS AND METHODS
2.1 Study Area
Kumasi (Fig. 1) is a city in southern central Ghana's Ashanti region. Kumasi is the second largest city in Ghana
also the capital of the Ashanti region.
Figure1. Map of Kumasi
The climate is typically tropical, with total annual rainfall of about 1400 mm, the average maximum and minimum
temperatures are about 35ͦC and 23ͦC which occurs in February and August respectively [10]. The potential
evapotranspiration (PET) is estimated at 1450mm/y. The average humidity during the wet season is typically high
(86%) and falls to about 57% in the dry period [11]. The major rivers and streams in Kumasi include Subin,
Wewe, Susan, Aboabo, Oda, Owabi, Suntreso, Akrubu, Acheamponmene and Asuoyeboa.
3. Revision of the Rainfall Intensity Duration Frequency Curves for the City of Kumasi-Ghana Journal ..
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2.2 Data Collection
The data used in this study was obtained from the Ghana meteorological Services Department. The data consists
of annual maximum series (AMS) of rainfall depth over a period of twenty-two years for nine (9) laps of time:
12min, 24min, 42min, 1hour, 2hours, 3hours, 6hours, 12 hours, and 24 hours.
Table 1: Summary of Data Gathered
Duration(hrs) No. of years with some records
0.2 22
0.4 22
0.7 22
1.0 22
2.0 22
3.0 21
6.0 20
12.0 19
24.0 18
2.3 Development of IDF Curves
The data set was subjected to frequency analysis to determine the distribution of which best characterize the data
set. The frequency of the rainfall is usually defined with reference to the annual maximum series, which consists
of the largest values observed in each year. The annual maximum series were found to be drawn from the Gumbel
distribution whose parameters were computed by fitting the statistics to the data. The fitting involves calculating
the 1, 2, 5, 10, 20, 30 and 50 return intervals for each duration. Frequency precipitation T
P (in mm) for each
duration with a specified return period Tr (in year) is given by:
T ave
P P K S ....................................................................................................................................(1)
Where K is the Gumbel frequency given by:
6
0 .5 7 7 2 1 6
1
T
In In
T
..................................................................................................(2)
For Tr < 2 years, K is given by:
2 3
6 1 1 1
0 .5 7 7 2
2 2 4 8
In T
T T T
..................................................................(3)
In utilizing Gumbel’s distribution, the arithmetic average in Eq. (1) is used:
1
1
n
a ve i
i
P P
n
........................................................................................................................................(4)
Where i
P is the individual extreme value of rainfall and n is the number of events or years of rainfall records.
The standard deviation (S) in equation (1) is given by:
1
2
2
1
1
1
n
i ave
i
S P P
n
................................................................................................................(5)
The rainfall intensity, T
I (in mm/hr) for a particular return period, T is then obtained by:
T
T
d
P
I
t
..................................................................................................................................................(6)
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The IDF Curves were then developed by plotting the rainfall intensity values, T
I against corresponding durations,
d
t for the different return periods.
III. RESULTS AND DISCUSSION
3.1 IDF Curves for the City of Kumasi
From the raw data, the maximum precipitation i
P and the statistical variables (average and standard deviation) for
each duration, d
t (12 min, 24 min, 42 min, 60, 1 hr, 2 hr, 3 hr, 6 hr, 12 hr and 24 hr) were computed. Table 2 shows
the computed frequency precipitation ( T
P ) values and intensities ( T
I ) for different return periods
Table 2: Computed frequency precipitation and Intensity values for different durations and return periods for the
City of Kumasi.
Computed Precipitation (PT) and Intensity (IT) using Gumbel Method
Tr
(year)
Duration
12 min 24 min 42 min
Pave=26.719 S=7.786 Pave=39.629 S=12.025 Pave=44.709 S=11.248
K PT IT(mm/hr) K PT IT(mm/hr) K PT IT(mm/h
r)
1 -0.970 19.8 99.15 -0.970 28.0 69.9 -0.970 33.8 48.3
2 -0.164 25.4 127.2 -0.164 37.7 94.2 -0.164 42.9 61.2
5 0.719 32.3 161.6 0.719 48.3 120.7 0.719 52.8 75.4
10 1.305 36.9 184.4 1.305 55.3 138.3 1.305 59.4 84.8
20 1.866 41.3 206.3 1.866 62.1 155.2 1.866 65.7 93.9
30 2.189 43.8 218.8 2.189 66.0 164.9 2.189 69.3 99
50 2.592 46.9 234.5 2.592 70.8 177 2.592 73.9 105.5
1 hr 2 hr 3 hr
Pave=59.513 S=16.547 Pave=67.1
62
S=20.588 Pave=66.360 S=18.56
8
1 -0.970 43.5 43.5 -0.970 47.2 23.6 -0.970 48.4 16.2
2 -0.164 56.7 56.7 -0.164 63.8 31.9 -0.164 63.3 21.1
5 0.719 71.3 71.3 0.719 82 41 0.719 79.8 26.6
10 1.305 81 81 1.305 94 47 1.305 90.4 30.2
20 1.866 90.3 90.3 1.866 105.6 52.8 1.866 101.1 33.7
30 2.189 95.6 95.6 2.189 112.2 56.1 2.189 107.1 35.7
50 2.592 102.3 102.3 2.592 120.6 60.3 2.592 221.7 38.2
6 hr 12 hr 24 hr
Pave=66.562 S=16.789 Pave=66.5
78
S=21.053 Pave=59.554 S=19.39
3
1 -0.970 50.4 8.4 -0.970 45.6 3.8 -0.970 40.8 1.7
2 -0.164 63.6 10.6 -0.164 63.6 5.3 -0.164 55.2 2.3
5 0.719 78.6 13.1 0.719 81.6 6.8 0.719 74.4 3.1
10 1.305 88.2 14.7 1.305 93.6 7.8 1.305 84 3.5
20 1.866 97.8 16.3 1.866 105.6 8.8 1.866 96 4
30 2.189 103.2 17.2 2.189 112.8 9.4 2.189 103.2 4.3
50 2.592 109.8 18.3 2.592 121.2 10.1 2.592 110.4 4.6
5. Revision of the Rainfall Intensity Duration Frequency Curves for the City of Kumasi-Ghana Journal ..
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The IDF Curves for the city of Kumasi were then developed by plotting the rainfall intensity values, T
I against
corresponding durations, d
t for the different return periods. The IDF Curves for the city of Kumasi is presented in
figure 2.
Figure2: IDF curves for Kumasi
The IDF estimates resulting from this study (Figure 2 and Table 3) are in accordance with the general
properties of IDF curves. Thus for the same return period, high intensities are related to short durations and
secondly, the curves are parallel; they do not cross each other.
3.2 Comparison of New IDF estimates and Existing Dankwa [7] IDF estimates for Kumasi City
Comparing the IDF results in this study to the existing Dankwa [7] IDF estimates for Kumasi, there are
variations in the intensities. In order to picture the degree of variation, the new IDF estimates and the existing
Dankwa [7] IDF estimates and their incremental rate of change are presented in table 3 below.
Table 3: Comparison of New IDF estimates and Dankwa [7] IDF estimates for Kumasi City
5 Year 10 Year 25 Year 50 Year
ankwa New % incr. Dankwa New % incr. Dankwa New % incr. Dankwa New % incr.
12 min 137.2 161.6 +17.8 153.7 184.4 +20.0 176.5 213.2 +20.8 191.8 234.5 +22.3
24 min 118.1 120.7 +2.2 127.0 138.3 +8.9 154.9 160.5 +3.6 170.2 177.0 +4.0
42 min 93.7 75.4 -19.6 104.1 84.8 -18.5 122.9 96.7 -21.3 134.9 105.5 -21.8
1hr 77.2 71.3 -7.7 83.8 81.0 -3.3 101.9 93.3 -8.4 112.0 102.3 -8.7
2hrs 45.7 41.0 -10.3 53.3 47.0 -11.8 64.8 54.6 -15.7 73.7 60.3 -18.2
3hrs 33.0 26.6 -19.4 38.6 30.2 -21.8 45.2 34.8 -23.0 50.3 38.2 -24.1
6hrs 19.3 13.1 -32.1 22.9 14.7 -35.8 27.4 16.8 -38.7 30.7 18.3 -40.4
12hrs 10.4 6.8 -34.7 12.4 7.8 -37.1 15.2 9.1 -40.1 17.3 10.1 -41.6
24hrs 5.3 3.1 -41.8 6.4 3.5 -45.3 7.9 4.1 -48.1 8.9 4.6 -48.3
6. Revision of the Rainfall Intensity Duration Frequency Curves for the City of Kumasi-Ghana Journal ..
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The results obtained indicate that:
The New IDF estimates are higher for shorter durations. The percentage increase ranges between 2% and
25%.This might be as a result of low precipitation trends for shorter durations in 1970s.
New IDF estimates are lower for longer durations. The percentage decrease ranges between 3% and 49%.
This might be as a result of high precipitation trends for longer durations in 1970s.
IV. CONCLUSION AND RECOMMENDATION
This work involves the revision of the Rainfall Intensity Duration Frequency (IDF) Curves for the city of Kumasi.
Annual Maximum Rainfall depths of various durations over twenty-two years for Kumasi were subjected to
frequency analysis to determine the distribution of which best characterize the data set. The annual maximum
series were found to be drawn from the Gumbel distribution whose parameters were computed by fitting the
statistics to the data. The Chi-square test and the Kolmogorov-Smirnov test prove the appropriateness of the
fitting.
The IDF estimates resulting from this work have been compared with the existing IDF curves prepared by
Dankwa [7]. The results show that for shorter durations (12 min and 24 min), the new IDF Curves give higher
intensities for the same return period; the percentage increase ranges between 2% and 25%, whiles for longer
durations (42min, 1 hr, 2hr, 3hr, 6hr, 12hr and 24 hr), the new IDF Curves give lower intensities for the same
return period with the percentage decrease ranging between 3% and 49% when compared with the existing
Dankwa [7] IDF Curves. This might be as a result of low precipitation trends for shorter durations and high
precipitation trends for longer durations in 1970s and before.
These therefore call for the revision and updating of the existing Dankwa [7] IDF Curves for all the major cities
and towns in Ghana to take into account the effect of climate change.
REFERENCES
[1]. V.T. Chow, Handbook of Applied Hydrology (McGraw-Hill Book, 1988).
[2]. B.S. Dupont, and D.L. Allen, Revision of the Rainfall Intensity Duration Curves for the Commonwealth of Kentucky, Kentucky
Transportation Center, College of Engineering, University of Kentucky, USA, 2000.
[3]. C.L. Chen, Rainfall intensity-duration-frequency formulas, Journal of Hydraulic Engineering,109(12), 1983, 1603-1621.
[4]. P.S. Yu, T.C. Yang, and C.S. Lin, Regional rainfall intensity formulas based on scaling property of rainfall, Journal of Hydrology,
295(1), 2004, 108-123.
[5]. B. Mohymont, G.R. Demaree, and D.N. Faka, Establishment of IDF Curves for Precipitation in the Tropical Area of Central Africa-
Comparison of Techniques and Results, Natural Hazards and Earth System Science,4(3), 2004, 375-387.
[6]. L. Oyebande, Deriving rainfall intensity-duration-frequency relationships and estimates for regions with inadequate data,
Hydrological Sciences Journal, 27(3), 1982, 353-367.
[7]. J.B. Dankwa, Maximum Rainfall Intensity Duration Frequencies in Ghana, Ghana Meteorological Services Department, 1974.
[8]. A. Mailhot, S. Duchesne, D. Caya, and G. Talbot, Assessment of future change in intensity–duration– frequency (IDF) curves for
Southern Quebec using the Canadian Regional Climate Model (CRCM), Journal of hydrology, 347(1), 2007, 197-210.
[9]. P. Prodanovic, and S.P. Simonovic, Impacts of changing climatic conditions in the Upper Thames River Basin, Canadian Water
Resources Journal, 32(4), 2007, 265-284.
[10]. World Weather Information Service–Kumasi, World Meteorological Organization, Retrieved 14 June 2015.
[11]. WARM, Ghana’s Water Resources, Management Challenges and Opportunities, Water Resources Management Study, Government
of Ghana, Accra. 1998.