Year 2010, Volume 34 , Issue 3, Pages 171 - 188 2010-03-01

Flood frequency analysis using Mathematica
Flood frequency analysis using Mathematica

Mohammad Ali GHORBANI [1] , Heikki RUSKEEP\"{A}\"{A} [2]


This study analyzes flood frequencies using discharge data from 6 gaging stations in the Aji River basin in Iran. Eighteen different distributions are fitted to the maximum annual discharges from each of these stations, and parameters of these distributions are estimated using the method of maximum likelihood and the method of moments. Calculations are performed with Mathematica}, a computer algebra system developed by Wolfram Research. The advantage of using this software is that the symbolic, numerical, and graphical computations can be combined and all quantities can be accurately calculated; in particular, there is no need to resort to any approximate methods for the calculation of quantiles. There is a ready-to-use command for calculating quantiles from distributions that are built in Mathematica}, while for other distributions they can be easily and accurately calculated by inverting the cumulative distribution functions or by solving nonlinear equations where the inversion is not possible. The best distribution is selected based on the root mean square error (RMSE), the coefficient of determination (R2), and the probability plot correlation coefficient (PPCC). Relations between the distributions' parameters and the area, average discharge, and time of concentration are explored. The complete Mathematica} code and sample data files are included in http://users.utu.fi/ruskeepa/.
This study analyzes flood frequencies using discharge data from 6 gaging stations in the Aji River basin in Iran. Eighteen different distributions are fitted to the maximum annual discharges from each of these stations, and parameters of these distributions are estimated using the method of maximum likelihood and the method of moments. Calculations are performed with Mathematica}, a computer algebra system developed by Wolfram Research. The advantage of using this software is that the symbolic, numerical, and graphical computations can be combined and all quantities can be accurately calculated; in particular, there is no need to resort to any approximate methods for the calculation of quantiles. There is a ready-to-use command for calculating quantiles from distributions that are built in Mathematica}, while for other distributions they can be easily and accurately calculated by inverting the cumulative distribution functions or by solving nonlinear equations where the inversion is not possible. The best distribution is selected based on the root mean square error (RMSE), the coefficient of determination (R2), and the probability plot correlation coefficient (PPCC). Relations between the distributions' parameters and the area, average discharge, and time of concentration are explored. The complete Mathematica} code and sample data files are included in http://users.utu.fi/ruskeepa/.
Primary Language tr
Journal Section Articles
Authors

Author: Mohammad Ali GHORBANI

Author: Heikki RUSKEEP\"{A}\"{A}

Dates

Publication Date : March 1, 2010

Bibtex @ { tbtkengineering144966, journal = {Turkish Journal of Engineering and Environmental Sciences}, issn = {1300-0160}, eissn = {1303-6157}, address = {}, publisher = {TUBITAK}, year = {2010}, volume = {34}, pages = {171 - 188}, doi = {10.3906/kim-1202-34}, title = {Flood frequency analysis using Mathematica}, key = {cite}, author = {GHORBANI, Mohammad Ali and RUSKEEP\\"\{A\}\\"\{A\}, Heikki} }
APA GHORBANI, M , RUSKEEP\"{A}\"{A}, H . (2010). Flood frequency analysis using Mathematica. Turkish Journal of Engineering and Environmental Sciences , 34 (3) , 171-188 . Retrieved from https://dergipark.org.tr/en/pub/tbtkengineering/issue/12129/144966
MLA GHORBANI, M , RUSKEEP\"{A}\"{A}, H . "Flood frequency analysis using Mathematica". Turkish Journal of Engineering and Environmental Sciences 34 (2010 ): 171-188 <https://dergipark.org.tr/en/pub/tbtkengineering/issue/12129/144966>
Chicago GHORBANI, M , RUSKEEP\"{A}\"{A}, H . "Flood frequency analysis using Mathematica". Turkish Journal of Engineering and Environmental Sciences 34 (2010 ): 171-188
RIS TY - JOUR T1 - Flood frequency analysis using Mathematica AU - Mohammad Ali GHORBANI , Heikki RUSKEEP\"{A}\"{A} Y1 - 2010 PY - 2010 N1 - DO - T2 - Turkish Journal of Engineering and Environmental Sciences JF - Journal JO - JOR SP - 171 EP - 188 VL - 34 IS - 3 SN - 1300-0160-1303-6157 M3 - UR - Y2 - 2020 ER -
EndNote %0 Turkish Journal of Engineering and Environmental Sciences Flood frequency analysis using Mathematica %A Mohammad Ali GHORBANI , Heikki RUSKEEP\"{A}\"{A} %T Flood frequency analysis using Mathematica %D 2010 %J Turkish Journal of Engineering and Environmental Sciences %P 1300-0160-1303-6157 %V 34 %N 3 %R %U
ISNAD GHORBANI, Mohammad Ali , RUSKEEP\"{A}\"{A}, Heikki . "Flood frequency analysis using Mathematica". Turkish Journal of Engineering and Environmental Sciences 34 / 3 (March 2010): 171-188 .
AMA GHORBANI M , RUSKEEP\"{A}\"{A} H . Flood frequency analysis using Mathematica. Turkish Journal of Engineering and Environmental Sciences. 2010; 34(3): 171-188.
Vancouver GHORBANI M , RUSKEEP\"{A}\"{A} H . Flood frequency analysis using Mathematica. Turkish Journal of Engineering and Environmental Sciences. 2010; 34(3): 188-171.

Authors of the Article
Mohammad Ali GHORBANI [1]
Heikki RUSKEEP\"{A}\"{A} [2]