Intercomparison of Log Normal and Weibull Distributions for Frequency Analysis

N. Vivekanandan*
Scientist-B, Central Water and Power Research Station, Pune, Maharashtra, India.
Periodicity:May - July'2017
DOI : https://doi.org/10.26634/jfet.12.4.13628

Abstract

Quantitative information on the low-flows regime of a stream is of utmost importance while making decisions on varied water resources management issues. The paper details a study on estimation of low-flows using 2-parameter Log- Normal (LN2) and Weibull (WB2) distributions for river Periyar at Neeleswaram site. The maximum likelihood method is used for determination of parameters of the distributions. Goodness-of-Fit (GoF) tests, viz., Chi-square and Kolmogorov- Smirnov are used for checking the adequacy of fitting of LN2 and WB2 distributions to the series of annual minimum d-day average flows for different durations of 'd', such as 7-, 10-, 14-, and 30-days. Model Performance Indicators, viz., correlation coefficient and root mean square error is used to evaluate the performance of the probability distributions adopted in frequency analysis of low-flows with a specific objective to identify the best suitable distribution amongst LN2 and WB2 studied for estimation of low-flows. The GoF test results and values of MPIs indicate the WB2 is better suited distribution for estimation of low-flows at Neeleswaram site. Low-flow frequency curves using LN2 and WB2 distributions are developed and presented in the paper.

Keywords

Chi-square Test, Correlation, Kolmogorov-Smirnov Test, Low-flow, Log-Normal, Mean Square Error, Weibull.

How to Cite this Article?

Vivekanadan,N. (2017). Intercomparison of Log Normal and Weibull Distributions for Frequency Analysis. i-manager’s Journal on Future Engineering and Technology, 12(4), 20-26. https://doi.org/10.26634/jfet.12.4.13628

References

[1]. Ahn, T. J., Lyu, H. J., Yo, W. S., & Park, J. E. (1998). Frequency analysis of low flows at gaged points of the Ansung stream. KSCE Journal of Civil Engineering, 2(1), 23-33.
[2]. Ang, H. S., & Tang, H. W., (1984). Probability Concepts in Engineering Planning and Design. M/s John Wiley and Sons Publications Limited, USA.
[3]. Arora K., & Singh, V. P., (1987). On statistical intercomparison of EV1 estimators by Monte Carlo simulation. Advances in Water Resources, 10(2), 87-107.
[5]. D'Agostino, R. B. & Stephens, M. A. (1986). Goodnessof- Fit Techniques. M/s Marcel Dekkar Inc., New York 10016, USA.
[6]. Durrans, S.R. (1996). Low-flow analysis with a conditional Weibull tail model. Water Resources Research, 32(6), 1749–1760.
[7]. Gotvald, A.J., (2017). Methods for estimating selected low-flow frequency statistics and mean annual flow for ungaged locations on streams in North Georgia. U.S. Geological Survey Scientific Investigations Report 2017– 5001.
[8]. Horn, S.D., (1977). Goodness-of-Fit tests for discrete data; A Review and an application to a health impairment scale. Biometrics, 33(1), 237-248.
[9]. Jain, S. K., Agarwal P. K., & Singh, V. P. (2007). Hydrology and Water Resources in India. Water Science & Technology Library, M/s Springer Link Publications, Netherlands, ISSN No. 0921-092X, Vol. 57.
[10]. Lee, K. S., & Kim, S. U. (2008). Identification of uncertainty in low-flow frequency analysis using Bayesian MCMC method. Journal of Hydrological Processes, 22(12), 1949–1964.
[11]. Nathan, R. J., & McMahon, T. A. (1990). Practical aspects of low-flow frequency analysis. Water Resources Research, 26(9), 2135-2141.
[12]. Önöz, B., & Bayazit, M. (2001). Power distribution for low streamflows. Journal of Hydrologic Engineering, 6(5), 429–435.
[13]. Randall, A. D., & Freehafer, D. A., (2017). Estimation of low-flow statistics at ungaged sites on streams in the Lower Hudson River Basin, New York, from data in geographic information systems. U.S. Geological Survey Scientific Investigations Report 2017–5019, 1-42.
[14]. Ries III, K. G., (2012). Estimation of low-flow duration discharges in Massachusetts. United States Geological Survey, Water-Supply Paper No. 2418.
[15]. Vogel, R. M., & Kroll, C. N. (1990). Generalised lowflow frequency relationships for ungauged sites in Massachusetts. Water Resources Bulletin, 26(2), 241-253.
[16]. Yue, S., & Wang, C.Y. (2004). Possible regional probability distribution type of Canadian annual stream flow by L-moments. Water Resources Management, 18(5), 425–438.
If you have access to this article please login to view the article or kindly login to purchase the article

Purchase Instant Access

Single Article

North Americas,UK,
Middle East,Europe
India Rest of world
USD EUR INR USD-ROW
Pdf 35 35 200 20
Online 35 35 200 15
Pdf & Online 35 35 400 25

Options for accessing this content:
  • If you would like institutional access to this content, please recommend the title to your librarian.
    Library Recommendation Form
  • If you already have i-manager's user account: Login above and proceed to purchase the article.
  • New Users: Please register, then proceed to purchase the article.