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Maximum Design Flow Estimates for Large Basins Using the Local Frequency Analysis (LFA) and the Most Probable Maximum Hydrograph (MPMH) Methods – a Critical Analysis

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Abstract

Statistical and deterministic methods have been severely criticized regarding their ability to calculate peak flows. The recently proposed method denominated as Most Probable Maximum Hydrograph (MPMH), applicable to large hydrographic basins, promises to overcome the difficulties faced in the most traditional methods (statistical and deterministic). The method not only uses the peak flow as in the statistical methods, and not requires detail information about the physical and meteorological characteristics of the hydrographic basin as in the deterministic method. The MPMH method takes information from observed hydrographs as base time, maximum flow and its respective volume. Using simple linear regression equations or simple exponential distribution adjusted to mean hydrograph volumes, the MPMH method is used to calculate design hydrograph, based on observed hydrographs volumes and the respective return periods. This paper assesses the applicability of the MPMH method by evaluating the influence of data characteristics as size of data series, removal of outliers and lowest values of the flow series on the peak flow estimates. In this paper it is shown that the MPMH method has great potential for estimation of design flows when compared to traditional methods. Besides that, it is shown that the difficulty in the use the MPMH method lies in deciding the base time (duration of the direct runoff hydrograph) of the standard hydrograph for the basin, which proved to be a decisive factor to estimate the peak flow and hydrograph volumes.

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Abbreviations

B:

Biased

EV1:

Gumbel Distribution or Extreme Values type – I

EXP:

Exponential Distribution

GAM:

Gamma Distribution

GEV:

Generalised Distribution of Extreme Values

GLOG:

Generalised Logistic Distribution

GPAR:

Generalised Pareto Distribution

HPP:

Hydroelectric Power Plant

k*:

Relation between peak and mean flow observed (dimensionless)

LFA:

Local Frequency Analysis

LN2:

2 parameter Log-Normal Distribution

LN3:

3 parameter Log-Normal Distribution

LOG:

Logistic Distribution

LPIII:

Log-Pearson type III Distribution

MD:

Maximum Percent Differences (%)

ML:

Maximum Likelihood Estimation

MM:

Moment Method

MPMH:

Most Probable Maximum Hydrograph

PIII:

Pearson type III Distribution

PM:

Probability Weighted Moments

Q10,000 :

Daily Maximum estimated flow for return period of 10,000 years [L3T−1]

QB :

Base flow hydrograph [L3T−1]

Qmax :

Maximum flow of naturalised or observed data series [L3T−1]

QP :

Daily peak flows of design considering the MPMH method [L3T−1]

QProject :

Design flow or design flood [L3T−1]

QTB :

Mean flow with TB duration [L3T−1]

s.e.d.:

Simple Exponential Distribution

s.l.r.:

Simple Linear Regression

SEM:

Standard Error of the Mean [L3T−1]

SSRH:

Subsecretaría de Recursos Hídricos de la Nación Argentina in Spanish

T:

Return period (years)

TB:

Base time of Design Hydrograph (days)

UB:

Unbiased

W:

Weibull Distribution

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Acknowledgments

The authors acknowledge the financial support of CNPq (the National Counsel of Technological and Scientific Development in Brazil) for the development of this study through scholarships granted to them. The authors would like to thank also Professor Fazal Hussain Chaudhry and anonymous reviewers for their helpful comments that permitted improvements to the manuscript.

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Authors and Affiliations

  1. Department of Hydraulics and Sanitary Engineering, University of São Paulo, Av. Trabalhador Saocarlense, 400, 13.566-590, São Carlos, São Paulo, Brazil

    Daysy Lira Oliveira Cavalcanti & Luisa Fernanda Ribeiro Reis

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  1. Daysy Lira Oliveira Cavalcanti
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  2. Luisa Fernanda Ribeiro Reis
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Correspondence to Daysy Lira Oliveira Cavalcanti.

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Dimensions used correspond to International System of Units (S.I.)

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Cavalcanti, D.L.O., Reis, L.F.R. Maximum Design Flow Estimates for Large Basins Using the Local Frequency Analysis (LFA) and the Most Probable Maximum Hydrograph (MPMH) Methods – a Critical Analysis. Water Resour Manage 31, 127–141 (2017). https://doi.org/10.1007/s11269-016-1514-4

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