Outlier detection in a few catchments of the Godavari river basin: A case study

The efficiency of the Grubbs-Beck test and the multiple Grubbs-Beck tests to detect discordant observations are compared in this research using a few catchment areas of the Godavari river basin in Maharashtra, India. The Multiple Grubbs-Beck tests are proven to be more effective than the original Grubbs-Beck tests when applied to the Weibull distribution. When using the Grubbs test, only one lower discordant observation was identified in all of the river stations, and no lower discordant observation was found in the Somanpally river station when using the Multiple Grubbs Beck test (MGBT) five survey catchments.

Illustrations explain the paper; charts are replotted from the paper's own table values.

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No of discordant observation for Grubbs test and No of discordant observation for MGB Test: Bhadrachalam vs Tumnar vs Sirpur vs Sabari vs SomanpallyClose ×

Replotted from Table 1 (page 3) of the original paper. Every bar is the paper's own table value.

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Introduction

Flood frequency analysis is a method for estimating the design flood necessary for bridges, culverts, flood embankments, and other water infrastructure, as well as for flood management and flood insurance research. Flood estimating attempts to extract as much information as can from the supplied data, while also remaining robust to the distribution model and achieving a low discordant. Furthermore, very low values can result in inaccurate estimates of huge inundation quantiles. In comparison to current levels of stream gauges with longer annual peak flow records, Griffs and Stedinger (2008) [18] discovered that flood size and frequency predictions utilizing river monitoring stations with short yearly peak flow data records have a greater standard error or uncertainty. Probability distributions are frequently chosen in flood frequency analysis based on statistical tests or graphical methods, which play a useful role in the selection of correct distributions. Cohn et al, (2013) [17] , 𝑝(𝑘; 𝑛) function accurately explains whether the 𝑘 𝑡ℎ smallest observation in a normal sample of n variates is rare. Because inward sweep tests are more sensitive to masking, an outward sweep is preferable to avoid the problem. A flood record may contain more than one low discordant, causing the original GB test statistic to fail to distinguish the smallest observation as a discordant, causing the original GB test statistic to fail to distinguish the smallest observation as a discordant. ROSNER employs a two-sided outward sweep. The MBG test is also based on a one-sided critical value of 10% significance of a normally distributed sample, but it's designed to look at ordered sets of data, which aren't included in the other tests. The detection of lower discordant in flood data is an important stage in flood frequency analysis. Lower discordant is a very tiny observation of flood data that deviates dramatically from the patterns of the rest of the data. Lower discordant identification and treatment is a critical topic in flood frequency analysis, as such observations might have a major impact. Discordant observation is an extra variable that disturbs the whole observation in flood data series. This arises due to different causes, when the observation is different from the selected samples, measurement error or missing of observation, mostly observation is from the different population of most of the data. The Weibull probability distribution with three parameters was used in this investigation for single or multiple discordant detection approaches. The continuous distribution is one of the three parameters of the Weibull distribution, which is mostly employed in extreme field events such as flood data, survival analysis, and so on. The sample features of quantile estimates based on the maximum likelihood (ML), Method of Moments (MOM), and probability-weighted moments (PWM) approaches were used to compute the Weibull distribution used in the regional flood frequency study (2001) [21] . The researchers conducted an empirical performance evaluation of discordant identification techniques for Weibull or extremevalue distributions (2007). The Grubb statistic G' scored well in tests for lower discordant. For the labelled slippage, Mann's W was much poorer than the others [22] . The purpose of this research is to use the Grubb's test and the multiple Grubb's-beck tests with the Weibull distribution to detect discordant observations in the five rivers stations.

Methodology

Methodology

Weibull distribution

The three parameters Weibull distribution is mainly used for this analysis. The Weibull distribution was first distinguished by (Frechet Maurice 1927) [20] . This distribution is a continuous probability distribution named given by Swedish mathematician Waloddi Weibull. It can work efficiently, even with small sample sizes, and can be used precisely in frequency analysis and obtaining parameter estimates. Let 𝑋 1 , … , 𝑋 𝑛 be independent random variables from a Weibull distribution with location, scale and shape parameters as 𝜇, 𝜎, 𝑎𝑛𝑑 𝛾 respectively.

For case I: When the observations are smaller than the location parameter 𝜇, 𝑒. ∀, 𝑥 𝑖 < 𝜇; 𝑖 = 1, … , 𝑛, then pdf is given by Probability density function (pdf)

Where, μ is the location parameter, σ is the scale parameter that decides the appearance or shape of the distribution and γ is the shape parameter.

Proposed test statistic

The original Grubbs-Beck tests uses the field logarithms of the peak flow data, to calculate a critical value at a significance level of 10% on one side of a normally distributed sample. Multiple peak flows recorded by the flow meter can be smaller than the critical Grubbs

Conclusion

This paper estimates the discordant observation for the five river stations of the Godavari basin. To find out a single discordant and multiple discordant, two methods Grubbs test and Multiple Grubbs beck test was used for comparison and its quantile value ware also observed with the help of simulation technique. For all the river stations single lower outlying observation is found with the help of the Grubbs test while using the method of Multiple Grubbs Beck test (MGBT). It also concluded that the when the variation between the flood discharge is low then the Grubbs test and Multiple Grubbs Beck test not found any discordant observation.

Figures and tables from the paper

S. No	River Station	No of discordant observation for Grubbs test	No of discordant observation for MGB Test
1	Bhadrachalam	1	0
2	Tumnar	1	8
3	Sirpur	1	12
4	Sabari	1	15
5	Somanpally	1	12

Table text extracted from the original PDF; superscript letters are shown inline. The original table image is below.

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Table 1Close ×

Comparison of single Grubbs test and multiple Grubbs Beck test in five rivers station of Godavari Basin

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Original paper tableSource PDF · page 3 ↗

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Table 2Close ×

Estimated Quantile value by Weibull Distribution of five river station for Godavari Basin using Grubbs test and Multiple Grubbs Beck

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Original paper figureSource PDF · page 3 ↗

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