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Assessment of temporal changes in frequency characteristics of annual maximum rainfall of daily duration over Bangladesh

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Understanding the changes in the frequency characteristics of extreme rainfall can lead to building an appropriate frequency model which ultimately plays a pivotal role in assessing flood risk. However, little attention is invested into the temporal changes of frequency characteristics of extreme rainfall in a monsoon dominated region like Bangladesh. This study assesses the temporal change in extreme rainfall frequency behaviour using a number of methods in an innovative way based on annual maximum rainfall data of 1-day duration over Bangladesh. The probable teleconnection of extremes with large-scale climate indices is also examined. Results suggested that the extreme rainfall data can be aptly described by the generalised extreme value distribution. The trend analysis shows interesting results: over 60% of stations show significant trends in all the three parameters; amongst them, about 75% show significant negative trends of location parameter which lead to decrease in the mean of extremes, while about 62% show unbounded trends of shape parameter which direct the increase of quantiles at the high return period. The correlations with climate indices show that the El Niño-Southern Oscillation has more influence on rainfall extremes than Indian Ocean Dipole; however, the outcome is inconclusive. Overall, majority of the stations display significant variation of frequency behaviour over time and non-stationary frequency analysis could be an option in estimating the extremes.

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Data availability

The observed daily rainfall data were obtained from the Bangladesh Meteorological Department. The data that support the findings of this study are available on request from the corresponding author. The data are not publicly available due to privacy or ethical restrictions.

Code availability

The study primarily used FORTRAN subroutines developed by Hosking (1996) for the estimation of extreme value with L-moments. The R (R Core Team 2021) packages including “trend” and “ggplot2” are used for trend analysis and graphical plotting respectively.


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The authors thank three anonymous reviewers for their critical comments, which helped improve the quality of the manuscript.

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Conceptualization: Samiran Das; methodology: Samiran Das; data collection: Samiran Das, Abu Reza Md. Towfiqul Islam; formal analysis and investigation: Samiran Das; writing—original draft preparation: Samiran Das, Abu Reza Md. Towfiqul Islam; writing—review and editing: Samiran Das; funding acquisition: Samiran Das; supervision: Samiran Das.

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Correspondence to Samiran Das.

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The GEV with three parameters, location (ξ), scale (α) and shape (κ), has the following cumulative form (Hosking and Wallis 1997):

$$F(p)={e}^{-{e}^{-y}},y=\left\{\begin{array}{c}-{k}^{-1}\mathit{\log}\left\{1-\frac{k\left(p-\xi \right)}{\alpha}\right\},k\ne 0\\ {}\left(p-\xi \right)/\alpha, k=0\end{array}\right.$$

The shape parameter decides the tail behaviour: for κ = 0, the distribution reduces to Gumbel distribution (EV1); for κ < 0 , the distribution is upper unbounded whereas for κ > 0 the distribution is upper bounded.

The estimated quantiles in terms of return period have the following form:

$${P}_T=\left\{\begin{array}{c}\xi +\frac{\alpha \left\{1-{\left(-\mathit{\log}\left(1-1/T\right)\right)}^k\right\}}{k},k\ne 0\\ {}\xi -\alpha log\left(-\mathit{\log}\left(1-1/T\right)\right),k=0\end{array}\right.$$

The parameters estimated by L-moments with 1st L-moment (λ1), 2nd L-moment (λ2) and L-Skewness (τ3) have the following expressions:

$$k\approx 7.8590c+2.9554{c}^2,c=\frac{2}{3+{\tau}_3}-\frac{\mathit{\log}2}{\mathit{\log}3}$$
$$\alpha =\frac{\lambda_2k}{\left(1-{2}^{-k}\right)\Gamma \left(1+k\right)}$$
$$\xi ={\lambda}_1-\alpha \left\{1-\Gamma \left(1+k\right)\right\}/k$$

where Γ is the complete gamma function.

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Das, S., Islam, A.R.M.T. Assessment of temporal changes in frequency characteristics of annual maximum rainfall of daily duration over Bangladesh. Theor Appl Climatol 153, 323–334 (2023).

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