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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi Zero : Jurnal Sains, Matematika, dan Terapan
Syukri Arif Rafhida
IPB University
Agriculture, Biological Sciences & Forestry Chemistry Mathematics Physics

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Evaluation of Best-Fit Probability Distribution Models for Monthly Rainfall in the Lake Toba Region Syukri Arif Rafhida; Sri Nurdiati; Retno Budiarti; Mohamad Khoirun Najib
ZERO: Jurnal Sains, Matematika dan Terapan Vol 9, No 2 (2025): Zero: Jurnal Sains Matematika dan Terapan
Publisher : UIN Sumatera Utara

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30829/zero.v9i2.25688

Abstract

Understanding rainfall's statistical distribution is crucial for effective water resource management, disaster mitigation, and climate adaptation in tropical regions. This study identifies the best-fit probability distributions for monthly rainfall in the Lake Toba region, Indonesia, based on long-term data from 34 rain gauge stations. Ten commonly used probability distributions were evaluated, with parameters estimated via Maximum Likelihood Estimation (MLE). The Kolmogorov-Smirnov (KS) test was applied to assess model goodness-of-fit at each station and month. Results indicate that the Generalized Extreme Value (GEV), Gamma, and Weibull distributions consistently provide the best fit for most stations and regencies, while Exponential and Inverse Gaussian distributions perform poorly. Spatial analysis reveals notable variation in best-fit models among regencies, emphasizing the influence of local topography and microclimate. These results highlight the need to select flexible probability models for hydrological planning and climate risk assessment in complex tropical regions. The findings provide valuable references for rainfall modeling and bias correction elsewhere.
Numerical Solution of 2D Advection-Diffusion for River Pollutant Transport using the Finite Element Method Muhamad Adzka Rizkia; Rahma Alya Zahrani; Zelisha Pitriatuz Zahra Fauzi; Foky Michelin; Najwaa Alifya Azka; Faiza Mayla Sabita; Mualim Arya Ilyas Wiradinata; Ferdy Aliansyah Hasyim; Mochamad Tito Julianto; Sri Nurdiati; Mohamad Khoirun Najib; Syukri Arif Rafhida
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 2 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i2.42814

Abstract

Pollutant dispersion in rivers is governed by advection, diffusion, and the physical characteristics of the channel. This paper models two-dimensional pollutant transport using the advection-diffusion equation and solves it numerically with the Finite Element Method (FEM) under five scenarios: constant flow with a single pollutant source, flow that follows a meandering channel, constant flow with two sources, the presence of a rock obstacle, and an irregular river domain. Simulations are implemented in Mathematica through domain construction, mesh generation, and a Finite Element-based numerical solution. The results show that flow velocity is the primary driver of plume movement, while diffusion smooths concentration gradients. Comparative analysis across the five scenarios demonstrates that obstacle-containing and irregular domains produce the widest plume spreading and the strongest concentration deformation compared to the straight-channel case. Peak concentrations also decrease more rapidly in multi-source and irregular-flow scenarios due to enhanced mixing and plume interaction. Physical obstacles and channel irregularities generate loacal recirculation zones and plume deviation, producing more realistic pollutant transport behavior than simplified channer models. These findings highlight the importance of geometry-aware flow representations for understanding river pollutant transport in numerical modelling studies.
Co-Authors Faiza Mayla Sabita Ferdy Aliansyah Hasyim Foky Michelin Mochamad Tito Julianto Mualim Arya Ilyas Wiradinata Muhamad Adzka Rizkia Najib, Mohamad Khoirun Najwaa Alifya Azka Rahma Alya Zahrani Retno Budiarti Sri Nurdiati Zelisha Pitriatuz Zahra Fauzi