This study presents a method for assessing drought events by integrating Standardized Precipitation Index (SPI) and Standardized Precipitation Evapotranspiration Index (SPEI) into the Power Law Process (PLP) model. The method begins with identifying drought events based on SPI and SPEI, followed by the Cramér-von Mises goodness-of-fit test to ensure the drought data meets PLP assumptions. Parameter estimation is performed using Maximum Likelihood Estimation (MLE) with a time-truncated approach, treating drought as a random process within a defined observation period. Model validation is conducted by comparing actual drought events with predictions from the cumulative PLP function, while event probabilities are determined using the Nonhomogeneous Poisson Process. Applied to 24 regencies/cities in South Sulawesi, the method showed that 14 regions fit the PLP based on SPI, and 13 regions based on SPEI. Predictions indicate that over the next 12 months, drought will occur for one month based on SPI and two months based on SPEI. This method contributes to the development of drought monitoring and early warning systems, supporting mitigation and adaptation strategies in South Sulawesi. The main contributions of this study include:•The development of a novel methodological framework by integrating SPI and SPEI into the PLP for drought analysis•Practical applications in drought early warning systems and drought risk management in South Sulawesi.

Rainfall is a natural process that is often characterized by significant variability and uncertainty. Stochastic models of rainfall typically involve the use of probability distributions to describe the likelihood of different outcomes occurring. This study aimed to model the annual maximum of daily rainfall in Makassar City, Indonesia for the period 1980–2022, specifically focusing on the rainy season (November to April) using probability distributions to estimate return periods. The study used the Generalized Extreme Value (GEVD) and Gumbel distributions. The Kolmogorov-Smirnov test was used to determine the suitability of each distribution, and the likelihood ratio test was employed to determine the best-fit model. The Mann-Kendall test was used to detect any trends in the data. The results indicated that the Gumbel distribution was the best-fit model for data in November, December, January, March, and April, while GEV was appropriate for February. No trends were observed in any of the months. The study then estimated the maximum rainfall for various return periods. January produced the highest maximum rainfall estimates for the 2, 3, and 5-year return periods, while February produced the highest maximum rainfall estimates for the 10 and 20-year return periods. Information about maximum rainfall can be valuable for the government and other stakeholders in developing flood prevention strategies and mitigating the effects of heavy rainfall, particularly during the peak months of the rainy season in Makassar City, which are December, January, and February.

The shift from manual weather measurements to automation is almost inevitable. When switching to AWS (Automatic Weather Station), WMO requires parallel data testing between automatic and manual measurements to be performed. The purpose of this paper is to conduct a parallel test of AWS data using a simple statistical test that has been applied to three main weather parameters, namely temperature, pressure, humidity, rainfall, and wind direction and speed. The months of January and June were used as samples to represent the character of the wet and dry seasons in the Makassar monsoon area. The results of the analysis show that during the rainy season, only pressure and temperature are identical and homogeneous. Meanwhile, in the dry season, apart from these two parameters, humidity and wind speed are also homogeneous and rainfall is a non-homogeneous parameter in January and June. Both AWS and manual observations show that the influence of land-sea winds in Makassar is very strong. Considering that there are inhomogeneous parameters, it is highly recommended to test for a longer time, taking into account the season, the influence of other global phenomena, the effect of missing data and incorrect data testing various methods of homogeneity and characteristics in each place and their effect on forecasts.

Improving the accuracy of rainfall forecasts is related to the number of rain gauges needed in an area, so determining the optimal number of rain gauges is very important. This study aimed to determine the best method for calculating the optimal number of rain gauges. Generally, the calculation of the optimal number of rain gauges using the coefficient of variation only takes into account the accumulation of rainfall at the station. The distance between the location and height of the rain gauge is not taken into account. The phenomenon of rain that occurs in the tropics is very dynamic, where one place compared to another tends to have different rain intensity and duration. In addition, the height and distance factors also greatly affect the measured rainfall. Therefore, it is very important to know the best method to calculate the optimal number of rain gauges needed in a particular area. This study implements 3 methods to determine the appropriate method to be used in determining the optimal rain gauge number for urban areas: namely, World Meteorological Organization (WMO) criteria, coefficient of variation, and Kagan-Rodda. In this study, rainfall data from 2010 to 2019 at 5 locations in Makassar were used in calculating the optimal number of rain gauges required. The results showed that the optimal number of rain gauges in Makassar as an urban area following the WMO recommendation was 9–18, where small islands around it are not considered. Another result obtained is that if the rainfall data for the Sudiang area, which is located at the coordinates (119.522° E, 5.085° S), is not included in the calculation, it will greatly reduce the accuracy in determining the optimal number of rain gauges in the Makassar area.

For a simple graph G with a vertex set V(G) and an edge set E(G), a labeling f : V(G)∪^​E(G)⟶{1,2, ⋯, k} is called a vertex irregular total k − labeling of G if for any two different vertices x and y in V(G) we have wt(x) ≠ wt(y) where wt(x) = f(x) + ∑_u∈V(G)f(xu). The smallest positive integer k such that G has a vertex irregular total k − labeling is called the total vertex irregularity strength of G, denoted by tvs(G). The lower bound of tvs(G) for any graph G have been found by Baca et. al. In this paper, we determined the exact value of the total vertex irregularity strength of the hexagonal cluster graph on n cluster for n ≥ 2. Moreover, we show that the total vertex irregularity strength of the hexagonal cluster graph on n cluster is (3n² + 1)/2.