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<p>The Earth’s surface plays a critical role in environmental regulation, supporting clean air and water and contributing to climate stability, which aligns with Sustainable Development Goals on Life on Land and Climate Action. This study develops a novel mathematically robust model named as Topp-Leone Exponentiated Exponential (TLEE) Distribution to examine Aerosol Optical Depth (AOD) patterns across Pakistan, focusing on statistical properties to capture spatial and temporal variability in AOD. Using monthly AOD data at 550&#xa0;nm from the Moderate Resolution Imaging Spectroradiometer. (MODIS) (MOD08_M3 v6.1) dataset spanning 2000 to 2022, the model is constructed as a mixture distribution with key properties, including survival functions, hazard and cumulative hazard functions, and quantile-based measures, providing a comprehensive analysis of AOD distribution. Estimation methods for parameters, likelihood maximization, and mixture component optimization enhance the model’s theoretical rigor, allowing for robust seasonal and regional characterizations of AOD. A comparison with alternative statistical families demonstrates the model’s superior fit, with log-likelihood = − 312.47, AIC = 628.94, and BIC = 636.52, while results show AOD fluctuations between 0.3 and 0.5 and a notable dip below 0.3 during the COVID-19 pandemic. The 22-year average AOD was 0.38 (SD = 0.07), safely below the hazardous international threshold of 0.6, though seasonal variability highlights the need for continued monitoring. This approach underscores the value of advanced statistical techniques, providing theoretically grounded insights into air quality trends and their environmental implications. The results indicate pronounced seasonal patterns in AOD levels, with statistically significant increases during specific months. It is therefore recommended that policy interventions be optimally timed to coincide with periods of peak AOD, informed by the model’s predictive capabilities, to maintain environmental stability and air quality in Pakistan.</p>

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Modeling aerosol optical depth variability using the Topp-Leone exponentiated exponential distribution: insights from MODIS data for climate and space science in Pakistan

  • 期刊论文

  • 发表日期：

    2025年10月13日

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  • Shan-E-Fatima,
  • Hina Khan,
  • Aamir Sanaullah,
  • Kanwal Javaid

摘要

The Earth’s surface plays a critical role in environmental regulation, supporting clean air and water and contributing to climate stability, which aligns with Sustainable Development Goals on Life on Land and Climate Action. This study develops a novel mathematically robust model named as Topp-Leone Exponentiated Exponential (TLEE) Distribution to examine Aerosol Optical Depth (AOD) patterns across Pakistan, focusing on statistical properties to capture spatial and temporal variability in AOD. Using monthly AOD data at 550 nm from the Moderate Resolution Imaging Spectroradiometer. (MODIS) (MOD08_M3 v6.1) dataset spanning 2000 to 2022, the model is constructed as a mixture distribution with key properties, including survival functions, hazard and cumulative hazard functions, and quantile-based measures, providing a comprehensive analysis of AOD distribution. Estimation methods for parameters, likelihood maximization, and mixture component optimization enhance the model’s theoretical rigor, allowing for robust seasonal and regional characterizations of AOD. A comparison with alternative statistical families demonstrates the model’s superior fit, with log-likelihood = − 312.47, AIC = 628.94, and BIC = 636.52, while results show AOD fluctuations between 0.3 and 0.5 and a notable dip below 0.3 during the COVID-19 pandemic. The 22-year average AOD was 0.38 (SD = 0.07), safely below the hazardous international threshold of 0.6, though seasonal variability highlights the need for continued monitoring. This approach underscores the value of advanced statistical techniques, providing theoretically grounded insights into air quality trends and their environmental implications. The results indicate pronounced seasonal patterns in AOD levels, with statistically significant increases during specific months. It is therefore recommended that policy interventions be optimally timed to coincide with periods of peak AOD, informed by the model’s predictive capabilities, to maintain environmental stability and air quality in Pakistan.