Quantitative research methods in physical geography, climate science, and meteorology: A synopsis approach

Quantitative methods underpin the measurement, explanation, and prediction of Earth system processes across physical geography, climate science, and meteorology. Although these fields share common analytical foundations, methods are often developed and applied within disciplinary silos, limiting methodological coherence and cross-disciplinary learning. This work presents a synoptic review of core quantitative approaches employed across the three disciplines, synthesizing spatial statistics and geostatistics, time-series and spectral analysis, trend detection, extreme-value modeling, process-based and statistical modeling, and emerging machine-learning techniques. Rather than providing an exhaustive literature inventory, the study adopts a comparative framework that organizes methods according to problem typologies, data structures, and evaluation criteria. The analysis highlights common inferential challenges, including non-stationarity, spatial and temporal dependence, scale mismatches, and uncertainty propagation, while illustrating how similar techniques are adapted for land-surface mapping, climate analysis, and weather forecasting. Particular attention is given to model verification and to distinguishing between aleatoric and epistemic uncertainty, emphasizing their implications for predictive reliability and decision-making. By explicitly addressing methodological convergence and divergence, the study offers a structured guide for enhancing reproducibility, rigor, and policy relevance in Earth system science.