Scientific logic and spatio-temporal dependence in analyzing extreme-precipitation frequency: negligible or neglected?

Abstract. Statistics is often misused in hydro-climatology, thus causing research to get stuck on unscientific concepts that hinder scientific advances. In particular, neglecting the scientific rationale of statistical inference results in logical and operational fallacies that prevent the discernment of facts, assumptions, and models, thus leading to systematic misinterpretations of the output of data analysis. This study discusses how epistemological principles are not just philosophical concepts but also have very practical effects. To this aim, we focus on the iterated underestimation and misinterpretation of the role of spatio-temporal dependence in statistical analysis of hydro-climatic processes by analyzing the occurrence process of extreme precipitation (P) derived from 100-year daily time series recorded at 1106 worldwide gauges of the Global Historical Climatology Network. The analysis contrasts a model-based approach that is compliant with the well-devised but often neglected logic of statistical inference and a widespread but theoretically problematic test-based approach relying on statistical hypothesis tests applied to unrepeatable hydro-climatic records. The model-based approach highlights the actual impact of spatio-temporal dependence and a finite sample size on statistical inference, resulting in over-dispersed marginal distributions and biased estimates of dependence properties, such as autocorrelation and power spectrum density. These issues also affect the outcome and interpretation of statistical tests for trend detection. Overall, the model-based approach results in a theoretically coherent modeling framework where stationary stochastic processes incorporating the empirical spatio-temporal correlation and its effects provide a faithful description of the occurrence process of extreme P at various spatio-temporal scales. On the other hand, the test-based approach leads to theoretically unsubstantiated results and interpretations, along with logically contradictory conclusions such as the simultaneous equi-dispersion and over-dispersion of extreme P. Therefore, accounting for the effect of dependence in the analysis of the frequency of extreme P has a huge impact that cannot be ignored, and, more importantly, any data analysis can be scientifically meaningful only if it considers the epistemological principles of statistical inference such as the asymmetry between confirmatory and disconfirmatory empiricism, the inverse-probability problem affecting statistical tests, and the difference between assumptions and models.