A Constraint-Convergent Framework for Tornado Formation (the ARCH Equation)

Tahir Rahman 

Despite significant advances in meteorological observation and modeling, the precise prediction of tornado occurrence remains a persistent challenge. Traditional forecasting approaches often rely on additive or probabilistic frameworks, assuming that the likelihood of a tornado increases as favorable parameters accumulate. However, many environments that appear highly conducive to tornadoes fail to produce them, while tornadoes occasionally form in marginal conditions. This paper proposes a conceptual shift: viewing tornado genesis as a constraint-convergent execution event, governed by the simultaneous satisfaction of multiple independent and necessary conditions. Drawing on analogies from systems biology, the ARCH equation is a conjunctive, multiplicative model in which tornado formation requires the co-occurrence of surface boundary presence, thermodynamic instability, contextual dynamics, upper-level forcing, and phase alignment. Case studies and integration with statistical, machine learning, and numerical modeling approaches demonstrate how this framework explains both false alarms and unexpected tornadoes. The constraint-convergent perspective also clarifies the limitations of existing composite indices and highlights the importance of identifying specific failure modes in tornado prediction. Beyond tornadoes, this logic applies to other threshold-governed atmospheric phenomena, suggesting a broadly applicable systems approach to meteorological transitions. The ARCH model offers new avenues for empirical research, interdisciplinary collaboration, and operational application, with the potential to improve warning systems, risk communication, and resilience in a changing climate.