The physics-based NWP (Numerical Weather Prediction) methodology appears increasingly difficult to enhance the NWP model’s forecasting capabilities. This is caused largely by catastrophe/tipping phenomena in the atmosphere as well as the multiplicity of NWP equation solutions. Classical physics from Newtonian mechanics to Einstein’s general relativity is essentially the theory of various kinds of smooth behavior other than catastrophe phenomena (water suddenly boils, a cell doubles cancerously etc.) while catastrophe theory (CT) provides a methodology for mathematical treatment of continuous action producing a discontinuous result, and has broad application prospects in numerous subjects. Studies of catastrophe have never stopped but the closely related terminology (tipping) changed subtly, and thus similarities and differences between catastrophe and tipping as well as the rhetoric course of change and development with tipping points have been ascertained in this article with the result showing that CT itself never declines and it gets a new replacer only. Both problems of the NWP development bottleneck and the highly acclaimed AI-weather models enslaved to its knowledge quality could be basically attributed to the emergence of catastrophic/tipping points owing to the nonlinearity of model equations. In this Critical Review, via a comprehensive review and the relevant analyses, we are led to the conclusion that it would be sagacious to first determine which one is the “physical solution” and/or incorporate (e.g.) the second law of thermodynamics as an additional constraint into the NWP model so as to reduce the number of solutions.