Gradient-Based Scaling for the Mellor–Yamada Model and the Master-Length Scale Conundrum

Abstract Consideration of a nondimensional form of the Mellor–Yamada Level-2 model within the gradient-based scaling framework leads to a closed equation set where all the relationships between scaled variables can be resolved without any additional closure hypothesis. In particular, this regards the master-length scale which can be found as a function of the Richardson number and the buoyancy height scale. While this fact has been noticed in our previous work, the next logical step is to extend it to the implementation in a single-column numerical model framework. Here, we present the full equation set of the Level-2 model cast in the gradient-based scaling, its analysis and the results of numerical simulation of stable boundary layer evolution with the Level-3 version, compared against literature data.