Computing precipitations with a 1D vertical (radiative-convective) model using zero parameterizations.

The main philosophy in building a climate model is to represent the most possible number of phenomena, with the purpose of answering the most possible number of questions, with one unique perfect model. For this purpose, climate models have historically evolved from energy balance models, to radiative-convective models, to general circulation models, to the earth system model, with growing complexity. While this approach is relevant in some domains (e.g. climate services), more simple models could answer simple questions (e.g. calculate the mean temperature or precipitations for paleoclimates). Moreover, all climate models use parameterizations to represent the processes with unknown or not numerically solvable physical laws. Moreover, to make them accurate, all climate models tune their parameters. For example, in the atmosphere in the vertical direction, the energy flux often obeys a Fourier-like law with a "conductivity" coefficient tuned to fit observations. The approach we use is entirely different, and because of that, we need to rebuild everything from scratch. We want to construct a simple atmospheric model with no parameterizations (the ultimate goal could be to couple it to a vegetation or an ice model and run long simulations). We use the MEP hypothesis (maximum entropy production) to do so. This hypothesis has been used in realistic cases with parameterizations, or without parameterizations in more theoretical cases (like 2-box models). However, we aim to construct a full climate model with the MEP hypothesis. First, we restrict ourselves to a vertical tropical atmosphere: a radiative-convective model. Only stationary states are considered. Also, the relative humidity is fixed at 100%. A realistic radiative code is used, and convection is computed with the MEP hypothesis. The computed temperatures fit well with the observations. Also, precipitations can be computed and are coherent with observations. This means that almost only the knowledge of radiative transfer is needed to obtain a good order of magnitude of precipitations. In recent developments, the model has allowed deep convection, leading to slightly different precipitations. When relative humidity is allowed to vary; in the simple convection case, the MEP solution gives a 100% relative humidity almost everywhere; and the deep convection case gives a non-trivial relative humidity profile. Because MEP is only a hypothesis, we still need to find out if the MEP solution is the exact solution. However, it must represent some upper bound in the system because it corresponds to a maximum. It is already interesting to explore what this upper bound is.