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The Community Earth System Model (CESM) is described as a
fully-coupled, global climate model that provides state-of-the-art computer simulations of the Earth's past, present, and future climate states
I've come across "coupling" and "coupled model" many times but still have trouble with the term. What does "coupling" and "fully coupled" mean? Does refer to the physics or numerical aspects?
In Earth-system models, the term "coupling" is often used in two ways. The first is "offline" coupling, where output from one model is passed to another model for computation of some variable. The second is "online" coupling, where the feedbacks are allowed to pass between the two models. Online coupling is synonymous with "fully coupled".
A good example is when wildfires are modeled with coupled meteorology-chemistry models. Historically, the aerosol emissions from the fire would be modeled by a separate chemistry model that only used the meteorology model as an input (e.g. offline coupling). However, now you can fully couple (e.g. online coupling) the chemistry with the weather such that the heat and aerosol released from the fire perturbs the meteorological/radiation calculations in the next iterated time step.
Coupling refers to communication and interchange of information between models.
For example a typical standalone atmospheric model may be initialized with information about sea surface temperature. Depending on the model the ocean may be treated as a heat reservoir and may or may not affect any change to the SST. The ocean itself is not modeled. Similarly an ocean model may parameterize the atmosphere and only care about surface temperature and moisture fluxes (and perhaps momentum fluxes for waves) which may be static or prescribed values.
Contrast this to a coupled model where the atmosphere and ocean models exchange data with each other so that they can evolve as a whole. Rather than the atmosphere seeing a static SST, it sees the modeled SST from the ocean model. Because the ocean is modeled even more information than just SST is available to the atmosphere model.
CESM in particular is a family of models that all talk to each other to model earth, air and water as a whole system.
Coupling is used in the context of feedback between various processes. It can be weak or strong. E.g, if you heat a rod it expands mechanically due to thermoelastic effects (strong coupling) but when you mechanically compress it the temperature rise is insignificant (weak coupling). On the other hand for a poroelastic material the coupling is strong both ways.
In climate/weather codes the term is used at a rather higher level, i.e., coupling between atmospheric, land and oceanic processes. It does refers to physics but it also has numerical implications.
