@ -503,25 +503,25 @@ In \Sec{sec:exchange_grid_and_flux_calculator}, the term exchange grid was synon

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In the following we want to refer to this (in fact) \textit{special case} of an exchange grid, as the \textit{intersection grid}.

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The two alternative exchange grid cases that are apparent, can then be constructed from either the \textit{atmospheric model grid} or the \textit{ocean model grid}themselves.

The two alternative exchange grid cases that are apparent, can then be constructed from either the \textit{atmospheric model grid} or the \textit{ocean model grid}itself.

Since for a typical coupled model setup, the atmospheric grid has the lower resolution than the ocean model, the two resulting alternative exchange grids can differ quite substantially.

Since for a typical coupled model setup, the atmospheric grid has the lower resolution than the ocean model, the two resulting alternative exchange grids can differ quite substantially from each other as well as from the intersection grid.

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In any case both alternatives will have (by construction) a lower resolution than the intersection-type exchange grid, see again \Sec{sec:exchange_grid_and_flux_calculator}.

With these more general formulation for the exchange grid we are now able to consider three different kind of coupling approaches on equal footing.

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With this more general conception of an exchange grid we are now able to consider three different kind of coupling approaches on equal footing.

First, we employ the approach introduced in this manuscript and calculate fluxes by the flux calculator with state variables locally resolved on the intersection grid and subsequently communicate the fluxes to the models.

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Second and third, we employ one of the model grids as the exchange grid and calculate fluxes with spatially averaged fields and communicate then the fluxes to the involved models.

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These cases include also the ``standard'' coupling approach, i.e. using a conservative mapping of state variables from the ocean to the atmospheric model accompanied by the flux calculation via the latter and the communication back to the former~\open{\cite{citation-needed}}.

These two last cases include also the ``standard'' coupling approach, i.e. using a conservative mapping of state variables from the ocean to the atmospheric model accompanied by the flux calculation via the latter and the communication back to the former~\open{\cite{citation-needed}}.

Importantly, the flux calculator enables to investigate all three approaches with the very same infrastructure.

Importantly, the developed flux calculator methodology enables to investigate all three approaches with the very same infrastructure.

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The only differences are in the exchange grid and the resulting mapping matrices to and from the model grids.

The only differences lie in the exchange grid and the resulting mapping matrices to and from the model grids.

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The different mapping matrices are visualized in \Fig{fig:remappings}.

These different mappings are visualized in \Fig{fig:remappings}.

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\begin{figure*}

\centering

@ -561,7 +561,7 @@ The different mapping matrices are visualized in \Fig{fig:remappings}.

For further description see text.

}

\end{figure*}

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As it can be seen therein, the different mapping matrices for different exchange grids can be distinguished at which phase of the coupling spatial averaging is performed.

For instance in case of the intersection grid, \Fig{fig:remappings-intersection}, the weights are all equal to one when the model's state variables are mapped to the exchange grid, see white grid cell areas in the left panels therein and note the color bar and figure caption.