1DONE: Symbolic notation¶

The symbolic notation in this document is structured as $X^{descriptor}_{discretisation}$. Central to this symbolic notation is the symbol of the variable group ($X$ in the example above) which helps the reader to understand whether the symbol represents a flux, a mass, or a dimension, to mention a few of the common variable groups used in this document (Table 1). When appropriate, the symbol is complemented with a subscript that denotes the spatial and temporal discretisation. Where multiple subscripts are needed, they are separated by a comma to maintain readability. As c is a constant and there is no spatial and temporal discretisation, its name is in the subscript.

The majority of the calculations is performed within a single discrete time step $t$. When this is the case, the time dimension is omitted from the symbolic notation to enhance readability. Where variables from another time step than the current one are used (e.g., $t-1$ or $t+1$), this is indicated in the subscript of the symbolic notation.

Several processes have been discretised for different vertical atmospheric, canopy, and soil layers. Different layers are represented by the subscripts $i$, $k$, and $l$. The subscript $l$ strictly refers to the different circumference classes of forests. Note that subscripts $i$ and $k$ may represent different discretisation schemes between different sections in the document. When different spatial discretisations apply at the same time, the subscripts are separated by a comma.

The superscript contains an explanatory descriptor of the variable. Most often this descriptor is explicit and specifies the process underlying the flux, i.e., $F^{gpp}$, or the litter pool for which the biomass is given, i.e., $M^{structural}$. When the same calculations are applied to different biomass components such as plant organs or litter qualities, a general descriptor, $o$, is used in the symbolic notation, i.e., $M^{o}$. When several keywords are used for the explanatory descriptor, they are separated by a comma.

The numbering of the parameters is relative to each section: the parameters $c_1$, $c_2$,... from different sections have different meaning and values. Where the same parameters are used across sections, this is explicitly mentioned in the text.

The majority of the calculations in ORCHIDEE v4.2 are performed for each PFT present in a grid cell. Calculations thus have to be repeated for the different PFTs within a grid cell and for the different grid cells within the spatial domain of the simulation. Where the calculations follow this nesting approach, the PFT and grid cell dimensions are omitted from the symbolic notation to enhance readability.