3.7. Surface fractions

Because a single grid cell can be part land, part ocean and part sea ice, the mediator tracks the fraction of each surface type on every component grid. These fractions are the weights in essentially every merge and in the fractional normalization of many mappings, so getting them right is central to conservation (Core concepts). The machinery lives in med_fraction_mod.F90, and the fractions are stored per grid in the internal-state fraction bundles FBfrac(comp).

3.7.1. Key assumptions

The fraction bookkeeping rests on a few assumptions that are important to keep in mind:

The ocean and sea ice must share the same grid (and the same mask). Ice and ocean fractions are therefore computed together and mapped together.
The ocean grid has no partial land. Every ocean gridcell is either entirely ocean or entirely land — the ocean mask is binary (0 or 1) per cell, never a fractional value.
The land fraction is derived from the ocean mask. The fraction of land on the land grid is obtained by mapping the ocean mask onto the land grid (land is the complement of the mapped ocean fraction), rather than being prescribed independently.
The cross-grid maps have specific forms. The ocean-to-atmosphere and ice-to-atmosphere maps are masked maps, while the land-to-atmosphere map is a global map.

3.7.2. The fraction fields

The fractions for each component are held in an ESMF FieldBundle. These are the internal-state array FBfrac(:) — one bundle per component, allocated to ncomps in med_internalstate_mod.F90 (“fraction data for various components, on their grid”). They are initialized and subsequently updated in med_fraction_mod.F90. Each such fraction bundle can carry the following fields (not all on every grid):

lfrac — fraction of land on the grid
ofrac — fraction of ocean on the grid
ifrac — fraction of sea ice on the grid
ifrad / ofrad — the ice / ocean fractions as of the last radiation timestep

The set carried on each grid is fixed per component, for example:

atm : ifrac ofrac lfrac aofrac
ocn : ifrac ofrac ifrad ofrad
ice : ifrac ofrac
lnd : lfrac
glc : gfrac lfrac
rof : rfrac lfrac

On the atmosphere grid the surface fractions are self-consistent and sum to one:

\[f_{lfrac} + f_{ofrac} + f_{ifrac} \approx 1\]

3.7.3. How the fractions are set

3.7.3.1. Relative versus total fractions

Component fractions delivered at run time are relative fractions — the fraction of the active region a surface covers, not the fraction of the whole gridcell. For example, if a cell can be at most 50% ice and 50% land, an ice model reporting “half covered” sends an ice fraction of 0.5 (a relative value between 0 and 1). The mediator corrects these to total fractions so that, on every grid,

\[f_{ifrac} + f_{ofrac} + f_{lfrac} = 1\]

The fractions are seeded from a few fields the surface components provide (read from the diagonal FBImp bundles):

the ocean mask So_omask (FBImp(compocn,compocn))
the land-grid land fraction Sl_lfrin (FBImp(complnd,complnd)), itself a map of the ocean mask onto the land grid
the ice fraction Si_ifrac and ice mask Si_imask (FBImp(compice,compice))

In the sequences below, mapX2Y denotes a mapping from the X grid to the Y grid — for example mapo2a (ocean → atmosphere), mapl2a (land → atmosphere), mapa2l (atmosphere → land), mapi2o (ice → ocean), mapi2a (ice → atmosphere), mapl2r (land → river) and mapl2g (land → land-ice). These fraction and mask maps are all first-order conservative maps.

3.7.3.2. Initialization (`med_fraction_init`)

At initialization the ice fraction is taken to be zero everywhere; the ocean and land-grid fractions are taken from the components, mapped to the atmosphere, and the remaining fractions derived:

fractions_*(ifrac) = 0                            ! ice fraction initially zero
fractions_o(ofrac) = So_omask                     ! ocean mask from the ocean
fractions_l(lfrac) = Sl_lfrin                     ! land fraction (ocean-mask complement
                                                  !   on the land grid)

fractions_a(ofrac) = mapo2a(fractions_o(ofrac))   ! ocean fraction -> atmosphere grid
fractions_a(lfrac) = 1 - fractions_a(ofrac)       ! land is the complement
                                                  !   (truncated to 0 below 0.001)

fractions_r(lfrac) = mapl2r(fractions_l(lfrac))   ! land fraction -> river grid
fractions_g(lfrac) = mapl2g(fractions_l(lfrac))   ! land fraction -> land-ice grid

The land-fraction truncation (values below 0.001 set to zero) helps preserve non-land gridcells as fully non-land.

3.7.3.3. Run time (`med_fraction_set`)

Every coupling step the time-evolving fractions are recomputed from the current ice fraction — this is what the post_ice phase triggers when it “updates the surface fractions”:

fractions_i(ifrac) = Si_ifrac                     ! ice fraction from ice model
fractions_i(ofrac) = 1 - fractions_i(ifrac)       ! ocean = complement of ice
                                                  !   (relative -> total corrected)
fractions_o(ifrac) = mapi2o(fractions_i(ifrac))   ! -> ocean grid
fractions_o(ofrac) = mapi2o(fractions_i(ofrac))
fractions_a(ifrac) = mapi2a(fractions_i(ifrac))   ! -> atmosphere grid
fractions_a(ofrac) = mapi2a(fractions_i(ofrac))

Because the land fraction is static, only the ice and ocean fractions are updated at run time.

3.7.4. Where the fractions are used

The fractions feed the two operations of the previous pages:

Merges. A merge to the atmosphere is weighted by fractions_a (lfrac, ofrac, ifrac); a merge to the ocean is weighted by fractions_o (ofrac, ifrac) normalized to one.
Mapping normalization. Fraction-weighted mappings scale by a fraction before mapping and unscale by the mapped fraction after (Mapping) — for example mapo2a scales by fractions_o(ofrac) and divides by fractions_a(ofrac); mapi2a uses ifrac; mapl2a uses lfrac.