Clarifications to documentation

doc/source/science_guide/sg_itd.rst

@@ -106,14 +106,17 @@ In this theory, individual floes are identified with a size :math:`r` and area :
 distribution :math:`f(r,h) dr dh` is the fraction of grid surface area 
 covered by ice with thickness between :math:`h` and :math:`h + dh` and lateral floe
 size between :math:`r` and :math:`r + dr`. The FSTD integrates over all floe sizes and
-ice thicknesses to unity; over all floe sizes to the ITD; and over all thicknesses to the FSD.
+ice thicknesses to unity (:math:`\int_r \int_h F(r,h) dr dh =1`); over all floe sizes to the ITD (:math:`\int_r  F(r,h) dr =g(h)`); and over all thicknesses to the FSD (:math:`\int_h F(r,h)dh = f(r)`).
 
-For implementation in CICE,  the continuous function :math:`f(r,h)` is replaced
+For implementation in CICE,  the continuous function :math:`f(r,h)dr dh` is replaced
 with a product of two discrete variables: :math:`a_{in}` as defined above and :math:`F_{in,k}`. 
 :math:`F_{in,k}` is the fraction of ice belonging to thickness category :math:`n` with lateral 
-floe size belonging to floe size class :math:`k`, giving
+floe size belonging to floe size class :math:`k` (denoted ``afsdn`` in the code).
+We then have
 :math:`\sum_{n=0}^{N_C}\sum_{k=0}^{N_f} a_{in} F_{in,k} = 1` and :math:`\sum_{k=0}^{N_f}  F_{in,k} = 1`.
-:math:`F_{in,k}` is carried as an area-weighted tracer.
+:math:`F_{in,k}` is carried as an area-weighted tracer. The FSD (continuous function :math:`f(r)dr`
+or discrete function :math:`f_{k}`, denoted ``afsd`` in the code) is recovered via 
+:math:`\sum_{n=1}^{N_C} a_{in} F_{in,k} = f_{k}`.
 
 The FSD may be ignored when considering processes that only modify ice thickness
 (eg. vertical thermodynamics), and the ITD can be ignored when considering processes that only modify floe sizes (eg. wave fracture). For processes that affect both the ITD and the FSD, (eg. lateral melt), 
@@ -138,7 +141,7 @@ in thickness and lateral size, at a rate :math:`\mathbf{G} = (G_r,G_h)`. The thi
 term represents growth of new ice: new floes are created at a rate :math:`\dot{A}_p` 
 in the smallest thickness category and a given lateral size category. If wave forcing 
 is provided, the size of newly formed floes is determined via a tensile stress limitation 
-arising from the wave field (:cite:`Shen01`,:cite:`Roach19`); otherwise, all floes 
+arising from the wave field (:cite:`Shen01`, :cite:`Roach19`); otherwise, all floes 
 are presumed to grow as pancakes in the smallest floe size category resolved. 
 To allow for the joining of individual floes to one another, we represent
 the welding together of floes in freezing conditions via the fourth term, 
@@ -174,13 +177,13 @@ currently supports ``nfsd = 1, 12, 16, 24``.  Although ``nfsd = 1`` tracks the s
 is assumed when ``tr_fsd=false``, the processes acting on the floes differ.
 It is assumed that the floe size lies at the midpoint of each floe size category.
 
-If simulations begin without ice (``ice_init='none'``), the FSD can emerge without initialization. This
-is the recommended initialization for studies on the FSD itself. If simulations begin with ice cover, 
+If simulations begin without ice (``ice_init='none'``), the FSD can emerge without initialization. 
+If simulations begin with ice cover, 
 some initial FSD must be prescribed in ``init_fsd``. The default (used for ``ice_init='default'``) 
 is a simple relationship determined from point observations by :cite:`Perovich14`, but its basin-wide 
 applicability has not been tested. In Icepack, ``ice_init='default'`` is selected for the slab
 and the full ITD cells.
 
-
+The history output includes FSD tendency terms for each of the floe-size-modifying processes. Note that the sum of these does not equal the change in the FSD, as the FSD is also modified by changes in the ITD. 
 
 

doc/source/user_guide/ug_case_settings.rst

@@ -373,7 +373,7 @@ forcing_nml
    "", "``true``", "include frazil water/salt fluxes in ocn fluxes", ""
    "``ustar_min``", "real", "minimum value of ocean friction velocity in m/s", "0.005"
    "``wave_spec_type``", "``constant``", "wave data file is provided, constant wave spectrum, for testing", "``none``"
-   "", "``none``", "no wave data provided, no wave-ice interactions", ""
+   "", "``none``", "no wave data provided, no wave-ice interactions (not recommended when using the FSD)", ""
    "", "``profile``", "no wave data file is provided, use fixed dummy wave spectrum, for testing", ""
    "", "``random``", "wave data file is provided, wave spectrum generated using random number", ""
    "``ycycle``", "integer", "number of years in forcing data cycle", "1"