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dabail10 merged 2 commits into from
Jul 14, 2025
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Minor comments and documentation cleanup for sealvl ponds #7

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37b60d3
edit comments in code, fix doc grammar, remove whitespace
eclare108213 Jul 14, 2025
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eclare108213 Jul 14, 2025
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6 changes: 3 additions & 3 deletions columnphysics/icepack_mechred.F90
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Original file line number Diff line number Diff line change
Expand Up @@ -167,7 +167,7 @@ subroutine ridge_ice (dt, ndtd, &
fpond , & ! fresh water flux to ponds (kg/m^2/s)
fresh , & ! fresh water flux to ocean (kg/m^2/s)
fhocn , & ! net heat flux to ocean (W/m^2)
rdpnd ! pond drainage due to ridging (m w.e. avg. over cell)
rdpnd ! pond drainage due to ridging (m avg. over cell)

real (kind=dbl_kind), dimension(:), intent(inout), optional :: &
dardg1ndt , & ! rate of fractional area loss by ridging ice (1/s)
Expand Down Expand Up @@ -605,11 +605,10 @@ subroutine ridge_ice (dt, ndtd, &
enddo
endif
endif
! diagnostic for all non-topo pond schemes, which are virtual
if (present(fpond)) then
fpond = fpond - mpond ! units change later
endif
! For water conservation, mpond = 0 for all non-topo pond schemes, which are currently virtual
! For now, rdpnd is purely diagnostic
if (present(rdpnd)) rdpnd = mpond

!-----------------------------------------------------------------
Expand Down Expand Up @@ -1396,6 +1395,7 @@ subroutine ridge_shift (dt, hin_max, &
enddo
endif

! diagnostic for all non-topo pond schemes, which are virtual
if (tr_pond_lvl) then
mpond = mpond + ardg1n * trcrn(nt_apnd,n) &
* trcrn(nt_hpnd,n) &
Expand Down
191 changes: 95 additions & 96 deletions doc/source/science_guide/sg_thermo.rst
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Original file line number Diff line number Diff line change
Expand Up @@ -88,11 +88,11 @@ because the infiltration of snow by pond water accomplishes the gradual radiativ
transition for which the patchy-snow parameters were originally intended. When level-ice ponds
are not used, then a typical value for hs0 is 0.03.

With level-ice ponds, the pond water is allowed to infiltrate snow over the level ice area,
With level-ice ponds, the pond water is allowed to infiltrate snow over the level-ice area,
invisible to the radiation scheme, until the water becomes deep enough to show through the
snow layer. The pond fraction is computed during this process and then used to
set the snow fraction such that :math:`f_{snow}+f_{pond}=1`. The ponds are only on the level ice
area, and so there is still snow on the ridges even if the entire level ice area becomes filled
set the snow fraction such that :math:`f_{snow}+f_{pond}=1`. The ponds are only on the level-ice
area, and so there is still snow on the ridges even if the entire level-ice area becomes filled
with ponds.

See :cite:`Hunke13` for a discussion of the impacts of varying hs1, whose default value is 0.03.
Expand Down Expand Up @@ -444,8 +444,7 @@ given by the parameter :math:`\delta_p` (``pndaspect``),
:math:`\Delta V = \Delta h_p \Delta a_{p} = \delta_p\Delta a_p^2 = \Delta h_{p}^2/\delta_p`.
Here, :math:`a_{p} = a_{pnd} a_{lvl}`, the mean pond area over the ice.

Given the ice velocity :math:`\bf u`, conservation equations for level
ice fraction :math:`a_{lvl}a_i`, pond area fraction
Given the ice velocity :math:`\bf u`, conservation equations for level-ice fraction :math:`a_{lvl}a_i`, pond area fraction
:math:`a_{pnd}a_{lvl}a_i`, pond volume :math:`h_{pnd}a_{pnd}a_{lvl}a_i`
and pond ice volume :math:`h_{ipnd}a_{pnd}a_{lvl}a_i` are

Expand All @@ -470,7 +469,7 @@ and pond ice volume :math:`h_{ipnd}a_{pnd}a_{lvl}a_i` are
conservation of melt pond volume and pond ice volume, but in this form
highlight that the quantities tracked in the code are the tracers
:math:`h_{pnd}` and :math:`h_{ipnd}`, pond depth and pond ice thickness.
Likewise, the level ice fraction :math:`a_{lvl}` is a tracer on ice area
Likewise, the level-ice fraction :math:`a_{lvl}` is a tracer on ice area
fraction (Equation :eq:`transport-lvl`), and pond fraction :math:`a_{pnd}` is
a tracer on level ice (Equation :eq:`transport-apnd-lvl`).

Expand Down Expand Up @@ -672,7 +671,7 @@ where :math:`d_p` is a scaling factor (dpscale), and
dynamic viscosity.

*Conservation elsewhere.* When ice ridges and when new ice forms in open
water, the level ice area changes and ponds must be handled
water, the level-ice area changes and ponds must be handled
appropriately. For example, when sea ice deforms, some of the level ice
is transformed into ridged ice. We assume that pond water (and ice) on
the portion of level ice that ridges is lost to the ocean. All of the
Expand Down Expand Up @@ -702,26 +701,26 @@ The sealvl meltpond parameterization was developed based on the
following observations from field studies and high-resolution (<=1 m)
satellite and airborne imagery:

* Stage I and II of melt pond formation (initial formation and
drainage to sea level, respectively) last approximately 2 weeks (
:cite:`Eicken04`, :cite:`Polashenski12`, :cite:`Landy14`).
* Stage I and II of melt pond formation (initial formation and
drainage to sea level, respectively) last approximately 2 weeks
(:cite:`Eicken04`, :cite:`Polashenski12`, :cite:`Landy14`).
Therefore melt ponds spend most of their lifespan in Stage III (i.e.,
pond-air interfaces are at or near sea level and pond-ice interfaces
are below sea level)
* On the scale of a CICE grid cell (> 1 km), melt ponds are
simultaneously observed on thicker and thinner ice; and thinner ice
are below sea level).
* On the scale of a CICE grid cell (> 1 km), melt ponds are
simultaneously observed on thicker and thinner ice; thinner ice
does not need to be saturated with ponds for there to be ponds on
thicker ice (e.g., :cite:`Webster15`, :cite:`Webster22`).
* For pack ice in the Arctic, Stage III melt pond fraction is rarely
observed to be below 15% or above 45% on the scale of a CICE grid cell.
observed to be below 15% or above 45% on the scale of a CICE grid cell
(e.g., :cite:`Fetterer98`, :cite:`Tschudi01`, :cite:`Webster15`,
:cite:`Wright20`). Note, some remote sensing retrievals show higher
pond fractions immediately before the ice melts out (e.g.,
:cite:`Webster15`), but it is possible that melted-through ponds (i.e.,
:cite:`Wright20`). Some remote sensing retrievals show higher
pond fractions immediately before the ice melts out (:cite:`Webster15`),
but it is possible that melted-through ponds (i.e.,
open water) are being misclassified as ponds.
* Ponds are routinely observed on deformed ice (e.g., :cite:`Eicken04`).
* When MYI and FYI co-occur, observations do not clearly indicate
consistent differences in pond fraction, although there may be
* When MYI and FYI coexist, observations do not clearly indicate
consistent differences in pond fraction, although there may be
differences in timing (e.g., :cite:`Webster15`, :cite:`Wright20`).
* Ponded ice albedos do not rapidly increase as pond depth decreases
below 20 cm (e.g., :cite:`Light22`).
Expand All @@ -735,63 +734,63 @@ and meltwater does not laterally advect between categories on its own
ice thickness changes). The hypsometric curve is assumed to be linear.
For each category, the slope and intercept of the hypsometric curve are
parameterized such that when pond surfaces are at sea level and the
category is snow-free, the pond area fraction is equal to the namelist
parameter ``apnd_sl`` (notated as :math:`a_{p,sl}` in :eq:`pndasp`).
Unless otherwise specified, the sealvl parameterization uses the same
parameterizations as the level-ice pond scheme (e.g., the same approach is
used to set the effective surface fractions for the Delta-Eddington
shortwave calculations).
category is snow-free, the pond area fraction is equal to the namelist
parameter ``apnd_sl`` (notated as :math:`a_{p,sl}` in :eq:`pndasp`).
Unless otherwise specified, the sealvl parameterization uses the same
parameterizations as the level-ice pond scheme. For example, the same
approach is used to set the effective surface fractions for the Delta-
Eddington shortwave calculations).

*Hypsometry and Pond Depth-Area Relationship.*
*Hypsometry and Pond Depth-Area Relationship.*

Because sea ice is floating, the intercept of the hypsometric curve is
determined by buoyancy. In this construction, the slope of the
hypsometric curve is equal to double the pond aspect ratio
(:math:`pndasp`), which is defined such that:
Because sea ice is floating, the intercept of the hypsometric curve is
determined by buoyancy. In this construction, the slope of the
hypsometric curve is equal to double the pond aspect ratio
(:math:`pndasp`), which is defined such that

.. math::
h_p = a_p * pndasp

where :math:`h_p` is the mean depth of the ponded area of the
where :math:`h_p` is the mean depth of the ponded area of the
category and :math:`a_p` is the pond area fraction of the category.
Pond meltwater volume is apportioned into depth and area according to
:math:`pndasp`, with the exception that if the pond area completely
fills the category :math:`h_p` may exceed :math:`a_p*pndasp`
(:math:`h_p` is still subject to a freeboard constraint, see below).
Unlike in the level parameterization, this use of :math:`pndasp` means
that when drainage reduces pond volume, both pond area and depth
decrease (in the level parameterization just depth decreases). In the
sealvl parameterization, pond aspect is calculated by:
Pond meltwater volume is apportioned into depth and area according to
:math:`pndasp`, with the exception that if the pond area completely
fills the category :math:`h_p` may exceed :math:`a_p*pndasp`
(:math:`h_p` is still subject to a freeboard constraint, see below).
Unlike in the level-ice parameterization, this use of :math:`pndasp` means
that when drainage reduces pond volume, both pond area and depth
decrease; in the level-ice parameterization just depth decreases. In the
sealvl parameterization, pond aspect is calculated by

.. math::
pndasp = h_{in}*(\rho_w - \rho_{si}) / (\rho_{fresh} * (a_{p,sl})^2 - 2 \rho_w * a_{p,sl} + \rho_w)
:label: pndasp

where :math:`h_{in}` is the ice thickness of the category.
:math:`\rho_w`, :math:`\rho_{si}`, and :math:`\rho_{fresh}` are the
densities of ocean water, sea ice, and pond water respectively. Note
that for simplicity we use a constant sea ice density instead of using
where :math:`h_{in}` is the ice thickness of the category.
:math:`\rho_w`, :math:`\rho_{si}`, and :math:`\rho_{fresh}` are the
densities of ocean water, sea ice, and pond water respectively. Note
that for simplicity we use a constant sea ice density instead of using
the mushy parameterization.

The weight of the snow is omitted from the calculation of :math:`pndasp`.
The impact of this omission is that pond area and depth will tend to be
slightly higher while the category still has snow on it (i.e., in Stage
I). Since pond fractions are typically highest in Stage I (e.g.,
:cite:`Eicken04`, :cite:`Polashenski12`), this was seen as a
I). Since pond fractions are typically highest in Stage I
(:cite:`Eicken04`, :cite:`Polashenski12`), this was seen as a
desirable feature, although future work should explicitly parameterize
how the hypsometry and drainage evolves at different stages of pond
evolution.

The parameterized hypsometric curve is also used to compute the height
of the pond surfaces above the mean ice draft (:math:`hpsurf`), which is
then used in the calculation of hydraulic head for the drainage
parameterizations (below). :math:`hpsurf` is calculated by:
parameterizations (below). :math:`hpsurf` is calculated by

.. math::
hpsurf = h_{in} - pndasp + 2 * pndasp * a_{p}
:label: hpsurf

Unlike in the level-ice pond scheme, ponds are not limited to the level ice
Unlike in the level-ice pond scheme, ponds are not limited to the level-ice
fraction. Currently the parameterization of the hypsometric curve does
not account for the impacts of deformed ice due to limited data. Future
research should target this limitation.
Expand All @@ -800,76 +799,76 @@ research should target this limitation.

There are five mechanisms by which water can be lost from melt ponds in
the sealvl parameterization: percolation through the ice (sub-cm scale
drainage), drainage through macro-flaws in the ice (super-cm scale), an
drainage), drainage through macroscopic flaws in the ice (super-cm scale), an
ice freeboard constraint, drainage during ice deformation, and pond lid
refreezing. Meltwater is also lost when the ice melts. Unlike in the
level or topo schemes, the sealvl scheme does not use the 'runoff'
(``rfrac``) parameterization. nstead of draining a portion of the total
meltwater before it reaches the ponds via rfrac as in the topo and
level-ice schemes, this water is handled by the macro-scale drainage
level-ice or topo schemes, the sealvl scheme does not use the 'runoff'
(``rfrac``) parameterization. Instead of draining a portion of the total
meltwater before it reaches the ponds via rfrac as in the topo and
level-ice schemes, this water is handled by the macro-scale drainage
in the sealvl scheme.

* *Percolation Drainage.* Percolation drainage implemented in the mushy
thermodynamics scheme. The harmonic mean of the permeability of the
ice column is estimated, as is the hydraulic head (the height of the
* *Percolation Drainage.* Percolation drainage is implemented in the mushy
thermodynamics scheme. The harmonic mean of the permeability of the
ice column is estimated, as is the hydraulic head (the height of the
pond-air interface above sea level, see above). Then the drainage rate
is estimated assuming a Darcy flow. Percolation drainage in the sealvl
scheme is identical to the level scheme except for the calculation of
scheme is identical to the level-ice scheme except for the calculation of
the hydraulic head.

* *Macro-Flaw Drainage.* Melt water is transported laterally and drains
through macro-flaws: cracks, floe edges, enlarged brine channels,
seal holes, etc... (:cite:`Eicken04`, :cite:`Polashenski12`). In the
real system, the efficiency of this process depends on the
connectivity of lateral flow networks and the frequency of
macro-flaws, both of which evolve with ice conditions. In the sealvl
scheme, macro-flaw drainage is parameterized as an exponential decay
of pond height relative to sea level (a.k.a., the hydraulic head). So
macro-flaw drainage cannot remove pond water that sits below sea
level. The level-ice pond scheme is identical except that the exponential
decay is applied to the entire pond height. The decay constant is
controlled by the ``tscale_pnd_drain`` namelist parameter. Currently,
this decay constant is uniform in time and space, but future work
should consider how changing ice conditions impact macro-flaw
* *Macro-Flaw Drainage.* Melt water is transported laterally and drains
through macroscopic flaws: cracks, floe edges, enlarged brine channels,
seal holes, etc. (:cite:`Eicken04`, :cite:`Polashenski12`). In the
real system, the efficiency of this process depends on the
connectivity of lateral flow networks and the frequency of
macroscopic flaws, both of which evolve with ice conditions. In the sealvl
scheme, macro-flaw drainage is parameterized as an exponential decay
of pond height relative to sea level (a.k.a., the hydraulic head), so
macro-flaw drainage cannot remove pond water that sits below sea
level. The level-ice pond scheme is identical except that the exponential
decay is applied to the entire pond height. The decay constant is
controlled by the ``tscale_pnd_drain`` namelist parameter. Currently,
this decay constant is uniform in time and space, but future work
should consider how changing ice conditions impact macro-flaw
drainage.

* *Ice Freeboard Constraint.* For free-floating ice, pond water cannot
depress the mean ice surface below sea level when there are efficient
water transport pathways (i.e., Stage III melt ponds). The buoyancy
force from the ice drives the redistribution of water from above the
ice to below. Below-sea level pond bottoms are sustained by the weight
of adjacent ice and snow above sea level. The sealvl scheme assumes
that each ice category is rigid and mechanically uncoupled from the
other categories. If necessary, pond water is drained such that the
mean ice surface of the category is at sea level. I.e., the mean
* *Ice Freeboard Constraint.* For free-floating ice, pond water cannot
depress the mean ice surface below sea level when there are efficient
water transport pathways (i.e., Stage III melt ponds). The buoyancy
force from the ice drives the redistribution of water from above the
ice to below. Below-sea-level pond bottoms are sustained by the weight
of adjacent ice and snow above sea level. The sealvl scheme assumes
that each ice category is rigid and mechanically uncoupled from the
other categories. If necessary, pond water is drained such that the
mean ice surface of the category is at sea level. I.e., the mean
category ice freeboard is constrained to be greater than or equal to
zero. The level-ice pond scheme has the same constraint, except in the
level-ice pond scheme the ponded area of the category is assumed to be
zero. The level-ice pond scheme has the same constraint, except in the
level-ice pond scheme the ponded area of the category is assumed to be
mechanically uncoupled from the surrounding ice.

* *Drainage During Ice Deformation.* In all of the pond schemes, it is
* *Drainage During Ice Deformation.* In all of the pond schemes, it is
assumed that all pond water drains from ice undergoing deformation.

* *Pond Lid Refreezing.* Pond lid refreezing and melting in the sealvl
scheme is handled in the same manner as in the level scheme (above).
The only difference is that in the sealvl scheme the impact of the
* *Pond Lid Refreezing.* Pond lid refreezing and melting in the sealvl
scheme is handled in the same manner as in the level-ice scheme (above).
The only difference is that in the sealvl scheme the impact of the
removed/added pond water are distributed according to hypsometry.

*Pond Depth and Optical Property Relationship.*

When the Delta-Eddington radiation transport scheme
(:cite:`Briegleb07`) was implemented, there were not observations of
albedo in ponds shallower than 20 cm. For ponds shallower than a
transition depth (``hp0``, default 0.2 m), it was assumed that the
inherent optical properties (IOPs) were represented by a mixture of
When the Delta-Eddington radiation transport scheme
(:cite:`Briegleb07`) was implemented, there were no observations of
albedo in ponds shallower than 20 cm. For ponds shallower than a
transition depth (``hp0``, default 0.2 m), it was assumed that the
inherent optical properties (IOPs) were represented by a mixture of
ponded ice IOPs and bare ice IOPs, in proportions determined by the pond
depth. Additionally, if ponds are shallower than a cutoff depth
depth. Additionally, if ponds are shallower than a cutoff depth
(``hpmin``, default 0.005 m) they are assumed to have no impact on the
optical properties (i.e., bare ice IOPs are used). Subsequent research
optical properties (bare ice IOPs are used). Subsequent research
(e.g., :cite:`Light22`) does not support the assumption of a gradual
transition to bare ice IOPs below 20 cm pond depth. The presence of a
transition to bare ice IOPs below 20 cm pond depth. The presence of a
pond of any measured depth was sufficient to change the apparent optical
properties. Consequently, the sealvl scheme disables the pond to bare
properties. Consequently, the sealvl scheme disables the pond to bare
ice transition depth assumption (i.e., ``hp0`` = ``hpmin`` = 0.005 m).

.. _sfc-forcing:
Expand All @@ -891,8 +890,8 @@ heat flux, :math:`F_{L\downarrow}` is the incoming longwave flux,
the incoming shortwave flux, :math:`\alpha` is the shortwave albedo, and
:math:`i_0` is the fraction of absorbed shortwave flux that penetrates
into the ice. The albedo may be altered by the presence of melt ponds.
Each of the explicit melt pond parameterizations (CESM, topo and
level-ice ponds) should be used in conjunction with the Delta-Eddington
Each of the explicit melt pond parameterizations (topo, level-ice and
sealvl ponds) should be used in conjunction with the Delta-Eddington
shortwave scheme, described below.

Shortwave radiation: Delta-Eddington
Expand Down
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