Added science guide documentation for sealvlponds

doc/source/master_list.bib

@@ -252,6 +252,16 @@ @Article{Murray96
   pages = {251-273},
   url = {http://dx.doi.org/10.1006/jcph.1996.0136}
 }
+@Article{Fetterer98,
+  author="F. Fetterer and N. Untersteiner",
+  title="{Observations of melt ponds on Arctic sea ice}",
+  journal=JGRO,
+  year={1998},
+  volume={103},
+  number={C11},
+  pages={24821-24835},
+  url={https://doi.org/10.1029/98JC02034}
+}
 @Article{Lindsay98
   author = "R.W. Lindsay",
   title = "{Temporal variability of the energy balance of thick Arctic pack ice}",
@@ -334,6 +344,16 @@ @Article{Trodahl01
   pages = {1279-1282},
   url = {http://dx.doi.org/10.1029/2000GL012088}
 }
+@Article{Tschudi01,
+  author = "M.A. Tschudi and J.A. Curry and J.A. Maslanik",
+  title = "{Airborne observations of summertime surface features and their effect on surface albedo during FIRE/SHEBA}",
+  journal = JGRA,
+  year = {2001},
+  volume = {106},
+  number = {D14},
+  pages = {15335-15344},
+  url = {https://doi.org/10.1029/2000JD900275}
+}
 @Manual{Kauffman02
   author = "B.G. Kauffman and W.G. Large",
   title = "{The CCSM coupler, version 5.0.1}",
@@ -545,6 +565,15 @@ @Article{Lupkes12
   number = {D13},
   url = {http://dx.doi.org/10.1029/2012JD017630}
 }
+@Article{Polashenski12,
+  author="C. Polashenski and D. Perovich and Z. Courville",
+  title="{The mechanisms of sea ice melt pond formation and evolution}",
+  journal=JGRO,
+  year={2012},
+  volume={117},
+  number={C1},
+  url={https://doi.org/10.1029/2011JC007231}
+}
 @Article{Hunke13
   author = "E.C. Hunke and D.A. Hebert and O. Lecomte",
   title = "{Level-ice melt ponds in the Los Alamos Sea Ice Model, CICE}",
@@ -580,6 +609,16 @@ @Article{Jeffery14
   pages = {5891-5920},
   url = {http://dx.doi.org/10.1002/2013JC009634}
 }
+@Article{Landy14,
+  author="J. Landy and J. Ehn and M. Shields and D. Barber",
+  title="{Surface and melt pond evolution on landfast first-year sea ice in the Canadian Arctic Archipelago}",
+  journal=JGRO,
+  year={2014},
+  volume={119},
+  number={5},
+  pages={3054-3075},
+  url={https://doi.org/10.1002/2013JC009617}
+}
 @Article{Saha14
   author = "S. Saha and S. Moorthi and X. Wu and J. Wang and S. Nadiga and P. Tripp and D Behringer and Y. Hou and H. Chuang and M. Iredell and M. Ek and J. Meng and R. Yang and M.P. Mendez and H. van den Dool and Q. Zhang and W. Wang and M. Chen and E. Becker",
   title = "{The NCEP Climate Forecast System Version 2}",
@@ -619,6 +658,46 @@ @article{Roy15
 url = {https://doi.org/10.1002/2014JC010677},
 year = {2015}
 }
+@Article{Webster15,
+  author="M.A. Webster and I.G. Rigor and D.K. Perovich and J.A. Richter-Menge, and C.M. Polashenski and B. Light",
+  title="{Seasonal evolution of melt ponds on Arctic sea ice}",
+  year={2015},
+  journal=JGRO,
+  volume={120},
+  number={9},
+  pages={5968-5982},
+  url={https://doi.org/10.1002/2015JC011030}
+}
+@Article{Wright20,
+  author="N.C. Wright and C.M. Polashenski and S.T. McMichael and R.A. Beyer",
+  title="{Observations of sea ice melt from Operation IceBridge imagery}",
+  year={2020},
+  journal=TC,
+  volume={14},
+  number={10},
+  pages={3523-3536},
+  url={https://doi.org/10.5194/tc-14-3523-2020}
+}
+@Article{Light22,
+  author = "B. Light and M.M. Smith and D.K. Perovich and M.A. Webster and M.M. Holland and F. Linhardt and I.A. Raphael and D. Clemens-Sewall and A.R. Macfarlane and P. Anhaus and others",
+  title = "{Arctic sea ice albedo: Spectral composition, spatial heterogeneity, and temporal evolution observed during the MOSAiC drift}",
+  year = {2022},
+  journal = {Elem Sci Anth},
+  volume = {10},
+  number = {1},
+  pages = {000103},
+  url = {https://doi.org/10.1525/elementa.2021.000103}
+}
+@Article{Webster22,
+  author="M.A. Webster and M. Holland and N.C. Wright and S. Hendricks and N. Hutter and P. Itkin and B. Light and F. Linhardt and D.K. Perovich and I.A. Raphael and M.M. Smith and L.v. Albedyll and J. Zhang",
+  title="{Spatiotemporal evolution of melt ponds on Arctic sea ice: MOSAiC observations and model results}",
+  year={2022},
+  journal={Elem Sci Anth},
+  volume={10},
+  number={1},
+  pages={000072},
+  url={https://doi.org/10.1525/elementa.2021.000072}
+}
 @Article{Duarte17
   author = "P. Duarte and Coauthors",
   title = "{Sea ice thermohaline dynamics and biogeochemistry in the Arctic Ocean: Empirical and model results}",

doc/source/science_guide/sg_thermo.rst

@@ -116,7 +116,7 @@ be added to the melt pond liquid volume:
    \Delta V_{melt} = {r\over\rho_w} \left({\rho_{i}}\Delta h_{i} + {\rho_{s}}\Delta h_{s} + F_{rain}{\Delta t}\right) a_i,
    :label: meltvol
 
-where
+For the topo pond parameterization and the level pond parameterization
 
 .. math:: 
    r = r_{min} + \left(r_{max} - r_{min}\right) a_i
@@ -128,7 +128,10 @@ ponds, :math:`\rho_i` and :math:`\rho_s` are ice and snow densities,
 snow that melted, and :math:`F_{rain}` is the rainfall rate. Namelist
 parameters are set for the level-ice (``tr_pond_lvl``) parameterization;
 in the cesm and topo pond schemes the standard values of :math:`r_{max}`
-and :math:`r_{min}` are 0.7 and 0.15, respectively.
+and :math:`r_{min}` are 0.7 and 0.15, respectively. For the sealvl pond 
+parameterization, 100% of the melt water is added to the ponds 
+(:math:`r = 1.0`) and runoff is handled by the macro-flaw drainage 
+parameterization (see below).
 
 Radiatively, the surface of an ice category is divided into fractions of
 snow, pond and bare ice. In these melt pond schemes, the actual pond
@@ -692,6 +695,183 @@ same mean pond area in a grid cell after the addition of new ice,
 and solving for the new pond area tracer :math:`a_{pnd}^\prime` given
 the newly formed ice area :math:`\Delta a_i = \Delta a_{lvl}`.
 
+sealvl pond formulation (``tr_pond_sealvl`` = true)
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+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`).
+  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
+  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.
+  (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.,
+  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 
+  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`).
+
+The sealvl parameterization assumes that each ice thickness category
+within the grid cell has a subcategory distribution of ice surface
+height relative to sea level (a.k.a. a hypsometric curve). Meltwater
+is assumed to pool at the lowest ice surface height within the category
+and meltwater does not laterally advect between categories on its own
+(it is still handled as a tracer on ice area and hence advects with
+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 pond scheme (e.g., the same approach is 
+used to set the effective surface fractions for the Delta-Eddington 
+shortwave calculations).
+
+*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:
+
+.. math::
+   h_p = a_p * pndasp
+
+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: 
+
+.. 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 
+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
+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:
+
+.. math::
+   hpsurf = h_{in} - pndasp + 2 * pndasp * a_{p}
+   :label: hpsurf
+
+Unlike in the level 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.
+
+*Drainage and Pond Lid Refreezing.*
+
+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
+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. Physically, runoff is the same as drainage
+through flaws in the ice. So it is handled by the macro-scale drainage.
+
+* *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 
+  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 
+  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 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 
+  category ice freeboard is constrained to be greater than or equal to
+  zero. The level pond scheme has the same constraint, except in the 
+  level pond scheme the ponded area of the category is assumed to be 
+  mechanically uncoupled from the surrounding ice. So in the level pond
+  scheme, the freeboard constrains pond depth to be no greater than 10%
+  of the category ice thickness.
+
+* *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 
+  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 
+ponded ice IOPs and bare ice IOPs, in proportions determined by the pond
+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
+(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 
+pond of any measured depth was sufficient to change the apparent optical
+properties. Consequently, the sealvl scheme disables the pond to bare 
+ice transition depth assumption (i.e., ``hp0`` = ``hpmin`` = 0.005 m).
+
 .. _sfc-forcing:
 
 Thermodynamic surface forcing balance