diff --git a/columnphysics/icepack_mechred.F90 b/columnphysics/icepack_mechred.F90 index ebe923bf..7878f946 100644 --- a/columnphysics/icepack_mechred.F90 +++ b/columnphysics/icepack_mechred.F90 @@ -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) @@ -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 !----------------------------------------------------------------- @@ -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) & diff --git a/doc/source/science_guide/sg_thermo.rst b/doc/source/science_guide/sg_thermo.rst index 666adfe5..3b27f4ec 100755 --- a/doc/source/science_guide/sg_thermo.rst +++ b/doc/source/science_guide/sg_thermo.rst @@ -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. @@ -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 @@ -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`). @@ -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 @@ -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`). @@ -735,49 +734,49 @@ 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. @@ -785,13 +784,13 @@ 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. @@ -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: @@ -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