:tocdepth: 3

.. _index:

Index of primary variables and parameters 
==========================================

This index defines many of the symbols used frequently in the ice model
code. Values appearing in this list are fixed or recommended; most
namelist parameters are indicated ( :math:`E_\circ`) with their default
values. For other namelist options, see Section :ref:`tabnamelist`. All
quantities in the code are expressed in MKS units (temperatures may take
either Celsius or Kelvin units).  

.. csv-table:: *Alphabetical Index of Icepack Variables and Parameters*
   :header: " ", " ", " "
   :widths: 15, 30, 15, 1   

   "**A**", "", ""
   "a_rapid_mode", ":math:`\bullet` brine channel diameter", ""
   "ahmax", ":math:`\bullet` thickness above which ice albedo is constant", "0.3m"
   "aice_init", "concentration of ice at beginning of timestep", ""
   "aice0", "fractional open water area", ""
   "aice(n)", "total concentration of ice in grid cell (in category n)", ""
   "albedo_type", ":math:`\bullet` type of albedo parameterization (‘default’ or ‘constant’)", ""
   "albice", "bare ice albedo", ""
   "albicei", ":math:`\bullet` near infrared ice albedo for thicker ice", ""
   "albicev", ":math:`\bullet` visible ice albedo for thicker ice", ""
   "albocn", "ocean albedo", "0.06"
   "albpnd", "melt pond albedo", ""
   "albsno", "snow albedo", ""
   "albsnowi", ":math:`\bullet` near infrared, cold snow albedo", ""
   "albsnowv", ":math:`\bullet` visible, cold snow albedo", ""
   "algalN", "algal nitrogen concentration", mmol/m\ :math:`^3`
   "alndf", "albedo: near IR, diffuse", ""
   "alndr", "albedo: near IR, direct", ""
   "alvdf", "albedo: visible, diffuse", ""
   "alvdr", "albedo: visible, direct", ""
   "alndf_ai", "grid-box-mean value of alndf", ""
   "alndr_ai", "grid-box-mean value of alndr", ""
   "alvdf_ai", "grid-box-mean value of alvdf", ""
   "alvdr_ai", "grid-box-mean value of alvdr", ""
   "amm", "ammonia/um concentration", "mmol/m\ :math:`^3`"
   "aparticn", "participation function", ""
   "apeff_ai", "grid-cell-mean effective pond fraction", ""
   "apondn", "area concentration of melt ponds", ""
   "araftn", "area fraction of rafted ice", ""
   "ardgn", "fractional area of ridged ice", ""
   "aspect_rapid_mode", ":math:`\bullet` brine convection aspect ratio", "1"
   "astar", "e-folding scale for participation function", "0.05"
   "atm_data_format", ":math:`\bullet` format of atmospheric forcing files", ""
   "atm_data_type", ":math:`\bullet` type of atmospheric forcing", ""
   "atmbndy", ":math:`\bullet` atmo boundary layer parameterization (‘default’ or ‘constant’)", ""
   "awtidf", "weighting factor for near-ir, diffuse albedo", "0.36218"
   "awtidr", "weighting factor for near-ir, direct albedo", "0.00182"
   "awtvdf", "weighting factor for visible, diffuse albedo", "0.63282"
   "awtvdr", "weighting factor for visible, direct albedo", "0.00318"
   "**B**", "", ""
   "bgc_data_type", ":math:`\bullet` forcing type for biogeochemistry", ""
   "bgc_flux_type", ":math:`\bullet` ice-ocean flux velocity type", ""
   "bgc_tracer_type", "tracer_type for bgc tracers", ""
   "bgrid", "nondimensional vertical grid points for bio grid", ""
   "bignum", "a large number", ":math:`10^{30}`"
   "bphi", "porosity of ice layers on bio grid", ""
   "bTiz", "temperature of ice layers on bio grid", ""
   "**C**", "", ""
   "calc_strair", ":math:`\bullet` if true, calculate wind stress", "T"
   "calc_Tsfc", ":math:`\bullet` if true, calculate surface temperature", "T"
   "Cdn_atm", "atmospheric drag coefficient", ""
   "Cdn_ocn", "ocean drag coefficient", "" 
   "Cf", ":math:`\bullet` ratio of ridging work to PE change in ridging", "17."
   "cgrid", "vertical grid points for ice grid (compare bgrid)", ""
   "char_len", "length of character variable strings", "80"
   "char_len_long", "length of longer character variable strings", "256"
   "check_step", "time step on which to begin writing debugging data", ""
   "cldf", "cloud fraction", ""
   "cm_to_m", "cm to meters conversion", "0.01"
   "coldice", "value for constant albedo parameterization", "0.70"
   "coldsnow", "value for constant albedo parameterization", "0.81"
   "conduct", ":math:`\bullet` conductivity parameterization", ""
   "congel", "basal ice growth", "m"
   "coszen", "cosine of the zenith angle", ""
   "Cp", "proportionality constant for potential energy", "kg/m\ :math:`^2`/s\ :math:`^2`"
   "cp_air", "specific heat of air", "1005.0 J/kg/K"
   "cp_ice", "specific heat of fresh ice", "2106. J/kg/K"
   "cp_ocn", "specific heat of sea water", "4218. J/kg/K"
   "cp_wv", "specific heat of water vapor", "1.81x\ :math:`10^3` J/kg/K"
   "cp063", "diffuse fresnel reflectivity (above)", "0.063"
   "cp455", "diffuse fresnel reflectivity (below)", "0.455"
   "Cs", "fraction of shear energy contributing to ridging", "0.25"
   "Cstar", "constant in Hibler ice strength formula", "20."
   "**D**", "", ""
   "daice_da", "data assimilation concentration increment rate", ""
   "daidtd", "ice area tendency due to dynamics/transport", "1/s"
   "daidtt", "ice area tendency due to thermodynamics", "1/s"
   "dalb_mlt", "[see **icepack_shortwave.F90**]", "-0.075"
   "dalb_mlti", "[see **icepack_shortwave.F90**]", "-0.100"
   "dalb_mltv", "[see **icepack_shortwave.F90**]", "-0.150"
   "darcy_V", "Darcy velocity used for brine height tracer", ""
   "dardg1(n)dt", "rate of fractional area loss by ridging ice (category n)", "1/s"
   "dardg2(n)dt", "rate of fractional area gain by new ridges (category n)", "1/s"
   "daymo", "number of days in one month", ""
   "daycal", "day number at end of month", ""
   "days_per_year", ":math:`\bullet` number of days in one year", "365"
   "dbl_kind", "definition of double precision", "selected_real_kind(13)"
   "dbug", ":math:`\bullet` write extra diagnostics", ".false."
   "depressT", "ratio of freezing temperature to salinity of brine", "0.054 deg/ppt"
   "dhbr_bt", "change in brine height at the bottom of the column", ""
   "dhbr_top", "change in brine height at the top of the column", ""
   "dhsn", "depth difference for snow on sea ice and pond ice", ""
   "diag_file", ":math:`\bullet` diagnostic output file (alternative to standard out)", ""
   "diagfreq", ":math:`\bullet` how often diagnostic output is written (10 = once per 10 dt)", ""
   "divu", "strain rate I component, velocity divergence", "1/s"
   "divu_adv", "divergence associated with advection", "1/s"
   "dms", "dimethyl sulfide concentration", "mmol/m\ :math:`^3`"
   "dmsp", "dimethyl sulfoniopropionate concentration", "mmol/m\ :math:`^3`"
   "dpscale", ":math:`\bullet` time scale for flushing in permeable ice", ":math:`1\times 10^{-3}`"
   "dragio", "drag coefficient for water on ice", "0.00536"
   "dSdt_slow_mode", ":math:`\bullet` drainage strength parameter", ""
   "dsnow", "change in snow thickness", "m"
   "dt", ":math:`\bullet` thermodynamics time step", "3600. s"
   "dt_dyn", "dynamics/ridging/transport time step", ""
   "dT_mlt", ":math:`\bullet` :math:`\Delta` temperature per :math:`\Delta` snow grain radius", "1. deg"
   "dumpfreq", ":math:`\bullet` dump frequency for restarts, y, m or d", ""
   "dumpfreq_n", ":math:`\bullet` restart output frequency", ""
   "dvidtd", "ice volume tendency due to dynamics/transport", "m/s"
   "dvidtt", "ice volume tendency due to thermodynamics", "m/s"
   "dvirdg(n)dt", "ice volume ridging rate (category n)", "m/s"
   "**E**", "", ""                       
   "eice(n)", "energy of melting of ice per unit area (in category n)", "J/m\ :math:`^2`"
   "emissivity", "emissivity of snow and ice", "0.95"
   "eps13", "a small number", "10\ :math:`^{-13}`"
   "eps16", "a small number", "10\ :math:`^{-16}`"
   "esno(n)", "energy of melting of snow per unit area (in category n)", "J/m\ :math:`^2`"
   "evap", "evaporative water flux", "kg/m\ :math:`^2`/s"
   "**F**", "", ""
   "faero_atm", "aerosol deposition rate", "kg/m\ :math:`^2`/s"
   "faero_ocn", "aerosol flux to the ocean", "kg/m\ :math:`^2`/s"
   "fbot_xfer_type", ":math:`\bullet` type of heat transfer coefficient under ice", ""
   "fcondtop(n)(_f)", "conductive heat flux", "W/m\ :math:`^2`"
   "ferrmax", "max allowed energy flux error (thermodynamics)", "1x :math:`10^{-3}` W/m\ :math:`^2`"
   "ffracn", "fraction of fsurfn used to melt pond ice", ""
   "fhocn", "net heat flux to ocean", "W/m\ :math:`^2`"
   "fhocn_ai", "grid-box-mean net heat flux to ocean (fhocn)", "W/m\ :math:`^2`"
   "first_ice", "flag for initial ice formation", ""
   "flat", "latent heat flux", "W/m\ :math:`^2`"
   "floediam", "effective floe diameter for lateral melt", "300. m"
   "floeshape", "floe shape constant for lateral melt", "0.66"
   "flux_bio", "all biogeochemistry fluxes passed to ocean", ""
   "flux_bio_ai", "all biogeochemistry fluxes passed to ocean, grid cell mean", ""
   "flw", "incoming longwave radiation", "W/m\ :math:`^2`"
   "flwout", "outgoing longwave radiation", "W/m\ :math:`^2`"
   "formdrag", ":math:`\bullet` calculate form drag", ""
   "fpond", "fresh water flux to ponds", "kg/m\ :math:`^2`/s"
   "fr_resp", "bgc respiration fraction", "0.05"
   "frain", "rainfall rate", "kg/m\ :math:`^2`/s"
   "frazil", "frazil ice growth", "m"
   "fresh", "fresh water flux to ocean", "kg/m\ :math:`^2`/s"
   "fresh_ai","grid-box-mean fresh water flux (fresh)", "kg/m\ :math:`^2`/s"
   "frz_onset", "day of year that freezing begins", ""
   "frzmlt", "freezing/melting potential", "W/m\ :math:`^2`"
   "frzmlt_init", "freezing/melting potential at beginning of time step", "W/m\ :math:`^2`"
   "frzmlt_max", "maximum magnitude of freezing/melting potential", "1000. W/m\ :math:`^2`"
   "frzpnd", ":math:`\bullet` Stefan refreezing of melt ponds", "‘hlid’"
   "fsalt", "net salt flux to ocean", "kg/m\ :math:`^2`/s"
   "fsalt_ai", "grid-box-mean salt flux to ocean (fsalt)", "kg/m\ :math:`^2`/s"
   "fsens", "sensible heat flux", "W/m\ :math:`^2`"
   "fsnow", "snowfall rate", "kg/m\ :math:`^2`/s"
   "fsnowrdg", "snow fraction that survives in ridging", "0.5"
   "fsurf(n)(_f)", "net surface heat flux excluding fcondtop", "W/m\ :math:`^2`"
   "fsw", "incoming shortwave radiation", "W/m\ :math:`^2`"
   "fswabs", "total absorbed shortwave radiation", "W/m\ :math:`^2`"
   "fswfac", "scaling factor to adjust ice quantities for updated data", ""
   "fswint", "shortwave absorbed in ice interior", "W/m\ :math:`^2`"
   "fswpenl", "shortwave penetrating through ice layers", "W/m\ :math:`^2`"
   "fswthru", "shortwave penetrating to ocean", "W/m\ :math:`^2`"
   "fswthru_ai", "grid-box-mean shortwave penetrating to ocean (fswthru)", "W/m\ :math:`^2`"
   "fyear", "current data year", ""
   "fyear_final", "last data year", ""
   "fyear_init", ":math:`\bullet` initial data year", ""
   "**G**", "", ""
   "gravit", "gravitational acceleration", "9.80616 m/s\ :math:`^2`"
   "grow_net", "specific biogeochemistry growth rate per grid cell", "s :math:`^{-1}`"
   "Gstar", "piecewise-linear ridging participation function parameter", "0.15"
   "**H**", "", ""
   "heat_capacity", ":math:`\bullet` if true, use salinity-dependent thermodynamics", "T"
   "hfrazilmin", "minimum thickness of new frazil ice", "0.05 m"
   "hi_min", "minimum ice thickness for thinnest ice category", "0.01 m"
   "hi_ssl", "ice surface scattering layer thickness", "0.05 m"
   "hicen", "ice thickness in category n", "m"
   "highfreq", ":math:`\bullet` high-frequency atmo coupling", "F"
   "hin_old", "ice thickness prior to growth/melt", "m"
   "hin_max", "category thickness limits", "m"
   "hmix", "ocean mixed layer depth", "20. m"
   "hour", "hour of the year", ""
   "hp0", "pond depth at which shortwave transition to bare ice occurs", "0.2 m"
   "hp1", ":math:`\bullet` critical ice lid thickness for topo ponds (dEdd)", "0.01 m"
   "hpmin", "minimum melt pond depth (shortwave)", "0.005 m"
   "hpondn", "melt pond depth", "m"
   "hs_min", "minimum thickness for which :math:`T_s` is computed", "1.\ :math:`\times`\ 10\ :math:`^{-4}` m"
   "hs0", ":math:`\bullet` snow depth at which transition to ice occurs (dEdd)", "0.03 m"
   "hs1", ":math:`\bullet` snow depth of transition to pond ice", "0.03 m"
   "hs_ssl", "snow surface scattering layer thickness", "0.04 m"
   "Hstar", "determines mean thickness of ridged ice", "25. m"
   "**I**", "", ""
   "i0vis","fraction of penetrating visible solar radiation", "0.70"
   "ice_ic", ":math:`\bullet` choice of initial conditions", ""
   "ice_stdout", "unit number for standard output", ""
   "ice_stderr", "unit number for standard error output", ""
   "ice_ref_salinity", "reference salinity for ice–ocean exchanges", "4. ppt"
   "iceruf", "ice surface roughness", "5.\ :math:`\times`\ 10\ :math:`^{-4}` m"
   "idate", "the date at the end of the current time step (yyyymmdd)", ""
   "idate0", "initial date", ""
   "igrid", "interface points for vertical bio grid", ""
   "int_kind", "definition of an integer", "selected_real_kind(6)"
   "istep", "local step counter for time loop", ""
   "istep0", ":math:`\bullet` number of steps taken in previous run", "0"
   "istep1", "total number of steps at current time step", ""
   "Iswabs", "shortwave radiation absorbed in ice layers", "W/m\ :math:`^2`"
   "**J**", "", ""
   "**K**", "", ""
   "kalg", ":math:`\bullet` absorption coefficient for algae", ""
   "kappav", "visible extinction coefficient in ice, wavelength\ :math:`<`\ 700nm", "1.4 m\ :math:`^{-1}`"
   "kcatbound", ":math:`\bullet` category boundary formula", ""
   "kg_to_g", "kg to g conversion factor", "1000."
   "kice", "thermal conductivity of fresh ice (:cite:`Bitz99`)", "2.03 W/m/deg"
   "kitd", ":math:`\bullet` type of itd conversions (0 = delta function, 1 = linear remap)", "1"
   "krdg_partic", ":math:`\bullet` ridging participation function", "1"
   "krdg_redist", ":math:`\bullet` ridging redistribution function", "1"
   "krdgn", "mean ridge thickness per thickness of ridging ice", ""
   "kseaice", "thermal conductivity of ice for zero-layer thermodynamics", "2.0 W/m/deg"
   "ksno", "thermal conductivity of snow", "0.30 W/m/deg"
   "kstrength", ":math:`\bullet` ice stength formulation (1= :cite:`Rothrock75`, 0 = :cite:`Hibler79`)", "1"
   "ktherm", ":math:`\bullet` thermodynamic formulation (0 = zero-layer, 1 = :cite:`Bitz99`, 2 = mushy)", ""        
   "**L**", "", ""
   "l_brine", "flag for brine pocket effects", ""
   "l_conservation_check", "if true, check conservation when ridging", ""
   "l_mpond_fresh", ":math:`\bullet` if true, retain (topo) pond water until ponds drain", ""
   "Lfresh", "latent heat of melting of fresh ice = Lsub - Lvap", "J/kg"
   "lhcoef", "transfer coefficient for latent heat", ""
   "lmask_n(s)", "northern (southern) hemisphere mask", ""
   "log_kind", "definition of a logical variable", "kind(.true.)"
   "Lsub", "latent heat of sublimation for fresh water", "2.835\ :math:`\times` 10\ :math:`^6` J/kg"
   "Lvap", "latent heat of vaporization for fresh water", "2.501\ :math:`\times` 10\ :math:`^6` J/kg"
   "**M**", "", ""
   "m_to_cm", "meters to cm conversion", "100."
   "m1", "constant for lateral melt rate", "1.6\ :math:`\times`\ 10\ :math:`^{-6}` m/s deg\ :math:`^{-m2}`"
   "m2", "constant for lateral melt rate", "1.36"
   "m2_to_km2", "m\ :math:`^2` to km\ :math:`^2` conversion", "1\ :math:`\times`\ 10\ :math:`^{-6}`"
   "max_blocks", "maximum number of blocks per processor", ""
   "max_ntrcr", "maximum number of tracers available", "5"
   "maxraft", "maximum thickness of ice that rafts", "1. m"
   "mday", "day of the month", ""
   "meltb", "basal ice melt", "m"
   "meltl", "lateral ice melt", "m"
   "melts", "snow melt", "m"
   "meltt", "top ice melt", "m"
   "min_salin", "threshold for brine pockets", "0.1 ppt"
   "mlt_onset", "day of year that surface melt begins", ""
   "month", "the month number", ""
   "monthp", "previous month number", ""
   "mps_to_cmpdy", "m per s to cm per day conversion", "8.64\ :math:`\times`\ 10\ :math:`^6`"
   "mu_rdg", ":math:`\bullet` e-folding scale of ridged ice", ""
   "**N**", "", ""
   "n_aero", "number of aerosol species", ""
   "natmiter", ":math:`\bullet` number of atmo boundary layer iterations", "5"
   "nbtrcr", "number of biology tracers", ""
   "ncat", "number of ice categories", "5"
   "ndtd", ":math:`\bullet` number of dynamics/advection steps under thermo", "1"
   "new_day", "flag for beginning new day", ""
   "new_hour", "flag for beginning new hour", ""
   "new_month", "flag for beginning new month", ""
   "new_year", "flag for beginning new year", ""
   "nhlat", "northern latitude of artificial mask edge", "30\ :math:`^\circ`\ S"
   "nilyr", "number of ice layers in each category", "7"
   "nit", "nitrate concentration", "mmol/m\ :math:`^3`"
   "nlt_bgc_[chem]", "ocean sources and sinks for biogeochemistry", ""
   "nml_filename", "namelist file name", ""
   "npt", ":math:`\bullet` total number of time steps (dt)", ""
   "nslyr", "number of snow layers in each category", ""
   "nspint", "number of solar spectral intervals", ""
   "nt_<trcr>", "tracer index", ""
   "ntrcr", "number of tracers", ""
   "nu_diag", "unit number for diagnostics output file", ""
   "nu_dump", "unit number for dump file for restarting", ""
   "nu_forcing", "unit number for forcing data file", ""
   "nu_nml", "unit number for namelist input file", ""
   "nu_restart", "unit number for restart input file", ""
   "nu_rst_pointer", "unit number for pointer to latest restart file", ""
   "nx(y)_block", "total number of gridpoints on block in x(y) direction", ""
   "nyr", "year number", ""
   "**O**", "", ""
   "ocean_bio", "concentrations of bgc constituents in the ocean", ""
   "oceanmixed_ice", ":math:`\bullet` if true, use internal ocean mixed layer", ""
   "ocn_data_format", ":math:`\bullet` format of ocean forcing files", ""
   "ocn_data_type", ":math:`\bullet` source of ocean surface data", ""
   "omega", "angular velocity of Earth", "7.292\ :math:`\times`\ 10\ :math:`^{-5}` rad/s"
   "opening", "rate of ice opening due to divergence and shear", "1/s"
   "**P**", "", ""
   "p001", "1/1000", ""
   "p01", "1/100", ""
   "p025", "1/40", ""
   "p027", "1/36", ""
   "p05", "1/20", ""
   "p055", "1/18", ""
   "p1", "1/10", ""
   "p111", "1/9", ""
   "p15", "15/100", ""
   "p166", "1/6", ""
   "p2", "1/5", ""
   "p222", "2/9", ""
   "p25", "1/4", ""
   "p333", "1/3", ""
   "p4", "2/5", ""
   "p5", "1/2", ""
   "p52083", "25/48", ""
   "p5625m", "-9/16", ""
   "p6", "3/5", ""
   "p666", "2/3", ""
   "p75", "3/4", ""
   "phi_c_slow_mode", ":math:`\bullet` critical liquid fraction", ""
   "phi_i_mushy", ":math:`\bullet` solid fraction at lower boundary", ""
   "phi_sk", "skeletal layer porosity", ""
   "phi_snow", ":math:`\bullet` snow porosity for brine height tracer", ""
   "pi", ":math:`\pi`", ""
   "pi2", ":math:`2\pi`", ""
   "pih", ":math:`\pi /2`", ""
   "piq", ":math:`\pi /4`", ""
   "pndaspect", ":math:`\bullet` aspect ratio of pond changes (depth:area)", "0.8"
   "potT", "atmospheric potential temperature", "K"
   "PP_net", "total primary productivity per grid cell", "mg C/m\ :math:`^2`/s"
   "precip_units", ":math:`\bullet` liquid precipitation data units", ""
   "print_points", ":math:`\bullet` if true, print point data", "F"
   "Pstar", "ice strength parameter", "2.75\ :math:`\times`\ 10\ :math:`^4`\ N/m"
   "puny", "a small positive number", "1\ :math:`\times`\ 10\ :math:`^{-11}`" 
   "**Q**", "", ""
   "Qa", "specific humidity at 10 m", "kg/kg"
   "qdp", "deep ocean heat flux", "W/m\ :math:`^2`"
   "qqqice", "for saturated specific humidity over ice", "1.16378\ :math:`\times`\ 10\ :math:`^7`\ kg/m\ :math:`^3`"
   "qqqocn", "for saturated specific humidity over ocean", "6.275724\ :math:`\times`\ 10\ :math:`^6`\ kg/m\ :math:`^3`"
   "Qref", "2m atmospheric reference specific humidity", "kg/kg"
   "**R**", "", ""
   "R_C2N", "algal carbon to nitrate factor", "7. mole/mole"
   "R_gC2molC", "mg/mmol carbon", "12.01 mg/mole"
   "R_chl2N", "algal chlorophyll to nitrate factor", "3. mg/mmol"
   "R_ice", ":math:`\bullet` parameter for Delta-Eddington ice albedo", ""
   "R_pnd", ":math:`\bullet` parameter for Delta-Eddington pond albedo", ""
   "R_S2N", "algal silicate to nitrate factor", "0.03 mole/mole"
   "R_snw", ":math:`\bullet` parameter for Delta-Eddington snow albedo", ""
   "r16_kind", "definition of quad precision", "selected_real_kind(26)", ""
   "Rac_rapid_mode", ":math:`\bullet` critical Rayleigh number", "10"
   "rdg_conv", "convergence for ridging", "1/s"
   "rdg_shear", "shear for ridging", "1/s"
   "real_kind", "definition of single precision real", "selected_real_kind(6)"
   "refindx", "refractive index of sea ice", "1.310"
   "restart", ":math:`\bullet` if true, initialize using restart file instead of defaults", "T"
   "restart_age", ":math:`\bullet` if true, read age restart file", ""
   "restart_bgc", ":math:`\bullet` if true, read bgc restart file", ""
   "restart_dir", ":math:`\bullet` path to restart/dump files", ""
   "restart_file", ":math:`\bullet` restart file prefix", ""
   "restart_[tracer]", ":math:`\bullet` if true, read tracer restart file", ""
   "restore_bgc", ":math:`\bullet` if true, restore nitrate/silicate to data", ""
   "restore_ice", ":math:`\bullet` if true, restore ice state along lateral boundaries", ""
   "restore_ocn", ":math:`\bullet` restore sst to data", ""
   "rfracmin", ":math:`\bullet` minimum melt water fraction added to ponds", "0.15"
   "rfracmax", ":math:`\bullet` maximum melt water fraction added to ponds", "1.0"
   "rhoa", "air density", "kg/m\ :math:`^3`"
   "rhofresh", "density of fresh water", "1000.0 kg/m\ :math:`^3`"
   "rhoi", "density of ice", "917. kg/m\ :math:`^3`"
   "rhos", "density of snow", "330. kg/m\ :math:`^3`"
   "rhosi", "average sea ice density (for hbrine tracer)", "940. kg/m\ :math:`^3`"
   "rhow", "density of seawater", "1026. kg/m\ :math:`^3`"
   "rnilyr", "real(nlyr)", ""
   "rside", "fraction of ice that melts laterally", ""
   "rsnw_fresh", "freshly fallen snow grain radius", "100. :math:`\times` 10\ :math:`^{-6}` m"
   "rsnw_mlt", ":math:`\bullet` melting snow grain radius", "1000. :math:`\times` 10\ :math:`^{-6}` m"
   "rsnw_nonmelt", "nonmelting snow grain radius", "500. :math:`\times` 10\ :math:`^{-6}` m"
   "rsnw_sig", "standard deviation of snow grain radius", "250. :math:`\times` 10\ :math:`^{-6}` m"
   "**S**", "", ""
   "salinz", "ice salinity profile", "ppt"
   "saltmax", "max salinity, at ice base (:cite:`Bitz99`)", "3.2 ppt"
   "scale_factor", "scaling factor for shortwave radiation components", ""
   "sec", "seconds elasped into idate", ""
   "secday", "number of seconds in a day", "86400."
   "shcoef", "transfer coefficient for sensible heat", ""
   "shear", "strain rate II component", "1/s"
   "shlat", "southern latitude of artificial mask edge", "30\ :math:`^\circ`\ N"
   "shortwave", ":math:`\bullet` flag for shortwave parameterization ('default' or 'dEdd')", ""
   "sil", "silicate concentration", "mmol/m\ :math:`^3`"
   "sk_l", "skeletal layer thickness", "0.03 m"
   "snoice", "snow-ice formation", "m"
   "snowpatch", "length scale for parameterizing nonuniform snow coverage", "0.02 m"
   "skl_bgc", ":math:`\bullet` biogeochemistry on/off", ""
   "spval", "special value (single precision)", ":math:`10^{30}`", ""
   "spval_dbl", "special value (double precision)", ":math:`10^{30}`", ""
   "ss_tltx(y)", "sea surface in the x(y) direction", "m/m"
   "sss", "sea surface salinity", "ppt"
   "sst", "sea surface temperature", "C"
   "Sswabs", "shortwave radiation absorbed in snow layers", "W/m\ :math:`^2`"
   "stefan-boltzmann", "Stefan-Boltzmann constant", "5.67\ :math:`\times`\ 10\ :math:`^{-8}` W/m\ :math:`^2`\ K\ :math:`^4`"
   "stop_now", "if 1, end program execution", ""
   "strairx(y)", "stress on ice by air in the x(y)-direction (centered in U cell)", "N/m\ :math:`^2`"
   "strairx(y)T", "stress on ice by air, x(y)-direction (centered in T cell)", "N/m\ :math:`^2`"
   "strax(y)", "wind stress components from data", "N/m\ :math:`^2`"
   "strength", "ice strength (pressure)", "N/m"
   "stress12", "internal ice stress, :math:`\sigma_{12}`", "N/m"
   "stressm", "internal ice stress, :math:`\sigma_{11}-\sigma_{22}`", "N/m"
   "stressp", "internal ice stress, :math:`\sigma_{11}+\sigma_{22}`", "N/m"
   "strintx(y)", "divergence of internal ice stress, x(y)", "N/m\ :math:`^2`"
   "strocnx(y)", "ice–ocean stress in the x(y)-direction (U-cell)", "N/m\ :math:`^2`"
   "strocnx(y)T", "ice–ocean stress, x(y)-dir. (T-cell)", "N/m\ :math:`^2`"
   "strtltx(y)", "surface stress due to sea surface slope", "N/m\ :math:`^2`"
   "swndf", "incoming shortwave radiation, near IR, diffuse", "W/m\ :math:`^2`"
   "swndr", "incoming shortwave radiation, near IR, direct", "W/m\ :math:`^2`"
   "swvdf", "incoming shortwave radiation, visible, diffuse", "W/m\ :math:`^2`"
   "swvdr", "incoming shortwave radiation, visible, direct", "W/m\ :math:`^2`"
   "**T**", "", ""
   "Tair", "air temperature at 10 m", "K"
   "tday", "absolute day number", ""
   "Tf", "freezing temperature", "C"
   "Tffresh", "freezing temp of fresh ice", "273.15 K"
   "tfrz_option", ":math:`\bullet` form of ocean freezing temperature", ""
   "thinS", "minimum ice thickness for brine tracer", ""
   "time", "total elapsed time", "s"
   "time_forc", "time of last forcing update", "s"
   "Timelt", "melting temperature of ice top surface", "0. C"
   "TLAT", "latitude of cell center", "radians"
   "TLON", "longitude of cell center", "radians"
   "tmask", "land/boundary mask, thickness (T-cell)", ""
   "tmass", "total mass of ice and snow", "kg/m\ :math:`^2`"
   "Tmin", "minimum allowed internal temperature", "-100. C"
   "Tmltz", "melting temperature profile of ice", ""
   "Tocnfrz", "temperature of constant freezing point parameterization", "-1.8 C"
   "tr_aero", ":math:`\bullet` if true, use aerosol tracers", ""
   "tr_bgc_[tracer]", ":math:`\bullet` if true, use biogeochemistry tracers", ""
   "tr_brine", ":math:`\bullet` if true, use brine height tracer", ""
   "tr_FY", ":math:`\bullet` if true, use first-year area tracer", ""
   "tr_iage", ":math:`\bullet` if true, use ice age tracer", ""
   "tr_lvl", ":math:`\bullet` if true, use level ice area and volume tracers", ""
   "tr_pond_cesm", ":math:`\bullet` if true, use CESM melt pond scheme", ""
   "tr_pond_lvl", ":math:`\bullet` if true, use level-ice melt pond scheme", ""
   "tr_pond_topo", ":math:`\bullet` if true, use topo melt pond scheme", ""
   "trcr", "ice tracers", ""
   "trcr_depend", "tracer dependency on basic state variables", ""
   "Tref", "2m atmospheric reference temperature", "K"
   "trestore", ":math:`\bullet` restoring time scale", "days"
   "Tsf_errmax", "max allowed :math:`T_{\mathit sf}` error (thermodynamics)", "5.\ :math:`\times`\ 10\ :math:`^{-4}`\ deg"
   "Tsfc(n)", "temperature of ice/snow top surface (in category n)", "C"
   "Tsmelt", "melting temperature of snow top surface", "0. C"
   "TTTice", "for saturated specific humidity over ice", "5897.8 K"
   "TTTocn", "for saturated specific humidity over ocean", "5107.4 K"
   "**U**", "", ""
   "uatm", "wind velocity in the x direction", "m/s"
   "umin", "min wind speed for turbulent fluxes", "1. m/s"
   "uocn", "ocean current in the x-direction", "m/s"
   "update_ocn_f", ":math:`\bullet` if true, include frazil ice fluxes in ocean flux fields", ""
   "use_leap_years", ":math:`\bullet` if true, include leap days", ""
   "ustar_min", ":math:`\bullet` minimum friction velocity under ice", ""
   "uvel", "x-component of ice velocity", "m/s"
   "**V**", "", ""
   "vatm", "wind velocity in the y direction", "m/s"
   "vice(n)", "volume per unit area of ice (in category n)", "m"
   "vicen_init", "ice volume at beginning of timestep", "m"
   "viscosity_dyn", "dynamic viscosity of brine", ":math:`1.79\times 10^{-3}` kg/m/s"
   "vocn", "ocean current in the y-direction", "m/s"
   "vonkar", "von Karman constant", "0.4"
   "vraftn", "volume of rafted ice", "m"
   "vrdgn", "volume of ridged ice", "m"
   "vsno(n)", "volume per unit area of snow (in category n)", "m"
   "vvel", "y-component of ice velocity", "m/s"
   "**W**", "", ""
   "warmice", "value for constant albedo parameterization", "0.68"
   "warmsno", "value for constant albedo parameterization", "0.77"
   "wind", "wind speed", "m/s"
   "write_restart", "if 1, write restart now", ""
   "**X**", "", ""
   "**Y**", "", ""
   "ycycle", ":math:`\bullet` number of years in forcing data cycle", ""
   "yday", "day of the year", ""
   "year_init", ":math:`\bullet` the initial year", ""
   "**Z**", "", ""
   "zlvl", "atmospheric level height", "m"
   "zref", "reference height for stability", "10. m"
   "zTrf", "reference height for :math:`T_{ref}`, :math:`Q_{ref}`, :math:`U_{ref}`", "2. m"
   "zvir", "gas constant (water vapor)/gas constant (air) - 1", "0.606"