Sea Ice Thermodynamics and
ITD considerations
Marika Holland
NCAR
Sea ice thermodynamics
Fsw
FLW
FSH
Fsw
FLH
• Simulate vertical
heat transfer
(conduction, SW absorption)
hs • Balance of fluxes at
hi
T1
T2
T3
T4
ice surface
(ice-atm
exchange, conduction, ice
melt)
-k dT/dz
Focn
• Balance of fluxes at
ice base (ice-ocn
exchange, conduction, ice
melt/growth)
Vertical heat transfer
• Assume brine pockets are in
thermal equilibrium with ice
• Heat capacity and conductivity
are functions of T/S of ice
• Assume constant salinity profile
• Assume non-varying density
• Assume pockets/channels are
brine filled
(from Light, Maykut, Grenfell, 2003)
(Maykut and Untersteiner, 1971; Bitz and
Lipscomb, 1999; others)
Albedo
(Perovich et al., 2002)
Parameterized albedo depends on
surface state (snow, temp, hi).
Issues: Implicit ponds, optically thick
snow, no snow aging, constant fraction
of SW absorbed in surface layer,
constant extinction coefficients
New Albedo Formulation
• High ice/snow albedo due to multiple scattering associated
with individual snow grains, inclusions of gas, brine, etc.
• New multiple-scattering sea ice radiative transfer has been
developed by Bruce Briegleb and Bonnie Light
• Dependent on snow/ice inherent optical (microscopic)
properties
• Allows for inclusion of soot, algae, etc in a general and
consistent manner (biological implications)
• Allows for improvements to numerous
parameterizations (e.g. snow aging effects, melt ponds)
(currently being tested within CCSM)
Melt Pond Albedo Parameterization
• Accumulate fraction of snow
and surface ice melt into pond
volume reservoir.
• Compute pond area/depth from
simple empirically-based
relationship.
• Pond volume advected as a
tracer.
• Albedo depends on pond
fraction and depth.
July Pond Concentration
(Based on Ebert and Curry, 1993)
Ice Thickness Distribution
Previous studies with
• Single Column Models (Maykut, 1982)
• Basin-scale models (Hibler, 1980)
• Coupled models of intermediate
complexity (simplified atmos)
• Fully coupled models (Holland et al)
Have shown ITD influences mean
climate state:
• Thicker ice
• Warmer SAT
• More saline Arctic Ocean
• Changes in atmosphere, ocean
circulation
Schramm et al., 1997
Ice Thickness Distribution
Evolution depends on: Ice growth, lateral melt, ice divergence, and
mechanical redistribution (riding/rafting)
(Thorndike et al., 1975)
Calculation of ITD - Mechanical Redistribution
• Parameterized after Rothrock ,1975; Thorndike et al.,
1975; Hibler, 1980; Flato and Hibler, 1995
• Convergence and shear produce ridges
• Thin ice replaced by smaller area of thicker, ridged ice
• Thinnest 15% of ice participates in ridging
• Distribution of ridged ice results
• Assumptions regarding ridge formation (participation
function, ridged distribution, etc.) and its relationship
to ice strength
• Sea ice simulations sensitive to these assumptions
• For example - What to do with snow on ridging ice?
Boundary layer exchange in presence of ITD
• Resolving an ITD improves ice-ocn-atm exchange
• But ocean and atmospheric boundary layers do not differentiate
between lead and ice covered surfaces
Near-term improvements for thermo/ITD
• SNOW - metamorphosis (aging, etc - important for
radiation), blowing snow, others?
• Soot, algae, other impurities in ice - important for
coupling to biology
• Sea ice "hydrology”: including melt ponds, brine pockets
and drainage, percolation and snow-ice formation
• Exchange with ocean/atm - new possibilities with ITD,
improvements based on observations (e.g. exchange
coefficients, double diffusion)
• Mechanical redistribution - observed studies to refine and
improve parameterizations
Albedo
• Most climate models use
- empirical formulae to calculate albedo (function of surface state)
- optically thick snow
- constant fraction of radiation absorbed in surface layer (1-io)
- constant extinction coefficient within ice
- tuned ice albedo to implicitly include effects of surface melt water
• Not consistently related to inherent optical properties of snow/ice
• Only loosely tied to physical properties of snow/ice system
• Difficult to generalize for improved treatments of snow, meltwater,
and impurities
Albedo
1. Existing scheme emphasizes albedo, absorption within ice and transmission to
ocean are secondary
• Absorption and transmittance are difficult to validate, yet important!
• Absorbed light immediately available for melting
• Transmitted light heats upper ocean, available for primary productivity
2. While a tuned albedo parameterization may produce reasonable results for a sea ice
model, the strength of the ice-albedo feedback and the character of radiative
interactions with the atmosphere may require a more complex treatment of shortwave
radiation (Curry et al., 2001)
For climate studies
Need to include processes that are important for:
• Representing climatological state
• Representing feedbacks
– realistic variability and sensitivity
• Physics appropriate to the models spatial scale
• Parameterize important non-resolved processes
Trade off between complexity and computational cost
Enhanced albedo feedback in ITD run
ITD (5 cat)
1 cat.
1cat tuned
Larger albedo change for thinner initial ice
With ITD have larger a change for ice with same initial thickness
Suggests surface albedo feedback enhanced in ITD run
Holland et al., 2006
Fundamentals - Thermodynamics
T  T
c
 k
 QSW
t z z
QSW
where

d
z
  ISW e
dz
(Beer’s Law)
ISW  i0 (1  )FSW
Fraction transmitted
below surface layer

Vertical heat transfer
Albedo
Fundamentals - Thermodynamics
T  T
c
 k
 QSW
t z z
Vertical heat transfer
c(T,S)  c0 
S
T2
S
k(T,S)  k0 
T
where   L0
and
Tm  S
(Maykut and Untersteiner, 1971)
 Non-varying density; assume brine filled

(from Light, Maykut, Grenfell, 2003)
pockets/channels

Fundamentals - Thermodynamics
T  T
c
 k
 QSW
t z z
Vertical heat transfer
Boundary Conditions:
Assume balance of fluxes at ice surface:
(1 i0 )(1  )FSW  FLW  FSH  FLH
dT
dh
k
 q(S,T)
dz
dt
And base:
T
dh
Focn  k
 q(S,T)
z
dt
Where q(S,T) is the amount of energy needed to melt ice
Boundary layer exchange in presence of ITD
• Resolving an ITD improves ice-ocn-atm exchange
• But ocean and atmospheric boundary layers do not differentiate
between lead and ice covered surfaces
• Observations indicate that this can be important
Ice Thickness Distribution
g

  ( fg)  L(g)   (vg)  (h,g,v )
t
h

(Thorndike et al., 1975)
Evolution depends on: Ice growth, lateral melt, ice divergence, and
mechanical redistribution (riding/rafting)