A model of the three-dimensional
evolution of Arctic melt ponds on first-year
and multiyear sea ice
Article
Published Version
Scott, F. and Feltham, D.L. (2010) A model of the three-
dimensional evolution of Arctic melt ponds on first-year and
multiyear sea ice. Journal of Geophysical Research, 115
(C12). C12064. ISSN 0148-0227 doi:
https://doi.org/10.1029/2010JC006156 Available at
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A model of the three‐dimensional evolution of Arctic melt ponds
on first‐year and multiyear sea ice
F. Scott
1
and D. L. Feltham
1,2
Received 27 January 2010; revised 15 July 2010; accepted 20 September 2010; published 28 December 2010.
[1] During winter the ocean surface in polar regions freezes over to form sea ice.
In the summer the upper layers of sea ice and snow melts producing meltwater that
accumulates in Arctic melt ponds on the surface of sea ice. An accurate estimate of the
fraction of the sea ice surface covered in melt ponds is essential for a realistic estimate of
the albedo for global climate models. We present a melt‐pond–sea‐ice model that
simulates the three‐dimensional evolution of melt ponds on an Arctic sea ice surface. The
advancements of this model compared to previous models are the inclusion of snow
topography; meltwater transport rates are calculated from hydraulic gradients and ice
permeability; and the incorporation of a detailed one‐dimensional, thermodynamic
radiative balance. Results of model runs simulating first‐year and multiyear sea ice are
presented. Model results show good agreement with observations, with duration of pond
coverage, pond area, and ice ablation comparing well for both the first‐year ice and
multiyear ice cases. We investigate the sensitivity of the melt pond cover to changes in ice
topography, snow topography, and vertical ice permeability. Snow was found to have an
important impact mainly at the start of the melt season, whereas initial ice topography
strongly controlled pond size and pond fraction throughout the melt season. A reduction in
ice permeability allowed surface flooding of relatively flat, first‐year ice but had little
impact on the pond coverage of rougher, multiyear ice. We discuss our results, including
model shortcomings and areas of experimental uncertainty.
Citation: Scott, F., and D. L. Feltham (2010), A model of the three‐dimensional evolution of Arctic melt ponds on first‐year and
multiyear sea ice, J. Geophys. Res., 115, C12064, doi:10.1029/2010JC006156.
1. Introduction
[2] The rate of decline of Arctic summer sea ice extent has
increased dramatically in recent years. A record minimum of
ice extent was recorded in 2007, beating the previous record
minimum in 2005. The 2007 extent minimum was almost
matched again in 2008. The decrease in sea ice area has
been accompanied by a decrease in sea ice volume. For
instance, Rothrock et al. [1999] observed a 40% reduction in
average ice thickness by analyzing submarine measurements
of sea ice draft from the 1970s and 1990s. Wider area esti-
mates of sea ice thickness, based on satellite altimetry [Laxon
et al., 2003; Giles et al., 2008], also reveal a reduction in ice
thickness.
[
3] Global warming is intensified in polar regions due to
the albedo feedback mechanism [e.g., Ebert et al., 1995]
and, as a result of this, Arctic sea ice is a sensitive indicator
of climate change, as well as being an important climate
component. Climate prediction studies using Global Climate
Models (GCMs), such as the Intergovernmental Panel on
Climate Change AR4 study, are unable to simulate the
observed rapid reduction o f sea ice extent [Solomon et al.,
2007]. The inability of GCMs to simulate the rapid reduc-
tion in Arctic summer sea ice extent, combined with satellite
and field observations demonstrating the importance of sea
ice melt, indicate the need for a more realistic representation
of sea ice melt processes. In particular, GCMs do not model
melt ponds on sea ice. As the melt season progresses, part of
the surface meltwater produced accumulates to form melt
ponds that cover an increasing fraction of the surface,
reaching around 50% at the end of the melt season.
[
4] Melt ponds are a persistent feature of the summertime
sea ice surface in the Arctic [Derksen et al., 1997; Fetterer
and Untersteiner, 1998; Tucker et al., 1999; Yackel et al.,
2000; Tschudi et al., 2001]. Melt ponds have a significant
impact on the both the albedo of sea ice and the amount of
sea ice melt. The albedo of pond‐covered ice is variable and
has been measured in field experiments to be between 0.1
and 0.5 [e.g., Perovich et al., 2002b; Eicken et al., 2004].
These albedo values are much lower than bare ice and
snow‐covered ice, which are relatively stable at 0.6–0.65
and 0.84–0.87 [Perovich, 1996]. Since the ice concentration
in the interior Arctic is greater than 85%, melt ponds con-
tribute significantly to the area‐averaged albedo, with an
1
Centre for Polar Observation and Modelling, Department of Earth
Sciences, University College London, London, UK.
2
British Antarctic Survey, Cambridge, UK.
Copyright 2010 by the American Geophysical Union.
0148‐0227/10/2010JC006156
JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 115, C12064, doi:10.1029/2010JC006156, 2010
C12064 1of37
approximately linear decrease in albedo with increasing
pond fraction [Eicken et al., 2004]. For example, an
uncertainty in pond fraction of 15% over the entire Arctic
Ocean is equivalent to an uncertainty of 10% in the total ice
area in the calculation of mean Arctic Ocean albedo.
[
5] Melt pond parameterizations that can be incorporated
into GCMs are now being developed [Flocco and Feltham,
2007; Pedersen et al., 2009; Flocco et al., 2010], however,
to ensure that parameterizations are realistic we need to
understand the physics that govern melt pond evolution so
that the parameterizations can be physically based.
[
6] Our objective here is to create a model of melt pond
evolution on sea ice, based on the physics believed to
govern pond formation and growth, that can be used to
determine the sensitivity of melt ponds to ice and snow
surface topography and uncertainty in sea ice permeability,
and thus improve our understanding of the evolution of melt
ponds. Our model uses the cellular automaton concept
described by Lüthje et al. [2006], with significant im-
provements described below, and the one‐dimensional,
vertical heat transport model described by Taylor and
Feltham [2004]. In the model the ice cover is represented
by a horizontal square grid of cells like a checker board and
each cell contains a column of ice, which may have a melt
pond or snow cover, see Figure 1.
[
7] The initial ice and snow topographies have been
generated using standard statistical methods so that first‐
year and multiyear ice can be modeled using the statistical
properties of necessarily limited observations. Ice surface
and base heights are generated separately leading to a sur-
face topography with some ice surface heights below sea
level init ially. The initial surface topography in the Lüthje
et al. [2006] model is based on ice freeboard measure-
ments and all cells have positive initial freeboard.
[
8] In our model the entire floe is in hydrostatic equilib-
rium, but not necessarily every cell, and sea level with
respect to the floe is recalculated every time step. This al-
lows vertical drainage to be realistically modeled using
Darcy’s law, rather than take place at a fixed rate as in the
Lüthje et al. [2006] model. Horizontal water transport
rates in our model vary from cell to cell depending on the
solid fraction in the ice. Therefore in the model described
in this paper there is spatial as well as temporal variation
in drainage rate.
[
9] The ice and snow melt rates in our model are calcu-
lated from the detailed thermal and radiative balances
described by Taylor a nd Feltham [2004]. In the [Lüthje et
al., 2006] model bare ice melts at a fixed rate and melting
beneath ponds take place at an enhanced rate using an ad
hoc algorithm motivated by observations. There is no basal
melting in the Lüthje et al. [2006] model and there is no
separate representation of snow cover.
[
10] In section 2 we present the melt‐pond–sea‐ice model
including the model of meltwater transport, an explanation
of how the cellular approach is combined with the one‐
dimensional thermodynamic model, and a description of the
construction of initial ice and snow topographies. In section
3 we present the results of two model runs that simulate the
evolution of melt ponds on first‐year ice and multiyear ice,
which are compared with field data and the results of Lüthje
et al. [2006]. In section 4 we present sensitivity studies for
both first‐year and multiyear sea ice in which we vary the
initial snow cover (depth and roughness), ice topography
(roughness), and vertical ice permeability, and compare
Figure 1. A schematic diagram of the cellular automaton. Each cell has an individual ice thickness, H,
and has a horizontal surface area of 25 m
2
. Melting decreases the ice thickness in a cell and allows a pond
to form on the surface. Water can drain through a cell or can be transported to adjacent cells.
SCOTT AND FELTHAM: EVOLUTION OF MELT PONDS C12064C12064
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these studies with observations. Finally, in section 5, we
summarize our results and state our main conclusions.
2. Model Description
[11] The automaton grid consists of cells that evolve
largely independently of each other, interacting through the
transport of water between cells, see Figure 1. Each cell
represents a 5 m × 5 m square area of sea ice and, within this
area, ice thickness, meltwater depth and snow cover are
assumed to be uniform. The entire grid represents an 200 m
× 200 m area of a sea ice floe (40 cells per side). The area is
constrained to this size so that it can represent an arbitrary
section of a sea ice floe without the complication of having
to take edge effects into consideration. The boundaries are
periodic so that meltwater transported out of one edge cell is
transported back into the opposite edge cell. A time step of
the model consists of the following five stages:
[
12] 1. One‐dimensional thermodynamic equations fol-
lowing Taylor and Feltham [2004] are solved in the vertical
direction in every cell to calculate the heat flux through ice,
snow and meltwater (if it exists). These calculations estab-
lish the albedo, volume of meltwater produced, basal abla-
tion and the saturation of snow on a cell by cell basis.
[
13] 2. Sea level with respect to the floe is established and
used to calculate the hydraulic head in each cell.
[
14] 3. Water is driven between adjacent cells by differ-
ences in hydraulic head between the cells. The volume of
horizontal water transport is calculated using Darcy’s law
for flow through a porous medium.
[
15] 4. Vertical drainage through the ice in each cell is
calculated using Darcy’s law and the hydraulic head.
[
16] 5. The volume of water transported into and out of
the cells is updated and one cycle of the automaton model is
complete.
[
17] Note the choice of the order of operation of (2)–(4),
which corresponds to the rapidity of the relevant physical
processes, is needed in order to calculate meltwater trans-
port accurately for all practical choices of model time step
(i.e., greater than about a minute). We used a model time
step of 1 h.
[
18] Each cell in the cellular model calls a separate one‐
dimensional thermodynamic model, as described by Taylor
and Feltham [2004]. The thermodynamic model model is
run at a lower vertical spatial and temporal resolution than
that by Taylor and Feltham [2004] (20 grid points and time
steps of 1 h, compared with 641 grid points and time steps
of 600 seconds in the original model runs), first due to time
constraints, to allow a model run to be completed on a
typical workstation in just over a week, and secondly to
ensure that the cellular automaton and thermodynamic
models are of comparable accuracy. The resolution of the
thermodynamic model was tested in isolation from the cel-
lular model to ensure that the lower‐resolution results were
not significantly different from higher‐resolution results.
The relatively coarse grid length of 5 m was chosen because
this is the average distance water is expected to travel in a
time step length of 1 h. A higher spatial (and temporal)
resolution calculation was found to have no substantial
impact on the results.
[
19] We describe the melt‐pond–sea‐ice model in the
following sections: section 2.1 describes the calculation of
meltwater transport and drainage, section 2.2 briefly de-
scribes the thermodynamic and radiative model used to
calculate melt rates, and section 2.3 describes the generation
of the sea ice and snow topographies.
2.1. Calculation of Meltwater Transport and Drainage
[
20] The surface of sea ice is deformed by mechanical
processes such as ridging, or thermodynamic processes such
as the formation and drainage of melt ponds and the freezing
over of partially drained ponds [Fetterer and Untersteiner,
1998] and therefore in places the sea ice surface is likely
to have a negative freeboard. In this model the entire floe/
computational domain is in hydrostatic equilibrium but not
individual cells. Sea level with respect to the floe is estab-
lished initially using the assumption that the entire floe is in
hydrostatic equilibrium and is then updated as mass is
removed from the surface and base of the ice.
[
21] Mean draft, D, is calculated every time step from
D ¼
P
x
i
þ x
s
þ x
p
A
; ð1Þ
where x is the mass of ice, snow and water in each cell, where
index i represents ice, s represents snow, and p represents
melt pond, r is ocean density, and A is total floe area.
[
22] The area covered in melt ponds is affected by hori-
zontal and vertical water transport [Eicken et al., 2002]. In
this model water can be removed from the grid by vertical
drainage and can be transported between cells, depending on
differences in hydraulic head between cells. We model
vertical and horizontal water transport in each cell using
Darcy’s law and we assume for simplicity that sea ice is a
saturated porous medium. In the vertical direction the Darcy
velocity, v, reduces to
v ¼
v
g
m
y
H
; ð2Þ
where p
v
is the vertical ice permeability, g is gravitational
acceleration, m is dynamic viscosity, which, for water, is
10
−3
kg m
−1
s
−1
, r
m
is the density of meltwater, which is
initially formed from melted snow and is taken to be
1000 kgm
−3
, y is the height of the melt pond surface above
sea level, and H is ice thickness. In the horizontal direction the
Darcy velocity, u, is given by
u ¼
h
g
m
r ; ð3Þ
where p
h
is the ice permeability in the horizontal direction,
and y is the fluid surface height.
[
23] The structure of sea ice is such that the upper surface
and several centimeters below the sea ice surface is often a
highly porous, crusty layer of sea ice [Eicken et al., 2002].
We assume that most horizontal water transport is limited by
flow through this porous crust. The solid fraction in the sea
ice crust is lower than that in the ice below and therefore the
permeability will be greater here than at any other depth in
the sea ice. The permeability at the base of the ice in the
summer melt season is small enough to make horizontal
water flux greater than vertical water flux for the same
pressure gradient, and therefore is the dominant way in
which water is transported. In our model horizontal water
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