A model of the three-dimensional evolution of Arctic melt ponds on first-year and multiyear sea ice
Abstract: 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.
Summary (4 min read)
- The rate of decline of Arctic summer sea ice extent has increased dramatically in recent years.
- The inability of GCMs to simulate the rapid reduction 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.
- Horizontal water transport rates in their model vary from cell to cell depending on the solid fraction in the ice.
- In section 3 the authors 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. .
2. Model Description
- The automaton grid consists of cells that evolve largely independently of each other, interacting through the transport of water between cells, see Figure 1.
- One‐dimensional thermodynamic equations following Taylor and Feltham  are solved in the vertical direction in every cell to calculate the heat flux through ice, snow and meltwater (if it exists).
- Water is driven between adjacent cells by differences in hydraulic head between the cells.
- A higher spatial (and temporal) resolution calculation was found to have no substantial impact on the results. .
2.1. Calculation of Meltwater Transport and Drainage
- 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.
- The area covered in melt ponds is affected by horizontal and vertical water transport [Eicken et al., 2002].
- In their model horizontal water 3 of 37 flux is calculated before vertical water flux in a given time step and vertical water flux is calculated if there is any water remaining in the cell. .
- In the model described here vertical flow is limited by the lowest permeability in a vertical column.
2.2. Heat Transport Model
- The vertical heat transport model is the same as the melt‐pond–sea‐ice model described by Taylor and Feltham .
- A simple snow model was utilized, following Maykut and Untersteiner .
- The thermodynamic model of the sea ice component (including the ice lid) was described using the equations describing a mushy layer [Feltham et al., 2006], i.e., the sea ice is assumed to consist of a solid matrix of pure ice surrounded by brine (with no air pockets).
- The albedo depends (through the upwelling irradiance) on the presence and saturation of snow, the presence and depth of meltwater, the presence and depth of an ice lid on top of the melt pond, the depth of the sea ice beneath the melt pond, and the scattering and absorption coefficients of these media. .
2.3. Topography Model and Standard First‐Year and Multiyear Sea Ice Topographies
- Due to the limited availability of sea ice topography and snow topography data, and in particular combined data, some assumptions have been made in modeling the snow and ice topographies.
- The mean and variance of snow or ice depth is needed, which can be recovered from field data, and a covariance model is used to determine the correlation between snow or ice thicknesses at separate locations as the distance between locations increases.
- To create an ice topography two ice topographies were initially generated, one representing ice draft below a putative sea level and one representing freeboard ice height above a putative sea level.
- A mean ice thickness of 1.70 m was selected for the first‐year ice standard case, this is a mean ice thickness of first‐year ice with a thin snow cover as observed by Perovich et al. [2002b].
- This is most likely unrealistic and indicates a deficiency in using a simulated rather than measured topography.
3.1. Standard Case Simulation Results
- Day 140 is several days before the snow begins to melt.
- Mean pond area reaches its maximum at the same time, however mean pond depth continues to increase due to enhanced melting beneath ponds and water being transported across the surface to the cells with the smallest ice surface height.
- The percentage decrease in mass over the modeled melt season is 62.2% and the total ice ablation is 1.01 m.  (b) Change in mean snow depth (light blue), mean pond depth (red), and mean ice thickness with time for the standard first‐year ice case, with dashed lines representing the corresponding values for the alternative first‐year ice case.
- In the multiyear ice case the mean surface albedo decreases rapidly as snow melt produces ponds and continues to decrease more slowly until the ponds freeze over.
3.2.1. Comparison of Standard Case Simulations With Observations
- There is typically substantial variation between observations of melt ponds since observations are made at different points in the melt season and at different locations.
- The maximum pond fraction observed by Perovich et al. [2002a] was around day 174,early in the season, after this pond fraction decreased, which is a pattern seen in both the first‐year ice and multiyear ice modeled standard cases where there is a peak in pond coverage after snow cover is removed.
- The mean albedo of the ice surface over the melt season in the first‐year ice case is 0.64 and over the entire domain (which includes open ocean) is 0.56.
- The authors briefly compare the results of the model presented in this paper with that of Lüthje et al.  to 14 of 37 indicate the impact of the more realistic physics.
- The total ablation for first‐year ice in the Lüthje et al.  model of 0.75 m, was much less than the total ablation of 1.33 m in the model described here, this is due to the greater mass of water available in their model, due to the separate snow layer and the greater ice mean ice thickness. .
4. Sensitivity Studies: Results and Discussion
- Below the authors present sensitivity studies that examine the impact on pond cover and ice and snow ablation of changes in snow topography, ice topography, and vertical perme- ability for first‐year ice and multiyear ice.
- Unless otherwise indicated, all parameters are the same as for the appropriate standard case.
- Tables 2 and 3 summarize the important results for the sensitivity studies (and the standard cases for reference) for first‐year ice and multiyear ice, respectively.
- FYI denotes first‐year sea ice and MYI denotes multiyear sea ice.
4.1.1. Sensitivity of FYI Pond Coverage to the Snow Cover
- The following studies examine the sensitivity of pond evolution and ablation to snow depth and roughness.
- The snow topography used here represents the snow cover that would be expected on hummocky ice [Sturm et al., 2002], the standard deviation is increased from 0.15 m for the standard case to 0.25 m.
- There was an increase in maximum mean pond area from 219 m2 in the standard case to 315 m2 in the rough snow case and mean pond area exceeds the standard case pond area between days 185 and 195, when pond fraction is at its greatest.
- The smooth snow case differs from the standard first‐year ice case most obviously at the start of the season as the smaller variability in snow depth results in snow melting at the same rate across the grid causing initial pond fraction (not shown) and mean pond area to be greater than the standard case.
- The dashed lines represent the corresponding values for the standard first‐year ice case.
4.3. Discussion of Sensitivity Studies
- Tables 2 and 3 summarize the important results for the standard case runs and the sensitivity studies presented in this paper. .
- The dashed lines represent the corresponding values for the standard multiyear ice case.
- Such surface flooding was not observed in the multiyear ice case due to the deeper depressions in the ice, limiting the horizontal transport of water. .
- Change in mean snow depth (light blue), mean pond depth (red), and mean ice thickness with time for the smooth ice case.
5. Conclusion and Further Work
- The authors model uses the cellular automaton concept described by Lüthje et al. , with significant improvements, and the one‐dimensional vertical heat transport model described by Taylor and Feltham .
- The area‐averaged surface albedo of the summer ice cover is largely determined by the area of the sea ice covered in melt ponds and the open ocean fraction.
- (top) Variation in the fractional distribution of surface area with time for the low‐permeability case, where mean ice thickness is 2.50 m, standard deviation in ice thickness is 1.10 m, mean snow thickness is 0.30 m, and standard deviation in snow thickness is 0.25 m.
- The dashed lines represent the corresponding values for the standard multiyear ice case.
- Since the underlying ice topography plays such a central role in determining the location and extent of pond formation, detailed measurements of topography, in conjunction with observations of the pond evolution and surface forcing, will enable a stricter test of the melt‐pond–sea‐ice model. .
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...Although these existing data are too limited to fully validate the simulated melt pond distribution, the general pattern and evolution of time are within the range of field observations and detailed process studies, which were verified with observations (33, 34)....