The document analyzes geometric and topological characteristics of polygonal networks formed by freezing and thawing of soils in Adventdalen, Svalbard, Norway. Over 10,000 polygons across 120 networks were mapped from aerial imagery. 17 networks were analyzed in detail. Larger networks had smaller average polygon sizes while some networks with larger polygons showed signs of subdivision into smaller polygons over time. Networks with higher percentages of intersections with 4 sides (tetravalent vertices) and smaller, more uniform polygon sizes showed progression toward an equilibrium cracking pattern.

1. Geometric and Topologic Characterization of Periglacial Polygonal Networks
in Adventdalen, Svalbard, Norway
J. Saraiva (1,3), M. Lousada (1) , P. Pina (1) , L. Bandeira (1), and G. Vieira (2)
(1) Instituto Superior Técnico, Lisboa, Portugal, (2) CEG / IGOT, Lisboa, Portugal, (3) UNIS, Longyearbyen, Norway.
Research developed within the project ANAPOLIS (PTDC/CTE-SPA/099041/2008),funded by FCT (Portugal)
INTRODUCTION AND OBJECTIVES
Polygonal terrain patterns commonly occur in periglacial regions of the Earth, where seasonal processes of freezing and thawing cause the soil to expand and contract, leading to
the formation and growth of cracks. Understanding the formation of this type of networks on Earth and tracing their evolution can provide us with many insights into the history
of similar patterns on Mars. Thus, analogue studies of this type of structure on Earth are important. In this work, the objectives are to describe the geometric and topologic
characteristics of a number of networks of ice-wedge polygons occurring in a coastal valley, the Adventdalen, on the Norwegian archipelago of Svalbard, in the Arctic, at 78⁰ N.
METHODS RESULTS Adventdalen Topographic Map and ESRI Base Maps
A NETWORK MAPPING More than 10,300 individual polygons in 120 networks were identified and digitized into a GIS. Networks where polygons present a smaller average area have a larger
average in the number of neighbours.
Mapping was conducted through the analysis of remotely sensed imagery: Geometrical and topological analysis was conducted for 17 selected networks. There is a direct relation between a higher average in the number of
53 orthophotomaps (four-band RGB+NIR and 0.2 m/pixel of spatial
neighbours and the percentage of tetravalent vertices in a network.
resolution), acquired by the Norwegian Polar Institute.
The mean axis of a polygon is defined as the average between its major and minor orthogonal
B GEOMETRICAL CHARACTERIZATION axes; the aspect or elongation ratio corresponds to the division of the minor by the major axis.
The values in the table are averages for each of the networks selected.
Neighbours Vs. Areas and Neighbours Vs.
Vertices (tri) for the 17 Networks
Neighbours Vs. Areas and Neighbours Vs.
Vertices (tetra) for the 17 Networks
Network Network Nb. Mean Axis (m) Aspect Ratio
Area (m2) Polygons Average Min Max Average Min Max
1 20,572 95 17.08 9.14 31.83 0.67 0.32 0.93
2 49,157 262 15.58 5.24 36.69 0.69 0.24 1.00
3 270,529 1,666 14.68 3.50 46.65 0.71 0.19 1.00
4 114,631 671 14.49 4.51 65.04 0.71 0.28 0.99
5 28,882 95 19.87 7.86 53.98 0.66 0.31 0.95
6 264,199 821 20.29 5.43 71.62 0.71 0.31 1.00
7 88,612 253 21.67 6.22 50.76 0.72 0.37 0.98
8 178,501 264 28.77 6.23 95.69 0.69 0.28 0.98
9 255,783 328 32.28 8.46 100.92 0.67 0.30 0.99
Network 3 is the largest in area; its polygons, Network 9 is also among the largest, but its 10 59,781 116 21.51 6.70 162.99 0.69 0.25 0.96
however, are among the smallest, according to polygons are much larger, with a mode over 11 87,118 161 26.67 5.73 63.58 0.68 0.30 0.95
the average value of their mean axis; the mode 25 m and almost 80% of polygons with
is 10 to 15 m, and the large majority of the mean axis between 20 and 40 m. 12 99,110 216 24.43 4.44 67.92 0.70 0.35 0.99
polygons sit between 10 and 20 m. 13 112,765 215 26.57 8.69 58.69 0.70 0.29 0.98 % of Vertex (tri and tetra) Vs. Average
14 139,684 197 31.01 8.56 67.08 0.67 0.21 1.00 Polygon areas for the 17 Networks
15 154,644 294 25.78 7.67 99.19 0.69 0.33 0.98
C TOPOLOGICAL CHARACTERIZATION 16 129,783 215 28.08 9.42 59.83 0.68 0.28 0.96
17 130,645 357 21.01 4.85 83.02 0.68 0.25 0.97
The 17 networks selected for this analysis all contain at
least 20 interior polygons (after stripping the two outer Tetravalent Vertex (field views) Trivalent Vertex
layers). Topological analysis was conducted considering
only those interior polygons, and consisted on the Considering the global set of 17 networks, the
percentage of trivalent vertices rises with
computation of the number of neighbours and of the
increasing average polygon areas; for tetravalent
valence of each vertex.
vertices, the inverse situation occurs. This may
Network Nb. of Nb. of Neighbours Vertices reflect a process of subdivision of formerly large
Polygons polygons, creating new tetravalent vertices and
Average Min Max Nb % Tri %Tetra % Penta Network 3 has a large number of small Network 13 has a lower mean in thus increasing their representation in the
1 21 6.62 5 9 46 69.57 30.43 ---
polygons, with the highest mean for number of neighbours, and the network, while also augmenting the average of
the number of neighbours and seven mode is six; the percentage of
2 44 6.75 4 10 97 63.92 34.02 2.06 as the mode; it also shows a high tetravalent vertices is much lower.
the number of neighbours of its polygons.
3 1,132 6.98 3 12 1,875 68.00 31.57 0.43 percentage of tetravalent vertices.
4 415 6.78 3 11 737 75.98 24.02 ---
5
6
7
25
433
108
6.64
6.73
6.25
5
4
3
9
14
9
58
822
70.69
74.94
29.31
24.57
---
0.49 CONCLUSION
249 89.16 10.84 --- It is generally admitted that the first polygons to be formed are large. After
8 43 6.02 4 8 134 88.06 11.94 ---
9 108 6.29 3 10
repeated seasonal freezing and thawing, it is very likely that new cracks form
265 88.68 11.32 ---
10 35 6.66 5 9 70 64.29 35.71 --- inside them, leading to their subdivision into smaller ones. Thus, the
11 37 6.03 4 11 100 89.00 11.00 --- proportion of tetravalent vertices in a network might be seen as an indicator
12 56 6.27 4 9 147 84.35 15.65 --- of its evolution stage. The fact that, according to our data, the networks with
13 69 6.13 4 10 168 88.69 11.31 --- high percentages of tetravalent vertices and small polygons also exhibit a
14 58 6.53 3 11 141 83.69 15.60 0.71
15 146 6.44 4 11 303 84.82 14.19 0.99
smaller variation in polygon size, points toward the existence of a process
16 40 6.18 3 8 108 85.19 14.81 --- conducing to an equilibrium which is reflected in a more regular pattern of
17 77 6.27 4 9 201 82.59 17.41 --- cracks.