Now that I had a municipality attribute in my coastline dataset, I was able to calculate the length of each segment and used Excel to summarize the calculations per municipality.
Scale-dependant result
To double check that my results were coherent, I looked for official figures online. I knew already the information didn’t exist for all municipalities, since I had done that search before doing my calculations, but some municipalities separately publish their figures. Vordingborg, for instance, is the municipality with the longest coastline, which was also what I had found. However, on the official website of Frederikshavn (one of the first municipalities to be updated in Trap), the figure given is 105 km.. while I had calculated 163 km. Actually, there are so many islands, that the length of the continental coastline is only 150 km. The dataset I used was the highest accuracy available; so I decided to do the same calculations with the other scales: 1:500,000 and 1:20,000,000, to see if the ‘official figure’ was taken from one of these datasets.
Exploring these differences
As expected, the other scales did not have as much coastal details, and some islands were not included. The 1:10,000 scale included every single turns and meanders in the coast, including the crenels on sea defences! As a results, for most municipalities, the higher the scale, the shorter the coastline. There were also some parts that can be considered as an aberration when looking at the coast: for instance in Odense the entire estuary was included, making the coast much longer at the 1:10,000 scale than the others.
The harbours also are not always detailed in the same way, as shown here in Frederikshavn:
When included in the higher scales, the details of the coast of the islands can be quite different. For instance, Christiansø (one of the islands furthest east of Denmark, in the Baltic Sea) has a very different coastline depending on the scale.
Finally, there were also issues of points density, like in Frederikshavn (again!):
In both scales we can see aberrations: at 1:10,000 (in black), we see the crenels of the sea defences in the southern most coast; while at the 1:500,000 scale, there are obvious parts of the coast that have been generalised.
Conclusion
The differences between the length at different scales is therefore:
- the inclusion of some features of the coast (estuary, coast, islands, ..)
- the density of points used to draw the coastline
It is very difficult to find any authoritative figure. The danger in choosing a scale with very fine details is that we eventually measure something that does not exist. In Frederikshavn, even some of the sea defences crenels are included. Is that really the coast? But selecting a scale that does not show what exist is neither satisfactory, since it hides some real coast.
Appendix
Here is the table of results of my calculations:
| Kommune | Length 1:10.000 (km) | Length 1:500.000 (km) | Length 1:2.000.000 (km) |
|---|---|---|---|
| Vordingborg | 398 | 339 | 321 |
| Guldborgsund | 332 | 281 | 263 |
| Lolland | 307 | 267 | 254 |
| Thisted | 258 | 233 | 222 |
| Sønderborg | 258 | 239 | 232 |
| Ringkøbing-Skjern | 252 | 205 | 192 |
| Aalborg | 232 | 192 | 182 |
| Slagelse | 222 | 182 | 176 |
| Skive | 207 | 187 | 175 |
| Morsø | 201 | 170 | 156 |
| Kalundborg | 189 | 169 | 160 |
| Svendborg | 189 | 163 | 151 |
| Bornholm | 188 | 122 | 116 |
| Langeland | 188 | 168 | 159 |
| Læsø | 168 | 114 | 101 |
| Frederikshavn | 163 | 120 | 117 |
| Syddjurs | 161 | 134 | 129 |
| Odsherred | 160 | 139 | 137 |
| Norddjurs | 157 | 127 | 124 |
| Nordfyns | 155 | 122 | 110 |
| Kerteminde | 153 | 132 | 128 |
| Lemvig | 152 | 122 | 117 |
| Tønder | 121 | 121 | 110 |
| Frederikssund | 150 | 110 | 100 |
| Struer | 149 | 137 | 128 |
| Jammerbugt | 139 | 121 | 112 |
| Haderslev | 138 | 121 | 108 |
| Samsø | 137 | 114 | 105 |
| Faaborg-Midtfyn | 130 | 110 | 105 |
| Mariagerfjord | 123 | 103 | 97 |
| Ærø | 123 | 106 | 100 |
| Middelfart | 120 | 107 | 105 |
| Esbjerg | 119 | 87 | 85 |
| København | 118 | 72 | 70 |
| Randers | 115 | 97 | 88 |
| Tårnby | 112 | 60 | 46 |
| Aabenraa | 73 | 66 | 63 |
| Vesthimmerlands | 110 | 103 | 94 |
| Assens | 104 | 91 | 88 |
| Holbæk | 103 | 81 | 78 |
| Næstved | 103 | 77 | 75 |
| Odder | 98 | 77 | 73 |
| Holstebro | 91 | 76 | 66 |
| Varde | 87 | 76 | 75 |
| Hedensted | 80 | 74 | 69 |
| Horsens | 76 | 65 | 63 |
| Aarhus | 73 | 56 | 55 |
| Fanø | 73 | 51 | 49 |
| Lejre | 73 | 57 | 54 |
| Halsnæs | 64 | 45 | 44 |
| Hjørring | 63 | 53 | 52 |
| Kolding | 63 | 59 | 57 |
| Nyborg | 56 | 47 | 46 |
| Roskilde | 50 | 38 | 35 |
| Fredericia | 48 | 40 | 39 |
| Stevns | 44 | 40 | 40 |
| Viborg | 44 | 39 | 38 |
| Helsingør | 35 | 26 | 25 |
| Odense | 35 | 12 | 11 |
| Vejle | 34 | 30 | 29 |
| Faxe | 34 | 30 | 29 |
| Gribskov | 32 | 31 | 31 |
| Køge | 25 | 21 | 21 |
| Dragør | 20 | 14 | 14 |
| Brønderslev | 18 | 13 | 12 |
| Greve | 15 | 12 | 12 |
| Fredensborg | 13 | 9 | 9 |
| Hvidovre | 12 | 10 | 10 |
| Solrød | 12 | 8 | 8 |
| Gentofte | 10 | 8 | 8 |
| Rudersdal | 9 | 6 | 6 |
| Hørsholm | 9 | 7 | 7 |
| Christiansø | 9 | 4 | 4 |
| Lyngby-Taarbæk | 4 | 3 | 3 |
| Ishøj | 4 | 8 | 7 |
| Brøndby | 3 | 8 | 9 |
| Vallensbæk | 0 | 3 | 3 |