# What is 'dissection rate'?

I am looking for a definition of this term for wikipedia, with a reference.

It's mentioned on Franz Josef Land where it's indicated that the units are km-2/km. I'm curious about how this would be measured.

I've found precious few mentions of this unit in the usual sources.

Thanks in advance!

## 2 Answers

I’ve actually just updated the article you referenced on Wikipedia.

In fact, there is no measure called “dissection rate” represented by these units that is used this way in earth science literature. The 3.6 number in the text is merely the ratio of the total area of Franz Josef Land to its total coastline length, that is, 16,134 sq km / 4,425 km = 3.65 sq km per coastline km.

This quantity shouldn’t really be called a rate, which in the Earth Sciences generally refers to a measurement whose units are divided by time, or otherwise a ratio describing the way in which one quantity changes in relation to another, because it is instead just a simple ratio of two known, fixed measurements: area and perimeter (i.e. coastline length).

This particular ratio describes the degree to which a a landmass has been dissected/eroded, highly dissected landmasses having a relatively long, complex, tortuous coastlines and thus smaller ”dissection rates”, and landmasses that have not been so heavily eroded having a coastline that is much smoother—the perfectly “un-dissected” landmass would be in the shape of a circle. A perfectly circular landmass with area equal to Franz Josef Land would have a “dissection rate” of 35.83, the highest possible number for that area. It is an imperfect measure because it is dependent on the area—the larger the area, the greater the maximum dissection rate. What would be a better measurement is the ratio of the square root of the total area to its coastline, which is constant and related to fractal dimension.

The “dissection rate” as calculated in this Wikipedia article is also poorly conceived because it has an inverse relationship with the degree of erosion—that is, more dissection in a landmass equals a lower number, whereas one would expect that “dissection rate” should be a quantity that gets higher with more dissection.

Because Franz Josef Land has been heavily glaciated since the Pleistocene and remains 85% glaciated, and because glaciers are by far the most erosive force on earth and also very massive, depressing the surface of the earth under their weight and causing more land to come into contact with the ocean at sea level, it has been thoroughly dissected.

### Ratios of total area to total coastline length for Arctic Archipelagos:

Archipelago Total Area, A (sq km) Coastline Length, l (km) A/l
Franz Josef Land 16,134 4,425 3.65
Severnya Zemlya 37,000 2,782 13.30
New Siberian Islands 38,400 2,611 14.71
Svalbard 62,045 3,587 17.29
Novaya Zemlya 83,000 4,400 18.86

As you can see in the table above, Franz Josef Land is much, much more dissected than any of the other archipelagos like it on the Eurasian Arctic passive margin, with a ratio of 3.65, compared to ratios of between 13 and 18.

Note: Coastline length data was not available in any reference I could find for Severnaya Zemlya and the New Siberian Islands. I calculated the coastline lengths of these archipelagos in GIS using the Natural Earth 10m coastline and minor islands coastlines datasets, merged. Additionally, the area given for New Siberian Islands on Wikipedia is incorrect—Encyclopedia Britannica provides the correct figure (which I also verified in GIS using an equal-area projection on the same data set).

• Although I would agree with what you've written on the whole, and in particular that the word 'rate' was misapplied here, it might be worth saying that this word is sometimes used where time is not involved, as for example, in exchange rates. Commented Aug 5, 2023 at 21:31
• @BillBell That’s absolutely correct, but I can’t think of a single example in the Earth Sciences, let alone the Physical Sciences, where “rate” is used in this way (maybe there is, though?). Most of the examples you speak of (e.g. exchange rate, literacy rate, interest rate, tax rate) occur in the areas of economics or sociology. If you search Earth Science, specifically geomorphological literature, you only ever come across a handful of uses of “dissection rate”, and they all refer to a quantity over time. However, I will edit my answer to limit what I say to the Earth Sciences. Commented Aug 10, 2023 at 22:57
• An Earth Sciences usage of rate in which time isn't involved? en.wikipedia.org/wiki/Lapse_rate is a common topic in meteorology (it's the amount something [usually temperature] changes vertically) Rates generally can be any ratio between two measures (Google rate's definition for verification), aka any derivative. But still don't disagree with your specific answer though! (I know nothing about it, and your sources/experience on the topic sound reasonable to me... and using it in geology in that way does sound weirder to me) Commented Aug 11, 2023 at 8:46
• @JeopardyTempest thanks—my domain is geology, and when it comes to meteorology I am a novice, so I learned something on that page. I think it’s worth noting that this “lapse rate” is a proper rate—i.e. it describes the quantity by which one variable changes in relation to another. Often, this is in relation to time, but it obviously doesn’t need to be. The “dissection rate” discussed in this question, however, has nothing to do with a change in the relationship of two quantities—it’s merely a ratio of two known measurements. I suppose this is at the heart of the problem I have with it. Commented Aug 18, 2023 at 12:01

In geological terms, "dissection" appears to refer to the creation of cuts in a landscape due to erosion e.g. by the flowing of streams. Dissection rate would then be the rate at which such cuts in the landscape form.

https://books.google.com/books?id=AIyIAAAAMAAJ&pg=PA221&lpg=PA221&dq=dissection+rate+geology&source=bl&ots=bFXfYFDmt3&sig=CiiKojDNHIkyQxzqVkBuSyL1Zr0&hl=en&sa=X&ved=0ahUKEwiVgpOLm8TZAhUKnOAKHXQQBMMQ6AEIUjAI#v=onepage&q=dissection%20rate%20geology&f=false