ISSN:
1573-8868
Keywords:
geomorphology
;
statistics
Source:
Springer Online Journal Archives 1860-2000
Topics:
Geosciences
,
Mathematics
Notes:
Abstract This paper is based on the study of shore line length of 12 Swedish lakes on various maps ranging in scale from 1:10,000 1:1,000,000. The lakes differ in size, from Lake Munksjön, which has an area of 1.1 km2, to Lake Vänern with an area of 5893 km2, and also in shore line irregularity, ranging from the rather regular basins of Lake Munksjön and Lake Erken to the very irregular basin of Lake Mälaren. A “new ” method, the checkered transparent paper method (the CTP-method), was adopted to measure the shore length of certain lakes on various maps. Length determination by this method can be executed quickly and easily, and in a statistically definable way, giving comparable data from various types of map. A formula defining the functional relationship between scale, shore irregularity, shore length, and lake area has been derived: $$NF = F(K_{2} - K_{1})/[K_{2} - log(s + a)]$$ or $$1_{n} = 1(K_{2} - K_{1} )/[K_{2} - log(s + a)]$$ where NF = the normalized shore development (shore irregularity) at a scale of 1:1; F = the shore development as determined on a given map scale; s = the scale factor (10,000, 50,000 etc); a = 105 ⋅ log A, where 105 = the area constant; A = the lake area in km2; K1 = log(s + a) for s = 1, i.e. the reference scale; K2 = log(s + a) for s = 6,000,000, where 6,000,000 is called the scale constant; 1 = the shore length as determined by the CTP-method on a given map; and 1n = the normalized shore length at a scale of 1:1. The formula offers a high degree of accuracy and the length of any closed geomorphic line can be determined independently of map scale, under given practical limitations. The length value obtain is the normalized length, that is the best approximation of the real, natural length at a scale of 1:1.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01032862
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