By Dr. Lars Håkanson (auth.)

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Table 8. 45 krn3 • Now, how can this value be corrected and what is the certainty of the volume determination? A correction factor is obtained from Table 9. 996 for Lake Vanern. 45 krn3. -<::: .. 5) / ; ; : ; / ' / ' /' Q. , J:. -8 ~:y// //. / / (%) / / f Fig. 26. S) Table 9. 9993 (see Table 10). 45). 6 %. Table. 10. 0000 1. 0004 This method to determine the lake volume is, in principle, valid for all lake types. However, for lakes with rather JIl)re complex relative hypsographic curves the correction factor has to be established in a different manner.

The mean slope and the median slope are primarily to be considered as descriptive parameters. (F, dimensionless); a measure of the degree of irregularity of the shoreline. l~~! /TflA where 10 = the normalized shoreline length in km; A = the total lake area in km2• 50 (24) 6 10 5 8 4 ~ 6 ~ - 3 "o Do f en U;4 2 2 1 o ~-'--~-'--~-1--'---r-~--r--+ o 20 40 I i i o 1000 2000 60 I 3000 100 (%) 80 I 4000 i 5000 I 6000 (km 2 ) Cumulative area Fig. 31. Detennination of the median slope (a,50) from the slope curve for Lake Vanern The F-value illustrates the relationship between the actual length of the shoreline and the length of the circumference of a circle with an area equal to the total lake area.

40 Fig. 25 . The ARIsro planimeter Volume (V _ ~n3); may be determined from the following two formulae: n VI = L i=O n Ie :r i=O V = L p lc (18) ~ (a. + a . 1) l. 1 1+ (a. • a i +l ' 1 1 (19) where Ie = the contour-line interval in m; a i = the total area (= the cumulative area) within the limits of the contour line Ii' in km2. 41 The VI-formula (eq. 18) is called the linear approximation of the volume, the Vp-formula (eq. 19) the parabolic approximation. Which of these two formulae should be used depends on the lake form (Hakanson, 1977a).