By Dr. Lars Håkanson (auth.)
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Extra info for A Manual of Lake Morphometry
E. the water surface. a = 5 648 km2 in Lake Vanern. 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.
The manual for lake volume determination will now be exemplified for Lake Vanern. Base data on depth and area values are given in Table 8. e. 5) and it has no point of inflexion (see Fig. 26). 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 %.
The total length of the contour lines in the bathymetric map is 11 400 km (see later part). 14 mm. This is practically equal to the width of the contour 24 Table 5. 65 1 lines on the map. Thus, the error may, for IIDst practical purposes, be regarded as negligible. g. concerning new deep holes or sub-aquatic tops of limited areal extension, and the configuration of certain contour lines, which would be altered since the interpolation would be carried out from a new track net. Those hypothetical IIDdifications can, however, only change details and not the general pattern of the contour lines in the bathymetric map of Lake Vanern.