T 55 r

200000

100000

100000 200000 300000 400000 500000 600000 700000 800000 900000

Longitude

Figure 4 A simulated lake region generated using a random number generator in Microsoft Excel™ to determine 2000 positions of pits and bumps in a 106 x 106 land-unit area. Pit or bump height was determined using the same random number generator to create relief features with an elevation of 0-100 units. The topography of the land surface was created using kriging and the lake shores were arbitrarily set at 27 units of elevation.

Pareto curves. These curves show similar rates of decline in abundance with lake size among many regions of the Earth.

Because the size-frequency distributions of lakes follow a Pareto distribution in many regions down to very small lake sizes (Figure 6), exhaustively censused (canonical) data on the abundance of the world's largest lakes allows eqn. [1] to be anchored at the upper end to permit estimation of the world-wide abundance of lakes across the full range of lake sizes. Two collections of exhaustively censused lakes are shown plotted on Figure 6. Considering only the 17357 natural lakes >10 km2 in area, eqn. [1] can be fitted by least squares regression as

Since the shape of Pareto distributions is similar among diverse regions of the Earth (Figure 6) and the parameters of this distribution are estimat-able from the canonical data sets, Downing and coworkers provided a means of estimating the global extent of ponds and lakes down to very small sizes.

Analyses of lake-size distributions based on the Pareto distribution (Table 3) reveal that, contrary to others' predictions, small lakes represent a greater lacustrine area than do large ones. The large lakes >10 000 km2 in individual lake area make up only about 25% of the world's lake area. Together, the two smallest size categories of lakes in Table 3 make up more area than the three top size categories. Thus, undercounting small lakes has resulted in the significant underestimation of the world's lake and pond area over the last century. World lakes and ponds account for roughly 4.2 x 106km2 of the land area of the Earth. This is more than double the historical estimates. Natural lakes and ponds >0.001 km2 make up roughly 2.8% of the non-oceanic land area; not 1.3-1.8% as assumed since the early 1900s.

"P1

20 0 20 40 60 Latitude

Figure 5 Measured latitudinal distribution of area of lakes, impoundments, and streams redrawn from Lehner and Doll's Figure 3. Areas of water bodies are summed over 3° increments of latitude. Lake areas are corrected following the work of Downing and coworkers by assuming that previous underestimates of lake areas have been distributed evenly across all latitudes. Areas of impoundments are likely to be correct but river areas are probably underestimated.

"P1

20 0 20 40 60 Latitude

Figure 5 Measured latitudinal distribution of area of lakes, impoundments, and streams redrawn from Lehner and Doll's Figure 3. Areas of water bodies are summed over 3° increments of latitude. Lake areas are corrected following the work of Downing and coworkers by assuming that previous underestimates of lake areas have been distributed evenly across all latitudes. Areas of impoundments are likely to be correct but river areas are probably underestimated.

10 000

te at

2 ra

1000

10 000

te at

2 ra

1000

Figure 6 Plots of data on the axes implied by eqn. [1]. Colored lines are high resolution GIS analyses of geographically dissimilar regions. The black lines represent canonical (complete) censuses of world lakes taken from publications by Herdendorf and by Lehner and Doll. This figure is redrawn from a publication by Downing and coworkers.

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