## Impoundments

Parallel with the analysis of natural lakes above, one can fit the Pareto distribution to the sizes of large impoundments. Downing and coworkers did this using data from the International Commission on Large Dams who publish data on dams around the world that are of safety, engineering or resource concern (e.g., Figure 7). These data are purposefully biased toward large dams so the data provide the most accurate estimate of impoundments with the largest impounded areas, and progressively less complete coverage of small ones. Fitting eqn. [1] to data on the 41 largest impoundments from the largest impoundment (13 500 km2) down to 1000 km2 yields:

This equation implies that the smallest of the large impoundments make up more surface area than the largest of them because the exponent is strongly negative. This dataset is intentionally biased to large dams so the exponent increases if small impoundments are included. If one considers all of the ICOLD impoundments down to 1 km2, the result will be biased toward underestimation of impoundment area, but is

This equation results in an underestimate of the area covered by impoundments because it ignores many impoundments formed by small dams. Calculations using this function and the Pareto distribution, however, show that there are at least 0.5 million impoundments >0.01 km2 in the world and they cover >0.25 million km2 of the Earth's land surface (Table 3). This calculation using the Pareto distribution yields a smaller area than estimates based on extrapolation but nearly identical to GIS-based estimates. Large impoundment data suggest that small impoundments cover less area than large ones (Table 3).

Most analyses of impoundment size distributions have ignored small, low-tech impoundments created using small-scale technologies. Farm and agricultural ponds are growing in abundance, world-wide, and are built as sources of water for livestock, irrigation, fish culture, recreation, sedimentation, and water quality control.

Figure 8 shows that the area of water impounded by agricultural ponds in several political units expressed as a fraction of farm land varies systematically with climate. In dry regions, farm ponds are rare, but up to about 1600 mm of annual precipitation, farm ponds are a rapidly increasing fraction of the agricultural landscape. In moist climates, farm ponds make up 3-4% of agricultural land. Downing and coworkers used this relationship (Figure 8) with data on area under farming practice, pond size, and estimates of annual average precipitation to estimate the global area covered by farm pond impoundments. They found that 76 830 km2, worldwide, is covered with farm ponds. These small impoundments are growing in importance at annual rates of from 0.7%

 Area range (km2) Number of Total area of Number of Total area of lakes lakes (km2) impoundments impoundments (km2) 0.001-0.01 277 400 000 692 600 76830 000a 76 830b 0.01-0.1 24120 000 602100 444800 12 040 0.1-1 2 097 000 523400 60 740 16 430 1-10 182300 455100 8 295 22440 10-100 15 905 392 362 1 133 30640 100-1000 1 330 329816 157 41 850 1000-10000 105 257 856 21 57140 10000-100000 16 607 650 3 78030 >100000 1 378119 All water bodies 304000 000 4 200000 77345 000 335 400 Percent of land area 2.80% 0.22%

Superscript 'a' indicates that the calculation was based on an average farm pond size of 0.001 km2. 'b' Indicates an estimate of the global area of farm ponds.

Superscript 'a' indicates that the calculation was based on an average farm pond size of 0.001 km2. 'b' Indicates an estimate of the global area of farm ponds.

1700 1800 1900 2000 Year

Figure 7 Rate of change in impounded area in the United States for all impoundments listed by the United States Army Corps of Engineers with dams listed as potential hazards, or low hazard dams that are either taller than 8 m, impounding at least 18500 m3, or taller than 2 m, impounding at least 61 675 m3 of water (after Downing and coworkers). All data were ignored where the date of dam construction was unknown (ca. 12% of impounded area) or natural lakes (e.g., Lake Superior) were listed as impoundments. The dashed line shows a semi-log regression (r2 = 0.95) based on the exponential phase of impoundment construction.

1700 1800 1900 2000 Year

Figure 7 Rate of change in impounded area in the United States for all impoundments listed by the United States Army Corps of Engineers with dams listed as potential hazards, or low hazard dams that are either taller than 8 m, impounding at least 18500 m3, or taller than 2 m, impounding at least 61 675 m3 of water (after Downing and coworkers). All data were ignored where the date of dam construction was unknown (ca. 12% of impounded area) or natural lakes (e.g., Lake Superior) were listed as impoundments. The dashed line shows a semi-log regression (r2 = 0.95) based on the exponential phase of impoundment construction.

per year in Great Britain, to 1-2% per year in the agricultural parts of the United States, to >60% per year in dry agricultural regions of India.

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