Modern Analyses of Limnicity and Lake Size Distribution

Nearly concurrently, Lehner and Doll and an international team of scientists working with Downing at the US National Center for Ecological Analysis and Synthesis applied modern GIS methods and updated geographic imagery to updating inventories of world lakes. These two efforts used divergent approaches but both had the objective of using new technologies to provide a more accurate estimate of the global extent and distribution of lakes and other water bodies.

The approach used by Lehner and Doll was to combine many data sources to create a global database of lakes and wetlands. This database was created by combining data sources, registers, and inventories focusing on descriptive attributes with analog or digital maps that show the spatial extent and locations of lakes and impoundments. This important step replaced the >13 published, list-based attribute tables with a GIS approach, which allows evaluation of area, shape, and location of lakes and impoundments. These two data sources allow some historical perspective, as well, since modern sources such as satellite images may not include long-term variations that can only be derived using local information. For example, the Aral Sea has decreased in area to less than 30% of its former area. Although the database was compiled to represent lakes >0.1 km2 in area, Lehner and Doll judged that even high-resolution satellite imagery under-samples lakes <1 km2. Therefore, this approach did not effectively inventory lakes smaller than about 100 ha in surface area but offered the most substantial advance in the inventory of world lakes since Halbfass's compilation of 1914.

Lehner and Doll confirmed previous estimates of both the size distribution (as area) of moderate-to-large lakes as well as the surface area of the Earth they occupy. They showed quantitatively that the number of lakes in a size category increases as a power function of decreasing area. They showed, for example, that although there are 105 lakes >1km2, there are only about 100 lakes >1000 km2 in area. They also confirmed the previous estimates of the global area covered by moderate-to-large lakes as being near to 2.5 million km2. More importantly, however, their use of GIS and satellite imagery allows a greatly improved understanding of how global lake area is distributed geographically (Figure 5) and how lake area is distributed compared with that occupied by rivers and impoundments. In this analysis, rivers were distinguished from lakes and impoundments based on their development ratio so that very long and narrow water bodies were called 'rivers'. Further, this analysis includes only medium-to-large lakes and likely includes only the largest of rivers (i.e., with a breadth of 100 m or more; Strahler order >5). The distribution of lake area is strongly skewed toward the north temperate zone (35-70° N) with a small increase also

Table 2 Some of the world's large lakes that are of great depth, arranged in decreasing order of maximum depth

Name

Latitude

Continent

Zmax (m)

Zmean (m)

Lake area (km2)

Baikal

54.0

Asia

1741

730

31 500

Tanganyika

-6.0

Africa

1471

574

32 900

Caspian

42.0

Asia

1025

209

374000

Nyasa

-12.0

Africa

706

273

22 490

Issykkul

42.4

Asia

702

277

6240

Great Slave

61.8

N. America

625

73

28568

Toba

2.6

Asia

529

249

1150

Tahoe

39.1

N. America

501

249

500

Kivu

-2.0

Africa

480

240

2370

Great Bear

66.0

N. America

452

76

31 326

Fagnano

-54.6

S. America

449

211

590

Nahuel Huapi

-41.0

S. America

438

206

550

Dead

31.5

Asia

433

184

1020

Superior

47.6

N. America

407

149

82100

Llanquihue

-41.1

S. America

350

133

800

Geneva

46.4

Europe

310

153

580

Titicaca

-15.8

S. America

304

103

8030

Aregentino

-50.2

S. America

300

120

1410

Iliamna

59.5

N. America

299

123

2590

Atlin

59.5

N. America

283

86

774

Michigan

44.0

N. America

282

85

57 750

Hovsgol

51.0

Asia

270

183

2620

Melville

53.8

N. America

256

97

3069

Constance

47.6

Europe

252

90

540

Ontario

43.7

N. America

245

86

19 000

Ladoga

61.0

Europe

230

52

17 700

Baker

64.2

N. America

230

93

1887

Huron

45.0

N. America

229

59

59500

Reindeer

57.3

N. America

219

17

6640

Mistassini

50.9

N. America

183

75

2335

San Martin

-48.9

S. America

170

68

1010

Nipigon

49.8

N. America

165

63

4848

Taupo

-38.8

Oceania

165

97

616

Van

38.6

Asia

145

55

3740

Vattern

58.4

Europe

128

40

1856

Onega

61.5

Europe

127

30

9700

Champlain

44.6

N. America

122

49

1100

Athabasca

59.2

N. America

120

26

7935

Edward

-0.4

Africa

117

35

2150

Flathead

47.9

N. America

113

50

500

Sakami

53.3

N. America

110

52

592

Grand

48.9

N. America

110

52

537

Vanern

58.9

Europe

106

27

5648

Biwa

35.3

Asia

103

41

688

Pyramid

40.0

N. America

101

54

510a

A superscripted 'a' indicates that a lake's area is variable in time and that the area may be nominal. Zmax Is the maximum depth and Zmean is the average depth. Latitudes are expressed in decimal degrees with latitudes in the southern hemisphere expressed as negative numbers. Data are after Herdendorf's publications.

A superscripted 'a' indicates that a lake's area is variable in time and that the area may be nominal. Zmax Is the maximum depth and Zmean is the average depth. Latitudes are expressed in decimal degrees with latitudes in the southern hemisphere expressed as negative numbers. Data are after Herdendorf's publications.

near the equator (Figure 5). This is consistent with what is known about the distribution of large lakes (North American Great Lakes and the Caspian Sea), the balance of precipitation and evaporation, and agrees well with satellite scans of open water (except where large numbers of small lakes could not be inventoried). This analysis suggested that lakes make up about 1.8% of the land area (2 428 000km2), impoundments about 0.2% (251 000 km2), and rivers about 0.3% (360 000km2).

The perennial problem in lake inventories has been that small water bodies have gone un-inventoried. This has been assumed, somewhat tautologically, to be of little consequence because small water bodies have been found to be numerically dominant but inconsequential in terms of the area of land surface they cover. On the one hand, as shown by Lehner and Doll, no worldwide GIS coverage exists that has high enough spatial resolution to resolve all of the world's small lakes. On the other hand, we have

1000^

1000 10000 100000 1 000000 Lake area (km2)

Figure 2 Relationship between lake area and maximum depth taken from data compiled and published by Herdendorf. The dashed line is an empirically derived lower limit to maximum depth (m) for lakes larger than 5000 km2, where A is the lake area in km2.

long-standing information on the size distribution of the world's lakes down to a size of 1-10 km2 as well as high-resolution GIS coverage on many regions that can be used to examine and characterize the size distribution of lakes down to the smallest sizes.

Downing and coworkers improved estimates of lake abundance and area by working on the small-lake under-sampling problem. They estimated the world abundance of natural lakes by characterizing the size distribution using a nearly universally applicable distribution function, testing its fit to data down to the smallest sizes of lakes, anchoring it in empirical data for large lakes, and solving the distribution function to calculate the world abundance of large and small lakes.

Because the relationship between dL and lake area (A) in Figure 1 appears to fit a power function, Downing and coworkers and Lehner and Doll suggested that lake-size distributions fit a size-frequency function of the form:

where Na>Ais the number of lakes of great or equal area (a) than a threshold area (A), and a and p are fitted parameters describing the total number of lakes in the dataset that would be of one unit area in size and the logarithmic rate of decline in number of lakes with lake area, respectively. This model corresponds to a Pareto distribution that is particularly versatile and used in fields from linguistics to engineering. It has also been found useful in describing lakes' size-frequency distributions, as long as the data are not truncated or censored.

Www Spatialresolution Gool Com
Figure 3 Illustration of the influence of scale of observation on the perceived size distribution of lakes. Source: earth.google. com. The images are centered on the same point but have improved spatial resolution from top to bottom.

To test lake size distributions for general fit to the Pareto distribution, Downing and coworkers collected exhaustive inventories of all lakes within a variety of geographical settings representing divergent topography and geology. Figure 6 shows that there are interregional similarities among slopes of

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