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GSA provides this and other forums for the presentation of diverse opinions and positions by scientists worldwide, regardless of their race, citizenship, gender, religion, or political viewpoint. Opinions presented in this publication do not reflect official positions of the Society. Geological Society of America Special Paper 370 2003 Lessons from large lake systems— Thresholds, nonlinearity, and strange attractors Kevin M. Bohacs* ExxonMobil Upstream Research Company, 3120 Buffalo Speedway, Houston, Texas 77098, USA Alan R. Carroll Department of Geology and Geophysics, University of Wisconsin, 1215 W. Dayton Avenue, Madison, Wisconsin 53706 USA Jack E. Neal ExxonMobil Exploration Company, 233 Benmar Street, Houston, Texas 77060-2598, USA ABSTRACT Lake systems are the largest integrated depositional complexes in the continental realm: modern lakes have areas up to 374,000 km2, and ancient lake strata extend up to 300,000 km2 in the Cretaceous systems of the south Atlantic and eastern China and the Permian system of western China. The largest lakes do not appear to form a significantly different population in many of their attributes. Their area, maximum depth, and volume closely follow power-law distributions with fractional exponents (–1.20, –1.67, –2.37 respectively), with minimal breaks between the largest lakes and the majority of lakes. Controls on lake size and stratigraphic extent are not straightforward and intuitively obvious. For example, there is little relation of modern lake area, depth, and volume, with origin, climatic conditions, mixis, or water chemistry. Indeed, two-thirds of the largest-area lakes occur in relatively dry climates (precipitation-evaporation ratio [P/E] <1.6). In ancient lake strata, deposits of largest areal extent and thickness tended to form mostly under rela- tively shallow-water, evaporitic conditions in both convergent and divergent tectonic settings. Geometric and dynamical thresholds appear to govern lake systems as complex, sen- sitive, nonlinear dynamical systems. Phanerozic examples worldwide indicate that the exis- tence, character, and stacking patterns of lake strata are a function of the interaction of rates of supply of sediment + water and potential accommodation change. Lake-system behavior reflects interactions of four main state variables: sediment supply, water supply, sill height, and basin-floor depth. The stratal record ultimately records five main modes of behavior indicating that nonmarine basin dynamical systems are governed by two funda- mental bifurcations and five strange attractors in the sediment + water supply – potential accommodation phase plane: fluvial, overfilled lake, balanced filled lake, underfilled lake, and aeolian/playa. Thus, extremely large lakes are highly dependent on intricate convolu- tions of climatic and tectonic influences and occur in a variety of settings and climates. Keywords: aeolian, Caspian Sea, climate, climate change, continental depositional sys- tems, contingency, fluvial, fractal, lacustrine, lake, lake size, mixis, nonlinear dynamics, non- marine depositional systems, paleoclimate, paleolatitude, playa, rift basin, rivers, sag basin, tectonics, topography, water chemistry. *[email protected] Bohacs, K.M., Carroll, A.R., and Neal, J.E., 2003, Lessons from large lake systems—Thresholds, nonlinearity, and strange attractors, in Chan, M.A., and Archer, A.W., eds., Extreme depositional environments: Mega end members in geologic time: Boulder, Colorado, Geological Society of America Special Paper 370, p. 75–90. ©2003 Geological Society of America 75 76 K.M. Bohacs, A.R. Carroll, and J.E. Neal INTRODUCTION lakes, and discusses insights that large lakes provide for all lacus- trine and continental depositional systems. Large lakes have intrigued and fascinated humans since Our main data sources cover 253 modern lakes from an time immemorial; indeed, a significant portion of early hominid extensive compilation by Herdendorf (1984) of modern lakes evolution transpired around the large lakes of east Africa. As greater than 500 km2 in extent, and 211 ancient lakes from Cam- with any familiar object, there are numerous clashes between brian to Pleistocene (from Gierlowski-Kordesch and Kelts, 1994, facts and hypotheses, between what “everybody knows” and 2000; Carroll and Bohacs, 1999; and Bohacs et al., 2000a, along comprehensive observations. Ptolemy, in about 154 A.D., with other ExxonMobil proprietary studies). All of the data on reported quite accurately on the location and sizes of the large modern systems are available in GSA Data Repository item east African lakes, Victoria, Tanganyika, and Malawi. Later, 99161; most of the ancient examples are covered to some degree natural philosophers of the Enlightenment era thought these in the publications cited. huge inland seas to be fabulous, for they reasoned that no large Based on these observations, our hypotheses are that large bodies of water could exist beneath the scorching equatorial sun lakes do not form a particularly distinctive population and that (Guadalupi and Shugaar, 2001). It took the intensive efforts of lake size is not a particularly strong function of climate, latitude, mid-nineteenth century European explorers to “discover” and altitude, origin, mixis, or water chemistry. We do see that lake map these lakes, complete with native towns and fishing and size is an intricate function of four main factors: sill height, basin- trading fleets (Burton, 1860; Speke, 1863; Baker, 1866). Analo- floor depth, water supply, and sediment supply. We suggest that a gous clashes of thought and observations about lakes persist variety of combinations of these factors can yield large lakes— even into our day; although very large lakes are commonly that bigness is an accidental, and not an essential, attribute of a termed “inland seas,” they do not behave like small oceans, at lake system. least in the stratigraphic or geochemical sense (e.g., Bohacs, 1999, Bohacs et al., 2000c; Buoniconti, 2001). Additionally, MODERN LACUSTRINE SYSTEMS one might tend to think of large lakes as somehow distinctive and special in their origin and behavior. This thought does not, When discussing large lakes, the first issue to be addressed is however, stand up under close scrutiny of either modern or the measure of size, or which dimension of the lake is to be con- ancient lakes (Bohacs et al., 2000b). sidered: volume, depth, area, or some combination of these mea- Numerous observations of modern lakes and Phanerozoic sures (e.g., Hutchinson, 1957; Cole, 1979). The answer depends lacustrine strata strongly indicate that lake size, shape, chemistry, on the scope and focus of one’s investigation: in general, volume and ecology are not simple functions of climatic humidity or tec- is of interest for investigating system hydrology and ecosystem tonic subsidence. All lakes owe their existence and character to the issues; depth correlates mainly with mixis, distribution of biota, nonlinear interaction of rates of potential accommodation increase and water-sediment interactions; and area relates to trophic state, and supply of sediment and water; potential accommodation is the energy influx, and the lateral extent of lacustrine strata. space available for sediment accumulation below a lake’s sill or There is only a weak relation among these three measures spillpoint (Carroll and Bohacs, 1999). A lake’s size, chemistry, of lake size. Table 1 lists the largest 10 in each size category and and biota can vary rapidly, and lake strata are punctuated by many shows an imperfect correspondence among rankings. For widespread breaks (Gierlowski-Kordesch and Kelts, 1994; instance, Lake Baikal is second in volume, first in depth, but sev- Sladen, 1994; Bohacs et al., 2000a). Rates of change can be enth in area. Analysis of the lake data reveals a key insight: the extreme: lake level changes of 300 m in 10–20 k.y. are common deepest lakes are not necessarily the lakes with largest areal throughout the Pleistocene (e.g., Street-Perrott and Roberts, 1983; extent (Fig. 1A). Also, it appears that maximum lake depth is the Street-Perrott and Harrison, 1984, 1985; Contreras and Scholz, strongest factor in determining lake volume, and area is only a 2001). For example, Lake Victoria changed from totally desic- weak factor: r2 = 0.64 for depth versus volume, but r2 = 0.03 for cated to the largest area lake in Africa, populated with over 300 area versus volume (even allowing for the auto-correlation inher- fish species in less than 25 k.y. (Johnson et al., 1996). ent in these relations; Figs. 1B and C). Areal extent is the main The responses of lake systems to climatic, tectonic, and other focus of this paper because it forms the strongest link between forcing functions are complex, and their stratigraphic records can depositional environment and the extent of its stratal record, but be difficult to interpret. Lacustrine strata record various modes of first we examine the other two measures of lake size. lake response to changes in forcing conditions as a function of cli- The volumes of modern lakes follow a very strong trend mate, tectonics, sediment supply, and inherited topography. As with rank along a power-law distribution with a fractional expo- with so many other geological phenomena, the origin and exis- nent or dimension of 2.37 (r2 = 0.97, n = 253; Fig.