Constraints on the Origin of Paleolake Expansions in the Central Andes

Home , Cabana (ancient lake), Lake Minchin, Lake Tauca, Lake Titicaca, Mataro (ancient lake)

Earth Interactions • Volume 1 (1997) • Paper No. 1 • Page 1

Troy A. Blodgett,* John D. Lenters,** and Bryan L. Isacks* *Department of Geological Sciences, Cornell University, Ithaca, New York **Atmospheric Science Program, Cornell University, Ithaca, New York

Received 11 March 19; accepted 6 December 1996.

ABSTRACT: During the late Pleistocene, at least one episode of lake expansions occurred in the internally draining high plateau region of Bolivia. Some researchers have advocated that a wetter climate associated with a change in atmospheric circulation caused the development of the large paleolakes, while others have hypothesized that deglaciation contributed to the water source for the expanding lakes. From estimates of the potential meltwater stored in the glaciers during their maximum extents, the authors conclude that insuf®cient meltwater was available to ®ll the large paleolakes. However, the meltwater hypothesis remains viable south of the main plateau region where, in ®ve small drainage basins, the volume of available glacial meltwater was 3±16 times greater than the volume of water in the paleolakes. Pollen, dunes, and other eolian features indicate that the region surrounding the Altiplano was much drier during at least one interval of the late Pleistocene. Although the timing of the dry period with respect to the paleolakes is still unknown, a pluvial explanation for the existence of paleolakes seems unlikely. Decreased evaporative loss, however, remains a possible explanation. To understand what factors could have been associated with a decrease in evaporation rates over the drainage basin, an evaporation model is developed based on the energy

* Corresponding author address: Troy Blodgett, 2112 Snee Hall, Cornell University, Ithaca, NY 14853. E-mail address: [email protected]

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balance and bulk transfer methods. The model indicates that a 10ЊC drop in air temperature or a doubling in cloud cover could have caused the paleolakes to reach their highest levels. Alternatively, a 50% increase in precipitation rate could have also maintained the paleolakes. KEYWORDS: Paleoclimatology Evapotranspiration Geomorphology Hy- drologic budget Snow and ice

1. Introduction 1.1. Evidence of paleolakes Evidence of former lakes in the central Andes was ®rst documented in the mid- 1800s when explorers observed lacustrine deposits and high shorelines around Lake Titicaca and identi®ed algal-carbonate beach ridges 4 m above the basin ¯oor near Lake PoopoÂ (Figure 1) (Clapperton, 1993). Distinct erosional shore platforms and depositional gravel beach surround most of the salars and lakes between 15Њ and 23ЊS and throughout much of the internally drained portion of the central Andes. The modern climate encompassing the region of paleolake development is diverse and include both arid regions receiving less than 200 mm of precipitation per year and more humid areas receiving over 800 mm per year. Figure 1. Titicaca±Uyuni±Coipasa±PoopoÂ drainage basin. Within the numerous internally draining basins on the high plateau (Altipla- no), deposits and shorelines corresponding to several episodes of paleolake expansions have been identi®ed. The oldest and highest of the paleolakes identi®ed is Lake Mataro in the basin containing Lake Titicaca. Lake Mataro is tentatively dated as late Pliocene because it lies just above a 2.8 Ϯ 0.4 Ma ash bed (Lavenu, 1986). Evidence of two other paleolakes named Lake Cabana and Lake Ballivian have also been found within the Titicaca basin and are roughly mid- to late Pleistocene in age (Clapperton, 1993). During high paleolake phases in the southern Altiplano, the present PoopoÂ, Coipasa, and Uyuni drainage basins were integrated into one basin (Figure 1, Figure 2, Figure 3). Within the PoopoÂ±Coipasa±Uyuni drainage basin, Ahlfeld and Branisa (Ahlfeld and Branisa, 1960) identi®ed conspicuous erosional benches cut into the ¯anks of the volcanic stock Cerro Lipillipi at the elevations of 3680, 3685, 3710, and 3735 m. Based on radiocarbon ages of 26,700 to 28,300 yr BP, 25,700 to 26,900 yr BP, and an AMS (accelerator mass spectrometry) date of 30,640 to 31,750 yr BP, the four terraces and a higher depositional shoreline at 3760 m were originally associated with Lake Minchin, while a shoreline consisting of clayey and calcareous diatomites 2±5 m thick at 3720 m was considered evidence of another paleolake named Lake Tauca (Clapperton, 1993; Clayton and Clapperton, 1995; Servant and Fontes, 1978). Since dates acquired by Bills et al. (Bills et al., 1994) show that the maximum level of Lake Minchin (3760 m) was attained by the Tauca lake phase at about 13,790 yr BP, a distinction no longer exists between the maximum elevation of Lake Minchin and Lake Tauca. Additional AMS and uranium series dates corresponding to several lower lake levels indicate that either subsequent lesser high lake phases

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Figure 1. Titicaca–Uyuni–Coipasa–Poopo´ drainage basin. developed or the Tauca lake phase persisted until about 9500 yr BP (Clayton and Clapperton, 1995; Servant et al., 1995). To avoid confusion associated with new shoreline dates collected within the Uyuni±Coipasa±PoopoÂ basin, we simply consider the highest shoreline level (3760 m) to be the highest elevation attained by the Tauca lake phase. Lower shoreline elevations are considered lower levels of the Tauca lake phase. Although the age of the highest shoreline at 3825 m near the shores of Lake Titicaca has not been established, for our calculations we consider the 3825-m-level part of Tauca (3760 m), because a

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Figure 2. Paleolake and Pleistocene glacier reconstruction within the Titicaca– Uyuni–Coipasa–Poopo´ drainage basin. highstand in the Lake Titicaca basin is likely to have been contemporaneous with a highstand in the Titicaca±Uyuni±PoopoÂ±Coipasa basin (Wirrmann and Mourguiart, 1995). Servant and Fontes (Servant and Fontes, 1978) also dated shorelines within a small basin to the south that now contains Laguna Khota (Figure 4) at 11,000 to 12,500 yr BP. This small paleolake's age suggests that the cause of the Tauca phase may also have been felt outside of the Uyuni± Coipasa±PoopoÂ drainage basin. Glacial meltwater was one of the ®rst hypotheses proposed to account for

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Figure 3. Schematic proﬁle of modern drainage. Thick black lines represent relative slope length and slope gradients (slopes are vertically exaggerat- ed).

the paleolake expansions (Servant and Fontes, 1978). Kessler (Kessler, 1984) proposed as an alternative hypothesis that pluvial conditions accounted for the expanded lakes. He argued that the glaciers melted during a regressive lake phase and thus contributed no meltwater to the expansive lake phase. He further proposed that a southerly shift in the intertropical convergence zone had increased the amount of Amazonian moisture reaching the plateau and estimated that at least a 30% increase in precipitation would have been required to account for the Lake Tauca (3720 m) shorelines. A similar model was constructed by Hastenrath and Kutzbach (Hastenrath and Kutzbach, 1985), who also rejected the idea that glacial meltwater could account for the paleolakes. They estimated that the expansion of two of the Lake Tauca phases at 3720 and 3760 m resulted from precipitation increases of greater than 50% and 75%, respectively. A de®nitive test of the hypothesis that melting glaciers ®lled the basins would be to reconstruct the former glacier and lake water volumes to see which is greater. This is undertaken in the present study for the Titicaca±Uyuni±Coipasa± PoopoÂ basin as well as for ®ve small basins in the southern Altiplano (Figure 4). Furthermore, since reduced evaporation remains a potential explanation for the lake highstands, an evaporation model is constructed to investigate the sensitivity of evaporation rates to altered atmospheric conditions.

1.2. Modern and late Pleistocene drainage patterns Because many of the drainage basins on the Altiplano over¯owed and coalesced during the paleolake expansions, the modern series of drainage basins have been grouped into just two basins connected by the Desaguadero River (Figure 1, Figure 3). Evidence of basin coalescence has also been documented in modern

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Figure 4. Map showing extent of former glaciers, paleolakes, and present salars/ lakes in the southern Altiplano.

time. During the rainy season in the wet year of 1986, water not only reached Lake PoopoÂ as is typical, but the inundation also ¯ooded the Coipasa and Uyuni salars (Roche et al., 1991). One complication to this simple approach is that presently a small drainage area south of Lake Titicaca drains northward when Lake Titicaca is low but drains southward into the Desaguadero River watershed

Unauthenticated | Downloaded 09/25/21 01:08 PM UTC Earth Interactions • Volume 1 (1997) • Paper No. 1 • Page 7 when Lake Titicaca is high. For modeling present conditions, we include this alternating drainage as part of the Titicaca basin (Figure 1). However, since the highstand around Lake Titicaca was probably coincident with the Tauca lake phase, and the alternating drainage region area was likely to have drained directly into the Uyuni±PoopoÂ±Coipasa basin during inundation episodes, the alternating drainage area is considered part of the Uyuni±Coipasa±PoopoÂ basin during the Tauca lake phase. The combined area of the Titicaca±Uyuni±Coipasa±PoopoÂ drainage basin is 198,000 km2.

2. Comparison of former ice volume and paleolake volume 2.1. Methodology The maximum extent of moraines and their associated glacier headwalls were digitally mapped on Landsat Thematic Mapper (TM) images within the Uyuni± Coipasa±PoopoÂ and Titicaca drainage basins (Figure 1, Figure 2). Both TM images and topographic maps were used to digitize the basin divides. Fox (Fox, 1993) reconstructed the volume of 69 representative Pleistocene glaciers on the southern Bolivian Andes using a digital version of the method described by Porter (Porter, 1975) (Figure 5). Porter's method reconstructs former glacier surfaces using knowledge about modern glacier surfaces. Ice surface contours of topographic maps of typical existing alpine glaciers show that the accumulation zone's slope is concave and the slope of the ablation zone is convex. The contours cut straight across the glacier near the equilibrium line altitude (ELA). A toe-to- headwall altitude ratio (THAR) method was used to estimate the ELA by Char- lesworth (Charlesworth, 1957) and Meierding (Meierding, 1982). The THAR method was chosen in lieu of the accumulation area ratio (AAR) method, because AAR values for Andean glaciers range from 0.38 to 0.95 (Jordan, 1991). A THAR of 0.5 reliably determines the ELA of existing glaciers in the Bolivian cordillera (Oyarzun, 1987). Meltwater volume was determined by multiplying each glacier volume estimate by an assumed ice-to-water density ratio of 0.9. There are several possible sources of error in determining former glacier volumes. Mapping the glacial extent of moraines on Thematic Mapper images is relatively easy since moraines on the plateau are in general well preserved and wide enough to be discerned with a 30-m resolution. However, some moraines may have been overlooked especially in wetter regions where subsequent erosion has occurred. Missing sections of lateral moraines or end moraines are inferred based on the curvature of pieces that are well preserved. Because high-resolution maps are not available for some of the regions, we lack suf®cient numbers of glacier reconstructions for the largest glaciers. Thus, some of the largest glacier volumes were determined based on extrapolation. Figure 6 shows two curves that describe the relationship between former glacier area and ice volume (Klein, 1997). Studies for small modern temperate glaciers have shown that volume scales as a function of area: V ϭ cAb, where V is volume, A is area, and c and b are scaling factors (Meier and Bahr, 1995). Least squares curve ®tting was used to determine the linear scaling term (c)

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Figure 5. Longitudinal proﬁle of reconstructed glacier on Cerro Tunupa (a), reconstructed glacier surface (b), and physical dimensions of the glacier calculated using a geographic information system (c). (Fox,1993, Figure 3.12).

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Figure 6. Relationship between area and volume of 69 reconstructed Pleistocene glaciers. Red line represents best polynomial ﬁt. Blue line utilizes a theoretically based exponential scaling factor of 1.36 (Meier and Bahr,1995; Klein,1997 ).

estimated to be 0.048 (Klein, 1997). The Meier and Bahr relationship was derived from temperate glaciers; nevertheless, the empirical exponential scaling factor (b ϭ 1.36) is consistant with scaling factors determined theoretically (Meier and Bahr, 1995). We chose to evaluate ice volume estimates using the Meier and Bahr relationship, which yields an ice meltwater equivalent of about 11% less than volumes estimated from the best polynomial ®t used by Fox (Fox, 1993). The relationship between lake area and lake elevation was determined based on digitized 20-m contour intervals and the extent and elevations of lakes/salars from 1:50,000 maps (Figure 7). Islands of elevations higher than the lake surface were subtracted out. Because the lake expansions within the Titicaca basin are assumed to have been coincident with the Tauca lake phase of the Uyuni±Coi- pasa±PoopoÂ basin, the paleolake surfaces for each of the basins were combined to determine the total area inundated by the Tauca phases. Digitized 1:50,000 maps were used to determine the hypsometry of the Uyuni±Coipasa±PoopoÂ basin, but in the Titicaca basin, data gaps in the Peruvian region required some contour data to be inferred from maps at a scale of 1:500,000. For the ®ve isolated basins in the south, shorelines identi®ed and mapped on TM images were used to determine paleolake extent, since no ®eld measure-

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Figure 7. Relationship between paleolake area and paleolake level (Instituto Geogra´ﬁco Militar,1991). ments of the height of the paleolake highstands are available (Figure 1, Figure 4). The shoreline elevation was determined by superimposing the mapped shorelines on 1:50,000 topographic maps. The paleolake reconstruction represents the maximum extent of lake levels. Topographic contours (20-m interval) coinciding with or bracketing the highest shoreline were used as guides to map the perimeter of the paleolakes. To determine the relationship between lake volume and elevation, the average of paleolake areas bracketing each elevation increment was multiplied by the increment. The volumetric layers were then summed to produce a basinwide elevation versus volume relationship (Figure 8). The paleolake volume is given as the amount in excess of the modern lake volume. To account for the total volume attributed to the two levels of the Tauca lake phase, the volume of inundation in the Uyuni±Coipasa±PoopoÂ basin is combined with the increase in volume associated with two highstands identi®ed in the Titicaca basin (Figure 3).

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Figure 8. Hypsometric curve of Uyuni–Coipasa–Poopo´ basin showing relationship between paleolake volume (in excess of the modern volume ) and paleolake level.

2.2. Results: Titicaca–Coipasa–Uyuni–Poopo´ drainage basin The volume of glacier ice in the Titicaca±Uyuni±Coipasa±PoopoÂ drainage basin after the meltwater conversion yields a water volume of 1448 km3 This amount of water would have been available for ®lling the paleolakes assuming no loss of glacial meltwater to evaporation. The calculated volume of Lake Tauca at the 3760-m highstand is 3810 km3, whereas the Tauca (3720 m) volume was 1872 km3 (Figure 8). Glacial meltwater was insuf®cient to ®ll Lake Tauca to the 3760- m level but may have contributed substantially to ®lling Lake Tauca to the 3720- m level (Table 1). Hastenrath and Kutzbach (Hastenrath and Kutzbach, 1985) calculated that a deglaciation period of a century or less would have been required for glacial meltwater to ®ll Lake Tauca to its 3760-m level. They imply that the rate of deglaciation would have had to be implausibly fast. According to our more precise measurements of the volume of ice occupied by glaciers and the volume occupied by Tauca (3760 m) and Tauca (3720 m), even if the ice had melted instanta-

Unauthenticated | Downloaded 09/25/21 01:08 PM UTC Earth Interactions • Volume 1 (1997) • Paper No. 1 • Page 12 neously, glaciers could have only contributed a maximum of 43% of the water for paleolake Tauca (3760 m), but meltwater may have contributed 87% of the water for Tauca (3720 m). Moreover, our lake volume estimates probably underestimate the true volume of the paleolakes because isostatic rebound is not considered here (Bills et al., 1994). Nevertheless, meltwater was perhaps responsible for a 20-m lake-level rise from 3740 m to the Tauca highstand of 3760 m because there was suf®cient meltwater, and the event was interpreted by Clapperton (Clap- perton, 1993) to be short lived. The lack of erosional benches and stromatolite development of the degree seen at lower levels indicate a pulse of lake water out of equilibrium with climate (Clapperton, 1993). To account for paleolake Tauca (3760 m), either more precipitation fell within the drainage basin, or less water evaporated from the watershed. In section 3, we quantitatively explore these mechanisms through water budget and evaporation modeling.

2.3. Results: Five small drainage basins on the southern Altiplano The extent of former glaciation mapped from TM images shows that voluminous glaciers not only drained into the Altiplano drainage basin, but that many smaller lake basins just south of the Altiplano also supported glaciers that could have contributed signi®cantly to paleolake formation (Figure 4). Therefore, meltwater and lake volume comparisons were also made for this region. Stromatolite sam- ples collected from an intermediate shoreline level of one of the small lake basins, Laguna Chiar Khota (Laguna Khara), have ages of 10,740±11,200 yr BP, which implies that the stromatolite development was coincident with the development of Lake Tauca (Servant and Fontes, 1978). In all ®ve basins, the volume of water in the former glaciers greatly exceeded the additional paleolake volume (Table 2). Meltwater could have ®lled the lakes if the glaciers had melted instantaneously, but did melting occur fast enough to offset the effects of evaporation over the expanding lake areas? Given that the glaciers in each basin are situated not far from the valley ¯oors where each of the paleolakes developed, we assume that little meltwater was lost en route from the glaciers to the lakes. To address this question, we applied a simple model to the Laguna Khara basin (which has the smallest glacier/paleolake volume ratio). The glacial melting rate that would be needed to balance the evaporation from the paleolake was estimated using the maximum area of the lake as the surface area and the modern evaporation rate from Lake Titicaca. Changes in precipitation rates are not considered. Given the area occupied by the former glaciers, 7.48 ϫ 10Ϫ3 m of melt per day would have been required to balance evaporation from the paleolake. This melting rate is more than eight times less than a typical summer glacier surface melting rate observed in the Alps of 0.0622 m per melt- day (Oerlemans, 1986). We therefore conclude that suf®cient meltwater was available to ®ll the lakes in the small basins even when evaporation from the lake during deglaciation is considered. In internally draining basins to the west of the Titicaca±Uyuni±Coipasa±PoopoÂ drainage basin, changes in the covariance between 13C and 18O during the lake highstands imply that more meltwater was

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contributed to the paleolake during the highstands, thus implicating the glaciers as a primary water source for those paleolakes (Grosjean, 1994).

3. Water budget/evaporation model 3.1. Model description Having determined glacial meltwater to be of insuf®cient volume to ®ll Lake Tauca to its 3760- or 3720-m levels, we now examine the possibility that the enlarged lakes were the result of reduced evaporation or enhanced precipitation. The steady-state hydrologic balance for the closed Altiplano basin can be written as (Hastenrath and Kutzbach, 1985)

Pbas ϭ Eawwϩ E l(1 Ϫ a w) ϭ Ebas (1) or

Pbas Ϫ El aw ϭ , (2) EwlϪ E

where aw (referred to hereafter as the ``lake area ratio'') is the fraction of the basin's surface area that is covered by water, Pbas is the basin-averaged climatological precipitation rate, and E denotes the area-averaged evaporation rate over water (w), land (l), or the entire basin (bas). To investigate the effects of evaporation on aw, we assume Pbas to be constant and equal to the modern value. The problem, then, is to model Ew and El in terms of atmospheric variables and determine whether reasonable changes in atmospheric conditions yield a lake area ratio aw that matches that of the paleolake levels Tauca (3720 m) or Tauca (3760 m). Similarly, to examine the sensitivity of lake area to changes in basin-averaged precipitation rate, we ®x Ew and El at their modern values and vary Pbas. The sensitivity of Altiplano evaporation rates to changes in atmospheric conditions has been previously investigated by Kessler (Kessler, 1984) and Hastenrath and Kutzbach (Hastenrath and Kutzbach, 1985), but in a simpli®ed framework. Kessler (Kessler, 1984) uses a bulk transfer formula to estimate the sensitivity of Altiplano evaporation rates to changes in temperature and relative humidity. He concluded that a temperature depression of 3ЊC and a 5% increase in relative humidity would reduce evaporation rates by 27%, not enough to ®ll Lake Tauca to the 3720-m level. However, Kessler's model makes the simplifying assumption that the surface temperature of the lake and the local air temperature are the same, which is not true for the modern case and may be even more inappropriate for past conditions. Hastenrath and Kutzbach (Hastenrath and Kutzbach, 1985) estimated evaporation rates using the energy budget method and concluded that evaporation on the Altiplano is relatively insensitive to changes in temperature, relative humidity, or cloudiness. Again, the surface temperature and air temperature were taken to be identical. Furthermore, the Bowen ratio (the ratio of sensible heat to latent heat) of the water surface was assumed constant (i.e., insensitive to changes in atmospheric conditions). For this study we have constructed an evaporation model based on both the bulk transfer and energy budget methods. Doing so allows one to directly cal-

Unauthenticated | Downloaded 09/25/21 01:08 PM UTC Earth Interactions • Volume 1 (1997) • Paper No. 1 • Page 14 culate the surface temperature and Bowen ratio, thereby eliminating the above simplifying assumptions. The evaporation rate is (Brutsaert, 1982)

0.622CUfD E ϭ [ess(T ) Ϫ RHe sa(T )], (3) RTa where es is the saturation vapor pressure evaluated at the air temperature, Ta,or the temperature of the water or land surface, Ts. The moisture availability function f varies from 0 for a completely dry surface to 1 for a saturated surface. The remaining variables in (3) are de®ned in Table 3. The surface temperature is determined by solving the energy budget equa- tion,

Rsw Ϫ Rluϩ⑀R ld Ϫ H Ϫ LE ϭ 0, (4) where

pCDp Uc H ϭ (TsaϪ T ), (5a) RTa

Rswϭ R swc(1 Ϫ␣)[1 Ϫ (a ϩ bc)c], (5b)

4 Rluϭ⑀␴T s, (5c) and

RHe (T ) 1/7 R ϭ 1.24 sa ␴T4(1 ϩ aЈcb). (5d) ld100T a []a [Equations are adopted from Budyko (Budyko, 1974) and Brutsaert (Brutsaert, 1982) and are in mks units; see Table 3 for variable de®nitions.] A long-term average is assumed in (4), so no heat storage term is required. Equations (3)±(5) represent the model's governing equations and, given climatological inputs (U,

Ta, RH, p, and c ), provide estimates of annual mean surface temperature and heat ¯uxes (including evaporation rate). A Mathematica Notebook containing the evaporation model is available to download from the online version of this paper.

3.2. Model calibration

The solution of (3)±(5) requires knowledge of the surface drag coef®cient CD and moisture availability function f. These parameters are determined for the Altiplano basin by following a simple calibration procedure. First, the value of CD over water (f ϭ 1) is determined from (3)±(5) using Tsϭ13.0ЊC, the observed, annual mean surface temperature of Lake Titicaca (Carmouze, 1991). Climatological measurements of Ta, RH, and p are obtained from 15 years of station data (Car- mouze, 1991) at Puno, Peru, on the shore of Lake Titicaca, while average cloud fraction is taken from the 8-yr dataset of the International Satellite Cloud Cli- matology Project (ISCCP; Rossow, 1991). The annual mean wind speed over Lake Titicaca, is U ϭ 4.6msϪ1, the average value obtained by Kirkish and Taylor (Kirkish and Taylor, 1984; station Rocas Misteriosas). Although this estimate

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represents only an 11-month average (January±November 1982), the measurements of Kirkish and Taylor (Kirkish and Taylor, 1984) were actually obtained over Lake Titicaca. Land-based observations in the Titicaca region, while span- ning a longer time period, generally show wind speeds that are 2±3 times weaker than the overlake measurements. Using these climatological conditions as input, Ϫ3 (3)±(5) are solved for a drag coef®cient of CD ϭ1.25 ϫ 10 , which is within the typical range of 1±2 ϫ 10Ϫ3 (e.g., Imberger and Patterson, 1990).

The second step in the calibration procedure is to determine values of CD and f for land areas of the Altiplano. Because of the lack of good ground tem-

perature data for this region, we are forced to assume a value for CD. But since drag coef®cients over land are often taken to be 2±3 times larger than over water [at least in large-scale atmospheric models; e.g., Cook and Gnanadesikan, 1991)],

and CD and U always appear as a product in the model equations, we simply Ϫ3 Ϫ1 assume CDU ϭ 5.75 ϫ 10 ms , which is the same as that over water. Given that land-based wind speed measurements in the region of Lake Titicaca are

roughly 2±3 times smaller than over water (so the product of CD and U should be roughly the same), this assumption is not unreasonable. Land values of f are primarily a function of soil moisture, which varies signi®cantly from the dry, southern Altiplano to the more humid climate of the northern Altiplano. To account for this geographic variation, we ®rst calculate f separately for the Titicaca and Uyuni±Coipasa±PoopoÂ basins (Figure 1) and then form an area-averaged f, which is utilized in the model. For the Titicaca basin, Ϫ3 Ϫ1 using CDU ϭ 5.75 ϫ 10 ms and a land evaporation rate of E ϭ 585 mm Ϫ1 1 yr (from water budget estimates ), (4) can be solved for Ts ϭ 15.9ЊC, yielding f ϭ 0.346 [from Eq. (3)]. This corresponds to a Bowen ratio of B ϭ H/LE ϭ 0.76, which is reasonable for the semihumid climate of this region. For the drier southern Altiplano we simply assume a Bowen ratio of 2.45

(Hastenrath and Kutzbach, 1985) and solve (4) (with E ϭ H/LB) for Ts ϭ 22.6ЊC, yielding f ϭ 0.087. Climatological temperature, pressure, and humidity data representative of the southern Altiplano is taken from 2 years of measurements from a meteorological station in Oruro, Bolivia (see Figure 1; data obtained from the National Climatic Data Center), while cloud fraction is taken from the ISCCP dataset. To complete the calibration procedure, we calculate an area-averaged moisture availability function of f ϭ 0.165, which corresponds to a Bowen ratio of B ϭ 1.4 for basin-averaged climatic conditions. The calibration procedure described above is rather elementary and is meant only to capture the gross climatological characteristics of the Altiplano region. Improved calibration would require measurements of ground surface temperature and a much longer term meteorological database. Given the uncertainty in our

1 Land evaporation rates for the Titicaca basin are calculated from El ϭ [Pbas(1 Ϫ␭) Ϫ Ϫ1 Ewaw](1 Ϫ aw) [see Eq. (1)], where ␭ϭ0.09 is the fraction of precipitation lost to groundwater and river out¯ow [value taken from Serruya ( Serruya, 1983). A 20-yr annual mean precipitation map for the Titicaca basin (Roche et al., 1991) has been digitized and integrated to give a basin- Ϫ1 averaged precipitation rate of Pbas ϭ 737 mm yr . The modern Lake Titicaca evaporation rate Ϫ1 of Ew ϭ1270 mm yr is calculated from the evaporation model, and the modern lake area ratio

for the Titicaca basin is aw ϭ 0.1245.

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Figure 9a. Lake area ratio as a function of precipitation and air temperature.

estimates of CD and f (especially over land), it is worthwhile to examine the sensitivity of the model results to the values of these and other empirically derived parameters. We provide such an analysis at the end of this section.

3.3. Model results Using basin-averaged climatological conditions (from Puno and Oruro), the cal- ibrated evaporation model yields a modern basin-averaged evaporation rate of Ebas Ϫ1 ϭ 497 mm yr for a lake area ratio of aw ϭ 0.085 (estimated from digitized maps and satellite imagery). To investigate the effects of changes in atmospheric conditions and basin-averaged precipitation rate, we varied the air temperature, cloud fraction, relative humidity, and precipitation rate and calculated the corresponding lake area ratio from (2). The results are shown in Figure 9, with the paleolake levels Tauca (3720 m) (aw ϭ 0.25) and Tauca (3760 m) (aw ϭ 0.31) lake area ratios shown by the blue lines. Although ice cover is not considered in the evaporation model, in none of the climatic regimes shown in Figure 9 does the annual mean water or land surface temperature drop below freezing. In fact, the lowest annual mean surface temperature attained in the scenarios shown in Figure 9 is a water temperature of 4.1ЊC for Lake Tauca (3760 m) (c ഠ 0.7, RH ഠ 0.05). Presently, the annual mean surface temperature of Lake Titicaca is

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Figure 9b. Lake area ratio as a function of cloud fraction and relative humidity. roughly 2ЊC higher than the lowest monthly mean value (Carmouze, 1991), so an annual mean surface temperature of 4.1ЊC is not likely to result in signi®cant ice formation at any time of the year. Lake area increases with decreasing air temperature (Figure 9a) as a result of lower surface temperatures and associated evaporation rates. According to the model, temperature depressions of 7.4Њ and 9.7ЊC would be suf®cient to ®ll Lake Tauca to the levels of 3720 m and 3760 m, respectively. Figure 9a also indicates that, under modern evaporation rates, 35% and 48% increases in basin-averaged precipitation rate could also account for paleolake levels Tauca (3720 m) and Tauca (3760 m), respectively. These values are lower than previous estimates of 45%±50% (Tauca 3720 m) and 73%±78% (Tauca 3760 m) as determined by Hastenrath and Kutzbach (Hastenrath and Kutzbach, 1985). This primarily re¯ects the fact that our evaporation model simulates a lower water-to-land evaporation ratio, although Hastenrath and Kutzbach (Hastenrath and Kutzbach, 1985) also use lake area ratios for the paleolake level Tauca (3720 m) and modern lake phases that are lower than those used in this study. Our estimate of the required precipitation increase for the level Tauca (3720 m) is also less than that found by Kessler (Kessler, 1984), who calculated an 85% increase (with no change in evaporation), a 40% increase (with a 3ЊC temperature depression), and a 30% increase (with a 3ЊC temperature depression and 5% increase in relative humid-

Unauthenticated | Downloaded 09/25/21 01:08 PM UTC Earth Interactions • Volume 1 (1997) • Paper No. 1 • Page 18 ity). The results of the present model indicate that the latter two scenarios would only require 20% and 19% increases in precipitation, respectively. Cloud cover has a relatively strong impact on the lake area ratio through its in¯uence on surface temperature and, consequently, evaporation rate. For example, in the absence of other changes in atmospheric conditions, an increase in cloud fraction from 0.42 (modern) to 0.7 [Tauca (3720 m)] or 0.76 [Tauca (3760 m)] would reduce evaporation rates enough to ®ll the paleolakes (Figure 9b). Although these represent large (and perhaps unreasonable) changes in cloud cover, the point is that the effects of cloudiness on evaporation rate are signi®cant and cannot be overlooked. Relative humidity, on the other hand, has comparatively little in¯uence on the lake area ratio (Figure 9b) as a result of the competing effects of relative humidity on evaporation rate through downward longwave radiation [Eqs. (4) and (5d)] and the vapor pressure gradient [Eq. (3)]. As a result, paleolake levels Tauca (3720 m) and Tauca (3760 m) cannot be accounted for by a change in relative humidity alone. Nevertheless, an increase in humidity would reduce evaporation rates slightly and could be incorporated into the above scenarios to help explain the origin of the paleolakes. For example, 10% increases in cloud fraction and relative humidity (e.g., 0.45 becomes 0.495) together with decreases in temperature of 6.2Њ and 8.5ЊC would reduce evaporation rates enough to maintain paleolake levels Tauca (3720 m) and Tauca (3760 m), respectively. It is interesting to note that for a 10ЊC drop in air temperature, the modeled lake surface temperature drops by only 7.2ЊC as a result of the reduction in evaporative cooling. Thus the modern lake-to-air temperature differential of roughly 4ЊC actually increases as the air temperature is lowered. This indicates that the questionable approximation adopted by Kessler (Kessler, 1984) and Has- tenrath and Kutzbach (Hastenrath and Kutzbach, 1985), which assumes identical surface and air temperatures, is even less appropriate for colder conditions. As- sociated with this increased temperature differential is an increase in the sensible heat loss from the lake surface. Together with the reduction in evaporative cooling, this results in a signi®cantly increased Bowen ratio. For example, the Bowen ratio of the water surface increases from 0.15 to 0.38 for a 10ЊC drop in air temperature. Thus, the assumption of a constant Bowen ratio in an energy budget model (as in Hastenrath and Kutzbach, 1985) tends to underestimate the sensitivity of lake evaporation to changes in air temperature, at least for the Altiplano region.

3.4. Model sensitivities The evaporation model contains six empirically derived parameters that introduce some degree of uncertainty to the model results. To test the sensitivity of the model to these parameters, we calculated (one at a time) the air temperature depression (dT), cloud fraction increase (dc), relative humidity increase (dr), and percent precipitation increase (dP) that would be required to maintain a lake area ratio of aw ϭ 0.31 (Tauca 3760 m) and then reran the calculations after applying a 10% increase to one of the parameters. [A lake area ratio of 0.13 was used for the relative humidity calculations, since changes in relative humidity alone cannot

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maintain lake areas much greater than this value.] This was done for each of the six parameters, and the percent changes in dT, dc, dr, and dP were calculated and tabulated (Table 4). Temperature depression dT and precipitation increase dP show minimal sensitivity to a 10% increase in the shortwave and longwave cloud parameters but greater sensitivity to the drag coef®cient and moisture availability function. The cloud fraction increase dc is only moderately sensitive to three out of the four cloud parameters, while the relative humidity increase dr is most strongly affected by changes in the land surface drag coef®cient and moisture availability function (Table 4). The results of this sensitivity analysis indicate that the model calculations are not hypersensitive to any of the empirical parameters. In only one instance in Table 4 is there a greater than 1:1 sensitivity to one of the parameters, and that sensitivity is only 1.2:1. Most of the model results show a less than 0.5: 1 sensitivity. The sensitivities listed in Table 4 cannot be used to assign quantitative uncertainties to the model results, as the uncertainties in the parameters themselves are not known. However, one can determine an approximate range of suitable

values for CD and f from more easily estimated uncertainties in the modern climatological conditions, since these conditions were used in the calibration pro-

cedure that determined CD and f. For example, a 10% increase in CD (either water or land) corresponds to a 0.6ЊC drop in surface temperature. Since the annual mean surface temperature of Lake Titicaca is fairly well constrained (within about

1ЊC), the value of CD over water might, therefore, have a range of Ϯ17%. Land temperatures, on the other hand, are more poorly constrained (within about 3ЊC), so the value of CD over land might only be known to within 50%. With most of the sensitivities in Table 4 being less than 0.5:1, that would imply that the model results are certain to within about 25%. Similar arguments could be used to estimate the uncertainty in f, given that a 10% increase in its value corresponds to a 10% drop in Bowen ratio.

4. Discussion 4.1. Model limitations The results from the evaporation model clearly show that other climatic factors besides increased precipitation could have caused the lake expansions. However, it is important to note some of the model de®ciencies. First of all, the lack of a spatially and temporally comprehensive climatological dataset with which to cal- ibrate the model results in only a ®rst-order calibration. Improvements could be made by including land surface temperatures in the model calibration as well as explicitly accounting for geographic variability by extending the model to two dimensions. The inclusion of temporal variability (i.e., the seasonal cycle), which would require accounting for heat storage in the lake, would also be a worthwhile addition. Furthermore, more sophisticated bulk transfer formulations that include effects such as atmospheric stability could add signi®cant realism to the model. Finally, it would be worthwhile to validate the model's radiation parameterizations with observed radiation over the Altiplano to see if such parameterizations are

Unauthenticated | Downloaded 09/25/21 01:08 PM UTC Earth Interactions • Volume 1 (1997) • Paper No. 1 • Page 20 indeed appropriate for this particular region. Despite the model's shortcomings, the results are meaningful and can be used to constrain the climatic explanations for the late Pleistocene paleolakes.

4.2. Overﬂow hypothesis The well-developed paleolake terraces at four levels were all accompanied by stromatolite reefs. The reefs are clear of sediment, implying that the levels represent a falling succession of lake stages (Clapperton, 1993). Clapperton hypothesized that either static climatic periods or the altitude of an eroding over¯ow spillway caused the apparent steady-state conditions (Clapperton, 1993). Our ex- tensive topographic digitization and analysis of Altiplano relief indicates that a topographically controlled over¯ow did not regulate the height of the terrace levels in the Uyuni±Coipasa±PoopoÂ basin. According to the 1:50,000 topographic maps of the region, the lowest passage leading out of the basin is at about 3830 m (Figure 2), 70 m above the highest recognized shoreline. Still, the possibility remains that either the topographic maps are incorrect or that some tectonic or volcanic activity has sealed off an exit since Lake Tauca's development.

4.3. Timing of glaciers and lakes Based on the following geomorphic relationships and dating, we conclude that a major glacial stage coincided with the Tauca lake phase. Hanging deltas, identi®ed on Landsat TM images at several sites, can be traced back to end moraines demonstrating that the paleolake level was high during a glaciation or deglaciation phase (Figure 10a). An ice-marginal fan delta has been identi®ed and mapped in the ®eld by Clayton and Clapperton (Clayton and Clapperton, 1995). Shorelines identi®ed on TM truncate glacial outwash, showing that the major glaciations and glacier recession preceded the end of the Tauca lake phase (Figure 10b). Radio- carbon dates from the Cordillera Real and Chile indicate that a late glacial stage was coincident with the Tauca lake phase (Seltzer, 1992; Lowell et al., 1995). After the glacial stage, which culminated between 14,000 and 12,000 yr BP, many of the valleys in the eastern Cordillera of Bolivia and Peru were deglaciated by 8000 yr BP (Seltzer, 1992). Similarly, the Tauca lake level reached 3760 m at 13,790 yr BP, and by 9000 yr BP the Tauca lake phase was over (Servant et al., 1995; Bills et al., 1994).

4.4. Paleoclimate explanation In general, the paleolake highstands coincided with colder intervals and the paleolake lowstands coincided with warmer intervals. Dates that correspond to Lake Minchin indicate that the paleolake attained high levels between about 31,000 and 26,000 yr BP, which followed the warm interstadial from about 42,000 to 32,000 yr BP shown in the record from GISP II and Vostok (Bender et al., 1994; Clayton and Clapperton, 1995; Servant and Fontes, 1978). The level of Lake Tauca reached 13,790 yr BP during a colder interval according to interpretations from both pollen cores in Europe and ocean cores in the North Atlantic (Bard et

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Figure 10a. Glaciated Cerro Capia and glacioﬂuvial fans/deltas indicative of coincident glacier and paleolake expansions.

al., 1987; Woillard and Mook, 1982;). Pollen cores extracted from Peru, Colom- bia, and the Amazon basin concur (Colinvaux et al., 1996; Markgraf, 1989). A lake-level lowstand, judged from the deposition of gypsum evaporites and a 54- m drop in Lake Titicaca's level, is associated with the Holocene hypsithermal interval of greater warmth dated at 7700±7000 yr BP (Clapperton, 1993). In addition, Lake PoopoÂ was a salar during the hypsithermal (Wirrmann and Mour- guiart, 1995). The correlation of lake highstands with cold periods emphasizes the contribution of decreased evaporation to high lake levels. However, not all cold periods appear to be associated with highstands. Lake Titicaca depressed to a level equivalent to the hypsithermal lowstand between 20,000 and 21,000 yr BP, a period that coincides with a hiatus in paleolake expansions in the south based on a dearth of ages for high shorelines in that age range (Wirrmann et al., 1991). There is no evaporite layer associated with the older lowstand. Several climatologists have argued that fundamental changes in atmospheric circulation patterns were responsible for the observed ``pluvial episodes'' (Kes- sler, 1984; Hastenrath and Kutzbach, 1985). Advocates of this hypothesis cite the

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Figure 10b. Flank of glaciated Cerro Tunupa showing shorelines truncating glacial outwash. existence of paleolakes and the expansion of the glaciers as evidence for a pluvial climate. However, the extent of both glaciers and the lakes are sensitive to changes not only in precipitation, but to changes in air temperature as well. The climate proxy data collected to date demonstrate that 1) at least one dry interval existed in the late Pleistocene, 2) the regional circulation pattern in the past was similar to the present, and 3) the period coinciding with late Tauca phase was not signi®cantly wetter. Markgraf interprets from Altiplano pollen cores that the effective moisture was greater prior to 10,000 yr BP because of an increase in abundance of Gramineae and herbaceous taxa relative to Compositae (Mark- graf, 1989). However, Markgraf's interpretation does not support an extreme increase in basinwide precipitation on the order of 50%, as inferred by Hastenrath and Kutzbach (Hastenrath and Kutzbach, 1985). Based on pollen studies from the Junin region of the central Peruvian Andes, the glacial interval between 24,000 and 12,000 yr BP was interpreted to be cold and dry (Hansen et al., 1984). The Pantanal region directly east of the central Andes (17ЊS, 57ЊW ) has relict dunes and de¯ation basins, oriented north-northeast and north-northwest. Although the age of the eolian landforms is unknown, the composition of vegetation that oc-

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cupied the alluvial fans indicates that the predominant air masses of Amazon origin were dry (Klammer, 1982; Clapperton, 1993). Similarly, the Beni basin to the northeast of the plateau has eolian features indicative of a climate drier than present (Clapperton, 1993). The Chaco±Pampas plains south of the Altiplano also has relic sand dunes and loess deposits in which Pleistocene megafauna have been found (Iriondo, 1989; Bloom, 1990). Peruvian ice cores from HuascaraÂn contain more atmospheric dust during the late glacial stage, which is suggestive that land surface conditions during that period were drier (Thompson et al., 1995). Alnus and Podocarpus pollen derived from the eastern slopes of the Andes found in sediments dated about 14,000 yr BP in Laguna Lejia (23Њ30ЈS, 67Њ42ЈW) is indicative of a northeasterly airmass ¯ux, which is similar in direction to the present moisture ¯ux (Grosjean, 1994). In Chile, high lake levels and increased amounts of Gramineae, Compositae, and Chenopodiaceae pollen were dated at 12,000 yr BP (Grosjean, 1994). The lake expansions were restricted to elevations of approximately 3500±4000 m on the western side of the Altiplano, whereas no indicators for humid conditions such as high shorelines have been found below 3500 m (Grosjean, 1994). The elevation threshold implies that no additional moisture approached the central Andes from the west. The maximum extent of moraines are con®ned to higher elevations on the western side than on the eastern side of the Altiplano, demonstrating that an east-to-west decrease in precipitation existed then as it is observed today (Fox and Bloom, 1994).

4.5. Lake–atmosphere feedback

Air temperatures were depressed 5Њ±9ЊC in equatorial regions at low elevations during the last glacial maximum based on pollen and other data (Colinvaux et al., 1996). At high elevations, air temperatures were 8Њ±12ЊC lower than present during the last glacial stage based on the 18O record of the HuascaraÂn cores (Thompson et al., 1995). Our model shows that a depression of 10ЊC would have decreased evaporation rates enough to raise Lake Tauca to its highest level. In addition, we have identi®ed a possible source of increased localized precipitation caused by the differential depression of lake and land surface temperatures in the past relative to the present. Today the highest annual precipitation rates occur over the center of Lake Titicaca (Kessler and Monheim, 1968). One factor that contributes to this phenomenon and that could have been accentuated during the paleolake intervals is the convergence of nightly land breezes over the lake. The evaporation model predicts less temperature depression over the lake surface relative to land, indicating that land breezes are likely to have increased in strength. Consequently, more convection may have occurred over the paleolakes. These effects would have served to induce greater precipitation over the paleolakes with perhaps little effect on the rest of the basin. However, an offsetting mechanism is that an increased lake-to-air temperature differential in the past may have increased evaporation rates by reducing atmospheric stability over the lake. Local lake±atmosphere interactions have been cited as a contributor in the development of paleolakes Bonneville and Lahontan (Hostetler et al., 1994).

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4.6. Summary In summary, our model demonstrates that if air temperatures were depressed by 10ЊC, the lake surface area would have swelled to encompass paleolake Tauca (3760 m). Alternatively a doubling in cloud cover or a 50% increase in precipitation could have maintained Lake Tauca at its highest level. Changes in relative humidity have little in¯uence on evaporation rates over the lake. Differential changes in lake/land surface temperatures may have also contributed to a positive mass balance of the lake by altering the local climate. Paleoclimate proxies indicate that the Altiplano was cooler at the time of the Tauca highstand (3760 m) and warmer during the latest Titicaca lowstand. During at least one period in the late Pleistocene, the Amazon, which feeds moisture to the Altiplano, was drier, and drier conditions have been interpreted for the central Peruvian Andes during the Tauca lake phase. Nevertheless, proxies for precipitation rates on the Altiplano during the Tauca lake phase remain inconclusive. According to our volume calculations, melting glaciers probably played little or no role in the development of paleolake Tauca but can account for the paleolakes inferred to have existed in ®ve smaller lake basins south and west of the Titicaca±Uyuni±Coipasa±PoopoÂ lake basin.

Acknowledgments. We thank the former Cornell students and staff for their monumental efforts in digitizing the topography of the Altiplano. We especially appreciate Arthur Bloom and Andrew Klein for their continuous feedback and their suggestions, which have improved the manuscript signi®cantly. This work was sponsored by NASA EOS Grant NAGW-2638.

References Ahlfeld, F. and L. Branisa. 1960. GeologõÂa de Bolivia, Inst. Boliviano de PetroÂleo. D. Bosco. La Paz. 245.. Bard, E., M. Arnold, P. Maurice, J. Duprat, J. Moyes and J. Duplessy. 1987. Retreat velocity of the North Atlantic polar front during the last deglaciation determined by 14C accelerator mass spectrometry. Nature, 328, 791±794. Bender, M., T. Sowers, M. Dickson, J. Orchardo, P. Grootes, P. Mayewski, and D. Meese. 1994. Climate correlations between Greenland and Antarctica during the past 100,000 years. Na- ture, 372, 663±666. Bills, B. G., S. L. de Silva, D. R. Curry, R. S. Emenger, K. D. Lillquist, A. Donnellan, and B. Worden. 1994. Hydro-isostatic de¯ection and tectonic tilting in the central Andes: Initial results of GPS survey of Lake Minchin shorelines. Geophys. Res. Lett, 21, 293±296. Bloom, A. L. 1990. Some questions about the Pampean Loess. Int. Symp. on Loess, Mar del Plata,Argentina. Commission on the Quaternary of South America (Loess Commission). 29±31. Brutsaert, W. 1982. Evaporation into the Atmosphere. D. Reidel. Norwell, Mass. 299±31. Budyko, M. I. 1974. Climate and Life. Academic Press. San Diego, Calif. 508±31. Carmouze, J. P. 1991. El balance energeÂtico. El Lago Titicaca, C. Dejoux and A. Iltis. ORSTOM. Paris. 149±31. Charlesworth, J. K. 1957. The Quaternary Era. 2 vols., Edward Arnold. London. 1700±31. Clapperton, C. 1993. Quaternary Geology and Geomorphology of South America. Elsevier Sci. New York. 779±31. Clayton, J. D. and C. M. Clapperton. 1995. The last glacial cycle and paleolake synchrony in the

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southern Bolivian Altiplano: Cerro Azanaques case study. Bull. Inst. Fr. EÂ tudes Andines, 24, 563±571. Colinvaux, P. A., L. Kam-biu, P. De Oliveira, M. B. Bush, M. C. Miller, and M. S. Kannan. 1996. Temperature depression in the lowland tropics in glacial times. Clim. Change, 32, 19±33. Cook, K. H. and A. Gnanadesikan. 1991. Effects of saturated and dry land surfaces on the tropical circulation and precipitation in a general circulation model. J. Climate, 4, 873±889. Fox, A. 1993. Snowline depression and climate in the central Andes during the late Pleistocene glacial maximum. Ph.D. dissertation, Cornell University. Ithaca, N. Y. 504±889 [Available from Interlibrary Services, B42 Olin Library, Cornell University, Ithaca, NY 14853.]. Fox, A. N. and A. L. Bloom. 1994. Snowline altitude and climate in the Peruvian Andes (5±17Њ S) at present and during the latest Pleistocene glacial maximum. J. Geogr, 103, 867±885. Grosjean, M. 1994. Paleohydrology of the Laguna LejõÂa (north Chilean Altiplano) and climatic implications for the late-glacial times. Palaeogeogr., Palaeoclimatol., Palaeoecol, 109,89± 100. Hansen, B. C. S., H. E. Wright, and J. P. Bradbury. 1984. Pollen studies in the JunõÂn area, central Peruvian Andes. Geol. Soc. Am. Bull, 95, 1454±1465. Hastenrath, S. and J. Kutzbach. 1985. Late Pleistocene climate and water budget of the South American Altiplano. Quat. Res. (N. Y.), 24, 249±256. Hostetler, S. W., F. Giorgi, G. T. Bates, and P. J. Bartlein. 1994. Lake±atmosphere feedbacks associated with paleolakes Bonneville and Lahontan. Science, 263, 665±668. Imberger, J. and J. C. Patterson. 1990. Physical limnology. Adv. Appl. Mech, 27, 303±475. Instituto GeograÂ®co Militar. 1991. Bolivia 1:50,000 maps. Instituto GeograÂ®co Militar.. Iriondo, M. 1989. A late Holocene dry period in the Argentine plains. Quat. South America and Antarctic Peninsula, 7, 197±218. Jordan, E. 1991. Die Gletscher der bolivianishen Andes, Erdwissenschaftliche Forschung, Vol. 23, Stiener Verlag. Stuttgurt, Germany. 365±218. Kessler, A. 1984. The paleohydrology of the Late Pleistocene Lake Tauca on the southern Alti- plano (Bolivia) and recent climatic ¯uctuations. Late Cainozoic Palaeoclimates of the South- ern Hemisphere, J. C. Vogel. A. A. Balkema. Rotterdam, Netherlands. 115±122. Kessler, A. and F. Monheim 1968. Der wasserhaushalt des Titicacasees nach neueren messergeb- nissen. Erdkunde, 22, 275±283. Kirkish, M. H. and M. J. Taylor. 1984. Micrometeorological measurements at Lake Titicaca (Peru± Bolivia). Verh. Internat. Verein. Limnol, 22, 1232±1236. Klammer, G. 1982. Die PalaeovuÈste des Pantanal von Mato Grosso und die pleistozaÈne Klima- geschichte der brasilianischen Randtropen. Z. Geomorphol, 26, 393±416. Klein, A. 1997. Modern and late Pleistocene glacial studies in the central Andes of Bolivia and Peru: Application of remote sensing and digital terrain analysis. Ph.D. dissertation, Cornell University Ithaca, N. Y. 191±416 [Available from Interlibrary Services, B42 Olin Library, Cornell University, Ithaca, NY 14853.]. Lavenu, A. 1986. EÂ tude tectonique et neÂotectonique de l'altiplano et Cordillere Orientale des Andes Boliviennes. TheÂse doctoral, UniversiteÂ Paris-Sud. Paris. 240±416 [Available from Editions de L'ORSTOM Librairie-Diffusion 70, Route d'Aulnay, F 93140 Bondy Cedex, France.]. Lowell, T. V., C. J. Heusser, B. G. Andersen, P. I. Moreno, A. Hauser, L. E. Heusser, C. SchluÈchter, D. R. Marchant, and G. H. Denton. 1995. Interhemispheric correlation of late Pleistocene glacial events. Science, 269, 1541±1549. Markgraf, V. 1989. Palaeoclimates in Central and South America since 18,000 BP based on pollen and lake-level records. Quat. Sci. Rev, 8, 1±24. Meier, M. F. and D. B. Bahr. 1995. Counting glaciers: Use of scaling methods to estimate the number, size, and thickness distribution of glaciers of the world. Eos, Trans. AGU, 76,1± 183.

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Table 1. Volume of former glaciers and Tauca lake phase volumes (in excess of the modern lake volumes). Glacier water Paleolake volume Volume ratio: Glacier/ Basin equivalent (km3) (km3) paleolake Titacaca 1033 77 (3720 m) 11 (3720 m) 135 (3760 m) 6.4 (3760 m)

Uyuni±Coipasa±PoopoÂ 604 1795 (3720 m) 0.33 (3720 m) 3675 (3760 m) 0.16 (3760 m)

Titicaca±Uyuni±Coipasa±PoopoÂ 1637 1872 (3720 m) 0.87 (3720 m) 3810 (3760 m) 0.43 (3760 m)

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Table 2. Volume of former glaciers and paleolakes (in excess of the modern lake volumes) in ﬁve drainage basins. Salar/lake name Glacier water equivalent Paleolake volume Volume ratio: Glacier/ (km3) (km3) paleolake Yapi 5.0 1.6 3.1 Cachi 2.9 0.2 14.5 Khara 2.1 0.8 2.6 Capina 9.0 1.8 5.0 Colorada 62.0 4.0 15.5

Table 3. Deﬁnitions and values of variables used in the water budget/evaporation model for water (w) and land (l) surfaces. Parameters whose values are allowed to vary are indicated by an asterisk, in which case the value given is for modern annual mean conditions for the Titicaca–Uyuni–Coi- pasa–Poopo´ basin. Variable De®nition Value a Shortwave cloud parameter 0.39 aЈ Longwave cloud parameter 0.22 ␣ Surface albedo 0.07 (w), 0.2 (l)

aw Lake area ratio* 0.085 b Shortwave cloud parameter 0.38 bЈ Longwave cloud parameter 2.0 B Bowen ratio* 0.15 (w), 1.5 (l) c Cloud fraction* 0.42 Ϫ3 CD Surface drag coef®cient 1.25 ϫ 10 Ϫ1 Ϫ1 cp Speci®c heat of dry air 1004 J K kg E Evaporation rate* 1470 mm yrϪ1 (w), 407 mm yrϪ1 (l) ⑀ Surface emissivity 0.97 (w), 0.92 (l)

es Saturation vapor pressure* 1640 Pa (w), 2350 Pa (l) f Moisture availability function 1.0 (w), 0.165 (l) H Sensible heating rate* 17.6 W mϪ2 (w), 44.0 W mϪ2 (l) L Latent heat of vaporization 2.5 ϫ 106 JkgϪ1 p Air pressure 6.519 ϫ 104 Pa Ϫ1 Pbas Basin-averaged precipitation rate* 497 mm yr R Gas constant for dry air 287 J KϪ1 kgϪ1 RH Relative humidity* 0.45 Ϫ2 Rld Downward longwave radiation* 271 W m Ϫ2 Ϫ2 Rlu Upward longwave radiation* 376 W m (w), 386 W m (l) Ϫ2 Ϫ2 Rsw Net shortwave radiation* 247 W m (w), 213 W m (l) Ϫ2 Rswc Cloud-free shortwave radiation 345.7 W m ␴ Stefan±Boltzmann constant 5.67 ϫ 10Ϫ8 mϪ2 KϪ4

Ta Air temperature* 10.6ЊC

Ts Surface temperature* 14.4ЊC (w), 20.1ЊC (l) U Wind speed 4.6 m sϪ1

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Table 4. Model sensitivity to 10% increase in parameter value. Sensitivities are given in percent, with asterisks indicating less than 1% change. ⌬(dT) ⌬(dP) ⌬(dc) ⌬(dr) Parameter dT dP dc dr a **Ϫ6.4 Ϫ4.2 aЈ * * 3.5 1.9 b **Ϫ6.4 Ϫ1.7 bЈ ***Ϫ1.7

CD (water) 3.5 4.2 4.1 Ϫ2.1

CD (land) Ϫ4.8 Ϫ5.3 Ϫ2.6 Ϫ12 f (land) Ϫ6.7 Ϫ8.2 Ϫ5.2 Ϫ6.1

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