A Hydrologic-Isotopic-Balance Model for Application to Paleolake Systems Larry Benson University of Colorado at Boulder, [email protected]

A Hydrologic-Isotopic-Balance Model for Application to Paleolake Systems Larry Benson University of Colorado at Boulder, Great.Basin666@Gmail.Com

University of Nebraska - Lincoln DigitalCommons@University of Nebraska - Lincoln

USGS Staff -- ubP lished Research US Geological Survey

2002 HIBAL: a hydrologic-isotopic-balance model for application to paleolake systems Larry Benson University of Colorado at Boulder, [email protected]

Fred Paillet US Geological Survey

Follow this and additional works at: http://digitalcommons.unl.edu/usgsstaffpub

Benson, Larry and Paillet, Fred, "HIBAL: a hydrologic-isotopic-balance model for application to paleolake systems" (2002). USGS Staff -- Published Research. 784. http://digitalcommons.unl.edu/usgsstaffpub/784

This Article is brought to you for free and open access by the US Geological Survey at DigitalCommons@University of Nebraska - Lincoln. It has been accepted for inclusion in USGS Staff -- ubP lished Research by an authorized administrator of DigitalCommons@University of Nebraska - Lincoln. Quaternary Science Reviews 21 (2002) 1521–1539

HIBAL: a hydrologic-isotopic-balance model for application to paleolake systems Larry Bensona,*, FredPaillet b a US Geological Survey, 3215 Marine Street, Boulder, CO 80303, USA b US Geological Survey, MS 403, Denver Federal Center, Lakewood, CO 80225, USA Received18 May 2001; accepted30 August 2001

Abstract

A simple hydrologic-isotopic-balance (HIBAL) model for application to paleolake d18O records is presented. Inputs to the model include discharge, on-lake precipitation, evaporation, and the d18O values of these fluidfluxes. Monthly values of climatic parameters that govern the fractionation of 18O and 16O during evaporation have been extracted from historical data sets and held constant in the model. The ability of the model to simulate changes in the hydrologic balance and the d18O evolution of the mixed layer has been demonstrated using measured data from Pyramid Lake, Nevada. Simulations of the response in d18O to step- and periodic-function changes in fluid inputs indicate that the hydrologic balance and d18O values lag climate change. Input of reconstructedriver dischargesandtheir d18O values to PyramidandWalker lakes indicatesthat minima andmaxima in simulated d18O records correspond to minima and maxima in the reconstructed volume records and that the overall shape of the volume and d18O records is similar. The model was also used in a simulation of abrupt oscillations in the d18O values of paleo-Owens Lake, California. Publishedby Elsevier Science Ltd.

1. Introduction can be simulatedin modelruns that invoke step- function changes in the hydrologic state (open or closed) This paper consists of three separate but linked of the lake basin. sections. In this, the first section, we discuss concepts in modeling, previous applications of d18O models, and introduce the hydrologic-isotopic-balance (HIBAL) 1.1. Concepts in modeling model, details of which are provided in Appendix A. The secondsection consists of four parts. First, HIBAL The d18O value of a lake is the sum of its sources and is validated in a simulation of the measured d18O sinks andthe d18O value of water vapor leaving the lake evolution of PyramidLake surface water between 1985 is strongly influencedby its local climate. In the case of and1994. Second,a series of simulations are donethat lakes with watersheds in distant mountains, the climate illustrate the effect of hydrologic closure and overflow of of the watershedalso influences the d18O value of the PyramidLake on its d18O value. Third, simulations of lake through its effect on the d18O value of surface-water the response of lake volume and d18O to periodic input. In such watersheds, the value of precipitation is changes in river discharge are done to assess the degree not constant over time, being a function of the history of to which changes in d18O lag climate forcing. Fourth, the air parcel that carries the precipitation andthe HIBAL is usedin historical simulations of the response temperature at which the precipitation condenses. In of two different lake systems, PyramidandWalker addition, the d18O value of watershedprecipitation may lakes, to nearly identical climate forcings. In the last differ substantially from the d18O value of on-lake section of the paper, we apply the model to paleo-Owens precipitation. Lake, showing that abrupt changes in the d18O record Paleolake records of d18O are storedin carbonate precipitates. Given the fact that d18O records represent a complex integration of the elements of climate change, *Corresponding author. Tel.: +1-303-541-3005; fax: +1-303-447- 18 2505. how do we unravel climate history from the d O E-mail address: [email protected] (L. Benson). record? We must confront the fact that we are dealing

0277-3791/02/$ - see front matter Publishedby Elsevier Science Ltd. PII: S 0277-3791(01)00094-4 1522 L. Benson, F. Paillet / Quaternary Science Reviews 21 (2002) 1521–1539 with a highly underdetermined system, and that to 1.2. Previous applications of d18O models approximate the history of climate change from the d18O recordwe must make a number of assumptions High-resolution d18O records are increasingly being regarding the nature of the climate system. The usedas proxies of change in climate andhydrologic implication of this procedure is that no particular balance of paleo surface-water systems (e.g., Johnson solution will be unique. In some cases, additional et al., 1991; Lister et al., 1991; Fontes et al., 1993; Oviatt information on the climate system may be available et al., 1994; Phillips et al., 1994; Hodell et al., 1995; from other types of climate records, thereby eliminating Benson et al., 1997; Li andKu, 1997; Xia et al., 1997; part of the uncertainty implicit in the modeling exercise. Benson, 1999; Benson et al., 2001). Variation in d18O However, many climate proxies are poorly calibrated values of carbonates precipitatedfrom temperate-region anda multiproxy approach may often introduce as lakes with low-residence times and minimal evaporation many unknowns as solutions into the calibration losses have generally been attributedto variation in the equation set. d18O of precipitation falling in the watershedarea of the A question the modeler must initially address is lake (Stuiver, 1968, 1970; Fritz et al., 1975). Because the whether simulations of the entire d18O recordwill be d18O of precipitation is highly correlatedwith air attemptedor whether simulations will be confinedto temperature (Yurtsever, 1975), changes in the d18O ‘‘interesting’’ parts of the record. The latter strategy value of low-residence-time lakes has, therefore, been has a much higher chance of success in that some associatedwith changes in air temperature (Eicher and climate parameters tendto be relatively stable over Siegenthaler, 1976; Eicher, 1980). In contrast, for lake short time periods, and thus there is justification systems that are hydrologically closed or have long or for holding these parameters constant in the model. intermediate residence times, emphasis has often been Models can also be used to catalog the response of placedon change in the hydrologic balance as the d18O to various hypothetical climatic transitions. In principal process responsible for d18O variability (John- this mode, the model can be run a number of times son et al., 1991; Lister et al., 1991; Fontes et al., 1993; to test the sensitivity of d18O to initial conditions, Oviatt et al., 1994; Phillips et al., 1994; Hodell et al., lake-basin geometry, discharge rates, and overflow 1995; Benson, 1999). rates. Numerical modeling of the behavior of d18Ohas It is of paramount importance that the modeler has a usually been confinedto simulations of the measured thorough understanding of the system that is being d18O variability in lake water (e.g., Gat, 1970; Lewis, simulated. Historic climatic, hydrologic, physical, and 1979; Hostetler andBenson, 1994). Phillips et al. (1994) chemical data sets can be used to determine the have applieda lumped-parametermodel(Phillips et al., variability of various parameters over annual- and 1986, 1992) in an attempt to reproduce a mid-to-late- multi-decadal-time scales and their mutual interdepen- Wisconsin d18O recordfrom the Searles Lake basin, dencies. Historical data are also needed to validate the California. model. The model can be run eliminating or holding Hostetler andBenson (1994) coupledthe isotopic constant parameters that will not be available when derivations later published in Benson and White (1994) simulating paleo-d18O records. In this manner, limita- to a one-dimensional thermal model developed by tions of the model can be exposed. Hostetler andBartlein (1990). The coupledmodelwas One of the great difficulties in the use of HIBAL usedto simulate the d18O structure of PyramidLake for models to estimate past changes in the hydrologic the period 1985–1991. The system was well determined. balance of a lake system is that past values of climatic Inputs to the model included daily values of meteor- parameters must be assignedto the model.For lake ological andlake-thermal data(Hostetler andBenson, systems, we must exactly know the components of past 1993). Daily discharges of the Truckee River were climates that govern lake evaporation, inflow, andon- obtainedfrom US Geological Survey Water-Data lake precipitation in order to reconstruct past changes in Reports (1986–1992) andisotopic datasets were the hydrologic balance. This indicates that all lake- available for Truckee River input andPyramidLake modeling systems are mathematically underdetermined, surface water on a monthly or better frequency (Benson, forcing the modeler to make assumptions about the 1994). PyramidLake d18O profiles were available for nature of the past climate system. In the application of most months of the simulation andthe d18O value of our HIBAL model, we assume that the seasonal cycle of advected air was determined from a limited number of climate in low-elevation lake basins has remained fieldexperiments in which vapor-phase extractions were constant. The model has, therefore, been assigned conducted (Benson and White, 1994). constant monthly mean values of measuredclimatic Both wind-driven turbulent mixing (eddy diffusion) parameters. This implies that monthly evaporation rates and density-driven convective mixing were simulated andvalues of the evaporation fractionation factor in the model which divided Pyramid Lake into 1-m- remain constant from year to year. thick layers. Transport of oxygen isotopes (within the L. Benson, F. Paillet / Quaternary Science Reviews 21 (2002) 1521–1539 1523 water molecule) was accomplished by eddies and evaluate d18O records recovered from mid-latitude convection without preference for isotopic species (18O paleolake systems. HIBAL is a two-box model that and 16O). runs on a monthly time step. Model inputs are fluid 18 Because the fraction of advected air ðfadÞ was not fluxes andtheir d O values, depth of the mixed layer, measured, it was used as an adjustable parameter in the basin hypsometry, anda set of meteorological data simulations. Successful simulations were made using a that govern the fractionation of d18O during evapora- daily time step with fad set to 0.1 for the periods October tion (i.e., air temperature, water temperature, relative 1987 to October 1989 andfrom May 1991 through humidity, wind speed, and the fraction and d18O December 1991 (Figs. 3 and4 in Hostetler andBenson, value of air advected over the lake surface) and 1994). A 6.5 yr simulation also was made using a precipitation of CaCO3 (water temperature). The monthly time step andmonthly values of river structure of and inputs to the model are discussed fully discharge, on-lake precipitation, and their d18O values in Appendix A. (Benson, 1994). Monthly inputs of lake-surface temperature, relative humidity, evaporation rate, and depth of the mixedlayer were approximatedby averaging the 2. Validation and applications of HIBAL using historical output from the 1987 to 1989 daily simulations. The data sets model reproduced the trend in d18O between 1986 and 1992, but in some cases underestimated the magnitude 2.1. Simulation of Pyramid Lake historical (1916–1997) of seasonal fluctuations in surface d18O values (Fig. 1). volume The inability of the model to reproduce seasonal d18O variability is thought to result from two factors. Use of In order to determine if the hydrologic balance of mean-monthly mixed-layer thicknesses is probably a PyramidLake couldbe simulatedusing fixedmean- poor approximation for very wet andvery dryyears, annual values of evaporation andon-lake precipitation, andduringvery wet years, a thin layer of isotopically we usedestimatedvalues of these parameters (1.20 and light discharge water can persist on the surface of the 0.18 m yrÀ1, see Appendix A), together with estimated mixedlayer (meromixis). Thus, measured d18O values of values of Truckee River discharge at the Nixon gage the surface layer were not representative of the mean (Fig. 2), to calculate the change in PyramidLake volume d18O value of the mixedlayer. between 1916 and1997. The simulatedlake-volume The model successfully demonstrated that monthly recordwas a close match to the historical record averages of measured daily data obtained during a short (Fig. 3). time period(2 yr) couldbe appliedin modelsimulations that ran for several years when the lake was hydro- 2.2. Simulation of Pyramid Lake surface-water d18O logically closedandice free. between 1985 and 1994 The purpose of this paper is the introduction of a relatively simple HIBAL model that can be used to The Truckee River-PyramidLake surface-water system has been the object of intensive hydrologic, chemical, isotopic, and biological studies during the past several decades. The system is complicated by storage in natural lakes (Tahoe, Donner, andIndependencelakes) andman-madeupstream reservoirs (Prosser, Boca, and Stampede reservoirs) and by river diversion at the Derby Dam (Fig. 2). Cold-season precipitation falling in the Sierra Nevada is released to the Truckee River surface- water system as snowmelt in the spring andearly summer. Approximately 32% of Truckee River flow reaching the Faradgage in eastern California originates from overflow of Lake Tahoe and38% of Truckee River flow reaching the Faradgage passes through small-capacity reservoirs. The remaining 30% of the flow enters the river as surface andnear- surface flows (Benson, 1994). Above Farad, the Truckee River is largely unaffectedby diversion and downstream contributions of water are small. Ground- Fig. 1. Simulatedepilimnetic (mixedlayer) d18O values for Pyramid water input to PyramidLake is negligible. Prior Lake (solidline) comparedwith 1985 to 1992 measuredvalues to 1917, overflow to Winnemucca Lake occurred (Benson, 1994; Hostetler andBenson, 1994). frequently. 1524 L. Benson, F. Paillet / Quaternary Science Reviews 21 (2002) 1521–1539

In 1906, Derby Dam, located53 km upstream of PyramidLake, was completed.Since that time, an average of 54% of Truckee River flow has been diverted from the Truckee River basin, causing the level of Pyramid Lake to rapidly decline. Because of the decreases in inflow, Pyramid Lake has not overflowedto the Winnemucca Lake basin since 1917; it has remainedhydrologically closedfor the past 83 yr. We usedHIBAL to simulate the measured d18O evolution of the mixedlayer in PyramidLake between 1985 and1994. For this simulation, we usedan initial d18O value of –1.2%, an initial (January 1985) lake elevation of 1161.9 m, a constant annual on-lake precipitation rate of 0.18 m yrÀ1, anda constant annual evaporation rate of 1.20 m yrÀ1. For this andother simulations of the evolution of PyramidLake d18O, it was assumedthat Lake Tahoe contributed33% of the input to the Truckee River. Although HIBAL failedto capture the full variability of the annual cycle over the 8.5 yr period, the simulated trend in d18O values of the 18 mixedlayer ðd > OlakeÞ is similar to the measureddata (Fig. 4) andalso to the simulations of Hostetler and Benson (1994) (Fig. 1).

2.3. Response of Pyramid Lake d18O to changes in annual Truckee River discharge

Fig. 2. PyramidLake surface-water system showing location of Several 500 yr simulations were made with HIBAL to streamflow gages, weather stations, andtemperature profile site (Deep site). illustrate the effect of hydrologic closure and overflow of PyramidLake on its d18O value (Fig. 5, Table 1). In all

Fig. 4. HIBAL simulation of the d18O evolution of surface waters of PyramidLake between 1985 and1994. Much of the warm-season difference between simulated and measured values of d18O may be attributable to the fact that the model simulates the d18O value of a Fig. 3. PyramidLake measuredvolume (1916–1997) comparedwith well-mixedepilimnion, but the measured d18O values were taken from model simulations using Nixon flow data (modeled historical volume) the surface of the epilimnion which may be strongly affectedby and Farad flow data (modeled pristine volume). isotopic fractionation during evaporation. L. Benson, F. Paillet / Quaternary Science Reviews 21 (2002) 1521–1539 1525 simulations, the d18O response to a step-function change mean value), and0.80 km 3 yrÀ1. In these simulations, in the hydrologic balance consists of an initial transient, the total input (Vin) to PyramidLake increasedfrom lasting p100 yr, followedby an exponential decayto the 0.71 to 0.91 km3 yrÀ1. Results of the simulations indicate steady state. When climate switches to a wetter state, a progressive decrease in the steady-state value of 18 18 d O values first decrease, reflecting the initial dom- d Olake with increasing fluidinput to PyramidLake inance of discharge over evaporation on the hydrologic (increasing overflow to the Winnemucca Lake basin) andisotopic balances. In situations in which climate (Fig. 5A, Table 1). In the fourth overflow simulation, 18 3 À1 suddenly switches to a drier state, d O values first DTR was set to 0.70 km yr andinitial lake depthwas increase, reflecting the initial dominance of evaporation set to 40 m (83 m below the spill point). The negative 18 over discharge on the hydrologic and isotopic balances, 4.1% transient in d Olake indicates the effect of then the d18O values slowly decay to their steady-state dumping a large volume of isotopically light river water value. into a small-volume lake. For three of the four overflow simulations, initial lake In two of the three simulations that testedthe depth was set to 100 m (23 m below Pyramid Lake’s spill response of a hydrologically closed Pyramid Lake to a 18 point), d Olake was set to 0.0%, anddischarge of the step-function change in the hydrologic balance, Lake Truckee River (DTR) was set to 0.60, 0.70 (the historical Tahoe was allowedto contribute one thirdof the inflow

Fig. 5. HIBAL simulations of the response of d18O to step-function perturbations in climate (input). (A) Simulations in which PyramidLake overﬂows. (B) Simulations in which Pyramid Lake is hydrologically closed. The d18O response is characterizedby an initial transient whose magnitude is proportional to the input volume : lake volume ratio weighted by their respective d18O values. The steady-state d18O value in the hydrologically open simulations is proportional to the overﬂow volume : lake volume ratio. Under hydrologically closed conditions, the steady-state d18O value of the lake is equal to the input d18O value minus the output d18O value.

Table 1 Input data and results of simulations of Pyramid Lake d18O response to changes in Truckee River dischargea

18 3 À1 18 18 3 À1 18 18 di (m) d Oi (%) D (km yr ) d OTR (%) Pol (m) d Ool (%) E(m) Vin (km yr ) d Otrans (%) d OSS (%) Hydrologically open simulations 100 0.0 0.60 À11.6 0.20 À10.6 1.20 0.71 À0.3 1.2 100 0.0 0.70 À11.6 0.20 À10.6 1.20 0.81 À0.9 0.0 100 0.0 0.80 À11.6 0.20 À10.6 1.20 0.91 À1.5 À1.0 40 0.0 0.70 À11.6 0.20 À10.6 1.20 0.81 À4.1 0.0

Hydrologically closed simulations 100 0.0 0.30 À11.6 0.20 À10.6 1.20 0.36 2.5 2.2 100 0.0 0.40 À11.6 0.20 À10.6 1.20 0.48 4.2 2.2 122 0.0 0.25 À14.6 0.20 À10.6 1.20 0.27 6.0 À0.8

a 18 18 18 18 18 di; initial lake depth; d Oi, initial lake d O; D; Truckee River discharge; d OTR, Truckee River d O; Pol; on-lake precipitation; d Ool, on-lake 18 18 18 18 precipitation d O; E; evaporation; Vin; total input to PyramidLake; d Otrans, initial transient in d O; d OSS, steady state value of Pyramid Lake d18O. 1526 L. Benson, F. Paillet / Quaternary Science Reviews 21 (2002) 1521–1539 to PyramidLake. Initial lake depth was set to 100 m, deal of similarity in the overall shape of the forcing and 18 d Olake was set to 0.0%, and DTR was set to 0.30 and response functions. The high-frequency responses, how- 0.40 km3 yrÀ1 (Fig. 5B, Table 1). The steady-state d18O ever, were not nearly as variable as the high-frequency value achievedin both simulations was exactly the same forcing. (2.2%), illustrating that under closed-basin conditions 18 the d Olake value is dependent only on the difference 18 18 18 between the d O values of inflow ðd Oin ¼À11:6%Þ 2.5. Comparison of reconstructed d O and lake-volume 18 andthe evaporation fractionation factor ðd Oevap À records for Pyramid and Walker Lakes, Nevada 18 d Olake ¼À13:8%Þ: In order to determine the response of Pyramid Lake To this point we have examinedthe modeledresponse d18O to severe drought sufficient to cause Lake Tahoe to of d18O to hypothetical step-function andperiodic fall below its spill point, the depth of Pyramid Lake was changes in the hydrologic balance under either hydro- 3 À1 set to 122 m and DTR was set to a value of 0.25 km yr . logically closed or hydrologically open conditions. In The results of this simulation indicate that d18O initially this section, we use reconstructeddischarges of the experiences a 6.0% transient before achieving a steady Truckee (Benson et al., 2001) andWalker rivers (Milne, state value of À0.8%. In this simulation, the steady-state 1987) to simulate pristine volume andaragonite 18 18 d O value was negatively shifted3.0 % relative to the ðd OCaCO3 Þ records for Pyramid and Walker lakes since results of the other two closed-basin simulations 1916 (Fig. 8). With pristine (reconstructed) flows, (Fig. 5B, Table 1). This shift reflects the loss of Walker Lake wouldhave remaineda hydrologically isotopically heavy Lake Tahoe input to the Truckee closedsystem, but PyramidLake wouldhave shifted 18 River system; i.e., d Oin was 3.0% less (–11.6 to – from open to closed conditions when its level dropped 14.6%) with closure of Lake Tahoe. below 1177 m andits volume fell below 36.2 km 3.Itis apparent from its reconstructedlake-volume recordthat 2.4. Lags in the response of Pyramid Lake volume and PyramidLake wouldhave fallen below its spill point d18O to climate change during severe droughts that occurred during the late 1920s andthroughout the 1930s, duringthe late 1940s Simulations of the response of lake volume and d18O andearly 1950s, duringthe early 1960s andlate 1970s, to periodic climate forcing (changes in river discharge) andduring the late 1980s andearly 1990s (Fig. 8A). were made in order to assess how much d18O lags Each of these droughts is also indicated as minima in the climate change, andthe degree to which d18O mimics the Walker Lake volume record. shape of the climate forcing. Two sets of simulations Walker Lake has a geographic setting similar to were made under hydrologically open (Fig. 6) and PyramidLake. It is fedby a single stream (Walker hydrologically closed conditions (Fig. 7). We used the River) which also receives its moisture from Sierran following periodic function to generate discharge snowmelt. Reconstructedannual discharges of the 3 À1 wavelengths of 10, 50, and100 yr andan amplitudeof Walker River to Walker Lake average 0.38 km yr 0.1 km3: andare available from 1871 to 1986 (Milne, 1987). The evaporation rate for Walker Lake (1.3 m yrÀ1) is similar 2pt À1 y ¼ Amaxsin þ D; to that of PyramidLake (1.2 m yr ), andfor the l simulation of the historical d18O evolution of Walker 3 where y is the discharge in km , Amax the maximum Lake, we used identical climatic, isotopic, and hydro- amplitude in km3, t the time in yr, l the wavelength in logic inputs (excepting discharge). The initial depth of 3 À1 yr, and Din the mean discharge in km yr . Walker Lake was set to its 1916 reconstructedvalue of 18 PyramidLake overflows when Vin ¼ Din >0.58; 86.6 m andits initial d O value was set to À1.0%. In the 3 À1 18 18 therefore, Din was variedbetween 0.63 and0.73 km yr simulations, d Olake was convertedto d O values of a 18 in the open-system simulations. The results of these carbonate precipitate ðd OCaCO3 Þ using equations from simulations indicate that d18O andvolume responses O’Neil et al. (1969). 18 were nearly identical, and that both responses lagged Comparison of the simulated d OCaCO3 records for discharge periodicities of 10, 50, and 100 yr by 1.5, 11, PyramidandWalker lakes with their reconstructed 18 18 and15 yr (Fig. 6A–C). Thus the d O lag time varied volumes shows that minima andmaxima in d OCaCO3 from B15 to B20% of the periodof climate forcing. occur at the same time as minima andmaxima in 18 For the closed-system simulations,Din was varied volume (Fig. 8A, B). This illustrates that d Oisa between 0.30 and0.40 km 3 yrÀ1. The d18O lag time also faithful recorder of the timing and direction of change in variedfrom B15 to B20% of the periodof climate the hydrologic balance of both lakes. In addition, the 18 forcing in these simulations (Fig. 7A–C). Comparison of overall shape of the Walker Lake volume and d OCaCO3 the composite forcing (discharge data) with the compo- records are remarkably similar, suggesting that even site d18O response (Figs. 6D and7D) indicates a great though volume and d18O cannot be linkedby an L. Benson, F. Paillet / Quaternary Science Reviews 21 (2002) 1521–1539 1527

Fig. 6. HIBAL simulations of the response of d18O to periodic perturbations in climate (discharge) under overflow conditions. (A) Perturbations with a 10 yr wavelength. (B) Perturbations with a 50 yr wavelength. (C) Perturbations with a 100 yr wavelength. (D) Composite recordof the 10 yr, 50 yr, and100 yr perturbations. The d18O records lag the climate perturbations by 15–20% of the perturbation wavelength, but their form is strongly similar to the form of the perturbation. equation of state, they do tend to exhibit similar shapes the oscillations as being causedby abrupt changes in the over, at least, decadal time scales. The magnitudes of hydrologic balance of Owens Lake; i.e., its change from 18 negative maxima in the PyramidLake d OCaCO3 record a hydrologically open to a hydrologically closed system. are not reflectedin the volume recordduringoverflow. In the following, we usedHIBAL to simulate the This ‘‘excess’’ volume is insteadreflectedin the amount response of d18O to closure andspill of Owens Lake of water spilledto the adjacentWinnemucca Lake basin. during the Pleistocene-Holocene transition. Given the paucity of historic andprehistoric climate andlake data sets, we were forcedto make several simplifying 3. Applications of HIBAL to a Late Pleistocene d18O assumptions, including the following: record 18 (1) When short-livedheavy ( d OCaCO3 > 24%) excur- 3.1. Simulations of d18O variations in the Owens Lake sions in d18O values occurred, we assumed that the system during the Pleistocene–Holocene transition climate hadbeen either warm anddry(historic mode) or cold and dry (interstadial mode). For Between 15 and10 cal ka BP, four relatively brief, simulations involving the historic mode, we used 6–9% oscillations in d18O were recorded in Owens Lake, historic PyramidLake climate andlake datasets California (Fig. 9). Benson et al. (1997) have interpreted (Appendix A) because they were the only data 1528 L. Benson, F. Paillet / Quaternary Science Reviews 21 (2002) 1521–1539

Fig. 7. HIBAL simulations of the response of d18O to periodic perturbations in climate (discharge) under closed-basin conditions. (A) Perturbations with a 10 yr wavelength. (B) Perturbations with a 50 yr wavelength. (C) Perturbations with a 100 yr wavelength. (D) Composite recordof the 10 yr, 50 yr, and100 yr perturbations. As in the case of an overﬂowing lake, the d18O records lag the climate perturbations by 15–20% of the perturbation wavelength, andtheir form is strongly similar to the form of the perturbation. Note, however, that the high-frequency part of the composite- discharge record is not clearly reproduced in the d18O record.

available andbecause the climatic settings of Owens coldest and warmest months were set, respectively, andPyramidLakes are similar. For the historic to 11C and14 1C. The temperatures of the interven- mode, Owens Lake evaporation and on-lake pre- ing months were scaledbetween these values using cipitation rates were set to their estimatedhistoric the modern distribution of Pyramid Lake water values of 1.5 and0.1 m yr À1 (Hollett et al., 1991). temperatures. In addition, the depth of the mixed (2) When light d18O values (18–21%) dominated the layer was reduced to reflect the decrease in heat Owens Lake record, we assumed the climate had gainedby the lake over the annual cycle. This been cold and wet (stadial mode). For the cold was accomplishedby scaling the depth of the stades and interstades, we adjusted Pyramid Lake mixedlayer to its water temperature using historical values of air temperature, water temperature, relationships (Appendix A). Evaporation rate mixed-layer depth, and Owens Lake evaporation was set to 0.75 m yrÀ1 (about half the Owens andon-lake precipitation rates in accordancewith Lake historical value) andon-lake precipitation the results of Hostetler andBenson (1994) who was set to 0.30 m yrÀ1 (about three times its simulatedthe conditions responsible for the rise of historical value). late-Pleistocene Lake Lahontan. 71C was subtracted 18 from the PyramidLake monthly air-temperature To simulate the effects of overflow on d OCaCO3 ; the distribution and the water temperature of the initial depth of Owens Lake was set to 10 m (55 m below L. Benson, F. Paillet / Quaternary Science Reviews 21 (2002) 1521–1539 1529

Fig. 8. Reconstructed(A) volume and(B) d18O records for Pyramid and Walker lakes since 1916. Reconstructed discharge for the Walker River used to calculate Walker Lake volumes are available only through1986 (Milne, 1987). its spill point). The model was then run to simulate the effects of a step-function change to a coldandwet (stadial mode) climate. Three different discharge volumes were input to the model, 0.56, 0.84, and 1.69 km3 yrÀ1, representing 2, 3, and6 times the volumes necessary to cause overflow. The model was run for 18 300 yr. The initial d Olake value was set to 0.0%, and d18O values of river discharge and on-lake precipitation were set to their stadial values (À17%, Benson, 1999, p. 212). The results of the three simulations (Table 2, Fig. 10A, B, first 300 yr) indicate an abrupt 10.4 to 18 13.5% decrease in d OCaCO3 ; followedby exponential decay over a 100–200 yr interval to steady-state 18 d OCaCO3 values. The discontinuity in the exponential decay indicates the time that Owens Lake began to overflow. As the volume of the hydrologically closed Fig. 9. d18O recordfor Owens Lake between 15 and10 cal ka BP 18 CaCO3 Owens Lake increases, d Olake decreases, reflecting the D1,D2,D3, andD 4 signify times of climatic drying. addition of isotopically light river discharge; the faster 18 the volume increase, the greater the decrease in d Olake andthe more negative the value of the d18O transient. When Owens Lake overflows, the steady state d18O spill, lessening the effect of evaporation on the 18O/16O value of the overflowing lake water is proportional to ratio of the spilling lake. the ratio of the spill rate (Vspill) relative to maximum Two additional sets of simulations were run to 18 lake volume (Vlake). This is because the residence time of demonstrate the effect on d OCaCO3 of a return of water in the spilling lake decreases with increased rate of Owens Lake to hydrologic closure associated with either 1530 L. Benson, F. Paillet / Quaternary Science Reviews 21 (2002) 1521–1539

Table 2 Input data and results of simulations of Owens Lake d18O response to abrupt changes in its hydrologic balancea

18 3 À1 18 18 18 18 di (m) d Oi (%) D(km yr ) d OOR (%) Pol (m) d Ool (%) E (m) d Otrans (%) d OSS,CC (%) Cold and wet simulations (stadial mode, adjusted Pyramid Lake data used) 10 0.0 0.56 À17 0.30 À17 0.75 À10.4 26.5 10 0.0 0.84 À17 0.30 À17 0.75 À11.7 25.2 10 0.0 1.69 À17 0.30 À17 0.75 À13.5 22.1

Warm and dry simulations (historic mode, Pyramid Lake historical data used) 65 À5.5 0.36 À15 0.10 À15 1.50 8.3 28.9 65 À6.8 0.36 À15 0.10 À15 1.50 9.4 28.9 65 À9.9 0.36 À15 0.10 À15 1.50 11.9 28.9

Cold and dry Simulations (interstadial mode, adjusted Pyramid Lake data used) 65 À5.5 0.17 À17 0.30 À17 0.75 9.1 o29.5b 65 À6.8 0.17 À17 0.30 À17 0.75 10.2 o29.5b 65 À9.9 0.17 À17 0.30 À17 0.75 12.8 o29.5b

a 18 18 18 18 18 di, initial lake depth; d Oi, initial lake d O; D; Owens River discharge; d OOR, Owens River d O; Pol; on-lake precipitation; d Ool, on-lake 18 18 18 18 18 precipitation d O; E; evaporation; d Otrans, initial transient in d O; d OSS,CC, steady state value of Owens Lake calcium carbonate d O. b Not run to ﬁnal steady state.

a warm-dry or a cold-dry climate. Both sets of 18 simulations were initializedusing steady-state d Olake values resulting from the three overflow simulations. Initial lake depth was set to its overflow value of 65 m. The warm-dry simulations are meant to approximate modern-day drought conditions and the cold-dry simulations are meant to approximate drought conditions that are possibly more typical of the glacial- interglacial transition. For the warm-dry simulations, Owens River discharge was set to a value (0.36 km3) that wouldallow the lake to achieve a steady-state depth of B10 m. d18O values of river discharge and on-lake precipitation were set to their historic values (À15%, Benson, 1999, p. 212). For the cold-dry simulations, the model was run in its stadial mode with evaporation set to 0.75 m yrÀ1 and precipitation set to its historical value of 0.10 m yrÀ1. Owens River discharge was set to a value (0.17 km3) that wouldallow the lake to achieve a steady-state depth of B10 m. d18O values of river discharge and on- lake precipitation were set to their stadial values (À17%). Results of both sets of the warm-dry and cold-dry simulations (Table 2, Fig. 10A, B, 300–600 yr) indicate 18 an abrupt transient increase in d OCaCO3 of 8.3 to 12.8% followedby a 150- to 300-yr exponential decayto steady-state d18O values of 28.9% (Fig. 10A) and 18 o29.5% (Fig. 10B). During the dry intervals, d Olake 18 increases as the lake shrinks, reflecting the dominance of Fig. 10. Simulations of changes in d OCaCO3 resulting from overflow andhydrologic closure of Owens Lake California. The results of three evaporation on the hydrologic and isotopic balances. 18 sets of simulations are indicated. The first set of results show the Simulations of the response of Owens Lake d OCaCO3 to 18 response of d OCaCO precipitatedfrom a shallow (10 m) closedlake to 18 3 overflow andhydrologicclosure yield d OCaCO3 excur- step-function increases in the hydrologic balance during the first 300 yr sions of similar magnitude and duration to those of the simulations. The secondandthirdset of results indicate how 18 hydrologic closure during the next 300 yr of the simulations affects observedin the actual Owens Lake d O recordbetween 18 15 and10 cal ka BP (Fig. 9 and10), supporting the d OCaCO3 during the transition from a cold-wet climate to either a warm-dry climate (A) or a cold-dry climate (B). concept that the abrupt oscillations in d18O resulted L. Benson, F. Paillet / Quaternary Science Reviews 21 (2002) 1521–1539 1531 from step-function changes in the hydrologic balance. HIBAL model, a discussion of its application to We have therefore shown that HIBAL can be usedto PyramidLake, a description of the behavior of d18O simulate ‘‘interesting’’ parts of a paleolake d18O record. in the Truckee River-PyramidLake system, anda discussion of the data used as inputs to the HIBAL model. Inputs to simulations of the Walker Lake and 4. Discussion Owens Lake systems are discussed in the text. HIBAL is written in FORTRAN; a hardcopy of the Pyramid We have presenteda simple hydrologic-isotopic- Lake version together with input files is available from balance model for application to lake and paleolake the senior author ([email protected]). d18O records and have demonstrated the ability of the model to simulate changes in the hydrologic balance and A.1. Governing equations the d18O evolution of the lake, using measureddata from PyramidLake andWalker Lake, Nevada,and The isotopic mass balance of a lake is given by Owens Lake, California. Simulations of the response in 18 qðdVÞ d O to step- andperiodic-function changes in the ¼ðPdP À EdevapÞA þ VD;idDi À VD;odDo hydrologic balance indicate that d18O tends to lag qt climate change on time scales similar to that which þ VG;idGi À VG;odGo; ðA:1Þ 18 volume lags climate change. The d O response to a where t is time, V is lake volume, P is the amount of on- step-function perturbation in the hydrologic balance 18 lake precipitation, dP is the d O value of precipitation, consists of an initial transient that lasts several decades. 18 E is the amount of evaporation, devap is the d O value of Because climate varies on all time scales, the hydrologic water vapor leaving the lake surface, A is the surface balance always changes before the steady-state d18O area of the lake, VD;i is the discharge volume, dDi is the value is achievedandusually prior to the endof the 18 18 d O value of discharge, VD;o is the volume of surface transient response. This implies that the lacustrine d O 18 water lost from the lake as overflow, dDo is the d O recordis composedof a sequence of initial transient value of overflow, VG;i is the volume of groundwater responses to high- and middle-frequency climate per- 18 input to the lake, dGi is the d O value of ground-water turbations that are superimposedon a low-frequency discharge, VG;o is the volume of ground-water output backgroundof climate change. Neither lake volume nor 18 18 from the lake, and dGo is the d O value of the output d O ever reach equilibrium with climate forcing which groundwater (Gonfiantini, 1965). can be envisionedas occurring as a series of step- 18 For a closed-basin lake in which in which ground- functions. Even though the d O response lags climate water flux is negligible andsurface overflow doesnot forcing, the initial phase of the transient always reflects occur, Eq. (A.1) reduces to the immediate hydrologic response; i.e., when volume increases, d18O decreases and vice versa. Thus, the qðdVÞ ¼ðPdP À EdevapÞA þ VD;idDi: ðA:2Þ derivative of d18O will yieldthe directionof climate qt change; i.e., whether climate is becoming drier or wetter Benson andWhite (1994) derivedan expression for (Benson et al., 2001). Because the shape (amplitude) of devap basedon the conceptual modelof Craig and 18 the d O transient is dependent on lake size at the time Gordon (1965), deviating from their seminal derivation of the hydrologic perturbation, it cannot be used to in four ways: assess how wet or how dry the climate was unless the initial lake level is known. We have, however, illustrated 1. The derivation of the basic set of equations that that the d18O response of a hydrologically closed lake describe isotopic fraction was done in terms of ratios does tend to mimic its volume change. of isotopic species, Ri; allowing conversion of laboratory values of di to Ri; using 3 di ¼ðRi À 1Þ10 ; ðA:3Þ Acknowledgements 18 16 where bold-type Ri is the O: O ratio of a sample The authors thank Steve Hostetler of the US (Ri) divided by the corresponding isotopic ratio of a Geological Survey andJohn Andrewsof the University standard (Rstd). of Colorado for their reviews of this paper. 2. The derivation includes an expression for the 18O:16O ratio of evaporating moisture ðRevapÞ in terms of the fractions of advected and lake-derived Appendix A. The HIBAL model and its inputs moisture. 3. The equilibrium andkinetic fractionation of 18O and This appendix contains governing equations used in 16O are separately treatedin the derivation, allowing the isotopic mass-balance of a lake, a description of the the use of Merlivat andJouzel’s (1979) determina- 1532 L. Benson, F. Paillet / Quaternary Science Reviews 21 (2002) 1521–1539

18 18 18 tions of the dependence of the kinetic fractionation ðd Oevap À d OlakeÞ; d O fractionation can be dis- 18 factor on windspeed. playedas a function of fad; RH, d Oad; and Tlake using 4. Benson andWhite (1994) also derivedan expression Eqs. (A.3) and(A.4). When fad ¼ 0; the fractionation of for the net vapor flux that avoids introduction of d18O decreases B0.6% with a 10% increase in RH; gross evaporation andback-condensationfluxes, however, with an increase in fad; the fractionation of quantities that are nearly impossible to measure. d18O becomes increasingly sensitive to the value of d18O ; e.g., when f ¼ 0:2; d18O À d18O de- According to Benson and White (1994), the 18O:16O ad ad evap lake creases 0.5% with every 3% decrease in d18O ratio in water vapor releasedfrom the lake surface ad (Fig. 11A). Fractionation of d18O during evaporation during evaporation ðRevapÞ is given by decreases B0.09% with each 1 K increase in Tlake Rlake=aeq À RHfadRad (Fig. 11B). Revap ¼ ; ðA:4Þ ð1 À RH=akinÞþRHð1 À fadÞ where R and R are the 18O:16O ratios in lake water lake ad A.2. Model description and its application to Pyramid andadvectedwater vapor, fad is the fraction of advected water vapor in the boundary layer over the lake, RH is Lake the relative humidity of the boundary layer, and aeq and a are the equilibrium andkinetic fractionation HIBAL is a two-box ‘‘forward’’ model that runs on a kin monthly time step. For inputs, the model requires fluid factors. 18 If all the water vapor overlying the lake is derived by fluxes, their associated d O values, depth of the mixed evaporation, f ¼ 0 andEq. (A.4) becomes layer, basin hypsometry, anda set of meteorological ad data that govern the fractionation of d18O during akin 1 Revap ¼ Rlake : ðA:5Þ evaporation andprecipitation of CaCO 3. aeq 1 À RH þ RHakin Monthly values of normalizedon-lake precipitation # Isotope ratios can be convertedto del( d) values using ðPÞ; mixed-layer depth ðdmlÞ; lake-surface temperature Eq. (A.3) andvalues of the equilibrium fractionation ðTlakeÞ; relative humidity ðRHÞ; normalizeddischarge # # factor, aeq; can be calculatedfrom ðDÞ; normalizedevaporation ðEÞ; andthe polynomials that relate volume (V) andsurface area ( A) to lake depth a ¼ expð1137TÀ2 À 0:4156TÀ1 À 2:066710À3ÞðA:6Þ eq lake lake (d) are readfrom within HIBAL. There are two external where the temperature of lake surface water, Tlake; is in input files. The ‘‘flow’’ file contains a list of annual À1 K (Majoube, 1971). For windspeeds o6.8 m s , akin ¼ discharges. The ‘‘parameter file’’ includes values of 0:994 andfor windspeedsbetween 6.8 and12.5 m s À1, annual evaporation (E) andon-lake precipitation ( P), values of akin range from 0.9955 to 0.9975 (Merlivat and initial lake depth ðdiÞ; the fraction of advected moisture Jouzel, 1979). (fad) in the boundary layer over the lake, the fraction of If we define the fractionation of d18O during inflow from Lake Tahoe (0.333), the value of Truckee evaporation as the difference between d18O in the water River discharge (at the Farad gage) at which Lake vapor andthe d18O in evaporating lake water Tahoe ceases to overflow (0.28 km3), and d18O values for

18 18 Fig. 11. (A) The evaporation fractionation factor ðd Oevap À d OlakeÞ as a function of the fraction of advected vapor (fad), relative humidity, (RH), 18 18 18 18 andthe d O value of advected vapor (d Oad). (B) The evaporation fractionation factor ðd Oevap À d OlakeÞ as a function of surface-water temperature (Tlake). L. Benson, F. Paillet / Quaternary Science Reviews 21 (2002) 1521–1539 1533 the following: PyramidLake water, snowmelt, on-lake River-PyramidLake surface-water system. In that precipitation, advected moisture, and Lake Tahoe out- study, the weighted average d18O of precipitation at flow. Tahoe Meadows (Fig. 2) was found to be identical to the After the inputs are read, the program performs the À14.6% value of shallow groundwater in the Lake following sequence of calculations: For the first month, Tahoe area (Table 3). The À14.6% value represents the isotopic composition of overlandflow andshallow 1. Initial lake volume andsurface area are calculated groundwater that discharge to the Truckee River at from the initial depth. its headwaters. The d18O value of the Truckee River at

2. Fractionation factors (akin;aeq;aH2O2CaCO3 ) are readin the Faradsite, however, is heavier, oscillating between or computed. extremes of BÀ7% and À13% over the annual cycle 3. Discharge and on-lake precipitation are added to the (Fig. 12), due to the mixing of Lake Tahoe overflow lake. (d18O=À5.6%) (Fig. 2, Table 3) with À14.6% water 18 4. Volume-weighted d O values of discharge and derived from snowmelt (Fig. 13). The fraction of Tahoe- precipitation are combinedwith the volume-weighted derived water entering the Truckee River system is not 18 d O value of the mixedlayer. constant, but tends to increase sharply between July and 5. The new volume is comparedwith the overflow September (Fig. 14). volume. If the new volume is greater than the During wet years, the d18O value of PyramidLake’s overflow volume, the excess volume is subtracted; epilimnion (mixedlayer) decreases in response to the i.e., the overflow is routedto the adjacentWinne- large volume of isotopically light Truckee River water mucca Lake basin that flows into the lake (Fig. 15). Throughout the 6. Evaporation is subtractedfrom the lake. evaporation season, the lake warms andthe mixedlayer 18 7. The volume-weighted d O value of the vapor deepens (Fig. 16), and the d18O value of the mixedlayer 18 16 phaseðd OevapÞ is calculatedandthen subtracted increases in response to the preferential loss of O to the 18 from the volume-weighted d O value of the mixed atmosphere (Fig. 15). In January, the lake becomes layer. 8. The base of the mixedlayer is movedto the next month’s depth, and if the base penetrates the hypolimnion volume, the volume-weighted d18O value of the entrainedhypolimnion volume is mixed with the volume-weighted d18O value of the mixed layer.

Output consists of a listing of input variable values D; d; and V for each model year together with monthly 18 18 values of d Olake and d OCaCO3 : The model was also testedwith evaporation being subtractedbefore the excess volume was subtracted, using measured Nixon discharge values from 1916 through 1996. Simulated lake level and d18O records were identical in both simulations.

A.3. The behavior of d18O in the Truckee River-Pyramid Lake surface-water system

The study by Benson (1994) provides the basis for our understanding of the behavior of d18O in the Truckee Fig. 12. The d18O values of water from the Faradsite.

Table 3 Oxygen-18 values for precipitation, ground-water, and river water samples from the Pyramid Lake drainage basin

Sampling site Sample type Ave d18O Wt Ave d18O No. samples

Tahoe meadows Precipitation À14.2 À14.6 134 Sutcliﬀe Precipitation À9.8 À10.6 52 Lake Tahoe area wells Groundwater À14.6 NA 8 Truckee River, Tahoe City River water À5.6 À5.6 30 Truckee River, FaradRiver water À10.3 À10.1 55 Truckee River, Nixon River water À10.4 À9.9 61 1534 L. Benson, F. Paillet / Quaternary Science Reviews 21 (2002) 1521–1539

Fig. 13. Farad d18O and d2H values plottedon a mixing diagram.The solidline indicatesvalues of the two isotopes that wouldresult from mixing of Lake Tahoe overﬂow with snowmelt. Fig. 15. Proﬁles of d18O from PyramidLake taken duringearly summer (7/6/93), autumn (9/8/92), andlate winter (1/21/93). Note that the lake becomes isothermal in January, fully mixing andhomogeniz- ing its isotopic composition.

Fig. 14. The d18O values of water at the Faradsite plottedas a function of lunar month. The data indicate that most of the water passing the Faradsite in the late autumn is derivedfromLake Tahoe overflow. isothermal andfully mixes (Fig. 16), homogenizing the epilimnion andhypolimnion d18O values (Fig. 15). 18 Fig. 16. Depth of the mixedlayer in PyramidLake over the annual With regardto the use of d O values in historical cycle. Solid dots indicate base of a somewhat unstable mixed layer. 18 simulations of the evolution of PyramidLake d O, the Open circles indicate the base of a stable mixed layer. Data were observedseasonal distribution of Truckee River d18O provided by the Pyramid Lake Paiute Resources Group. (Fig. 14) was ignoredandit was assumedthat when Lake Tahoe overflowed, it contributed one-third d18O value of on-lake precipitation was set to the of the total Truckee River discharge to Pyramid Lake. weighted-mean value measured at Sutcliffe (À10.6%) Thus, discharge was given a d18O value of –11.6%. The (Table 3). L. Benson, F. Paillet / Quaternary Science Reviews 21 (2002) 1521–1539 1535

Fig. 17. Plots of Pyramid Lake hypsometric data (Benson and Miﬄin, 1986). (A) Surface area vs. depth. (B) Volume vs. depth.

Table 4 Precipitation data from selected weather stations located in the PyramidLake drainagebasin

Weather station Recordlength (yr) Annual precip. (m)

Tahoe meadows 23 1.3170.52 Reno airport 54 0.1870.06 Sutcliﬀe 20 0.2170.08 Nixon 40 0.1670.07 Wadsworth 17 0.1770.08

A.4. Model inputs

Monthly mixed-layer depths were fit to data taken on a more-or-less monthly basis between October 1985 andJanuary 1999 (Fig. 16). The lake undergoes complete mixing throughout the first two lunar months. Polynomials were fit to available surface area-depth and volume-depth data (Benson and Mifflin, 1986) Fig. 18. Precipitation from weather stations near PyramidLake for the PyramidLake basin (Fig. 17A,B). Hydrologic comparedto Reno, Nevada,precipitation. Data were obtainedfrom the Western Climate Data Center, Desert Research Institute, Reno, andmeteorological input datasets were tabulatedfor Nevada. lunar months of the calendar year. The choice of lunar month is arbitrary but dispenses with the necessity of ‘‘weighting’’ Julian-month data given their unequal lengths. Wadsworth and Reno (Fig. 19). The mean-value of Monthly values of on-lake precipitation were calcu- precipitation obtainedin this manner is statistically latedusing data from four weather stations locatedat indistinguishable from the non-weighted annual mean of Sutcliffe, Nixon, Wadsworth, and Reno, Nevada all four weather stations (Table 4). The monthly (Fig. 2). These stations are in low-elevation basins distribution of precipitation was calculated by averaging locatedeast of the Sierra Nevadaandthey exhibit monthly values of the station nearest PyramidLake annual values of precipitation that are statistically (Sutcliffe) with the site having the longest record(Reno) indistinguishable (Table 4). Correlation of annual values (Table 5) andthe monthly distribution was then of near-lake precipitation with Reno precipitation is normalized(Table 6). satisfactory, suggesting that data from any one of the The annual evaporation rate was calculatedby two four stations can be usedwhen only from only one methods. Calendar-year discharge and precipitation station is available (Fig. 18). Mean-annual historical values, together with lake-level data (converted to values of on-lake precipitation were estimatedusing, in volume andsurface area) for the period1932–1996, order of preference, monthly data from Sutcliffe, Nixon, were usedto calculate a hydrologic-balance evaporation 1536 L. Benson, F. Paillet / Quaternary Science Reviews 21 (2002) 1521–1539 rate of 1.2170.16 m yrÀ1. We also fit an optimized using a class A pan was 0.8970.08 m yrÀ1 for the period annual-evaporation rate using calendar-year discharge, 1957 through 1992. To distribute the annual evapora- precipitation, andmeasuredlake level for the tion of 1.2 m yrÀ1 over the annual cycle, monthly period1938–1996, obtaining a value of 1.18 m yr À1 modeled evaporation rates calculated by Hostetler and (Fig. 20). The optimization was basedon the minimiza- Benson (1994)(Table 4) were normalized(Table 6) and tion of the root-mean-square difference between mea- the annual value multipliedby each of the monthly suredandcomputedwater levels over the periodof normalizedvalues record. Annual andmonthly values of Truckee River Long-term pan-evaporation data suggest that a single discharge were obtained from the Farad and Nixon value of evaporation can be usedfrom year to year. The gaging stations (Fig. 2)(US Geological Survey Water- uncorrectedvalue of E measuredat Fallon, Nevada Data Reports, 1916–1996). The Faraddatarepresent an approximation of pristine Truckee River flows that wouldreach PyramidLake; i.e., most consumptive use of water occurs below the Faradsite. Data from the Nixon gage indicates the amount of water that actually reaches PyramidLake. Before construction of the Derby Dam (1906), FaradandNixon discharges were nearly equivalent. Gaging at the Nixon site commencedin 1958. To extendthe Nixon recordto 1916, annual discharges recorded at the gaging station located below Derby Dam were correlatedto Nixon discharges (Fig. 21). We elected to distribute annual Farad and Nixon discharges using the Faraddistribution. We first comparedthe individual monthly data for both sites, noting that they were similar in form before we averagedthe Farad monthly discharges (Table 5). We then checked to see that the shapes of the flow distributions were similar during high- and low-flow years (Fig. 22), prior to normalization of the Faradmonthly data(Table 6). In the model, annual discharges are multiplied by monthly normalized discharge values in order to obtain monthly flows. We electedto use normalizeddischarges as Fig. 19. Histogram of annual precipitation in the PyramidLake area (1900–1997). A single year’s data came from a single site. When data opposed to measured-monthly discharges because mea- for multiple sites were available, data were taken from the site closest sureddataare not available for surface-water systems to the lake. prior to 1900.

Table 5 Lunar monthly hydrologic and climatic data for the Pyramid Lake basina

Lunar Faraddischarge On-lake Evaporation Water temp Sutcliﬀe air RH Windspeed month (km3) precip (m) (m) (1C) temp (1C) (%) (m sÀ1)

1 0.03770.031 0.0292 0.0436 6.6670.54 2.3372.72 73 3.17 2 0.04270.035 0.0230 0.0372 7.0871.24 3.8873.12 68 2.82 3 0.05070.041 0.0198 0.0462 7.8372.17 7.2172.64 55 3.52 4 0.07770.049 0.0106 0.0772 10.0571.92 9.9372.65 47 3.49 5 0.11570.071 0.0140 0.1045 13.0773.74 13.7672.76 47 3.87 6 0.10570.075 0.0169 0.1295 16.4172.84 17.5973.03 46 4.14 7 0.06070.046 0.0060 0.1693 20.7772.18 22.3872.23 35 4.09 8 0.03870.017 0.0057 0.1753 23.1570.93 24.9771.86 37 3.98 9 0.03370.011 0.0060 0.1636 22.3471.32 22.5072.05 32 3.67 10 0.03070.014 0.0110 0.1232 20.0071.68 17.6672.39 41 3.33 11 0.02670.012 0.0101 0.0910 16.6171.89 11.8172.94 50 2.83 12 0.03070.028 0.0218 0.0821 12.6271.45 6.4872.40 64 3.61 13 0.03770.040 0.0255 0.0727 9.0270.90 2.8373.07 67 3.90

a Note: Monthly evaporation data are from a thermal simulation made by Hostetler and Benson (1994). All other data are measured values. See text for discussion. L. Benson, F. Paillet / Quaternary Science Reviews 21 (2002) 1521–1539 1537

Table 6 Normalizedlunar monthly values of discharge, on-lake precipitation andevaporation

Lunar month Faraddischarge On-lake precip Evaporation (normalized) (normalized) (normalized)

1 0.0543 0.146 0.033 2 0.0625 0.115 0.028 3 0.0731 0.099 0.035 4 0.1127 0.053 0.059 5 0.1696 0.070 0.079 6 0.1543 0.084 0.098 7 0.0882 0.030 0.129 8 0.0559 0.029 0.133 9 0.0491 0.030 0.124 10 0.0443 0.055 0.094 11 0.0381 0.051 0.069 12 0.0436 0.109 0.062 13 0.0542 0.129 0.055

Fig. 21. Correlation between annual (calendar-yr) discharges measuredat gages locatedbelow the Derby Dam andat Nixon, Nevada (Fig. 2).

Fig. 20. OptimizedPyramidLake annual-evaporation rate obtained using calendar-year discharge, precipitation, and measured lake levels for the period1938–1996. The optimization was basedon the minimization of the root-mean-square difference between measured andcomputedwater levels over the periodof record. Fig. 22. Plot of Farad monthly discharges during very wet (solid diamonds) and very dry (solid dots) years relative to mean values of Faraddischarge(open circles). Note that peak flows occur at the same times in all distributions. Instantaneous measurements of PyramidLake surface-water temperature between 1985 and1998 at the Deep Site (Fig. 2) were usedto calculate monthly mean values (Table 5). Measurements of air temperature at the Sutcliffe weather station, bordering the west monthly mean values of this parameter (Table 5). Daily shore of PyramidLake (Fig. 2) were also usedto values of windspeedfrom the same source were also calculate monthly mean values (Table 5). Relative examined (Fig. 23) in order to ensure that most daily humidity data available for October 1987 to October windvelocities couldbe associatedwith an akin value 1989 Hostetler andBenson (1993) were usedto calculate of 0.994. 1538 L. Benson, F. Paillet / Quaternary Science Reviews 21 (2002) 1521–1539

Eicher, U., Siegenthaler, U., 1976. Palynological andoxygen isotope investigations on late-glacial sediment cores from Switzerland. Boreas 5, 109–117. Fontes, J.C., Melieres, F., Giber, E., Qing, L., Gasse, F., 1993. Stable isotope andradiocarbonbalances of two Tibetan lakes (Sumxi CO, Longmu CO) from 13,000 BP. Quaternary Science Reviews 12, 875–887. Fritz, P., Anderson, T.W., Leqis, C.F.M., 1975. Late quaternary climatic trends and history of Lake Erie from stable isotope studies. Science 190, 267–269. Gat, J.R., 1970. Environmental isotope balance of Lake Tiberias. In: Isotopes in Hydrology. International Atomic Energy Agency, pp. 109–127. Gonfiantini, R., 1965. Isotopic effects in the evaporation of salt water. Atti Society Toscana National Science Pisa 72, 5–22. Hodell, D.A., Curtis, J.H., Brenner, M., 1995. Possible role of climate in the collapse of classic Maya civilization. Nature 375, 391–394. Hollett, K.J., Danskin, W.R., McCaffrey, W.F., Walti, C.L., 1991. Geology andWater Resources of Owens Valley, California. US Geological Survey Water-Supply Paper 2370. Hostetler, S.W., Bartlein, P.J., 1990. Simulation of lake evaporation with application to modeling lake level variations of Harney– Fig. 23. Daily (24 h) wind-speed data for water years 1988 and 1989 Malheur Lake, Oregon. Water Resource Research 26, (Hostetler andBenson, 1993). 2603–2612. Hostetler, S.W., Benson, L.V., 1993. Meteorological andwater- temperature data for Pyramid Lake, Nevada 1987–89. United States Geological Survey Open-File Report 92–159, 15pp. Hostetler, S., Benson, L.V., 1994. Stable isotopes of oxygen and hydrogen in the Truckee River-Pyramid Lake surface-water system. 2. A predictive model of d18O and- d2H in PyramidLake. References Limnology Oceanography 39, 356–364. Johnson, T.C., Halfman, J.D., Showers, W.J., 1991. Paleoclimate of Benson, L.V., 1994. Stable isotopes of oxygen andhydrogen in the the past 4000 years at Lake Turkana, Kenya, basedon the isotopic Truckee River-PyramidLake surface-water system. 1. Data composition of authigenic calcite. Palaeogeography, Palaeoclima- analysis andextraction of paleoclimatic information. Limnology tology, Palaeoecology 85, 189–198. andOceanography 39, 344–355. Lewis, S., 1979. Environmental isotope balance of Lake Kinneret as a Benson, L.V., 1999. Records of millennial-scale climate change from tool in evaporation rate estimation. In: Isotopes in Hydrology. the Great Basin of the Western UnitedStates. In: Clark, P., Webb, International Atomic Energy Agency, Vienna, pp. 33–53. R., Keigwin, L. (Eds.), Mechanisms of Global Climate Change at Li, H., Ku, T., 1997. d13–d18 covariance as a paleohydrological Millennial Time Scales, American Geophysical Union Monograph indicator for closed-basin lakes. Palaeogeography, Palaeoclimatol- 112, pp. 203–225. ogy, Palaeoecology 133, 69–80. Benson, L.V., Mifflin, M.D., 1986. Reconnaissance bathymetry of Lister, G.S., Kelts, K., Zao, C.K., Yu, J., Niessen, F., 1991. Lake basins occupiedby Pleistocene Lake Lahontan, Nevadaand Qinghai, China: closed-basin lake levels and the oxygen isotope California. UnitedStates Geological Survey Water-Resource recordfor Ostracodasince the latest Pleistocene. Palaeogeography, Investigation Report 85–4262, 14pp. Palaeoclimatology, Palaeoecology 84, 141–162. Benson, L.V., White, J.W.C., 1994. Stable isotopes of oxygen and Majoube, M., 1971. Fractionnement en oxygene-18 et en deuterium hydrogen in the Truckee River-Pyramid Lake surface-water system entre l’eau et sa vapeur. Journal de Chimie Physico 197, 1423–1436. 3. Source of water vapor overlying PyramidLake. Limnology and Merlivat, L., Jouzel, J., 1979. Global climatic interpretation of the Oceanography 39, 1945–1958. deuterium-oxygen 18 relationship for precipitation. Journal Geo- Benson, L.V., Burdett, J.W., Lund, S.P., Kashgarian, M., Mensing, S., physical Research 84, 5029–5033. 1997. Nearly synchronous climate change in the Northern Milne, W., 1987. A comparison of reconstructedlake-level records Hemisphere during the last glacial termination. Nature 388, since the mid-1800s of some Great Basin lakes. Unpublished 263–265. Thesis, Colorado School of Mines. Benson, L.V., Kashgarian, M., Rye, R., Lund, S., Paillet, F., Smoot, O’Neil, J.R., Clayton, R.N., Mayeda, T.K., 1969. Oxygen isotope J., Kester, C., Mensing, S., Meko, D., Lindstrom,. S., 2002. fractionation in divalent metal carbonates. Journal of Chemical Holocene multidecadal and multicentennial droughts affecting Physics 51, 5547–5558. Northern California andNevada.Quaternary Science Reviews Oviatt, C.G., Habiger, G.D., Hay, J.E., 1994. Variation in the 21, 659–682. composition of Lake Bonneville marl: a potential key to lake-level Craig, H., Gordon, L.I., 1965. Isotopic oceanography: deuterium and fluctuations andpaleoclimate. Journal of Paleolimnology 11, oxygen 18 variations in the ocean andmarine atmosphere. In: 19–30. Schink, D.R., Corless, J.T. (Eds.), Marine Geochemistry. Uni- Phillips, F.M., Person, M.A., Muller, A.B., 1986. A numerical model versity, Rhode Island, pp. 277–374. for simulating the isotopic evolution of closed-basin lakes. Journal Eicher, U., 1980. Pollen- undSauerstoffisotopenanalysen an sp- of Hydrology 85, 73–86. atglazialen. Profilen vom Gerzensee, Faulensee undregenmoos ob Phillips, F.M., Campbell, A.R., Kruger, C., Johnson, P., Roberts, R., boltigen. Mitteilungen der Naturforschenden Gesellschaft in Bern Keys, E., 1992. A reconstruction of the response of the 37, 65–80. water balance in western UnitedStates lake basins to L. Benson, F. Paillet / Quaternary Science Reviews 21 (2002) 1521–1539 1539

climatic change. Water Resources Research Institute Report 269, UnitedStates Geological Survey 1916–1996. Water resources datafor 154pp. Nevada. United States Geological Survey Water-data Report Phillips, F.M., Campbell, A.R., Smith, G.I., Bischoﬀ, J.L., 1994. Series. Interstadial climatic cycles: a link between western North America Xia, J., Haskell, B.J., Engstrom, D.R., Ito, E., 1997. Holocene climate andGreenland?Geology 22, 1115–1118. reconstructions from tandem trace-element and stable-isotope Stuiver, M., 1968. Oxygen-18 content of atmospheric precipitation composition of ostracodes from Coldwater Lake, North Dakota, during the last 11,000 years in the Great Lakes region. Science 162, USA. Journal of Paleolimnology 17, 85–100. 994–997. Yurtsever, Y., 1975. Worldwide survey of stable isotopes in precipita- Stuiver, M., 1970. Oxygen andcarbon isotope ratios of fresh-water tion. In: Reports Section of Isotope Hydrology, International carbonates as climatic indicators. Journal of Geophysical Research Atomic Energy Agency, pp. 567–585. 75, 5247–5257.