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Stable Isotopes of Oxygen and Hydrogen in the Truckee River-Pyramid Lake Surface-Water System, 2

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Stable Isotopes of Oxygen and Hydrogen in the Truckee River-Pyramid Lake Surface-Water System, 2 University of Nebraska - Lincoln DigitalCommons@University of Nebraska - Lincoln USGS Staff -- ubP lished Research US Geological Survey 1994 Stable isotopes of oxygen and hydrogen in the Truckee River-Pyramid Lake surface-water system, 2. A predictive model of δ18O and δ2H in Pyramid Lake S. W. Hostetler US Geological Survey Larry Benson U.S. Geological Survey, [email protected] Follow this and additional works at: https://digitalcommons.unl.edu/usgsstaffpub Part of the Geology Commons, Oceanography and Atmospheric Sciences and Meteorology Commons, Other Earth Sciences Commons, and the Other Environmental Sciences Commons Hostetler, S. W. and Benson, Larry, "Stable isotopes of oxygen and hydrogen in the Truckee River-Pyramid Lake surface-water system, 2. A predictive model of δ18O and δ2H in Pyramid Lake" (1994). USGS Staff -- Published Research. 1013. https://digitalcommons.unl.edu/usgsstaffpub/1013 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. Limnol. Oceanogr., 39(2), 1994, 356-364 0 1994, by the American Society of Limnology and Oceanography, Inc. Stable isotopes of oxygen and hydrogen in the Truckee River-Pyramid Lake surface-water system, 2. A predictive model of a1*O and cY~Hin Pyramid Lake S. W. Hostetler and L. V. Benson U.S. Geological Survey, 32 15 Marine St., Boulder, Colorado 80303 Abstract A physically based model of variations in WO and 6*H in Pyramid Lake is presented. For inputs, the model uses measurements of liquid water inflows and outflows and their associated isotopic compositions and a set of meteorological data (radiative fluxes, air temperature, relative humidity, and windspced). The model simulates change of lake volume, thermal and isotopic stratification, evaporation, and the isotopic composition of evaporation. A validation of the model for 1987-1989 and 199 1 indicates that it can reproduce measured intra- and interannual variations of 6’*0 and 6*H. Three applications of the model demonstrate its ability to simulate longer term responses of VO to change in the hydrologic balance and hydrologic characteristics (opening and closing) of the lake. Annual variations of the isotopic (al80 and measured data, however, they are limited to a2H) composition of Pyramid Lake are asso- applications within the period of calibration ciated by Benson (1994) with annual patterns and to lakes where sufficient measured data of precipitation, evaporation, streamflow dis- are available. In addition, except for the model charge, and lake mixing (stratification). Larger, of Lewis, a vertically homogeneous water col- long-term changes in isotopic composition are umn is assumed, and the effects of seasonal linked to change in the hydrologic balance and thermal and isotopic stratification on isotopic the hydrologic state (e.g. whether the lake is composition are not considered. open or closed) of the lake. In this paper, we To broaden the range of applicability of iso- present a model used to simulate variations in tope models, we have developed a calibration- 6180 and 62H in Pyramid Lake that occur in free model for Pyramid Lake that can simulate response to change in the hydrologic balance the seasonal behavior of 6180 and a2H. Both and climate. external forcing (atmospheric and hydrologic) Several steady state and dynamic models of and internal processes (seasonal stratification al80 and 62H have been developed and applied and mixing) that affect the isotopic composi- to lakes (e.g. Gat 1984; Zimmerman and Eh- tion are treated in the model. For inputs, the halt 1970; Zimmerman 1977; Fontes et al. model requires inflows and outflows of liquid - 1979; Phillips et al. 1986). The models have water and their associated isotopic composi- been successfully used to evaluate hard to mea- tions and a set of atmospheric data (air tem- sure components of the hydrologic budget perature, humidity, windspeed, solar radia- (typically evaporation). In such applications, tion, and atmospheric radiation). The model a model is calibrated on measured hydrologic simulates evaporation, change of volume (lev- and isotopic data, and the hydrologic com- el), and patterns of thermal and isotopic strat- ponent of interest is estimated indirectly by ification of the lake. The model may be gen- calculating the residual that is required to bal- erally applicable to closed or open freshwater ance the isotopic budget of the lake. Lewis lakes and will be modified in the future to (1979), for example, used a two-box represen- reconstruct past hydrologic change from iso- tation of the epilimnion and hypolimnion to topic variations evidenced in the sedimentary reproduce the isotopic composition and evap- record of the Lahontan basin. oration rate of Lake Kinneret. The model was In this paper, we describe the model and calibrated with (among other measured inputs) then validate it. We present three applications values of water temperature and thermocline that demonstrate the potential of the model depth. Applications such as this arc useful for for deriving hydrologic information from past determining components of the hydrologic variations of isotopic composition. The first budget. Because the models are calibrated with application is a simulation of the 1986- 199 1 356 ii180 and 6211model 357 change in monthly values of 6180 that occurred Notation in response to historical extreme variations in nA Lake surface area, m* streamflow discharge into Pyramid Lake. The C Heat capacity of water, J (kg “C) -’ second application is an equilibrium simula- E Evaporation, m t ’ tion (300 yr) in which the model was run on I, 0 Surface inflow and outflow, m3 t-’ a daily time step to demonstrate the depen- G,, Go Groundwater inflow and outflow, m3 t-l Vertical eddy diffusivity, m* d- ’ dence of isotopic equilibrium on the kinetics K, 4 Vertical eddy diffusion of 5, m* d-l of hydrologic equilibrium. In the third appli- Nm Mass-transfer coefficient, kPa-I cation, the model is run on an annual time step P Precipitation, m t-l to demonstrate the isotopic response of the RH Relative humidity, dimensionless lake as it changes from a closed basin to an T Lake temperature, “C T&V Temperature of the water surface, “K open basin andthen back to a closed basin. u2 2-m windspeed, m s-l V Lake volume, m3 e,, e. Atmospheric air and surface-saturated vapor Model description pressure, kPa Model equations -The hydrologic and iso- Fraction advected air, dimensionless Molecular diffusivity, m* d- ’ topic balances of the lake are computed in the Molecular diffusion of 4, m* d I model from the standard mass-balance equa- Latent and sensible heat flux, W m-* tion (Gonfiantini 196 5): Time, d Lake depth, m Heat source term, W m-* y = (Pap - E6,)A Isotopic enrichment factor, 9~ Ratio of isotopic diffusivities, dimensionless + I6,i - 06,, + Gi6gi - Go6go. (1) Shortwave albedo, dimensionless Isotopic composition of advected air and V is lake volume, 6 represents either 6180 or evaporative vapor, 9~6 J2H, t is time, P is on-lake precipitation, 6, is Isotopic composition of groundwater inflow isotopic composition of the precipitation, E is and outflow, 9~ Isotopic composition of lake water and pre- lake evaporation, 6, is isotopic composition of cipitation, 9~ the evaporative vapor, A is surface area of the Isotopic composition of surface inflow and lake, I is surficial inflow to the lake, 6,i is iso- outflow, 9m topic composition of the inflow, 0 is surficial 6, 4.7 Incoming atmospheric and solar radiation, W outflow from the lake, a,, is isotopic compo- m-* Outgoing longwave radiation, W m-* sition of the outflow, Gi is groundwater inflow 6180 or 6*H 9 9m into the lake, 6, is isotopic composition of the groundwater inflow, G, is groundwater outflow from the lake, and 6, is isotopic composition of the groundwater outflow (units are given in T is lake temperature, z is lake depth, A(z) is the list of notation). The isotopic compositions lake area at depth z (a vertical resolution of 1 of the liquid-water terms in Eq. 1 are readily m is used here), kh is molecular diffusivity, determined by analysis, and the composition &(z, t) is vertical eddy diffusivity, C is the of the evaporative flux is evaluated here by heat capacity of water, and @ is a heat-source modeling. term representing subsurface absorption of so- For daily time steps, our isotope model lar radiation. The surface boundary condition makes use of an existing one-dimensional for Eq. 2 is model (Hostetler and Bartlein 1990) that sim- ulates the thermal structure and evaporation of a lake. The equation of the thermal model is = (1 - %&.3 + 41 + 67 + 4/e + 4h- (3) -=dT -- 1 d A(z)W, CY,,is the shortwave albedo of the lake surface, at A(z) dz i 4, is incoming solar radiation, +I is incoming atmospheric radiation, &, is outgoing long- I 1 -- 1 dA(z)@ wave radiation from the lake surface, qle is la- CA(z) dz * (2) tent heat flux, and qh is sensible heat flux. For 358 Ilostetler and Benson Pyramid Lake, we assume that no heat is trans- isotopic diffusivities in the boundary layer ferred between lake water and underlying sed- (Merlivat and Jouzel 1979). iments which leads to the bottom boundary The isotopic enrichment factor a(,,, varies condition of [k, + &(z, t)]dT/dz = 0. A mea- with isotopic species and is a function of lake sured or estimated temperature-depth profile temperature (Majoube 197 1). For 6180, provides the initial conditions for Eq. 2. a!eq = exp(1,137Twe2 - 0.4156T,+,-1 Bulk evaporation is computed from mean atmospheric conditions by a mass-transfer - 0.00207); (64 equation (Brutsaert 19 8 2): for 62H, E = N,,.JJ,(e, - e,).
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