Stable isotopes of oxygen and hydrogen in the Truckee River-Pyramid Lake surface-water system, 2. A predictive model of Î ́18O and Î ́2H in Pyramid Lake

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 intraand 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 a2H) composition of Pyramid Lake are associated by Benson (1994) with annual patterns of precipitation, evaporation, streamflow discharge, and lake mixing (stratification). Larger, long-term changes in isotopic composition are linked to change in the hydrologic balance and the hydrologic state (e.g. whether the lake is open or closed) of the lake. In this paper, we present a model used to simulate variations in 6180 and 62H in Pyramid Lake that occur in response to change in the hydrologic balance and climate. Several steady state and dynamic models of al80 and 62H have been developed and applied to lakes (e.g. Gat 1984; Zimmerman and Ehhalt 1970; Zimmerman 1977; Fontes et al. 1979; Phillips et al. 1986). The models have been successfully used to evaluate hard to measure components of the hydrologic budget (typically evaporation). In such applications, a model is calibrated on measured hydrologic and isotopic data, and the hydrologic component of interest is estimated indirectly by calculating the residual that is required to balance the isotopic budget of the lake. Lewis (1979), for example, used a two-box representation of the epilimnion and hypolimnion to reproduce the isotopic composition and evaporation rate of Lake Kinneret. The model was calibrated with (among other measured inputs) values of water temperature and thermocline depth. Applications such as this arc useful for determining components of the hydrologic budget. Because the models are calibrated with measured data, however, they are limited to applications within the period of calibration and to lakes where sufficient measured data are available. In addition, except for the model of Lewis, a vertically homogeneous water column is assumed, and the effects of seasonal thermal and isotopic stratification on isotopic composition are not considered. To broaden the range of applicability of isotope models, we have developed a calibrationfree model for Pyramid Lake that can simulate the seasonal behavior of 6180 and a2H. Both external forcing (atmospheric and hydrologic) and internal processes (seasonal stratification and mixing) that affect the isotopic composition are treated in the model. For inputs, the model requires inflows and outflows of liquid water and their associated isotopic compositions and a set of atmospheric data (air temperature, humidity, windspeed, solar radiation, and atmospheric radiation). The model simulates evaporation, change of volume (level), and patterns of thermal and isotopic stratification of the lake. The model may be generally applicable to closed or open freshwater lakes and will be modified in the future to reconstruct past hydrologic change from isotopic variations evidenced in the sedimentary record of the Lahontan basin. In this paper, we describe the model and then validate it. We present three applications that demonstrate the potential of the model for deriving hydrologic information from past variations of isotopic composition. The first application is a simulation of the 1986199 1