δ13C–δ18C covariance as a paleohydrological indicator for closed-basin lakes
The relationship between δ18O and δ13C in a closed-basin lake is a function of hydrological change, vapor exchange, lake productivity, and total CO2 (or carbonate alkalinity) concentration. Covariance of δ18O and δ13C usually occurs in lake sediments under the condition of hydrological closure for time periods of the order of 5000 yr or longer. On shorter time scales, however, certain subtleties in the use of the δ13C–δ18O covariance as a hydrology history indicator must be recognized. The covariant trend may not be found in hyper-alkaline lakes because of the insensitivity of δ13C to lake volume changes. For less alkaline closed-basin lakes, covariance of δ13C–δ18O will result from relatively rapid increase or decrease of lake volume, with the rapid-decrease condition giving rise to heavy and narrow-ranged isotopic values for both δ13C and δ18O due to the coupled evaporation-productivity effect. When the lake volume remains stable (as is the case for an over-flowing open lake), poor δ13C–δ18O covariance will ensue, due to the effect of vapor exchange with the atmosphere. 
 
We have used the measured δ13C–δ18O covariance in carbonate sediments of Mono Lake, California, to deduce paleo-hydrological and lake-water alkalinity (and salinity) variations and found the results in consonance with Holocene lake-level history derived from the δ18O and other information.