Tracer relations in mixed lakes in non-steady state

Abstract Tracer concentration in mixed lakes was usually calculated under assumption of steady hydrologic state, i.e., constant input, output, and volume. Departures from steady state were treated by the use of average flow or weighting the concentration by inflow values. An exact analytical solution indicates the limits of validity of the above approximations. The exact solution can be adapted for multiple inputs and outputs, exchange with atmospheric moisture, evaporation with isotope fractionation and formation of epilimnion. The solution is simplified for certain types of connection between outflow and volume.