A lake as a natural integrator of linear processes: Application to Lake Kinneret (Israel) and Lake Biwa (Japan)

The major hydrological variables that may cause long-term salinity changes in fresh water lakes are the volume of the lake, stream and/or groundwater inflows and outflows, direct rainfall, stream, groundwater, and rainfall salinity and evaporation. Measurements of these variables are usually subject to natural fluctuations and unavoidable errors of the measured data. Therefore, evaluation of the contribution of each component to the long-term salinity trends is difficult. In this work, it is shown that since salinization processes are linear, lakes are able to retain a ‘solute influx memory’, which records information about their lake–watershed–climate relationship in the past. Our objective was to test and verify a system approach method, which evaluates this ‘memory’, i.e. investigates the causes of long-term salinization processes in fresh water lakes. With this approach, a general expression is developed that represents the lake as a natural integrator of linear processes in space and time. The long-term change of the chloride concentration in the lake (representing salinity) reflects the long-term changes in each of the various past hydrological variables. The general theory of the lake as a natural integrator was tested by examination of the long-term salinity changes in Lake Kinneret, Israel, and Lake Biwa, Japan. The hydrology and salinity of both lakes are well monitored for several decades. In the analysis of Lake Kinneret, the long-term measurements of inflows, outflows and lake salinity were used to verify that the salinization mechanism follows the theory of complete mixing (system identification). In Lake Biwa the same approach was used, however, we assumed that the salinization mechanism was ‘complete mixing’, and the long-term measurements of the lake hydrology were used to investigate the reasons for increasing salinity (system detection). Since the system analysis is affected by uncertainties of the measured variables, a stochastic component was added, in order to take these uncertainties into account.