A simple approach to the evaluation of the actual water renewal time of natural stratified lakes

In natural lakes, where thermal stratification hinders complete mixing, the theoretical value T 0
of the water renewal time provides a low-order approximation to the time T 37 when 37% of the original
water is still present within the lake; this time could be operatively regarded as the actual value of the water
renewal time. In this paper, we present a simple nonparametric model to estimate the age distribution of
water within stratified natural lakes, taking into account fundamental aspects of its mass exchange and ther-
mal evolution. This distribution provides a straightforward way to compute T 37 . The model is presented as a
system of ordinary differential equations along with a MATLAB script for its numerical solution, so that it
can be easily applied to lakes where a minimum of limnological data are available, without the need of
extensive meteorological data set and modeling expertise that an hydrodynamic model would require to
the same purpose. The case of a deep oligomictic Italian prealpine lake (Lake Iseo) is considered: after a pos-
itive comparison with the results obtained using a 1-D lake hydrodynamic model, the reiterated application
to the available time series allows to approximate the water age probability distribution. This distribution is
used to compute the actual value of the water renewal time, that resulted T 37 5 1.6T 0 .