Computing the transport time scales of a stratified lake on the basis of Tonolli’s model

This paper deals with a simple model to evaluate the transport time scales in thermally stratified lakes that do not necessarily completely mix on a regular annual basis. The model is based on the formalization of an idea originally proposed in Italian by Tonolli in 1964, who presented a mass balance of the water initially stored within a lake, taking into account the known seasonal evolution of its thermal structure. The numerical solution of this mass balance provides an approximation to the water age distribution for the conceptualised lake, from which an upper bound to the typical time scales widely used in limnology can be obtained. After discussing the original test case considered by Tonolli, we apply the model to Lake Iseo, a deep lake located in the North of Italy, presenting the results obtained on the basis of a 30 year series of data.