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A simple approach to the evaluation of the actual water renewal time of natural stratified lakes
Author(s) -
Pilotti Marco,
Simoncelli Stefano,
Valerio Giulia
Publication year - 2014
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1002/2013wr014471
Subject(s) - thermal stratification , simple (philosophy) , hydrology (agriculture) , ordinary differential equation , stratification (seeds) , distribution (mathematics) , set (abstract data type) , natural (archaeology) , computer science , differential equation , mathematics , environmental science , geology , oceanography , geotechnical engineering , mathematical analysis , thermocline , paleontology , philosophy , epistemology , seed dormancy , germination , botany , dormancy , programming language , biology
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 thermal 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 positive 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 = 1 .6 T 0 .