J. Limnol., 69(1): 15-28, 2010 DOI: 10.3274/JL10-69-1-02 The residence time of the water in Lago Maggiore (N. Italy): first results from an Eulerian-Lagrangian approach Leonardo CASTELLANO*, Walter AMBROSETTI1), Luigi BARBANTI1) and Angelo ROLLA1) Matec Modelli Matematici, Via Rondoni 11, 20146 Milano, Italy 1)CNR Institute for Ecosystem Study, Largo V. Tonolli 50, 28922 Verbania-Pallanza, Italy *e-mail corresponding author: [email protected] ABSTRACT The paper describes a numerical study for estimating the spatial distribution of the hydraulic residence time in Lago Maggiore. A 3D eulerian time-dependent CFD code has been applied under real conditions, taking into account the effects of the monthly mean values of the mass flow rates and temperatures of all the tributaries, mass flow rate of the Ticino effluent and meteorological, hydrogeological and limnological parameters available from the rich data-base of CNR-ISE (Pallanza). The velocity distributions from these simulations were used to compute the paths of a number of massless markers with different initial positions and so evaluate their residence times within the lake. The results presented here follow a two-year simulation and show encouraging agreement with the mechanisms of mixing and of deep water oxygenation revealed by recent limnological studies carried out at CNR-ISE. Further studies are in progress to improve the results and extend the research over a time period of at least four years. Key words: residence time, hydro-meteorological parameters, eulerian mathematical model, CFD, lagrangian markers These difficulties can be particularly severe for large 1. INTRODUCTION natural water bodies with a long evolution time: apart from the material costs, any extreme meteorological An inspection of the technical literature reveals that event may destroy instruments, interrupt the acquisition various concepts of time scale designed to characterize of data, and even change the scenarios (a typical exam- transport phenomena in rivers, lakes and estuaries ple is the dramatic variation in the sections measuring emerge from research and studies on the quality of the the discharge of tributaries and effluents provoked by water in these ecosystems. high intensity rainfall). While essentially four different names (Residence One way of overcoming these difficulties or of com- Time, Transit Time, Age, Flushing Time) are used in (a plementing other studies is the increasing use of CFD range of) papers and reports, the same name quite often (Computational Fluid Dynamics) to evaluate the time- refers to parameters indicating dissimilar sets of physi- scale parameters of natural water bodies (Loga-Karpin- cal or physical-chemical mechanisms and/or different ska et al. 2003; Shen & Haas 2004; Jouon et al. 2006; approaches and experimental procedures. Wilde et al. 2006; Liu et al. 2008). The need to remove this confusion was first high- The application of this approach rests on the lighted more than 30 years ago by Bolin & Rodhe assumption that the interactions between a water body (1973), but it is only in recent years that sufficient and the external environment are only one-way (from attention has been devoted to the problem, e.g. by Mon- the latter to the former) and these interactions (in the sen et al. (2002) and Ji (2008). Definitions have conse- case of lakes: mass flow rate and temperature of the quently become increasingly detailed and precise, and at inflows/outflow, rain, runoff, wind, heat exchange with the same time the intrinsic difficulties of the problem the atmosphere) can be described using a relatively and the causes of the unavoidable approximation of the small number of known parameters or functions which solutions have become even clearer (Shelton & Alber represent a statistically valid description of the time 2002; Waugh et al. 2002; Ambrosetti et al. 2003; Rueda behaviour of the external phenomena over a fairly long & Cowen 2005; Delhez & Deleersnijder 2006; Oliveira period. 2006; Doos & Engqvist 2007; Lucas et al. 2009). A second indispensable precondition is the use of a Many of the difficulties involved in giving good es- well-tested computer code that has been proven to give timations even for a theoretically well-defined parame- satisfactory results over multiple spatial and time scales ter lie in the complexity of executing (and correctly and boundary conditions. interpreting) adequate experimental observations and The aim of this paper is to explain the guidelines of measurements on systems that strongly interact with the a campaign of numerical simulations devised to esti- atmosphere and surrounding aquatic environments. mate the time scales of the hydrodynamics and transport 16 L. Castellano et al. phenomena of Lago Maggiore and through them to As far as Lago Maggiore and other great lakes of the compile a detailed spectrum of the renewal times of its northern temperate zone are concerned, the relatively water. small thickness of the layer involved in the vertical mixing by convection of the waters at the end of the 2. BACKGROUND OF THE PRESENT STUDY limnological winter is of decisive importance. As shown Studies of applied limnology by today's scientific by Ambrosetti & Barbanti (2002), the reduction of the community can be divided into two broad areas: those deep recirculation is a consequence of the climate focused on developing the knowledge required to pre- change of the last decades, which has prevented the serve and/or improve the health of lakes, and those that homogenization of the water column and its density study lakes to find evidence of the climate change phe- with a related increase in vertical stability. In fact, the nomenon. measured data reveal that the waters of the deep In the first case, the lake is treated as a large bio- hypolimnion are practically isolated from the upper part chemical reactor in which the degree of development of of the lake and have almost no possibility of renewal. the biochemical phenomena depends mainly on the ratio All the above facts prompted the promotion of a between the Hydraulic Residence Time and the rate of campaign of numerical simulations designed to permit a the reactions (in addition to temperature and turbulent more realistic and more detailed evaluation of renewal mixing); in the second, it is regarded like a patient times. showing symptoms which are suspected of originating Many approaches have been developed in the field in some historical anomalies (for instance, traces of of mathematical modelling to improve the accuracy of these anomalies are clearly seen in the "Climatic Mem- the assessments. For instance, George & Harley (2003), ory" of the great subalpine lakes; Ambrosetti & Bar- suggested computing a residence time for each day of banti 1999; Ambrosetti & Sala 2008). the year by using the average lake volume for certain In both cases a sufficiently reliable estimate of the months, the average epilimnetic volume for the others Hydraulic Residence Time is required; this would also and the daily volume of water entering the lake; the be used as a reference value for other time scales that algorithm is applied in "hindcast" mode to prove that the could take into account other mechanisms apart from model is reliable for predicting future conditions. Con- that of pure motion, such as chemical or biochemical ceptually similar, but computationally more sophisti- decay, turbulent diffusion, macroscopic dispersion, cated, is a previous model devised by Rossi et al. (1975) adsorption, colonization, sedimentation and so on. for monomictic lakes, based on the same physical Focusing on lakes, as a first approximation the theo- assumptions adopted by Piontelli & Tonolli (1964) for retical value of the Hydraulic Residence Time, here Lago Maggiore, i.e., a) the outflow mass fluxes come indicated by the symbol τH, can be calculated by the only from the most superficial layers; b) the inflow relation: mass fluxes mix homogeneously only with the waters above the epilimnion in the summer and with the mixed τ = V / Q& (1 H layer in the winter. The application of this model to where Q& is the annual amount of water passing through Lake Lugano revealed differences up to one order of the water body and V the volume of the whole basin. magnitude between the water renewal times in different This is rather a rough definition, since it assumes the zones of the lake, thus pointing out the incorrectness of lake to be similar to a large river, morphologically defining a single value of hydraulic residence time for uncomplicated, in which the velocity field is almost uni- the whole water body. form and the most important physics of the seasonal Nowadays there is a widespread awareness of the cycle are absent. In contrast, in the course of their need to assess more than one value for this parameter of annual cycle the deep lakes show differentiated vertical pure hydraulic nature; and more subtle levels of analysis thermal structures which, depending on geographical, can be achieved by trying to describe the effects of the climatic and morphological conditions, give rise to one spatial scale and seasonal conditions. Efforts to reach or more periods of vertical thermal stratification during this objective have resulted in the introduction of more which the thickness of the layer involved in the water meaningful theoretical definitions and an improvement renewal, i.e. the layer mixed at the surface, represents in methods of measuring the relevant parameters. only a more or less large percentage of the whole water This aspect has already been discussed in the previ- mass. Of course, many other factors influence the river- ous section and will not be repeated here. It will be lake-river hydrological complex; of these, a consider- more useful to summarize the assumptions underlying able role is played by the system of currents and other the use of one or more sets of equations implemented in movements arising in the lake, the topography of the a CFD computer code.