Giovanni Pecenik

Modelling macroalgae (Ulva rigida) in the Venice lagoon: Model structure identification and first parameters estimation

Abstract The paper describes the definition and a first parametrization of a dynamic model of macroalgae ( Ulva rigida ) population. Based on specific literature, a two-step kinetic scheme is selected for modelling growth and uptake of nitrogen and, therefore, the intratissual concentration of nitrogen has been considered as a state variable of the model. Accordingly, Ulva r. growth rate depends on the concentration of phosphorus in the external medium and on the intratissual nitrogen concentration, which influences, in turn, the uptake rates of reduced and oxidized nitrogen. The influences of temperature and light intensity on Ulva r. photosynthetic activity are also discussed. The dynamics of dissolved oxygen has also been modelled and a specific mortality rate, depending on dissoved oxygen, has been adopted. The model has proved to be qualitatively consistent with the available literature, while a first parametrization yields results in quantitative agreement with short term laboratory experiments, regarding samples collected in the lagoon of Venice. The model has been applied to data sets collected in the lagoon of Venice and is capable of reproducing the main features of the seasonal dynamic of Ulva r. These results prompted its inclusion in a comprehensive 3D transport-water quality model of the Venice lagoon ecosystem.

Long term simulations of population dynamics of Ulva r. in the lagoon of Venice

Abstract The dynamic of macroalgae is implemented in a 3D transport-water-quality model of the central part of the lagoon of Venice. Ulva biomass density and nitrogen concentration in Ulva tissue have been added to the set of state variables previously considered, that is to phytoplankton and zooplankton densities, concentrations of nutrients in water, detritus and dissolved oxygen. The model shows that Ulva succeeds in the competition with the phytoplanktonic community in the shallower areas, where water temperature and irradiance levels reaching the bottom are sufficient to sustain growth. Long term evolutions of Ulva colonies, under different scenarios of forcing functions, show that adverse meteoclimatic conditions can be more effective in reducing Ulva biomass than a consistent decrease in the loads of Nitrogen.

Development of a mathematical eutrophication model of the lagoon of Venice

Abstract Integrated research on pollution and eutrophication problems in the central part of the lagoon of Venice is reported, together with a three-dimensional diffusion model. The latter was developed through preliminary elaboration of two other two-dimensional models of the same area, a diffusion and a advection-diffusion model. It was used to estimate, by calibration, the eddy diffusion constant incorporating the dispersive action of the tide. Both research and model were finalized with the objective of studying the temporal evolution and steady-state condition of the dispersion of pollutants and nutrients in the lagoon. The three-dimensional model is applied to simulate dispersion of eight representative variables: phytoplankton, zooplankton, NH 4 + , NO x − , PO 4 3− , dissolved oxygen, degradable organic compounds and temperature. Computer outputs, displaying the spatial distribution of the considered variables under peculiar hypereutrophic conditions, are presented. Additional detailed notes are introduced concerning the more relevant steps of the global study.

Local sensitivity analysis of a distributed parameters water quality model

Abstract A local sensitivity analysis is presented of a 1D water-quality reaction-diffusion model. The model describes the seasonal evolution of one of the deepest channels of the lagoon of Venice, that is affected by nutrient loads from the industrial area and heat emission from a power plant. Its state variables are: water temperature, concentrations of reduced and oxidized nitrogen, Reactive Phosphorous (RP), phytoplankton, and zooplankton densities, Dissolved Oxygen (DO) and Biological Oxygen Demand (BOD). Attention has been focused on the identifiability and the ranking of the parameters related to primary production in different mixing conditions.

Thermal exchanges at air-water interfacies and reproduction of temperature vertical profiles in water columns

Abstract For a 3-D eutrophication-diffusion macromodel of the central part of the Venice Lagoon, air-water heat fluxes are computed interpolating, through Fourier series expansion, meteoclimatic variables averaged over a thirty years survey. Also reproduced with the same interpolation methods, is the daily fluctuation of incident light as well as the annual variation of the photoperiod. With an interative procedure temperature values, to be assigned at each grids point and corresponding to each hour of a reference year, are computed also accounting for the thermal inertia of water columns of varying depths. By statistical examination of temperature vertical profiles, depth varying diffusivities are also estimated, which enables, without assumption of an instantaneous mixing, the reproduction of heat diffusion from the surface to the bottom water cells. Procedures, preliminary refined and verified for a one-dimensional vertical system input, are next implemented on a three-dimensional submodel of reduced size provided of “open boundaries”: this last submodel, under a continuous input of energy and of matter is seen to attain a steady states as well as to be capable of simulating regime conditions. A further validation is performed, on a submodel of 43 × 47 × 20 cells, encompassing a limited portion of the macromodel and presenting the actual lagoon bathymetry. Macromodels seasonalisation so achieved, enables for a more correct simulation of the periodical behaviour of light and of temperature, forcing functions governing the eutrophication phenomena.

A two-dimensional diffusion model of the Venice lagoon and relative open boundary conditions

Abstract A modellistic study aimed at describing the multi-dimensional diffusion of pollutants in the central part of the lagoon of Venice is presented. After a preliminary search for analytical solutions, a first numerical two-dimensional diffusion model is developed which is capable of undergoing further extension. In particular, an original solution is proposed for conditions at the ‘open’ boundaries, i.e., boundaries derived from restricting the modelled area and not from real physical delimitations; a delocalized Gaussian distribution involving an analysis with logarithmic finite differences was found to be the optimal solution. An appendix is included, in which procedures followed to solve the problem are described and an analysis is performed of the many possible physico-mathematical expressions used in dealing with this problem. The computer program is also described; results obtained with the proposed boundary conditions conform to reality better than do those yielded by commonly adopted methods.

Using parallel computers in environmental modelling: a working example

Abstract An application of the utilization of parallel supercomputers for a 3D eutrophication-diffusion macromodel of the Venice lagoon is presented. Problems encountered in program restructuration, in the choice and in the introduction of parallel algorithms for solving the diffusion equation are discussed, together with the approach used to exploit multitasking performances. Results obtained show that, through appropriate coding, execution times for a full year simulation of the model, involving the diffusion and the trophic interactions of eight state variables, with a time step of one hour, have been decreased by about an order of magnitude.

An advection-diffusion pollution model of the Lagoon of Venice

Abstract A two-dimensional advection-diffusion model of the central part of the Venice Lagoon, developed from a pre-existing pure diffusive model is presented. Tidal-current velocities are expressed with a time-dependent sinusoidal function multiplied by the sum of two vectors directed to the Lido and Malamocco mouths and with magnitudes inversely proportional to the distances between nodal points and both sea entrances. In consideration of its physical meaning, the explicit second ‘upstream’ method is adopted for integration, whereas the calculation of intracell advective-diffusive flux is performed, taking the depth of the shallower of two adjacent cells into account. The consistency and stability of the method are thoroughly examined and compared with those of other methods; Reynolds cell number and conservativity are also discussed, as well as transportivity. Although operative, the model requires a lengthy computation time to achieve the steady state; future refinements and modifications leading to improvement are suggested.

Tidal three-dimensional diffusion in a model of the lagoon of Venice and reliability conditions for its numerical integration

Abstract A three-dimensional model of the central part of the Venice Lagoon is presented: the model is of a pure eddy-diffusion type and embodies tidal mixing action on pollutant transport. The models asymptotic evolution to the steady state is examined, and it is shown that a pure diffusive process can achieve stationarity only in a system having more than two dimensions. Stability and consistency analysis of the implicit integration methods indicates that the two-time-levels Laasonen scheme is the most suitable for performing the integrations. Because of the closed vertical boundaries and of the larger vertical diffusion number, in respect to the horizontal, in a first version of the model, Laasonens scheme is adopted for only vertical diffusion. After solving the problems posed by non-linear conditions at the ‘open’ boundaries, the scheme is applied also for diffusion along all spatial coordinates. The diffusion constant adopted in the model is obtained by calibration with a previously developed advection-diffusion model. Utilization of the model for description of more complex, interconnected physico-chemical, biochemical and ecological processes is prospected.

A model for macroalgae and phytoplankton growth in the Venice Lagoon

Abstract The definition and a first parameterization of a dynamic model of macroalgal growth is described, aimed at including this species and related physico-chemical variables in a more comprehensive 3-D eutrophication-diffusion, water-quality model of the Venice Lagoon. Relevant physicochemical factors affecting macroalgal and phytoplankton competition and succession have been analyzed as a function of physiological and trophic conditions. Results of simulations show that while phytoplankton response to growth factors is more intense and of shorter duration, internal nutrient storage in macroalgae stabilizes the growth process and makes macroalgal communities relatively more independent of variations of chemical and external forcing functions. The model provides results which appear to be qualitatively and quantitatively consistent with available functional in situ measurements.