This work is a continuation of the study on modeling the propagation of microplastic (MP) in Lake Baikal. A three-dimensional Eulerian type model, represented by the advection-diffusion-reaction equation, is used to simulate the behavior of MP in the lake. To set the hydrodynamic background, a three-dimensional model of the hydrothermodynamics of the lake in a non-hydrostatic approximation is used. Some "climatic" scenarios of atmospheric influence are compiled to be used for MP propagation modeling. In addition to the traditional approach based on direct (forward in time) modeling, we consider its combination with inverse modeling methods, assuming to solve the actual problems of sensitivity, optimization and control, which are important in environmental protection and design. Based on hydrodynamic scenarios, we formulate some inverse problems for assessing the fate of MP in the lake. In particular, two hypothetical scenarios are considered to assess the informational significance of the virtual monitoring networks that "observe" the spread of MP in the lake.
KEYWORDS: Particles, Mathematical modeling, 3D modeling, Pollution, Climatology, Process modeling, Monte Carlo methods, Ecosystems, Diffusion, Coastal modeling
With the help of a transport model, the issues of the distribution of neutrally floating particles simulating microplastic (MP) in Lake Baikal are studied. A three-dimensional model of the lake hydro-thermodynamics in the non-hydrostatic formulation is used to produce the fields of currents and the other necessary parameters for the transport model. To give generality to the conclusions, we use a set of parameters that are conditionally combined into hypothetical scenarios. In them, we design the "climatic" scenarios of external influences, in accordance to which the fields of currents and temperature in the hydrodynamic model are calculated. Depending of the goals of the study, we also formulate the specific tasks for giving the impurity sources in the transport model. The results of calculations are presented, in which some possible locations of an increased concentration of impurities in the lake were revealed.
A three-dimensional model of the hydrothermodynamics of a lake in a non-hydrostatic approximation and an advectiondiffusion model are used to describe the processes of distribution of impurities in the Barguzin Bay of Lake Baikal. To give generality to the conclusions, we use a set of parameters, which are conventionally combined into "climatic" scenarios, according to which the hydrodynamic background is calculated. The distribution of impurities in the bay, as in the entire lake, is completely determined by hydrodynamic processes. The main natural source of impurities in the bay, which also plays an important role in hydrodynamics, is the Barguzin River. In addition to this source, a set of point sources located on the shore of the bay is specified that simulate objects of the tourism industry. The results of the hypothetic scenarios on the propagation of impurities from a given configuration of impurity sources and their mode of operation are presented.
Within the framework of many-year studies of the carbon cycle in the water-atmosphere system and in order to determine high-priority measures for conservation of the unique ecosystem of Lake Baikal, the specialized combined expedition was carried out in August 2019 in Barguzin and Chivyrkuy Bays of Lake Baikal. With the unique onboard instrumentation system, we have measured the gas content in the surface water and the near-water atmosphere, as well as concentrations of biogenic elements and organic matter at the sampling stations. The spatial distribution of the increased methane concentrations in the surface water of Barguzin Bay has been analyzed to determine the main direction of the Barguzin River’s water inflow into the bay. The observational data were compared with the results of scenario calculations by a large-scale model of currents in the lake. This model gives us some understanding of a general nature of water mass circulation in the bay. For modelling small-scale manifestations in the near shore zones, it is necessary to use higher resolution models for nested regions.
KEYWORDS: Mathematical modeling, 3D modeling, Climatology, Monte Carlo methods, Databases, Algorithm development, Visualization, Thermal modeling, Systems modeling
Using mathematical modeling methods, we study the possibility of spreading green filamentous algae Spirogyra cells from their original locations throughout the lake by currents. The simulation is performed using a three-dimensional model of lake hydrothermodynamics in a non-hydrostatic approximation and a model of impurity propagation against the background of hydrodynamic processes. Due to the significant uncertainties in the problem statement, a scenario approach is used to obtain possible solutions in the answers to the questions raised. An example of a hypothetical simulation scenario is given in which the impurity is distributed from sources located at four initial occurrence sites selected in different parts of the lake over two summer months.
Possible formulations of mathematical modeling problems intended for estimating transboundary transport are considered. Two approaches are possible. The first approach is related to direct modeling methods. It actually consists in obtaining forecasts of impurity distribution with all the necessary data to solve such problems. The second approach, using the methods of inverse modeling, makes it possible to obtain estimates of some functionals characterizing the desired solutions, for example, related to the search for possible sources of disturbances that led to transboundary transport. We develop both of these approaches based on the variational principle. Some remarks on both approaches are discussed.
Formulations of mathematical models and statements of problems for investigating the behavior of multiphase systems under natural conditions are discussed. In particular, here we consider the hydrodynamics of the liquid-solid system in the context of possible surges of gas hydrates from the bottom of Lake Baikal. The results of numerical experiments on the simulation of hydrodynamic processes in a system where the source of disturbances is the income of solid particles from the bottom of the lake are presented. Parametrizations of the interphase dynamic exchange are studied.
The results of numerical experiments on the modeling of hydrothermodynamics and the processes of transport and transformation of gas emerging from the sources at the bottom of the lake are presented. The problem of large-scale convection that arises due to the buoyancy of bubbles coming from deep and shallow sources into the stratified water environment in the Selenga shallows is considered. The behavior of the heterogeneous system during the development of the spring thermal bar is studied.
Ice is highly transparent to solar energy; therefore, the spring heating of the water begins under the ice before melting. As the water temperature near the lower edge of the ice is less than the temperature of maximum density at this depth, the heat flux launches the natural convection in the upper water layer. At the same time, the forced convection may occur in the lake. We associate the origin of forced convection with random events of ascent and dissociation of methane hydrates. Using mathematical models, we study the processes of natural and forced convection beneath the ice in a deep lake under the specific conditions of Lake Baikal. The results of numerical experiments have shown that the natural convection under the ice intensifies the process of forced convection.
To study the behavior of heterogeneous methane-water system, a mathematical model describing the joint processes of hydrodynamics, transport, and transformation of methane in a deep freshwater body is used. There are three phases of methane in the system: solid (hydrate), gaseous (bubbles) and dissolved in water. We discuss the physical origin of phase transitions in the specific conditions of Lake Baikal and possible mathematical formulations of problems. Some preliminary results of calculations are presented.
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