Geological ring structures of various sizes and ori gins are observed on the Earth's surface. In the past decade, ice ring structures on Lake Baikal were regu larly identified by satellites [1]. On April 4, 2009, these structures emerged in the western end of South Baikal and near the Svyatoi Nos Peninsula in Central Baikal [1][2][3] and were destroyed along with the ice at the end of April. The expedition for studying the ice and hydrophysical measurements in the area of the ring structure in South Baikal was organized on April 7. This work presents the results of the field studies and modeling of the currents and variations in the ice thickness.The MODIS satellite data in the visible range with a spatial resolution of 250 m (www.geol.irk.ru) were used for remote study of the ring structure. During the field studies, the ice thickness was measured and the ice cores were drilled along two sections, which transect the center of the ring structure at 51°40′35″ N, 103°52′15″ E (Fig. 1a). The measurement stations were placed in the center of the structure and 1, 2, 3, and 4 km from it along the sections and 7 and 8 km to the west and to the east, respectively, from the center along the EW section. The ice surface in the center of the structure, at its periphery, and in the area of the dark ring was visually similar. No water was visible on the ice surface, and the ice was made up of vertical crys tals. The ice thickness was 74 cm in the center, decreased to 43 cm at the distance of 2 km from the center, and increased up to more than 70 cm beyond the ring.The temperature and electric conductivity of the water column were registered by a SBE 19 profiler. The water in the center was warmer by 0.5°С and less saline (for 2 mg/kg) relative to the periphery (Fig. 1b). In spite of the higher temperature in the center, the ice thickness was similar to that beyond the structure; i.e., the temperature of the water layer was not the major factor responsible for the decrease in the ice thickness. The deepening of the thermocline in the center of the structure (Fig. 1b) indicated the presence of the ring anticyclonic current.According to the tracer movements, the maximum velocities of the water currents (3-4 cm/s) were observed at a distance of 2-3 km from the center of the Abstract-This work presents the results of complex analysis of the field data and of mathematical modeling of the ice ring structure more than 4 km across, which was identified by the space images of South Baikal in April 2009. The measurements revealed that the ice thickness was 74 cm in the center of the structure, decreased to 43 cm at a distance of 2 km, and increased up to 70 cm and more beyond the ring. The ice water in the central part was warmer by 0.5°C and less saline (for 2 mg/kg) relative to the periphery of the structure. According to the tracer movements, the maximum velocities of the ice currents (3-4 cm/s) were observed at a distance of 2-3 km from the center of the structure with minimum ice thickness. The event was modeled using several mathem...

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Air quality monitoring systems differ in composition and accuracy of observations and their temporal and spatial coverage. A monitoring system’s performance can be assessed by evaluating the accuracy of the emission sources identified by its data. In the considered inverse modeling approach, a source identification problem is transformed to a quasi-linear operator equation with the sensitivity operator. The sensitivity operator is composed of the sensitivity functions evaluated on the adjoint ensemble members. The members correspond to the measurement data element aggregates. Such ensemble construction allows working in a unified way with heterogeneous measurement data in a single-operator equation. The quasi-linear structure of the resulting operator equation allows both solving and predicting solutions of the inverse problem. Numerical experiments for the Baikal region scenario were carried out to compare different types of inverse problem solution accuracy estimates. In the considered scenario, the projection to the orthogonal complement of the sensitivity operator’s kernel allowed predicting the source identification results with the best accuracy compared to the other estimate types. Our contribution is the development and testing of a sensitivity-operator-based set of tools for analyzing heterogeneous air quality monitoring systems. We propose them for assessing and optimizing observational systems and experiments.

a r t i c l e i n f o MSC: 58E30 76R99 49Q12 81T80 65M06 65M32 65N99 65K10 Keywords: Variational principle Convection-diffusion Monotonic scheme Discrete-analytical approximation Numerical environment modelling Adjoint sensitivity problem Direct and inverse modelling a b s t r a c tA new method of constructing numerical schemes on the base of a variational principle for models including convection-diffusion operators is proposed. An original element is the use of analytical solutions of local adjoint problems formulated for the operators of convectiondiffusion within the framework of the splitting technique. This results in numerical schemes which are absolutely stable, monotonic, transportive, and differentiable with respect to the state functions and parameters of the model. Artificial numerical diffusion is avoided due to the analytical solutions. The variational technique provides strong consistency between the numerical schemes of the main and adjoint problems. A theoretical study of the new class of schemes is given. The quality of the numerical approximations is demonstrated by an example of the non-linear Burgers equation. These new schemes enhance our variational methodology of environmental modelling. As one of the environmental applications, an inverse problem of risk assessment for Lake Baikal is presented.

551.51+519.6The structure of mathematical models for studying the processes of thermodynamics and transfer of pollutants in a climatic system involving the atmosphere of an industrial region and a lake is presented. These models are used to solve the problems of climatic and ecological monitoring and prediction. The problems of constructing numerical schemes and simulation methods are discussed. An example for estimating the effect of pollutants from sources located in the northern hemisphere of the Earth on the Baikal region is given.Introduction. Mathematical models have become a multifunctional tool for studying processes in the atmosphere and water objects. In particular, for solving the problems of evaluation of the prospects of industrial regions with anthropogenic actions imposed on natural climatic and ecological factors, mathematical simulation is, apparently, the only means for obtaining information.The immediate effect of anthropogenic loads is primarily manifested in regions of local and mesoregional scales; therefore, it is important to study the possible preconditions for the appearance of ecologically unfavorable situations in each region that are caused mainly by its climatic conditions. From the viewpoint of monitoring and climatic-ecological prediction, Siberian industrial regions are not only interesting but also strategically important objects of investigation since their activity is mainly connected with raw materials.The Baikal region plays a specific role in the formation of climatic conditions and ecological environment in the south of Siberia. Taking into account this circumstance, we chose this region as a basic object for the development and application of ecologic-climatic models. The specific feature of the Baikal region is that Lake Baikal is a powerful climate-forming factor in the south of Siberia. The importance of this factor is amplified by the fact that this region is in the influence zone of the summer Sayan-Altai cyclogenesis and the winter Asian anticyclone. The interaction of background and local atmospheric processes forms unique "Baikal" mesoclimates, which, in turn, have a determining effect on the formation of mesoclimates and the quality of atmosphere in industrial zones of this region. The contrast of water-land temperatures, which is always observed in the open-water period, is a source of instability in the climatic system and leads to the fact that the zone of immediate influence of Lake Baikal, which was preliminarily estimated as 100-200 km from the coast line [1], becomes a potential accumulator of pollution not only from the territory of the region, but also from other territories of the northern hemisphere: Siberia, China, and Mongolia. All these processes should be studied to understand the ecological prospects of the region and the lake.Thus, forming a concept of studying climatic changes in the system lake-atmosphere, we do not confine ourselves to the scale of direct interaction of water and atmosphere, but consider mesoregional processes together with hem...