Introduction. Scenarios of development of the processes in the complex marine ecosystems are forecasted by the models developed for marine ecosystems. At that the method for formalizing the scheme of the cause-effect relations (impacts) is required. In other words, it is necessary to construct the equation system for the model variables connecting the functions representing the modeled processes. Data and Methods. Proposed are the methods for modeling the processes in the marine ecosystems based on the system principles of the adaptive balance of causes and informational unity of the processes' models and the corresponding observational data. Analysis of Results. It is shown that application of these principles permits to construct the adaptive models with negative feedbacks of the 1 st and the 2 nd orders between the model variables and the speed of their variation. These models provide automatic fitting of the model variables to each other and to the external effects; at the same time they preserve the matter balances in the substance transformation reactions in the marine environment. The simulation results reveal that the 2 nd order adaptive models are more sensitive to the external effects influencing the ecosystem and adapt to them quicker. Application of the adaptive modeling principles is illustrated by the data of hydrochemical observations in the Sevastopol Bay. Two methods of reconstructing dynamics of the nitrite concentration are comparatively analyzed using the time series of the ammonium and nitrate observations. Discussion and Conclusions. It is shown that the dynamic-stochastic equation provides much higher accuracy of reconstruction of the unobserved process of the nitrite concentration as compared to the method of the normalized relations of the mean values. Besides, the reconstruction accuracy increases with growth of length of the observation time series applied at constructing their covariance matrix.

The adaptive model of managing consumption of marine bio-resources by the coastal economic subsystem which is a part of the ecological-economic system coast-sea is constructed. The marine part of the model is represented by the adaptive version of the plankton dynamics and nitrogen cycle model in which the chlorophyll a concentration observations are assimilated. Management of the consumed bio-resources volume is based on tracing the deviations of the marine biodiversity index from its average (undisturbed) value which is represented as an estimate of the stationary value of the environment bio-resource capacity. The bio-resource capacity integral model controlling the balance between the rates of consumption and reproduction of marine bio-resources is proposed. The model equations are constructed by the method of adaptive balance of influences; at that the influence coefficients are expressed through the normalized ratios of the variables' mean values. To preserve the marine environment biodiversity, the right-hand sides of the equations contain the agents for managing the scenarios of ecological-economic processes. These agents ensure imposing fines for sea pollution caused by the coastal economic subsystem. Represented are the results of computational experiments confirming economic expediency of introducing new technologies in the coastal subsystem which, in their turn, contribute to economic efficiency of bio-resource consumption and preserve the marine environment bio-resource capacity. It is shown that the marine environment bio-resource capacity is an integral value of the biodiversity index determined for a certain time interval. Thus, in order to use rationally bio-resources of the sea coastal zone, it is necessary to control both biodiversity and bioresource capacity of the marine environment. These two indices indicating ecological state of the sea coastal zone serve the criteria for managing the integrated ecological-economic system coast-sea which are used to derive economic benefit from consumption of marine bio-resources provided that the marine environment quality is preserved.

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Adaptive model of managing consumption and reproduction of the recreational potential in the sea coastal zone is proposed. The recreational potential is assessed based on the nature and climate features, development of a resort infrastructure, quality of recreation services and level of the coastal zone pollution. The concepts of the recreational resource concentration and the resource capacity of a recreational unit which characterize its recreational potential are introduced. Constructed is the ecological-economic model of the recreational resource consumption consisting of the economic subsystem (rendering of recreational services) and the block of managing the environmental activity which controls pollution of the recreational and coastal areas. The model equations are constructed by the method of adaptive balance of causes including the logical management agents. Such an approach is applied in the model developing intended to monitor dynamics of the recreational capacity of the South Crimea coastal region. The aim of the study is to construct the spatial-temporal scenarios of the ecological and economic processes which characterize response of the model managing recreational services to seasonal variability of the recreational potential of the sea coastal zone. The scenarios of the modeled ecological and economic processes are given. To initiate the spatial variant of the model, a part of the South Crimea coast supplied with the digital map showing average estimates of its recreational attractiveness is used. The model response to seasonal changes in the recreational potential was investigated. It is shown that in order to maintain the quality of recreational services, it is necessary to manage the balance between the rates of consumption and reproduction of the recreational resource, which characterizes the recreational capacity of the sea coastal zone.

The model of the sea upper layer ecosystem based on the equations of the adaptive balance of causes method is proposed. The scheme of the cause-effect relations from the paper by Fasham, Ducklow and McKelvie constituting the nitrogen cycle reactions in the sea upper layer is used in the model. Parameterization of biochemical reactions of the substance interaction is substituted in this model for the normalized ratios of the substances' average concentrations resulted from analyzing the observations of the biochemical fields of the Black Sea northwestern shelf. The satellite-derived chlorophylla concentrations as well as the data on advection and diffusion obtained from calculations of intraannual variability of the current velocity field in the sea upper sea layer using the hydrodynamic model, are used as the external influencing factors. Being regarded as the external influencing factors, the information was used for calculating the deviations of the biochemical fields' concentrations from their average values assumed to be a stationary state of the ecosystem. The observations were assimilated through including the sources' additional functions (representing the assimilated data) to the right parts of the adaptive ecosystem model equations. The regional maps of the biochemical fields permitting to analyze their spatial-temporal variability in 2015 were constructed. The drawn conclusion confirms utility of the proposed approach used for mapping the biochemical fields of the sea upper layer.Keywords: adaptive balance of causes method, preservation of material balances, normalized influence coefficients, adaptive model of the sea upper layer ecosystem, maps of biochemical fields.Acknowledgements: the adaptive model of the marine ecosystem is developed at financial support of the Russian Fund of Fundamental Investigations and the Sevastopol Administration within the framework of the project No. 18-47-920001 "Study of the principles for constructing adaptive models of the ecological-economic systems and digital informational technologies for managing the scenarios of sustainable development of natural and economical complexes in the Seavastopol region". The computing experiments with the model are performed within the framework of the state task on the theme No. 0827-2018-0004 "Complex interdisciplinary investigations of the oceanologic processes which condition functioning and evolution of the coastal ecosystems of the Black and Azov seas".