Climate warming has been and will continue to be faster in the Arctic compared to the other domains of the world, which generates major challenges for human adaptation. Among others, the development of socio-economic infrastructure and strategic planning requires long-term projections of water availability and extreme hydrological events. In this context, it is preferable that the projections of river runoff should be performed statistically, allowing the evaluation of economical risks and costs for hydraulic structures, which are connected to changes in hydrological extremes. In this study, the hydrological model MARCS (MARcov Chan System) is suggested as a tool to simulate the parameters of probability density functions (PDFs) of maximal runoff or peak flow, based on climate projections of the Representative Concentration Pathways. Following that, the PDFs of the maximal runoff were constructed within the Pearson Type III distributions to estimate the runoff values of a small exceedance probability. To evaluate the risks and costs of a long-term investment based on the future projections of river maximal discharge of 1 % probability, simple calculations were performed for the new bridge over the Nadym River as an example.

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The dimensions of embedding spaces for maximum, annual, and minimum flows, as well as for lake levels and suspended alluvium flows, are estimated using the fractal diagnostics. The background distribution of the above dimension for the annual flow was mapped with GIS technology for Russia. With such estimates, we can define the number of differential equations necessary to stably describe statistical distributions widely applied in water-depending branches of economics and hydroecology according to regulations in force.

In last few years in hydrology an interest to excess factor has appeared as a reaction to unsuccessful attempts to simulate and predict evolving hydrological processes, which attributive property is statistical instability. The article shows, that the latter has a place at strong relative multiplicative noises of probabilistic stochastic model of a river flow formation, phenomenological display of which are "the thick tails" and polymodality, for which the excess factor "answers", by being ignored by a modern hydrology in connection to the large error of its calculation because of insufficient duration of lines of observation over a flow. However, it is found out, that the duration of observation of several decades practically stabilizes variability of the excess factor, the error of which definition appears commensurable with an error of other calculated characteristics used in engineering hydrology