The Substance of Uncertainty in Systemic Approach: Statistical Learning for Time Series of Geospheres: Natural Scientist's Point of View

In the natural sciences, statistical learning for the geosphere time series (atmosphere, hydrosphere, cryosphere, lithosphere and biosphere) addresses the substance of uncertainty by treating the Earth as a coupled, multi-scale cyber system (J. Krcho, 1970). The time series are sequences of observation in time that reflect results of interaction subsystems of the Geosphere obtained as sequences of observation in time. The systemic approach shifts analysis from one dimensional time series to discover, describe and model complex interactions and cybernetics feedback loops across scales.

Statistical learning allows extraction of Hilbert Spaces from observations with results defining the Geosystems as fuzzy time-spatial structures (Zadeh) with dimensionality and quantitative characteristics of variability reflected from data. The substance of uncertainty may be defined as an ability for models to describe variability in data. From a natural scientist's perspective, uncertainty is not merely "noise" but a property of the systemic approach to modeling the Earth system's complexity.

The Hydrosphere is the most dynamic of the Geospheres and connects with all of them. The Hydrosphere may be described with nine interacting fuzzy elements: water of seas & oceans, stream runoff shell, water of closed lakes, atmospheric water, water of glaciers, water of permafrost rocks, connate groundwater, water trapped in rocks & minerals of lithosphere, and water of biosphere. The stream runoff shell includes* terrestrial stream network.

Model definition (Minsky, 1969) here includes a concept and kinds of coordinate system; a hierarchy of watersheds in the Hydrosphere; representation results of analysis of empirical data; representation of some* knowledge and new concepts.

Visualization results will be presented following the above concepts with interpretation on the example of two watersheds (USGS 04010500 PIGEON RIVER AT MIDDLE FALLS NR GRAND PORTAGE MN, USGS 06191500 Yellowstone River at Corwin Springs MT). Besides six models of these two mesoscale watersheds based on statistical learning of three types of fuzzy structures, the concept will be illustrated with reference to hydrological maps based on time spatial structure obtained by Statistical Learning with use of empirical data from the Great Lakes watershed of North America.

These models for watershed as an element of cyber model for Geosphere and results obtained them illustrates that the systemic approach with statistical learning on empirical data may be successful to find interactions for other Geospheres and bigger natural systems.

The Scientific Hydrology growled out from multiscale cartography surface and groundwater interaction for evaluating regional and global water resources (a Report by Gilbrich and Struckmeier "50 Years of Hydro(geo)logical Cartography", 2014 UNESCO CGWM IAN BGR) unfortunately as parallel branch to Stochastic Hydrology (Klemeš, Koutsoyiannis). The modern cartography of water resources taking root in concepts from Horton, Strahler, Kudelin, using statistical learning for quantitative description time spatial variability, is the scientific branch of Hydrology. Union of those two branches with joint efforts of scientists and engineers is certainly coming.