Influence of climatological norms of the surface air temperature on the fractal dimensionality of the series of long-term river discharge

Geographic Pattern as a Determinant Factor of Interlinking Climatic and Hydrological Components of the Natural Resources

“…Therefore, if the models of runoff formation are really multidimensional, the empirical material should produce the above features of these solutions, to a certain extent and in some form. This is confirmed by the table (756 series of annual average water discharges of water basins located in the northern and southern hemispheres were processed [6]). As is known, the flatness and peakedness of distributions is determined by the kurtosis ε [9].…”

“…To mitigate this instability, a methodology [2] was developed that relied on the unloading of the multiplicative noise component by increasing dimensionality of the phase space where the flow formation is modelled. To perform fractal diagnosis, we used the correlation dimension recovered from the measurements of only one phase variable, according to the Takens theorem [4,5], applied to 756 annual runoff series (predominantly, rivers of the Northern hemisphere) and detected (see [6]) a previously unknown regular pattern, the parabolic dependence of the fractal dimension on the climatic norm of the surface air temperature (Fig. 1, a).…”

Hydrological Probabilistic Model MARCS and Its Application to Simulate the Probability Density Functions of Multi-year Maximal Runoff: The Russian Arctic as a Case of Study

“…However, the additional algorithms should be implemented to the model before developing regional-oriented schemes for the catchments located in the mid-latitudes. As the role of evaporation is more important in the general water balance on the south regions, this variable has to be considered (Kovalenko and Gaidukova 2011).…”

Theoretical and experimental substantiation of the correlation between the fractal dimension of long-term flow series and the climatic norm of surface air temperature

“…This problem may be solved by using fractal diagnostics. Fractal diagnostics (using the cor relation dimension, which is reconstructed in line with the Takens theorem [7], based on a single measured phase variable) of 756 series of the annual flow made it possible to reveal (see [2]) the previously unknown regularity of the parabolic correlation between the fractal dimension ξ and the climatic norm of surface air temperature T (as an indicator of environmental conditions): ξ = 0.0002T 3 -0.0071T 2 + 0.0523T + 1.548; the approximation confidence coefficient R 2 = 0.79 for the temperature range of -5 to +27°С. It appears that in the temperature range of approximately 2-7°С (more exactly 1.6-7°С) all three phase variables take part as statistically significant values in the flow forma tion in a third of all river basins ( Fig.…”