Abstract
Complex hydrological models find adequate formalization in co-nodal systems, given the abundance, multiplication, dynamics, relations of elements (hubs and nodes) and systems (basins and rivers), as well as chronologies. Hydrological models function on the principle of nodes and orientations. Hypo-cycloids (in the text: h-Cycloids) are time-spatial categories; the subject of hydrodynamic nonlinear analysis, they do not exist entirely realistically as recent flows, but are present only partially, phased, as partial flows. Hypo-cycloids are formed by summing cycles with a combination of overlapping and alternating flows. Cycles are time-spatial categories of co-nodal reconstruction. Fluvial dynamics is logically composed of nodal sets, hub systems, and junctions that are polyvalues (polyvalent, multi-oriented, cyclic) of a diverse model rather than a single-oriented output of just a simple physical model. The chapter examines four of the world's largest interfluviums: Parana-Paraguay, Euphrates-Tigris, Mississippi-Ohio, Danube-Tisza.
TopIntroduction
Complex hydrological models find adequate formalization in the co-nodal systems, given the abundance, multiplication, dynamics, relations of elements (hubs and nodes) and systems (basins and rivers) as well as chronologies. Hydrological models function on the principle of nodes and orientations. Temporal orientations are in paleo-hydrological analysis besides the spatial (geographical) and temporal categories. Geographic models are not only physical, spatial systems, but also complex and multi-dimensional, supra-geographical, linear compositions. The placement of geographic models is oriented in space and time, and therefore the basic geographical facts like the flow, orientation are not mono-dimensional but vector categories (Jerolmack & Paola, 2007; Kleinhans et al., 2008). Geographic elements are not physical but structured elements of a system. The contemporary theory involves a structured multidimensional, realistic, diffuse model versus a linear model in the classification of paleo-hydrological phenomena.
Key Terms in this Chapter
Nonlinear Function: A reversible, time-space, conditional, poly-oriented function. Implies the alternation of flows which are bifluviums or refluviums with several confluent points such as: quadrifluvium, double biconfluvium, or triconfluvium, such as: biconfluvium and active confluvium. Interaction implies the use of factors and factorials (partial outcomes) in order to form hydrodynamic product. Basically, every nonlinear function is a bifluvial relation.
Counterflow: A paleo-hydrological relation (factorial) of two rivers, in which chronologically the latter river flows in the opposite direction from the original direction of the previous river. Countercurrents occur at higher stages of paleohydrological development. These are high-ranking hydrodynamic phenomena, requiring a greater degree of fluvial and hub conditions: bifluvium, recon, or bicon.
Cycle: A cyclo-hydrological phenomenon that is formed by overlaps and additions of subcycles. Semi-hypocycloids are paleo-cyclo-hydrological phenomena that occur by alternating and overlapping cycles.
Complete Cycloid: A hydrocyclic phenomenon that is formed by the alternation of flows and the rotation of semi-cycloids. The subcycle is formed by cycling, the cycle by overlapping, the semicycloid by overlapping and alternating, and the perfect cycloid by rotating cycles.
Co-Nodal Analysis: An analysis of co-nodal system composed of nodules and flows, which describes oriented hydrological functions, river basin, set and subsets of river basins, are not just linear and unambiguous hydrological networks, as seen by conventional river basin theory, but by definition of the nodal theory are, multifaceted oriented networks (reversible, bidirectional, complementary).
Fluvial Cycle: A cycle usually made up of two rivers with an impressive palaeogenesis of one river, the dominant one. The cycle, the development of the dominant, can be rotational (with counterpoints and counter directions), alternative (with alternation of dominant and subdominant) and alternate-rotational (with two alternations and two subdominants).