Deterministic Tree Networks for River Drainage Basins

Fractals ◽  
1998 ◽  
Vol 06 (03) ◽  
pp. 245-261 ◽  
Author(s):  
M. R. Errera ◽  
A. Bejan
Keyword(s):  
Porous Medium ◽  
Flow Resistance ◽  
Drainage Basin ◽  
Drainage Basins ◽  
River Drainage ◽  
One Step ◽  
Local Properties ◽  
Flow Through ◽  
Internal Properties ◽  
Flow Medium

This paper shows that the dendritic patterns formed by low-resistance channels in a river drainage basin are reproducible and can be deduced from a single principle that acts at every step in the development of the pattern: the constrained minimization of global resistance in area-to-point flow. The river basin is modeled as a two-dimensional territory with Darcy flow through a saturated heterogeneous porous medium with uniform flow addition per unit area. From one step to the next, small elements of the porous medium are dislodged and removed in ways that minimize the global flow resistance. The removed elements are replaced by channels with lower flow resistance. The channels form a dendritic pattern that is deterministic, not random. The finest details of this structure are sensitive to internal properties and external forcing, i.e. variations in the local properties of the flow medium, and the manner in which the total area-to-point flow rate varies as the structure develops. Remarkably insensitive to such effects are the basic type and rough size of the flow structure (channels versus no channels, dendrite, number of branches) and the minimized global resistance to flow.

scholarly journals Evaluation of Satellite-Derived Products for the Daily Average and Extreme Rainfall in the Mearim River Drainage Basin (Maranhão, Brazil)

2021 ◽  
Vol 13 (21) ◽  
pp. 4393
Author(s):  
Ana Carolina Freitas Xavier ◽  
Anderson Paulo Rudke ◽  
Edivaldo Afonso de Oliveira Serrão ◽  
Paulo Miguel de Bodas Terassi ◽  
Paulo Rógenes Monteiro Pontes
Keyword(s):  
Drainage Basin ◽  
Daily Rainfall ◽  
Extreme Rainfall ◽  
Kendall Test ◽  
Drainage Basins ◽  
Satellite Precipitation ◽  
River Drainage ◽  
Monthly Scale ◽  
Precipitation Estimates ◽  
River Drainage Basin

Satellite precipitation estimates are used as an alternative or as a supplement to the records of the in situ stations. Although some satellite precipitation products have reasonably consistent time series, they are often limited to specific geographic areas. The main objective of this study was to evaluate CHIRPS version 2, MSWEP version 2, and PERSIANN-CDR, compared to gridBR, as daily mean and extreme inputs represented on a monthly scale and their respective seasonal trends of rainfall in the Mearim River Drainage Basin (MDB), Maranhão state, Brazil. Estimates of errors were calculated (relative error, pbias; root mean square error, RMSE, and Willmott concordance index, d), and the chances of precipitation were estimated by remote sensing (RES). In addition, trends in precipitation were estimated by the two-sample Mann–Kendall test. Given the overall performance, the best products for estimating monthly mean daily rainfall in the MDB are CHIRPS and PERSIANN-CDR, especially for rainy months (December to May). For daily extremes on the monthly scale, the best RES is PERSIANN-CDR. There is no general agreement between gridBR and RES methods for the trend signal, even a nonsignificant one, much less a significant one. The use of MSWEP for the MDB region is discouraged by this study because it overestimates monthly averages and extremes. Finally, studies of this kind in drainage basins are essential to improve the information generated for managing territories and developing regionalized climate and hydrological models.

scholarly journals A COMPARISON BETWEEN RANDOM AND DETERMINISTIC DYNAMICS OF RIVER DRAINAGE BASINS FORMATION

2009 ◽  
Vol 8 (1) ◽  
pp. 65
Author(s):  
C. A. Marin ◽  
M. R. Errera
Keyword(s):  
Flow Resistance ◽  
Network Formation ◽  
Drainage Basin ◽  
Low Flow ◽  
River Networks ◽  
Drainage Basins ◽  
Random Models ◽  
Mere Presence ◽  
Structure Configuration ◽  
Optimal Reduction

This work contributes to the discussion on how and why tree networks in drainage basin arises in nature. A fully deterministic erosion model recently developed was used to explain the spontaneous origin of river networks, which until then was assumed to be due to the optimal reduction of the flow resistance in a area to point flow. A random evolution model was devised in order to investigate the contribution of two separate features: the relative area size of the network and the structure (configuration) of the network. Two random models were applied, namely, restricted random choosing selection and fully random. Results showed that indeed the mere presence of low flow resistance portions of the basin does improve global performance and that randomness does not create networks. Further gain in performance is given by the network formation by erosion or by optimization. This suggest that local factors also are important to the explanation of the very existence of natural networks.

DRAINAGE BASIN AS A COMPLEX SOCIO-NATURAL HIERARCHICAL SYSTEM

2020 ◽  
Vol 42 (3) ◽  
pp. 293-303
Author(s):  
VALERIY BONDAREV
Keyword(s):  
Drainage Basin ◽  
Temporal Analysis ◽  
Large River ◽  
Hierarchical Level ◽  
Effective Management ◽  
Drainage Basins ◽  
Time Intervals ◽  
Natural Systems ◽  
Spatial And Temporal Analysis ◽  
Entire Complex

The theoretical and methodological basis of the systems hierarchical spatial and temporal analysis of a drainage basin, which addresses the problems of effective management in socio-natural systems of different ranks, is considered. It is proposed to distinguish 9 orders of forms that are relevant to the analysis of drainage basins, where the first level is represented by individual aggregates and particles, and the last - by basins of large and the largest rivers. As part of the allocation of geological, historical and modern time intervals, the specificity of the implementation of processes in basins of different scales from changing states, through functioning to evolution is demonstrated. The interrelation of conditions and factors that determine the processes occurring within the drainage basins is revealed. It is shown that a specific combination of conditions and factors that determine processes in the drainage basin is associated with the hierarchy of the objects under consideration, i.e. the choice of a spatial-temporal hierarchical level is crucial for the organization of study within drainage basins. At one hierarchical level, some phenomenon can be considered as a factor, and at another - as a condition. For example, tectonic processes can be considered as an active factor in the evolution of large river basins in the geological perspective, but for small drainage basin, this is already a conservative background condition. It is shown that at the historical time the anthropogenic factor often comes to the fore, with the appearance of which in the functioning of the drainage basin, there is a need to take into account the entire complex of socio-environmental problems that can affect the sustainable state of various territories, especially in the field of water and land use. Hierarchical levels of managing subjects are identified, which are primarily responsible for effective management at the appropriate hierarchical level of the organization of the socio-natural system within the catchment area, starting from an individual to humankind as a whole.

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