Retention capacity of correlated surfaces

Area of Science:

• Physics
• Geophysics
• Statistical Mechanics

Background:

• The water retention model by Knecht et al. (2012) provides a framework for understanding fluid behavior in porous media.
• Previous models often assumed uncorrelated properties of the underlying landscapes.

Purpose of the Study:

• To extend the existing water retention model to incorporate spatial correlations in random surfaces.
• To investigate the influence of these correlations on landscape retention capacity.
• To analyze the relationship between spatial correlations and power-law scaling in lake volume distributions.

Main Methods:

• Extension of the water retention model to correlated random surfaces.
• Analysis of discrete random landscapes with varying degrees of spatial correlation.
• Exact solution for the uncorrelated case on a small lattice.
• Derivation of bounds for the retention of uncorrelated landscapes.

Main Results:

• Spatial correlations in landscape heights strongly influence water retention capacity.
• The emergence of power-law scaling in lake volume distribution is linked to spatial correlations.
• Exact solutions and bounds were obtained for the uncorrelated case.

Conclusions:

• Spatial correlations are a critical factor in determining water retention in random landscapes.
• The findings provide new insights into fluid dynamics in complex, correlated geological formations.
• This work offers a more comprehensive understanding of water retention phenomena in natural environments.