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Exponential Distribution Theory and the Interpretation of Splash Detachment and Transport Experiments

Faculty of Earth and Life Sciences, Vrije Univ. Amsterdam, De Boelelaan 1085, 1081 HV Amsterdam, The Netherlands

View larger version (17K): [in a new window]   Fig. 1. The mass of soil splashed beyond a radial distance r from its point source (data from Riezebos and Epema, 1985). Exponential functions are fitted to the data, which represent splash resulting from artificial drops falling from indicated heights.

View larger version (14K): [in a new window]   Fig. 2. One-dimensional distribution of particles splashed from a source strip expressed as a density function of perpendicular distance x {vstrip(x); Eq. [5]} and as a transport function indicating the fraction of detached material splashed beyond distance x {vbeyond(x); Eq. [6]}. All variables have been made dimensionless; dashed lines represent approximate exponential functions. = average splash length.

View larger version (16K): [in a new window]   Fig. 3. Rates of splash transport [q(X)] onto 10-cm wide strips, placed at increasing distances from a soil tray subjected to artificial rainfall and filled with different soils (approximate median grain size indicated; data from Savat and Poesen, 1981) with Eq. [12c] fitted to the data.

View larger version (32K): [in a new window]   Fig. 4. Illustration of (a) the matrix used to model the distribution of particles splashed from a rectangular area (the meaning of the areas labelled SCREEN and CORNER is explained in the text); (b) a soil tray bordered by a very wide collecting screen having the same length; (c) a soil tray bordered by an infinitely large horizontal collecting screen; and (d) a soil tray bordered by a collector with vertical splash guards on three sides.

View larger version (24K): [in a new window]   Fig. 5. Splash transport onto (a) a wide screen having the same length as a side A, and (b) an infinitely large screen, both placed along a side A of a tray with dimensions A and B, as a function of the dimensionless length of that side, A/, and for a number of different values of the aspect (A/B) of the tray. Splash transport was made dimensionless by expressing it as a fraction of the transport from an infinitely large area of soil.

View larger version (11K): [in a new window]   Fig. 6. Relationship between dimensionless cup radius R/ and the amount of soil splashed out of the cup, expressed as a fraction of the total amount of detached sediment (FR).

View larger version (13K): [in a new window]   Fig. 7. Application of the theory for interpreting splash cup data (Eq. [16]) to data collected by Poesen and Torri (1988). The exponential equation proposed by Poesen and Torri (1988) is shown for comparison. mR = cup splash rate, R = radius.