Depth-transport functions and erosion-deposition diagrams as indicators of slope inclination and time-averaged traction forces: applications in tropical reef environments

The trigonometric relationship between slope inclination, the horizontally acting time-averaged traction force and the vertical depth of transport allows the estimation of one factor, when both others are known. Depth-transport functions can be deduced by comparing the depth distributions of living organisms and their skeletal remains, and this paper simplifies this comparison using foraminifera in which a single test represents an individual. Differences in distribution parameters between living individuals and empty tests allow depth-transport functions to be determined; these functions differ between species at a single transect according to the varying buoyancies of the tests. Within a single species, differences in depth-transport functions between locations are based on either slope inclination or traction intensities. After establishing a mean depth-transport function by averaging species-characteristic functions, the time-averaged traction force acting on the studied transect can be calculated. Transport intensities are also estimated using an erosion-deposition diagram that combines the relative frequency distributions of living individuals and empty tests. The proportion of 'eroded', 'parautochthonous' and 'allochthonous' tests mirrors the influence of both slope inclination and traction force for the deposition of empty tests. To test the model, six species of symbiont-bearing benthic foraminifers were investigated at two transects in front of a NW Pacific coral reef. One transect is distinguished by a strong slope flattening below the steep reef slope (30 m), whereas further steepening characterizes the equivalent part in the other transect. These differences are mirrored in the depth-transport functions as well as in the erosion-deposition diagrams of all species. The time-averaged traction forces differ in intensities between transects, because of the position of the reef front with respect to the predominant wind direction. However, the form of the functions is identical and distinguished by an increase from the surface to 35 m depth, followed by a decrease down to 105 m. This can be explained by successive onshore and offshore forces acting on the shallow slope, such as the tropical cyclones that cross the region every summer.