Predictive modeling of slope deposits and comparisons of two small areas in Northern Germany

- Relations of colluvium thickness (Mtotal) to topography are strongly non-linear.
- Close links are between Mtotal and horizontal (DH) and vertical (DV) distances.
- Exponential models based on DH and DV explain 70-93% of Mtotal spatial variation.
- Links slope-valley that describe Mtotal accumulation may be local or regional.
- Parameters that describe links slope-valley allow comparison of different terrains.

Methods for correct quantitative comparison of several terrains are important in the development and use of quantitative landscape evolution models, and they need to introduce specific modeling parameters. We introduce such parameters and compare two small terrains with respect to the link slope-valley for the description of slope deposits (colluvium) in them. We show that colluvium accumulation in small areas cannot be described by linear models and thus introduce non-linear models. Two small areas, Perdoel (0.29 ha) and Bornhöved (3.2 ha), are studied. Slope deposits in the both are mainly in dry valleys, with a total thickness Mtotal up to 2.0 m in Perdoel and up to 1.2 m in Bornhöved. Parent materials are mainly Pleistocene sands aged ~ 30 kyr BP. Exponential models of multiple regression that use a 1-m LiDAR DEM (digital elevation model) explained 70-93% of spatial variability in Mtotal. Parameters DH12 and DV12 of horizontal and vertical distances are introduced that permit to characterize and compare conditions of colluvium formation for various terrains. The study areas differ 3.7 times by the parameter DH12 that describes a horizontal distance from thalwegs at which Mtotal diminishes 2.72 times. DH12 is greater in Bornhöved (29.7 m) than in Perdoel (8.12 m). We relate this difference in DH12 to the distinction between types of the link slope-valley: a regional type if catchment area of a region outside a given small area plays an important role, and a local type when accumulation of colluvium from valley banks within a small area is of more importance. We argue that the link slope-valley is regional in Perdoel and local in Bornhöved. Peaks of colluvium thickness were found on thalwegs of three studied valleys by both direct measurements in a trench, and model surfaces of Mtotal. A hypothesis on the formation mechanism of such peaks is discussed. The parameter DV12 describes a vertical distance from a peak of colluvium thickness along valley bottom at which Mtotal diminishes 2.72 times; values of this parameter differ 1.4 times for the study areas. DV12 is greater in Perdoel (3.0 m) than in Bornhöved (2.1 m) thus indicating more sharp peaks of Mtotal in Bornhöved. Exponential models allow construction of predictive maps of buried Pleistocene surfaces for both the terrains and calculate colluvium volumes with an error 4.2% for Perdoel and 7.1% for Bornhöved. Comparisons of buried and present surfaces showed that the latter are more smoothed, more strongly in valleys where flow branching is increased.