Geometric constraints on tributary fluvial network junction angles

Abstract. The intersection of two non-parallel planes is a line. Howard (1990), following Horton (1932), proposed that the orientation and slope of a fluvial valley within a tributary network are geometrically constrained by the orientation and slope of the line formed by the intersection of planar approximations to the topography upslope from the tributary junction along the two tributary directions. Previously published analyses of junction-angle data support this geometric model, yet junction angles have also been proposed to be controlled by climate and/or optimality principles (e.g., minimum-power expenditure). In this paper, we document a test of the Howard (1990) model using ~10⁷ fluvial network junctions in the conterminous U.S. and a portion of the Loess Plateau, China. Junction angles are consistent with the predictions of the Howard (1990) model when the orientations and slopes are computed using drainage basins rather than in the traditional way using valley-bottom segments near tributary junctions. When computed in the traditional way, junction angles are a function of slope ratios (as the Howard (1990) model) predicts, but data deviate from the Howard (1990) model in a manner that we propose is the result of valley-bottom meandering/tortuosity. We map the mean junction angles computed along valley bottoms within each 2.5 km x 2.5 km pixel of the conterminous U.S.A. and document lower mean junction angles in incised late-Cenozoic alluvial piedmont deposits compared to those of incised bedrock/older deposits. To understand how this finding relates to the geometric model of Howard (1990), we demonstrate that, for an idealized model of an initially unincised landform, i.e., a tilted plane with random microtopography, lower ratios of the mean microtopographic slope to the large-scale slope/tilt are associated with lower mean junction angles compared to landforms with higher such ratios. Using modern analogs, we demonstrate that unincised late-Cenozoic alluvial piedmonts likely had ratios of mean microtopographic slope to large-scale slope/tilt that were lower (i.e., ~1) prior to tributary drainage network development than the same ratios of bedrock/older deposits (≫1). This finding provides a means of understanding how the geometric model of Howard (1990) results in incised late Cenozoic alluvial piedmont deposits with lower mean tributary fluvial network junction angles, on average, compared to those of incised bedrock/older deposits. This work demonstrates that the topography of a landscape prior to fluvial incision exerts a key constraint on tributary fluvial network junction angles via a fundamental geometric principle that is independent of any climate- or optimality-based principle.