Power law scaling of topographic depressions and their hydrologic connectivity

Abstract

Topographic depressions, areas of no lateral surface flow, are ubiquitous characteristics of the land surface that control many ecosystem and biogeochemical processes. High density of depressions increases the surface storage capacity, whereas lower depression density increases runoff, thus influencing soil moisture states, hydrologic connectivity, and the climate‐soil‐vegetation interactions. With the widespread availability of high‐resolution lidar‐based digital elevation model (lDEM) data, it is now possible to identify and characterize the structure of the spatial distribution of topographic depressions for incorporation in ecohydrologic and biogeochemical studies. Here we use lDEM data to document the prevalence and patterns of topographic depressions across five different landscapes in the United States and quantitatively characterize the probability distribution of attributes, such as surface area, storage volume, and the distance to the nearest neighbor. Through the use of a depression identification algorithm, we show that these probability distributions of attributes follow scaling laws indicative of a structure in which a large fraction of land surface areas can consist of high number of topographic depressions of all sizes and can account for 4 to 21 mm of depression storage. This implies that the impacts of small‐scale topographic depressions in the landscapes on the redistribution of material fluxes, evaporation, and hydrologic connectivity are quite significant.

Scale‐Dependent Patterning of Wetland Depressions in a Low‐Relief Karst Landscape

“…Negative feedbacks that induce regular patterning inhibit the development of features, limiting the prevalence of large features and thus truncating the distribution of feature sizes. As such, we predicted that wetland features in BICY will deviate from the power law scaling observed for wetland depressions where negative patterning feedbacks are absent (Le & Kumar, ; van Meter & Basu, ). Power law distributions of feature areas implies the action of scale invariant or fractal processes acting over many orders of magnitude (Brown et al, ; Scanlon et al, ) and would imply one dominant process of basin formation at all scales.…”

Wetlandscape hydrologic dynamics driven by shallow groundwater and landscape topography

“…The elevations of wetland bottoms and divides are results of the regional topography of the landscape, and thus can be derived from DEM data (Bertassello, Rao, Jawitz, et al, ; Le & Kumar, ). The procedure starts by evaluating the flow direction for each cell, and if the cell has no neighbours with lower elevation, it is identified as a sink, representing the bottom, z B , of potential wetlands ( N p ).…”

GPU-based high-performance computing for integrated surface–sub-surface flow modeling

“…In addition, these conjunctive models are being coupled to vegetation-hydrology dynamics (Ivanov et al, 2008), solute transport (VanderKwaak and Sudicky, 1999;Weill et al, 2011), and land-surface and atmospheric models (Maxwell and Miller, 2005;Maxwell et al, 2007). However, existing models have not been applied to capture the micro-topographic controls revealed by light detection and ranging (lidar) digital elevation model (lDEM) data (Le & Kumar, 2014). The goal of this paper is to present numerical scheme suited for Graphic Processing Unit (GPU) based computation to enable studies using lDEM over large areas.…”

“…The increasing availability of high-resolution topographic data from lidar technique has offered new opportunities for broader exploration of the control of landscape variability at fine scales such as water and nutrient dynamics (Lefsky et al, 2002;Schwarz, 2010;Ussyshkin and Theriault, 2011;Le & Kumar, 2014) and to explore behavioral response (Kumar, 2011). Previous studies have shown that depressions arising from micro-topographic variability can have significant effects on streamflow generation (Dunne et al, 1991;Frei et al, 2010;Thompson et al, 2010;Loos and Elsenbeer, 2011), soil moisture dynamics (Simmons et al, 2011), and the surface e sub-surface flow interactions (Frei and Fleckenstein, 2014).…”

“…Recent work has begun to identify and characterize the spatial distribution of topographic depressions as power laws for size and volume, using lidar data (Le & Kumar, 2014). Dynamics associated with these micro-topographic features need to be incorporated into conjunctive surface e sub-surface flow models to understand their impacts on the hydrologic and biogeochemical processes.…”