Abstract
Abstract. We revisit three variants of the well-known Stommel diagrams that have been used to summarize knowledge of characteristic scales in time and space of some important hydrologic phenomena and modified these diagrams focusing on spatiotemporal scaling analyses of the underlying hydrologic processes. In the present paper we focus on soil formation, vegetation growth, and drainage network organization. We use existing scaling relationships for vegetation growth and soil formation, both of which refer to the same fundamental length and timescales defining flow rates at the pore scale but different powers of the power law relating time and space. The principle of a hierarchical organization of optimal subsurface flow paths could underlie both root lateral spread (RLS) of vegetation and drainage basin organization. To assess the applicability of scaling, and to extend the Stommel diagrams, data for soil depth, vegetation root lateral spread, and drainage basin length have been accessed. The new data considered here include timescales out to 150 Myr that correspond to depths of up to 240 m and horizontal length scales up to 6400 km and probe the limits of drainage basin development in time, depth, and horizontal extent.
Highlights
The development of “physically based” and verifiable spatiotemporal scaling relationships is one of the important goals stated in the publication Opportunities in the Hydrologic Sciences (National Research Council, 1991), which helped guide the establishment of NSF’s Hydrologic Sciences Program in the Earth Sciences (EAR) Division
Given the possible influence of subsurface processes on drainage basin development, the seeming correspondence of the icons of the Stommel diagram in Fig. 3 that represent river basin development, and the apparent coincidence of plant root development and river path development along optimal paths in a highly heterogeneous environment, we propose investigating the spatiotemporal scaling of drainage basins in terms of Eq (1), which was found to predict the range of root lateral extent values in the subsurface over timescales up to 100 kyr
Ture of the porous medium as a network and flow rates as given by hydrologic variables. These individual relationships were confirmed separately by comparison with a great deal of data that examined their individual predictions for soil depths and vegetation growth
Summary
The development of “physically based” and verifiable spatiotemporal scaling relationships is one of the important goals stated in the publication Opportunities in the Hydrologic Sciences (National Research Council, 1991), which helped guide the establishment of NSF’s Hydrologic Sciences Program in the Earth Sciences (EAR) Division. Hydrogeologists and earth scientists occasionally organize (eco)hydrologic phenomena according to their spatial and temporal scales so as to locate them in a single figure (National Research Council, 1991, 2001; Bloeschl and Sivapalan, 1995; Loague and Corwin, 2006) Such figures, known as Stommel (1963) diagrams, are illustrative and can, under the right circumstances, trigger further useful work, such as testing hypotheses regarding appropriate spatiotemporal scaling relationships and the relevant space and timescales that enter in. The power s was chosen (Hunt, 2017b), for soil development, as the inverse of the percolation backbone dimensionality, 1/Db = 0.53, and, for vegetation growth, equal to the inverse of the 2D percolation optimal path exponent, 1/Dopt = 0.83 These non-linear exponents reflect diminishing connectivity of the network with increasing length scales. The relevance of Eq (1) using the same parameters x0 and t0 from Yu et al (2017a, b) and Hunt (2017b) will be tested further below by investigating its ability to frame the understanding of the Stommel diagrams
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