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The Perpetual Quest for Efficiency Part 2: Gradient and Morphological Selection

(Part 1 here)

Gradient Selection

Preferential flow phenomena are specific cases of what Phillips (2010, 2011) called the principle of gradient selection: the most efficient flux gradients are preferentially utilized, preserved, and replicated. Gradient selection is based on the twofold notion that (1) the most efficient potential flow paths are preferentially selected; and (2) use of or flow along these paths further enhances their efficiency and/or contributes to their preservation. While Phillips (2010) was concerned with hydrologic flows and geomorphic processes, the evolution of preferential flow paths by gradient selection has broader applicability.

Selection of more efficient paths is not perfect. This selection sometimes occurs deliberately, even intentionally, as when root growth seeks to optimize access to water and nutrients, or a human (or other large fauna) seeks to find the easiest path through thick brush. In other cases, potential transport paths of varying efficiency are encountered by chance (e.g., by sheet flow on a hillslope, or diffuse infiltration into soil). In both cases the mechanisms for route selection are imperfect, and the “decisions” are highly local—in the examples, neither the animal, root, or flowing water can “see” beyond its immediate surroundings.

Karst conduits exposed in a pocket valley, central Kentucky

The strongest forms of gradient selection involve positive feedback, where use of a pathway enhances its flux efficiency—for instance, when karst fracture flow enlarges the conduit by dissolution, or concentrated surface runoff incises a channel. A weaker version is when flow or use simply does not degrade the efficiency of a route. Sometimes this does happen, as for example when material transported by percolating water results in clogging of pores, or when overuse of an unpaved road or path renders it rutted and muddy.

Feedback and efficiency selection in surface runoff.

The positive feedbacks generally involve creating or enhancing features that are relatively resistant and tend to persist, such as gullies, stream channels, macropores, ground water conduits, and well-trampled footpaths. However, this does not always occur, and may be limited, for example when a conduit enlarges to the point of collapse or a trail becomes severely eroded and more difficult to traverse.

Morphological selection

In geomorphology there also exists morphological selection via resistance (Phillips, 2011). Weathering and erosion preferentially or more rapidly remove weaker, less resistant, less stable, and more exposed materials and features, thus preferentially preserving more resistant and stable ones. Sometimes positive feedback accelerates resistance selection via gradient selection, as mass and energy fluxes become concentrated along channels and other pathways cut into weaker materials.

Resistant sandstone, Three Sisters formation, Blue Mountains, New South Wales

But this does not always, inexorably lead toward increasing domination by the more resistant forms. In part this is because of the role of disturbances and changing boundary conditions. But we must also consider differential resistance of the same materials to different processes and in different contexts. Quartz sand, for instance is a strong, stable, low-solubility material that is highly resistant to modification by chemical weathering. However, sandy soils or sediments may be highly vulnerable to wind or water erosion, though even that will vary according to topographic settings, hydrological context, and vegetation cover. Similarly, many limestones have a high degree of physical strength and are resistant to mechanical erosion, but are soluble and have low resistance to dissolution.

Resistance may also change over time, sometimes due to the opposing forces or processes. Aging, senescence, death and decay of organisms and organic structures decreases resistance over time, for instance, and undercutting of slopes increases their propensity for failure. Erosion and weathering may eventually result in increased surficial resistance due to armoring, crusting or sealing, or case hardening. Rock weathering reduces rock mass strength, but also produces resistant residuals and secondary minerals.

Turtle-turbation on a sand bar, Sabine River, Texas/Louisiana. Quartz sand is highly resistant to chemical weathering, and more resistant to transport than silt, but otherwise relatively easy to move around by water, wind, and turtles.

Finally, denudational forces are often applied to layered regoliths, soils, and sedimentary rocks, and to materials and surfaces that are heterogeneous in three dimensions. Thus it is not unusual for the removal of weaker materials to expose more resistant ones.

Next: Barriers to Continuous Increases in Efficiency

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References:

Phillips, J.D. 2010. The job of the river. Earth Surface Processes and Landforms 35: 305-313.

Phillips, J.D. 2011. Emergence and pseudo-equilibrium in geomorphology. Geomorphology 132: 319-326.

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The Perpetual Quest for Efficiency and Stability in Earth Surface Systems

Fluxes of mass and energy in hydrological and geomorphological processes, and in environmental systems in general, preferentially select and reinforce the most efficient pathways. In doing so, they also tend to selectively preserve the most stable and resistant materials and structures, and remove the weaker and unstable ones. This suggests that Earth surface systems should generally evolve toward more efficient flux paths and networks, and a prevalence of stable and resistant forms. The purpose of this essay is to explore why the attractor condition of maximum efficiency and stability is not fully attained.

Numerous theories, hypotheses, and conceptual frameworks exist in geosciences that predict or seek to explain the development of flow paths in Earth surface systems (ESS). These include so-called “extremal” principles and the least action principle in hydrology and fluvial geomorphology, principles of preferential flow in hydrology, constructal theory, and various optimality principles in geophysics and ecology.

Extremal principles related to hydraulic geometry (interrelationships between fluvial channels and the flows within them) are consistent with respect to their fundamental hydrological and geomorphological implications, and Huang and Nanson (2000; Nanson and Huang, 2008; 2016) argue that all can be subsumed under a more general principle of least action (i.e., geomorphic work is performed with the minimum possible energy). Phillips (2010) generalized this even further, contending that water flows will be more prevalent along more efficient rather than less efficient pathways, and that emergent feedbacks cause these paths to be preferentially preserved and enhanced.

Guadalupe River, Texas

The least action principle (LAP) in physics states that the motion between any two points in a conservative dynamical system is such that the action has a minimum value with respect to all paths between the points that correspond to the same energy--in essence, that nature always finds the most efficient path. The general applicability and utility of the LAP in physics is not contested, though debate persists as whether the LAP is a true physical law. In ESS, the LAP is manifested by accomplishing work (e.g., fluvial sediment transport, ecosystem productivity, productivity, heat flux in fluids) with as little energy as possible.

With a given energy input, conservation laws coupled with maximum efficiency in accomplishing work dictates that energy dissipation via entropy must be maximized (Maximum Entropy Production; MEP). Thus there exists a general consistency among optimality principles based on energy, power, and entropy. This phenomenon also clarifies the superficial contradiction between extrema based on minimization and maximization, as minimization of energy to perform work implies maximization of dissipation and entropy. Note also that work itself is not necessarily minimized; only the energy deployed to perform that work. In stream channels, for instance, extremal principles do not suggest that sediment transport is minimized, but rather minimization of the energy used to accomplish a given amount of transport.

Fluvial transport of glacially-derived silt (rock flour), South Island, New Zealand

The concept of preferential flow has been principally associated with soil hydrology and physics, but Uhlenbrook (2006) noted that preferential flow applies to all hydrological phenomena at all scales. Preferential flow may be predetermined or influenced by pre-existing structures and spatial variability, but even in homogeneous materials preferential flows develop due to dynamical instabilities, with reinforcement of incipient preferential paths (Liu et al., 1994). Hunt (2016) linked subsurface water and solute flows to nutrient uptake and plant growth using critical path analysis and percolation theory, showing that similar phenomenologies exist among these processes.

Woldenberg (1969) developed a theory explaining how and why channelized flow systems evolve toward more efficient networks. A similar general principle was formalized by Bejan (2007) as the “constructal law:” “For a flow system to persist in time (to survive) it must evolve in such a way that it provides easier and easier access to the currents that flow through it.” Prevalence of preferential flow at a broad range of scales was reviewed by Lin (2010), who discussed the tendency for these to either develop into, or be controlled by, morphological features in soils and landscapes. Constructal-type behavior arises from traditional path-of-least-resistance reasoning if selection results in persistence of the preferring flow paths, though, contrary to constructal theory, flow patterns in ESS are often strongly influenced by factors other than the flow itself.

Next: Gradient & Morphological Selection

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References:

Bejan, A., 2007. Constructal theory of pattern formation. Hydrology and Earth System Sciences 11, 753–768.

Huang HQ, Nanson GC (2000) Hydraulic geometry and maximum flow efficiency as products of the principle of least action. Earth Surface Processes and Landforms 25: 1-16.

Hunt AG (2016) Spatio-temporal scaling of vegetation growth and soil formation from percolation theory. Vadose Zone Journal 15: DOI: 10.2136/vzj2015.01.0013.

Lin, H., 2010. Linking principles of soil formation and flow regimes. Journal of Hydrology 393, 3–19. 

Liu Y, Steenhuis TS, Parlange J-Y (1994) Formation and persistence of fingered flow fields in coarse-grained soils under different moisture contents. Journal of Hydrology 159: 187-195.

Nanson, G. C., & Huang, H. Q. (2008). Least action principle, equilibrium states, iterative adjustment and the stability of alluvial channels. Earth Surface Processes and Landforms, 33(6), 923-942.

Nanson, G.C., Huang, H.Q., 2016. A philosophy of rivers: equilibrium states, channel evolution, teleomatics and the least action principle. Geomorphology doi:10.1016/j.geomorph.2016.07.024.

Phillips, J.D. 2010. The job of the river. Earth Surface Processes and Landforms 35: 305-313.

Uhlenbrook S. 2006. Catchment hydrology--a science in which all processes are preferential. Hydrological Processes 20: 3581-3586.

Woldenberg MJ. 1969. Spatial order in ﬂuvial systems:Horton's laws derived from mixed hexagonal hierarchies of drainage basin areas. Geological Society of America Bulletin 80: 97–112.

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CONTINGENT ECOSYSTEM ENGINEERING

Many biogeomorphic ecosystem engineer organisms exert their biogeomorphic effects through intrinsic activities and behaviors that occur wherever the organism occurs. Ants, earthworms, sphagnum mosses, and marsh grasses, for example are going to have the same qualitative ecosystem engineering impacts wherever they occur. In other cases, however, biogeomorphic impacts may differ (or even occur) in different geomorphic settings or habitats. This can be called contingent ecosystem engineering, because the effects are contingent on the environmental setting. For example, beavers build dams to create suitable pond habitats, with attendant geomorphic effects on streams. However, where water is deep enough (that is, there is suitable habitat without damming a stream), they don’t bother building dams or lodges (though they do have different biogeomorphic impacts, via burrowing into banks for their lodges). Thus the ecosystem engineering impacts are contingent on the hydrophysical properties of the stream. An example of an organism where the existence (not just the nature or degree) of biogeomorphic effects is contingent is the sulfate reducing bacterium Desulfovibrio desulfuricans. This microbe is found in soil, water, and living organisms in a wide variety of settings. However, in water with high partial pressures of carbon dioxide (such as occur in karst environments), Desulfovibrio desulfuricans stimulates carbonate precipitation, which is an important geomorphic process in caves and karst settings.

Pathways for ecosystem engineering & nich construction. Where phenomenona in the shaded boxes depend on the environmental setting, contingent ecosystem engineering is possible.

This is the theme of the just-published Biogeomorphology and Contingent Ecosystem Engineering in Karst Landscapes (Progress in Physical Geography, vol. 40, p. 503-526). The paper highlights the phenomenon of contingent ecosystem engineering (CEE) in general, with a focus on karst. While CEE may be somewhat more common in karst than other geomorphic systems (we still don’t know enough yet to be sure), it is certainly not limited to karst. The paper also includes a consideration of a range of biotic-abiotic interactions in geomorphology (from a few completely abiotic landforms to some cases where landforms can be considered extended composite phenotypes, though whether any karst features fall into the latter category is still an open question.

Abstract of the article is below:

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SOIL DEEPENING BY TREES

Where soils are relatively shallow, tree roots penetrate into the underlying bedrock through joints and fractures and promote weathering by funneling water into the rock, and facilitating chemical weathering. In addition to these processes, mass displacement by tree growth and bedrock "mining" by tree uprooting help deepen soils and regoliths. While this ihas been demonstrated in several studies, it was unclear the extent to which these processes occur where the bedrock is flat-bedded sedimentary rocks, which offter fewer vertically oriented joints for root access. Soil deepening by trees and the effects of parent material addresses this question (yes, the same general processes do occur in horizontally-bedded rocks). The paper, just out in Geomorphology (vol. 269, p. 1-7) by (mostly) Michael Shouse and myself, also provides some heretofore unprecedented spatial resolution on the spatial variability of soil & regolith thickness attributable to effects of individual trees. The abstract is below.

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MEASURING COMPLEXITY OF EVOLUTIONARY SEQUENCES

Complexity of Earth Surface System Evolutionary Pathways has just been published in "online first" form in Mathematical Geosciences. The abstract:

Evolution of Earth surface systems (ESS) comprises sequential transitions between system states. Treating these as directed graphs, algebraic graph theory was used to quantify complexity of archetypal structures, and empirical examples of forest succession and alluvial river channel change. Spectral radius measures structural complexity, and is highest for fully connected, lowest for linear sequential and cyclic graphs, and intermediate for divergent and convergent patterns. The irregularity index b represents the extent to which a subgraph is representative of the full graph. Fully connected graphs have b = 1. Lower values are found in linear and cycle patterns, while higher values, such as those of divergent and convergent patterns, are due to a few highly connected nodes. Algebraic connectivity (m(G)) indicates inferential synchronization, and is inversely related to historical contingency. Highest values are associated with fully connected and strongly connected mesh graphs, whereas forking structures and linear sequences all have m(G) = 1, with cycles slightly higher. Diverging vs. converging graphs of the same size and topology have no differences with respect to graph complexity, so complexity change is dependent on whether development results in increased or reduced richness. Convergent-divergent mode switching, however, would generally increase ESS complexity, decrease irregularity, and increase algebraic connectivity. As ESS and associated graphs evolve, none of the possible trends reduces complexity, which can only remain constant or increase. Algebraic connectivity may increase, however. As improving shortcomings in ESS evolution models generally results in elaborating possible state changes, this produces more structurally complex but less historically contingent models.

Keywords complexity; evolutionary trajectory; directed graph; algebraic graph theory

Evolutionary sequence of soils in upland sites of the North Carolina Coastal Plain (Fig. 1 from the article).

Earth surface systems (ESS) develop and change over time. Theories of geomorphic, soil, hydrologic and ecosystem evolution call for either (or both) increasing or decreasing complexity as they develop. Thus, key questions across the Earth and environmental sciences involve the In this paper the focus in on complexity with respect to the evolutionary or successional pattern or pathway itself, rather than complexity of the individual elements. Thus, the concern is with the properties of, for instance, a phylogenetic tree rather than complexity of the taxa represented, or of the network of state transitions in geomorphic evolution or vegetation change rather than properties of the landforms or vegetation communities involved. The question is thus not whether, for example, ecosystems or soils become more complex over time, but whether the network of transitions among system states becomes more or less complex. This is addressed by applying algebraic graph theory methods to some archetype (representative idealized) patterns of ESS development to assess structural complexity, network irregularity, and historical contingency properties.

State-and-transition model of channel changes in alluvial rivers (Fig. 3 from the article).

Though I cannot claim to have intended for it to work out this way, this paper is part of a trilogy. Earlier papers sought to measure the degree of historical contingency in ESS and to quantify the robustness of chronosequences. In the first instance the networks were based on the idea of inheritance between temporal episodes—for example, given a set of relationships among geomorphic factors in a river, those that determine or influence the same factor in a subsequent developmental episode. In the second, chronosequences were used to define system states (stages or phases of the sequence) and possible transitions among them based on observed or inferred changes among states. The path stability (degree to which developmental trajectories are sensitive to disturbance) of the derived networks was determined. The new paper expands on the previous work by considering the actual network of changes over time and how complexity might changes as systems continue to evolve.

OK, so there is a general scientific urge to quantify and a temptation to measure something because you can, but there are also compelling reasons to assess the complexity of evolutionary sequences. Most obviously, if the complexity of such sequences is known or can be computed, questions of the evolution of complexity can be addressed once the (or an) appropriate sequential model has been identified. For several decades it has been widely recognized that simple progress-to-equilibrium models are incomplete and not always applicable, but the understanding of state transitions in ESS is still rudimentary in many cases. Further, as ESS evolve they “compute" intrinsically and store information. Information and complexity are closely related in a statistical sense, but methods for estimating stored information in historical data are currently restricted mainly to relatively long time series of integer or ratio-level numerical data. As entropy (and thus information) is directly related to graph spectral properties described below, the approach developed in the latest paper could be useful in assessing the information stored in an evolutionary sequence.

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evolution

THE TAO OF THE RIVER

When more rain falls than the soil can absorb or plants can use, it has to go somewhere, and that movement is driven by gravity. Because concentrated flows are more efficient than sheet flows, concentrated and channelized flow paths are more likely to occur than diffuse flows. These pathways are also more likely to be reused, and to be enhanced by erosion associated with those flows. Similarly, when two of these threads of flow meet, they typically combine (less total surface area for the same amount of water = greater efficiency). Thus these channelized flows tend to form branching channel networks.

The formation of stream and river channels and networks is thus an emergent property of efficiency selection--those most efficient flow paths are more likely to arise in the first place and to be preserved and enhanced. The fact that most of these systems eventually lead to the sea (though globally, a surprisingly large minority drain to interior continental basins) is due to the fact that the flows are gravity driven, and for water, the ocean is the low point.

There is no law of science or nature that requires that water be moved from continents to oceans, or sediment, or for any of the other things that fluvial processes do. Those are the work of the river; emergent outcomes of the job of the river, which is simply to move excess water. I made these points six(!) years back in an article titled The Job of the River.

I am thinking about this today as I sit alongside the Neuse River estuary, where Lynn and I are working on the home built by her late parents. It has long been one of my favorite spots--very near many of my research field sites from the 1990s, and near where I grew up. At this point the river is more than 6 km wide, and this place is situated with views both up and downriver.

NOAA nautical chart of the Neuse River estuary. I've always loved these maps for their combination of applied purpose and aesthetic quality.

Up, to the Neuse River, which rises in the North Carolina piedmont, flows through the insanely sprawling Raleigh area, and escapes that land of strip malls and perpetual highway construction near Smithfield. On it flows through Goldsboro, Kinston, and Fort Barnwell, forming the Neuse River estuary downstream of Street's Ferry; upstream of New Bern. Down, past Cherry Point, Minnesott Beach, and Cedar Island, to the Pamlico Sound. From there it is another 45 km, as the Pelican flies, to the Atlantic Ocean via Ocracoke Inlet.

Many times (we lived near here back in the 1990s, and will again; and I've visited this area every year since 1982) I've thought about this river. I've thought about its geomorphology, hydrology, and ecology. I thought about the way the water level changes according to which way the wind is blowing, and how hard, at Cape Hatteras, never mind the flow of the Neuse. I've thought about the fish and crabs that were so abundant in the early 1980s, and not so much now.

I'd like to thank somebody for this place.

I often think about river journeys, back when water was the main means of transportation, and even still for some adventurous sorts who pass by between the Intracoastal Waterway to the east and the sailing havens of New Bern to the west. I've thought (and researched, back in the day), about the sedimental journeys of eroded soil downstream from the piedmont, and inland from the fields of the Coastal Plain; the back-and-forth journeys of salt, nitrogen, blue crabs, and shad. I think about how I like to see the lights--but only a few--on the far shore, and the channel markers blinking up and down the estuary. About how when the moon is up over the water, always promising adventure and romance.

So you may wonder how I reconcile the romantic blathering just above, with the fairly clinical-sounding analysis based on efficiency selection and emergent properties farther above. How can one go effortlessly from principles of material fluxes to magic?

My father, who was a Methodist minister, never had any problem reconciling science and religion. Science deals with the how, he said, and religion with the why. And even if you don't rely on religion for the why, the how and why don't need to come from the same place. To me, imagining a creator who can get this done with only a simple principle of efficiency selection and gravity is far more inspiring than one who has to preordain every microbe and mountain range. And the beauty of it is, none of us have to believe in a creator, or the same one, to learn how it happened or to appreciate it.

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ROOTS, ROCK & REGOLITH

Just published in Earth-Science Reviews, and available via: http://www.sciencedirect.com/science/article/pii/S0012825216301143

I'm happy to have my name on this, and contributed enough to justfiy that, but this was not an equal contribution by all authors--Lukasz gets most of the credit!

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GEOMORPHIC IMPACTS OF TREES

I've just spent a couple of excellent weeks working on a project investigating biogeomorphic impacts of trees, particularly in old-growth forests. With Pavel Samonil (Forest Ecology Dept., Sylva Tarouc Inst., Brno) and his PhD student Pavel Danek, we visited a number of sites in the Czech Republic. There is much to be done--some of the impacts we identified have never been studied before; others have been studied enough to reveal some complex questions and uncertainties. A sampling of what we saw follows.

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REFERENCE: Phillips, J.D., 2016. Vanishing point: scale independence in geomorphic hierarchies. Geomorphology 266: 66-74.

VANISHING POINT

I’ve been working on and off on scale linkage problems for more than 30 years. The most recent effort, Vanishing Point: Scale Independence in Geomorphological Hierarchies, has just been published.

The abstract is below:

Scale linkage problems in geosciences are often associated with a hierarchy of components. Both dynamical systems perspectives and intuition suggest that processes or relationships operating at fundamentally different scales are independent with respect to influences on system dynamics. But how far apart is “fundamentally different”—that is, what is the “vanishing point” at which scales are no longer interdependent? And how do we reconcile that with the idea (again, supported by both theory and intuition) that we can work our way along scale hierarchies from microscale to planetary (and vice-versa)? Graph and network theory are employed here to address these questions. Analysis of two archetypal hierarchical networks shows low algebraic connectivity, indicating low levels of inferential synchronization. This explains the apparent paradox between scale independence and hierarchical linkages. Incorporating more hierarchical levels results in an increase in complexity or entropy of the network as a whole, but at a nonlinear rate. Complexity increases as a power aof the number of levels in the hierarchy, with aand usually < 0.6. However, algebraic connectivity decreases at a more rapid rate. Thus, the ability to infer one part of the hierarchical network from other level decays rapidly as more levels are added. Relatedness among system components decreases with differences in scale or resolution, analogous to distance decay in the spatial domain. These findings suggest a strategy of identifying and focusing on the most important or interesting scale levels, rather than attempting to identify the smallest or largest scale levels and work top-down or bottom-up from there. Examples are given from soil geomorphology and karst flow networks.

Keywords: scale linkage; scale hierarchy; graph theory; soil geomorphology, fluviokarst

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