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AXIOMS OF GEOMORPHOLOGY

Axiomatic approaches to science and mathematics depend on an underlying set of statements, principles, or propositions that apply to all situations within the domain of study. The axioms run the gamut from undisputed universal laws to widely or even universally accepted but unproved or unprovable generalizations, to propositional stipulations adopted for analytical convenience or because they raise interesting questions.

Examples abound in mathematics and formal logic, and in science, engineering and technological applications of math and logic. Although it is only occasionally referred to as such, the laws of stratigraphy (details in any geology textbook) form an axiomatic approach to sedimentology, sedimentary geology, and related palaeoenvironmental studies. The laws of original horizontality, lateral continuity, superposition, and cross-cutting relationships are assumed in this approach to apply to all sedimentary deposits, and therefore form an axiomatic system for interpretation.

Thinking about these matters inspired me to make a preliminary stab at a set of axioms for geomorphology, which are laid out below. There exist at least three different definitions or concepts of axiom: (1) a self-evident truth that requires no proof; (2) a universally accepted principle or rule; and (3) a proposition that is assumed without proof for the sake of studying the consequences that follow from it. I make no effort to distinguish the axioms below with respect to these categories, or to get into the semantics of axioms, laws, principles, maxims, propositions, guidelines, etc. I do not deny that these differences might be significant, but for me personally that sort of parsing bores me to tears.

Let me also note that there have been previous efforts to lay out a list of key general concepts or principles of geomorphology, admirably summarized by Gregory & Lewin (2014), and including my own 11 principles of Earth surface systems (Phillips, 1999), focusing on nonlinear dynamics.

(Proposed) Axioms of Geomorphology

These are based on the assumption that the ultimate goal of geomorphology is to explain the origin, evolution, and changes in landscapes. I acknowledge that some axioms are irrelevant to specific research problems (e.g., principles related to environmental and historical context are not directly relevant to laboratory experiments).

1. Landscape forms and patterns are indicators (clues) of formative processes and history. This has always been an underlying implicit or explicit assumption of our field, and in many cases is a necessary one, as the long timescales involved prevent direct observation.

2. Different aspects of the landscape are inherently no more or less important as clues or indicators. Key indicators and the ability to interpret them, however, will vary in different situations. This is intended to highlight that we cannot assume that “it’s all about” , for instance, topography or geochemistry in all situations, and that we cannot assume a priori that factors such as vegetation, soil type, grain size, etc. either are or are not key to the story to be told.

3. History matters. Landscapes cannot be fully explained and interpreted without considering their history, including inheritance, path dependence, event timing and sequence, and changes in environmental controls.

4. Geography matters. Landscapes make little sense outside their geographic (place and ecological) contexts.

We can learn a lot from abstract theory, models, and lab work. However, understanding landscapes ultimately requires boots on the ground.

 

5. Landscape processes, forms and patterns are underpinned and constrained by general laws and principles. These include laws per se and generally applicable principles of (at least) physics, chemistry, biology, geology, and geography. The most important, general, and inviolable are laws of conservation of matter and energy. Thus Landscape systems can be described and understood based on flows, transformations, and storage of energy and matter.  I can’t decide if this should be a separate axiom, or a corollary.

6. Laws, Place, History: landscapes can be understood as representing the combined, interacting effects of generally applicable rules or principles, location- or region-specific environmental influences and controls, and age, time or path-dependent factors (follows from 3, 4, 5).  An essay on this, discussing this axiom and providing some further explanation and justification for items 3-6, is available in online-first form here.

7. Scale matters. The relationships between, and the factors governing, landscape forms and processes vary with spatial and temporal scale or resolution.

8. Selection happens. More durable, resistant, resilient, stable, and efficient forms, patterns, and behaviors are preferentially preserved, and may be reinforced and replicated, relative to less durable, resistant, resilient, stable, and efficient entities. Previous posts on this theme are here, here, here, and there.

9. Selection is non-deterministic. Selection is an aggregate phenomenon, expressed in tendencies and probabilities. It does not always apply or occur in individual cases.

10. Dominant controls.  While many different law, place, and history factors may influence landscapes, for any particular landscape, a relatively small subset of these control landscape evolution and responses. The dominant controls concept holds that while there may exist a very large number of factors and processes that can influence a given phenomenon, in any given geomorphic system some will be irrelevant and others of comparatively negligible influence, leaving a few dominant controls to deal with. In another post I laid out five axioms underlying the DCC, and acknowledging its inspiration from the dominant processes concept in hydrology.  

Comments, critiques, additions, deletions are all welcome. Send ‘em to jdp@uky.edu.

 

 

 

Δ DELTAS

 

Several studies have noted the temporal coincidence between shoreline erosion around some major deltas (e.g., Nile, Mississippi, Ebro), and the reduction of stream sediment loads due to reforestation, soil conservation practices, and trapping of river sediment behind dams. There are, of course, excellent reasons to suspect a causal link, but the link itself has not, in my view, been fully established.

First, in many cases it has not been established that reduction of soil erosion within river basins and sediment trapping behind dams has reduced sediment delivery to the coastal zone. In some cases, particularly where rivers cross a coastal plain, there are sediment “bottlenecks” that limit sediment delivery to the coast. While the upstream changes do indeed reduce fluvial sediment loads in parts of the river, and may well reduce input to the bottlenecks upstream of the deltas/estuaries, it may be that even with the reduced loads there is still as much sediment as the river can carry in its lower reaches. Lower reaches of coastal plain rivers are often characterized by extensive sediment storage space, frequent overbank flow that delivers sediment to these storage zones, and very low stream power. It is often difficult to assess changes in sediment actually getting to deltas and estuaries because the downstream-most gaging station is well upstream of the coast, and of any lower-river transport bottlenecks (for more extensive discussions and case study evidence, see this, this, this, thisthis, and that).

Some studies also don’t pay attention to other factors that influence delta erosion and deterioration, such as (accelerated) sea-level rise, subsidence, compaction, and human modifications that either limit sedimentation (e.g., flood control levees), prevent avulsions that may be important in deltaic sediment distribution (e.g., channel stabilization), or contribute to delta wetland loss (dredging, canals, etc.). The point is that in some cases deltas could be experiencing net erosion even where river sediment supply is not decreasing.

False-color LANDSAT image of the Mississippi River delta. 

It is well established that human settlement and expansion dramatically increased soil erosion and river sediment loads in many cases due to deforestation, agriculture, mining, etc.  To the extent reforestation, soil conservation and sediment controls reduce erosion, and dams trap sediment, this could be viewed as returning the sediment regime to its pre-modern situation. Thus, if we want to say that choking off this excess anthropic sediment is starving deltas, shouldn’t we also observe that the excess anthropic sediment was resulting in delta progradation before?

I did a quick-and-dirty literature review on this. I was not thorough enough to draw any conclusions, but I did see enough to know this: the evidence is mixed and varied. There are some cases where accelerated soil erosion can be shown to have led to delta growth, some cases where this is unclear, and some where no evident delta growth occurred.

Resolving this question means evaluating each river and delta on a case-by-case basis, accounting for the possibility of sediment bottlenecks, and considering the other factors that influence delta growth or erosion. 

THE CYCLE OF EROSION

 

Out on the trails of Shaker Village at Pleasant Hill, Kentucky, this morning, I got to thinking about William Morris Davis’ “cycle of erosion” conceptual model (also called the geographical or geomorphological cycle). The drive-by, oversimplified version is that landscape evolution starts with uplift of a more-or-less planar, low relief surface. Weathering and erosion goes to work, and results in an initial stage of increasing relief as streams carve valleys, and slope processes operate on the slopes thereby created. Eventually, however, as the streams begin to approach base level, a new stage of decreasing relief begins as hilltops and drainage divides are lowered and valleys infilled. This continues until the entire landscape is about as close to baselevel as the geophysics of mass transport will allow, creating a low-relief, almost-planar surface called a peneplain. At some point a new episode of uplift occurs and the cycle begins anew.

I was thinking of this because many landscapes in the world, like the one I was viewing this morning, do give the impression of a dissected plateau or a low-relief surface into which denudational processes have cut.

Google Earth image of part of the landscape at Shaker Village, KY. 

As historians of Earth science—as well as almost anyone who’s had a geomorphology course—is aware, Davis’s cyclical concepts dominated geomorphology (as well as those aspects of historical and structural geology that overlap with geomorphology) for much of the 20th century. The theory is flawed, and a backlash began in the 1950s, and it is very much out of fashion, though it persists in areas of Earth science other than geomorphology.

Why was the Cycle of Erosion so successful, and so dominant, for so long? There are a number of historical, sociological, and political reasons that figure into this, but there are good scientific ones as well.

From a theoretical perspective, under the conditions Davis specified (an episode of uplift followed by a long period of no further uplift, erosion dominated by fluvial processes, and no major sea-level, climate or tectonic change), the postulated cycle of erosion is exactly what would happen, as physical models testify. Of course, those conditions have rarely (perhaps never) been met in Earth history for a long enough period to allow the cycle to run its course, but the reasoning was not at all unsound.

From the perspective of a landscape observer—a geographer, geologist, or layperson, and in the field or on maps and images—the cycle does provide a plausible explanation for the widespread occurrence of eroded landscapes where the ridges, peaks, and interfluves (the high bits) are, or at least appear to be, accordant (i.e., at approximately the same elevation). There are indeed many landscapes on our planet where the high parts appear to be part of a surface that has been dissected from the top down rather than the sticky-uppy parts having been raised from the bottom up.

I think some of the ideas in the Earth and environmental sciences about steady-state equilibrium are analogous to the Cycle of Erosion in several ways. First of all, they are (in many cases) seriously flawed and give misleading impressions about how nature works. Second, however, the reasoning behind them is often sound, though even more often based on highly simplified assumptions rarely met in nature. Third, they may provide at least superficially plausible explanations for observations. This is the case, for instance, with the steady-state model of graded stream profiles.

My ideas on the latter point are laid out in Phillips (2010; 2011), and my only contribution to debates on peneplains and such in Phillips (2002). There are many discussions and critiques of Davis’s cyclical ideas; several that I especially like are in Rhoads and Thorn’s (1996) edited volume The Scientific Nature of Geomorphology. 

HYDROPEDOLOGY: FLUX-STRUCTURE INTERACTIONS

Subfields such as biogeomorphology, ecohydrology, geoecology, soil geomorphology are areas of overlap between disciplines and subdisciplines. They are governed by the paradigms of the overlapping fields, and fit more or less comfortably within, and at the boundaries of, those fields. They do not have an independent paradigm or conceptual framework (which in no way reduces their importance or vitality).

Landscape ecology, by contrast, has developed its own paradigm—pattern, process, scale—that is independent from mainstream ecology, biogeography, and geospatial analysis.

Does, or can, hydropedology have such an independent paradigm? Is its development best served by, say, the ecohydrology or soil geomorphology model as an overlap field dominated by existing paradigms of pedology and hydrology? Or is a landscape ecology, separate paradigm direction more appropriate?

IF the latter is the case, what is an appropriate framework? Henry Lin’s papers on hydropedology (see, e.g., Lin, 2012 and http://www.hydrol-earth-syst-sci.net/14/25/2010/hess-14-25-2010.pdf) identify key foci as (1) soil indicators of flow & transport, (2) soil morphology as a signature of soil hydrology, (3) water movement over the landscape, and (4) hydrologic processes as a soil forming factor. This suggests the following as a paradigm for hydropedology: Flux—Structure Interactions, with structure meant in a broad sense to include morphology, topography, and spatial patterns, rather than soil structure per se.

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Lin, H. (editor). 2012. Hydropedology. Elsevier.

OPTIMALITY IN EARTH SURFACE SYSTEMS

 

A number of theories in geomorphology, ecology, hydrology, etc. are based on the idea that Earth surface systems (ESS) develop according to some optimal principle or goal function. That is, the ESS develops so as to maximize, minimize, equalize, or optimize some quantity—energy, exergy, entropy, work, mass flux, etc.  Some of these notions have some explanatory power and have resulted in some important insights. However, they have always bothered me--no one has ever been able to convince me that there is any inherent, a priori, rule, law, or reason that, e.g., a hillslope or a stream channel or a soil would operate so as to optimize anything. The conservation laws for mass, energy, and momentum are the only laws of nature that absolutely must hold everywhere and always.

So how does one explain the apparent success of some optimality principles in describing, and even predicting, real ESS behavior?

Suppose we use P to represent possible developmental pathways for an ESS. An optimality principle is essentially arguing that a particular P among all those possible is the most likely1. But the sufficient conditions for a particular path need not invoke any extremal or optimal goal functions.

Sufficient conditions for preferential development along trend or pathway Po, PoÍ Pi, i = 1, 2, . . . , n potential pathways are threefold:

1. Pois associated with processes or behaviors that confer advantages or higher probability of persistence or replication relative to other Pi. For instance, with respect to hydrological flow paths, concentrated pathways are favored over diffuse ones; and steeper and hydraulically more efficient routes over gentler and less efficient ones. With respect to hillslope gradients, angles less than the angle of repose persist, while those greater fail. In ecosystem or community composition, for example, more rapid or efficient resource use and cycling may confer competitive or selective advantages.

2. The ESS is at or approaching saturation (i.e., given enough time without change in boundary conditions or disturbance, it will become increasingly saturated). The “saturated” condition is associated with biological saturation (i.e., all available niches are filled) in ecology; with fully developed drainage systems in hydrology; and with relaxation time equilibrium in geomorphology. Condition 2 does not require the ESS to have reached saturation; only that if it has not, then (e.g.) niches will continue to be filled, drainage systems will continue develop, and geomorphic responses will continue until saturation is achieved.

3. There are no significant changes in boundary conditions, or clock-resetting disturbances.

In the absence of environmental change (no. 3 above), two conditions (1, 2 above) are sufficient.

Hypothesized “optimal” development does typically correspond or overlap with pathways that are advantageous in the sense of condition 1 above. Thus observations of supposedly optimal evolution are better explained as emergent outcomes of the simple selection principle indicated in item 1 above, subject to items 2 and 3.

I prefer the emergent explanation based on selection to the optimization hypotheses because it is simpler, it works at least as well2, and it requires no suppositions of goal functions for ESS.

 

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1Though in some cases it has been shown that there are many ways an ESS might be configured to achieve a particular optimum.

2”Works as well” refers to explanation and interpretation. For modeling, assuming a particular optimal condition often simplifies things immensely. However, in those cases the optimality principle should indeed be viewed as a simplifying assumption rather than a truth statement about ESS. 

DUST BOWL DYNAMICS

A conversation with other scientists about severe, dust-bowl type wind erosion and erosion risks got me to thinking about the key interrelationships involved. The severe erosion and land degradation in the U.S. Great Plains in the 1930s was a combination of a particular confluence of environmental factors that set up aeolian erosion risk (climate, periodic low soil moisture, topography), a prolonged drought, and human factors (replacing natural grassland vegetation with crops that left fields bare part of the year).  In other areas where the environmental risk factors are present, how stable or resilient is the landscape to severe wind erosion?

Archival photo from Kansas showing cropland degraded by wind erosion in the 1930s. 

They key factors, as I seem them, are wind erosion, soil moisture, and vegetation cover. The key interactions are shown below. Negative links in this case mean that a change in one component results in a change in the other in the opposite direction. Thus, for instance, a decrease in soil moisture, other things being equal, leads to an increase in wind erosion, and increased soil moisture to reduced erosion. A positive link indicates that a change in one component leads to a change in the other in the same direction. Thus the only positive link in the model below shows that increases or decreases in soil moisture lead to corresponding increases or declines in vegetation cover. The dotted lines in the figure are undetermined. The vegetation to soil moisture link could be positive or negative. Denser vegetation could increase soil moisture in some cases due to shade effects and the role of soil organic matter in promoting moisture storage. On the other hand, plants use water, and denser vegetation could draw down soil moisture. The erosion to soil moisture link could be negative (due to loss of soil moisture storage capacity as topsoil is lost) or negligible (i.e., no arrow), if topsoil or soil thickness is not limiting with respect to water storage. The self-limiting negative links reflect the fact that soil moisture, wind, and vegetation all may be limited by factors other than each other, such as climate, nutrients, geomorphic processes, etc.

The dynamical stability (resilience) of the system can be determined using the Routh-Hurwitz criteria. This analysis shows that instability is possible when the vegetation cover to soil moisture link is positive, and the aeolian erosion to soil moisture link is negative. Dynamical instability indicates that the system is vulnerable to small changes and disturbances (i.e., changes in soil moisture, wind erosion, or vegetation). If the vegetation to moisture link is negative, and the effects of erosion on soil moisture are unimportant, the system is stable and therefore resilient to non-catastrophic changes.

So what does this all mean? First, it may provide a framework for assessing vulnerability to land degradation by wind erosion. Second, it highlights key research needs to make such assessments—specifically, how soil moisture responds to soil loss from aeolian erosion and to changes in vegetation cover, which no doubt vary in specific environments.

A final note: instability is not always a bad thing. If the system is already degraded or threatened, dynamical instability suggests that measures such as erosion control or vegetation establishment can “flip” the system to a more preferable state. 

THE INHERENT EPHEMERALITY OF WETLANDS

As a citizen, an environmentalist, and a scientist, I am absolutely committed to the conservation and preservation of wetlands. The ecosystem services provided by wetlands are immense; their hydrologic, ecologic, economic, and aesthetic values are long since beyond serious question. However, as we strive to protect these inarguably valuable resources, we need to keep one thing in mind—marshes, swamps, bogs, and other wetlands are inherently and irreducibly subject to change.

First, many of them are geologically ephemeral. They are recently formed and very young in geological terms, and under no circumstances would they be expected to remain static—geomorphically, hydrologically, ecologically, or locationally—for very long. The estuaries of the Gulf coast of the U.S., for example—and their associated tidal flats, salt and freshwater marshes, mangrove swamps, freshwater swamps, etc.—were established in approximately their current locations only about 3000 years ago. That’s nothing in geological time. Even at that, both the external boundaries and internal dynamics have been anything but static in that time, and change is ongoing. This kind of youth and dynamism is the rule, not the exception, for wetlands around the world.

A seasonally-flooded wetland (and one of my favorite fishing spots) in Mercer County, KY. 

Second, the creation and maintenance of a particular type or form of wetland depends on a specific set of interactions among hydrologic, geomorphic, and ecological processes. All of those can change as sea-levels rise and fall, as climates get wetter or drier, as rivers migrate and shift their channels, as plants and animals disperse—not to mention any number of human modifications! All of those can also change due to the inherent, internal evolutionary dynamics of ground water flow systems, channels, soils, landforms, and biotic communities. And when any factor (topography, hydrology, vegetation, etc.) changes, it affects all the others.

Inventories, maps, or estimates of wetlands should recognize their dynamism—that is, these are inevitably snapshots (stills from a continuous movie, if you will). Detection of change in and of itself is not a cause for concern. The known or potential drivers of those changes, and net losses of wetlands (globally or locally) are a cause for concern. We can and should expect to continue to have wetlands, but we should not expect them to remain constant for long periods.

Protecting and conserving wetlands requires that we allow them to move. They have to be able to respond to these environmental changes geographically—sometimes by expanding or contracting; sometimes by shifting positions.

Protecting and conserving wetlands requires that we allow them to change. Some wetland changes wrought by human actions are avoidable and deleterious (certain wetland destruction is). However, we should be aware that they are gonna change, with or without humans. So we need to recognize that change per se—e.g., a shift in vegetation communities, the infilling of an oxbow lake, fringe erosion of a salt marsh—is not a cause for concern.

Protecting and conserving wetlands requires that we protect and conserve wetlands. Their inherent ephemerality and dynamism should never be used as an excuse to let miners, developers, etc. destroy and degrade wetlands. This may seem self-evident, and no more likely than someone arguing that it should be OK to kill protected species because new ones will be born. However, we’ve seen many arguments that we need do nothing about human impacts on climate because climate can change without human agency, so I thought I should make this point clear.

An example of my scientific efforts to measure/estimate the complexity of transitions in river, delta, and wetland environments is in the attached paper. 

Attachments:
STM.pdf (751.4 KB)

THRESHOLD MODULATION

 

Not too long ago (Phillips, 2014) I proposed that many geomorphic systems are characterized by divergent behavior driven by either self-reinforcing feedbacks, or by “competitive” mutually-limiting relationships. However, this divergent evolution cannot continue indefinitely, and is ultimately limited by some sort of thresholds. Watts et al. (2014) recently published a paper that I think provides a good example of this sort of behavior a bit different from the ones I cited.

In a low-relief karst wetland landscape in Florida, they found that feedbacks among vegetation, nutrient availability, hydroperiod, and rock weathering (dissolution) result in formation of isolated forested wetland depressions (cypress domes) amongst prairie-type wetlands. However, as the cypress dome (they are called domes because of the taller canopies, despite the depressional landform) features grow, water volume thresholds limit further growth. 

 

Phillips, J.D., 2014. Thresholds, mode-switching and emergent equilibrium in geomorphic systems. Earth Surface Processes and Landforms 39: 71-79.

Watts, A.C. & eight others, 2014. Evidence of biogeomorphic patterning in a low-relief karst landscape. Earth Surface Processes and Landforms 39: 2027-2037. 

Attachments:
modeswitch.pdf (232.37 KB)