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.

In 2011, a massive flood swept through the Lockyer Creek valley in southeast Queensland, Australia. The environmental, economic, and geomorphic impacts were immense, and Australian geoscientists immediately set out to document, understand, and contextualize them. The “Big Flood” project, led by Jacky Croke, has already produced 19 scientific journal articles, and they just this week went live with their web site, with numerous resources for scientists, managers, and the general public.

Floodwaters in Grantham, QLD, 2011 (http://www.thebigflood.com.au/whathappened.html)

The project has already produced some novel results with respect to flood geomorphology and hydrology, and is unique as far as I know with respect to direct efforts to integrate geoscience research with public policy, public education, and practical land and water resource management.

I recommend you check it out.

Last year our geography department underwent an external review, as we do every five years or so. One of the recommendations was that we seek to integrate our Earth surface systems and physical geography program with political ecology. We happen to have a couple of political ecologists who understand and appreciate physical geography, and vice-versa. But I wonder what, at the subdisciplinary rather than the individual level,  we really have to offer each other.

Despite the word "ecology" and a tradition early on in political ecology (PE) of careful analysis of environmental change, contemporary PE appears to have very little general concern with ecology as a science (as opposed to ecology as a general reference to the environment, nature, or natural resources) or to other Earth and environmental sciences. This is not true of all PE or political ecologists, of course, and to the extent it is true, is not meant as a criticism of the field. Political ecologists are free to define and practice their field as they see fit, and it is not up to a geomorphologist to decide how central biophysical sciences should be.

Imagine exploring and mapping a newly discovered cave opening. At this point, there is only one set of questions--how long, deep, tall, wide, etc. is the passage, and where does it go? But as you begin to map it, more often than not, other passages and fissures will be discovered (and many of them will lead to others, and so on). This opens up a whole new set of questions. Some of the passages can be mapped, assuming someone can get the time and resources. Others can't be no matter how skilled the spelunker; they are too small. But even these can possibly be explored later, perhaps with remote control or AI tiny robots or probes; or with imaging techniques that can see through rock.

This is a pretty good metaphor, I think, for research in general. The more you learn, the more you discover you don't know, and more potential pathways for research appear--some possible now, some awaiting new techniques.

A forest biogeomorphology two-fer, courtesy of my central European boyz, who have graciously allowed me to ride their coattails here in the twilight of my career. The first is one where Pavel Daněk took some of my ideas and methods on applying graph theory to soil geomorphology, and went places with them I never even imagined:

Daněk, P., Šamonil, P., Phillips, J.D., 2016. Geomorphic controls of soil spatial complexity in a primeval mountain forest in the Czech Republic. Geomorphology 273: 280-291.

The second is one  that arose when Pavel Samonil took me to one of his field sites, where I saw things I hadn't imagined:

Phillips, J.D., Šamonil, P., Pawlik, L., Trochta, J., Daněk, P., 2017.  Domination of Hillslope Denudation by Tree Uprooting in an Old-Growth Forest. Geomorphology 276: 27-36.

The abstracts are below.

In the brief biography on my departmental web page, I refer to myself as the "author of a vast number of widely-ignored articles."  This statement reflects the lifelong tug-of-war between my inherent boastful, egotistical leanings and the humility my parents tried, with mixed success, to instill. Thus the boastful "vast number" juxtaposed with the humble "widely ignored." The latter, by the way, is based on the relatively low number of citations and other metrics generated by ISI, etc., compared to the most popular and influential scholars.

I revisit this because I got an e-mail from a master's student working on a research paper who asked: "When going through the bio section of the webpage for the university you work for, it says that a lot of your work is widely ignored.  I am wondering why this is, as I have seen some of your work and think it is fascinating.  Maybe you could help me in this matter by explaining a little further?" The egomaniac within wants to answer that it is because I am so far out front that few have caught up with me; a genius-ahead-of-his-time narrative. The answer dictated by my upbringing (which in this regard is typical for anyone of my generation raised in the small-town or rural USA) is that I just need to try harder and do better (and thanks for the compliment!).

Hurricane Matthew devastated Haiti and other Caribbean areas, and did tremendous damage in Florida and South Carolina (I rode out the storm in Myrtle Beach, SC with my son Nate, his wife Morgan, and my delightful 2-year-old granddaughter Caroline). By the time it got to North Carolina, winds were down to gale force, but rain was ferocious (15 to 40 cm) in much of eastern N.C. Where I am at the moment, in Croatan, there was "only" about 10 cm of rain, and only gale force winds. However, that was enough, as it usually is, to get some geomorphic work done in the forest.

Below are some photos of trees uprooted by the storm in Croatan National Forest in the Flanner Beach area. Uprooting not only does significant soil mixing, but the pit-mound topography left behind significantly influences hillslope and soil processes for decades (and occasionally longer) thereafter.

Another example from a cemetery near Maysville, N.C.

(Part 1 here; Part 2 here)

The principle of gradient selection, along with a variety of “optimality” principles in geomorphology, geophysics, hydrology, and ecology (e.g., Patten, 1995; Fath et al., 2001; Lapenis, 2002; Ozawa et al., 2003; Kleidon et al., 2010; Quijano and Lin, 2014), is in essence a particular case of a broader principle of efficiency selection. Given this common behavior in many types of Earth surface systems, why do we not observe a general global trend toward ever more efficient routes and networks of flows?

First, note that gradient and efficiency selection are tendencies that (like natural selection in biological evolution) apply in the aggregate, and not to individual cases. Also recall from part 2 that gradient selection is imperfect even where it operates.

(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.