Karst development is strongly influenced by climate, both directly (via the moisture balance and temperature regime) and indirectly. The indirect effects include biogeomorphic impacts of biota, and base level changes associated with sea-level and river incision or aggradation. The literature on cave and karst landscape evolution has plenty on the general influence of climate on karstification, the role of base-level changes, and speleothems as proxy records of climate change.  There is little on how (or whether) direct effects of climate change influence the rate or nature of karst development.

There sometimes exists an intuitive or cognitive disconnect between the idea that Earth surface systems (ESS) may exhibit divergent evolution associated with dynamical instability and deterministic chaos; and the fact that ESS sometimes evolve so as to increase their complexity and interconnectedness.  Despite the initial apparent inconsistency, these two phenomena can and do happen simultaneously within the same ESS.

Instability/divergence and evolution of increasing complexity are readily reconciled when you realize that instability and chaos are scale-contingent, so that divergence and pseudo-randomness occur within firm limits. Also, these phenomena in effects expand the options an ESS has for its development, thus creating more room for evolution of complexity.

The ecologist Robert Ulanowicz developed the notion of ascendancy as a measure of the complexity and interconnectedness of a system. Ascendancy is influenced by the quantity of matter and energy throughputs, and the network of mass/energy exhanges between system components. Almost 10 years ago (!) I used the notions of ascendancy and Kolmogorov entropy to show how dynamical instability and chaos can increase ascendancy.

Geoscientists modeling landscape evolution overwhelmingly (not exclusively, but indeed overwhelmingly) emphasize geophysical aspects, mainly tectonic uplift and erosion. Erosion is typically modeled based on some form of the stream power law, where erosion rates are a power-law function of stream discharge and slope. Discharge is itself often assumed to be a function of drainage area.  There’s nothing wrong with studying the interactions of uplift and denudation without paying much heed to climate, biota, and other factors; I’ve dabbled in this myself.

More shameless self-promotion: The online first version of my new article in Progress in Physical Geography is now available: Biogeomorphology and Contingent Ecosystem Engineering in Karst Landscapes. It is not uncommon to acknowledge anonymous reviewers in an article, and I do so here, but it does not do justice to the breadth, depth, and insight of comments I received on an earlier version from three reviewers (which ran to 14 pages!). Whatever the flaws of the final product, it is a heck of a lot better as a consequence of their efforts. Thanks, whoever you are!

When we (scientists) talk and write about complexity in recent years, the focus is on complex nonlinear dynamics, and related phenomena such as deterministic chaos, dynamical instability, some forms of self-organization, fractal geometry, etc.  These are forms or sources of complexity that are intrinsic to the structure of dynamical systems, but these are hardly the only things that make systems complex. So, to make sure we don’t forget the elements of complexity that transcend so-called “complexity science,” I present the Top 10 Forms of Complexity in Earth Surface Systems (ESS). ESS is a blanket term that includes geomorphic systems, landscapes, ecosystems, soil systems, etc.  Even though the items are numbered, they are actually in no particular order. Many ESS may exhibit only a few of these forms, and still be quite complex!

The list I was gonna do has already been done (http://grogsmovieblogs.com/). 

Forms of Complexity in Earth Surface Systems

Hot off the press--more fun with graph theory!

Phillips, J.D. 2016. Identifying sources of soil landscape complexity with spatial adjacency graphs. Geoderma 267: 58-64.

In many of my writings I advocate an alternative to reductionist approaches to science. By alternative, I mean a complementary, different way of doing things, not a replacement for reductionism. Many excellent reviews of scientific approaches, viewpoints, and methodological stances exist by historians, philosophers and sociologists of science, and by scientists themselves. I do not intend to review or critique these various approaches here. Further, I have no intent to deny the value or necessity of reductionist science. The crux of my argument is that a reductionist approach, by itself, is inadequate or incomplete for understanding Earth.

The American Heritage Dictionary defines reductionism as an attempt or tendency to explain a complex set of facts, entities, phenomena, or structures by another, simpler set, and provides a quote from John Holland:

For the last 400 years science has advanced by reductionism ... The idea is that you could understand the world, all of nature, by examining smaller and smaller pieces of it. When assembled, the small pieces would explain the whole.

The characteristics of a place or system can be factors that are measurable or observable, or those that are not observed or observable. Of the observable phenomena, there are (at least) two different classes. First, there are those whose detection and interpretation does not vary among observers (allowing, of course, for the fact that among us there are humans exceptional in various ways). But the vast majority of humans beyond infancy will recognize, say, a rock, and will not be inclined to argue about whether or not the boulder in question is a rock or not. Suitably trained observers (e.g., geologists) may further agree that the rock is, say, granite.

Flows of mass and energy occur along the steepest gradients of potentials or concentrations.  The principle of gradient selection is simply that features associated with these gradients persist and grow. Take, for instance, the redistribution of excess (i.e., more than the ground can absorb or retain) surface water. Hydraulic selection principles favor the most efficient paths, which we can generally interpret as the fastest pathways. Thus the steepest slopes and/or the routes with the lowest resistance to flow attract more water. The most efficient paths persist and prevail; less efficient options dry up.  For example:

Standard flow resistance equations are of the general form

V = f(R^aS^bf^-c)

where R is hydraulic radius (cross-sectional area divided by wetted perimeter; typically roughly equal to mean depth), S is slope (hydraulic gradient), and f is a roughness or frictional resistance factor. The exponents a, b, c < 1. For example, the D’Arcy Weisbach equation is

V = 8g R^0.5 S^0.5 f^-0.5

Threshold modulation

Upper and lower limits

In terms of mass balances or budgets, geomorphic systems have three fundamental states, whereby losses or removals are either greater than, less than, or roughly equal to inputs or gains (i.e., steady-state). Thus a regolith cover, for instance, is either thinning, thickening, or maintaining steady-state relative to the rates of mass losses and inputs, and weathering and regolith formation.

The principle of threshold-mediated modulation holds that thresholds limit development on both ends (negative or positive mass balance), and that exceeding the thresholds may initiate development in the opposite direction. For instance, vertical accretion on alluvial floodplains is limited by an elevation at which regular flooding no longer occurs, thus limiting further accretion. In addition, confinement of flows within the channel may increase stream power and shear stress, thus ultimately resulting in stripping of the alluvium.