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The Importance of Fractal 1/f Slopes for Minesite Drainage



Minesite-drainage chemistry is a rather insular science. We use laboratory-based humidity cells, first developed around 1960, and acid-base accounts and hydrogen-peroxide tests developed about the same time. The Wheel Approach (e.g., Morin and Hutt, 1997, 1999, and 2001a), summarizing the various synergistic tests for predicting drainage chemistry around the world, has been around for decades.

Furthermore, experts in minesite-drainage chemistry (MDC) continue to predict full-scale minesite drainage using scaling factors applied to small samples (Morin and Hutt, 2007; Morin, 2013, 2014, and 2015a), because some people started using them for their simple convenience. There is no evidence that the typical selection of a handful of scaling factors used by MDC experts reliably predicts full-scale chemistry. Moreover, these scaling factors are applied across eight or more orders of magnitude of scale, and across thresholds where complex emergent conditions arise. Therefore, this extreme scaling ignores the fact that complex and dynamical systems like minesite components (Morin and Hutt, 1998) cannot be simulated or predicted based on their small parts (Morin and Hutt, 2001b).

With the analogy of sand "avalanches" down the sides of a steepened sand pile, Bak (1996) explained an avalanche could not be explained or predicted by looking closely at one grain of sand. Yet MDC experts look closely at a few, relatively small samples of rock or tailings, and proceed to predict full-scale behaviour. This does not work reliably in other sciences, and cannot not work reliably for minesite-drainage chemistry.

The ability to link the science of minesite-drainage chemistry to other sciences provides many benefits. For example,
- MDC would no longer be so insular.
- Our knowledge and understanding of MDC would increase vastly, in a short period of time, by borrowing the knowledge and understanding from other sciences.
- Published papers, books, conference proceedings, etc., from other sciences become relevant to MDC and, in turn, MDC documents would assist other sciences.

Dr. Per Bak discussed the linkages among sciences in his thoughtful and innovative book published in 1996, How Nature Works: the Science of Self-Organized Criticality. This book discusses many important concepts like criticality, 1/f slopes, fractal patterns, and complexity. Again, full-scale minesite components fall under the definition of "complexity".

"Complexity deals with common phenomena in different sciences, so the study of complexity benefits from an interdisciplinary approach. However, because of the sociology of science, it takes someone at the top to change the course of science. Most scientists in the rank and file do not venture into new areas that have not been approved from above. There is good reason for this since young scientists are dead in the water if they step out of traditional disciplines." (p. 115)

"Traditionally, cross-disciplinary research has not been very successful. The fundamental entities dealt with in the various sciences are competely different .... Attempts to find common ground have often been contrived and artificial.  At universities, the different sciences are historically confined to specialized departments with little interaction. This has lefty vast areas of science unexplored. However, a new view is emerging that there could be common principles governing all of those sciences, not directly reflected in the microscopic mechanisms at work in the different areas. Maybe similarities arise due to the way the various building blocks interact, rather than to the way they are composed." (p.115)

"No mechanism for changing directions [in scientific areas of specialization] exist, so more and more efforts go into more and more esoteric aspects of well-studied areas that once paid off.... Nobody has an incentive to step back and ask himself, 'Why am I doing this?' In fact, many scientists are put off if you ask this question." (p.115-116)

Therefore, the cross-disciplinary linkage of MDC to other sciences would not come easy, certainly not without moving away from focussed specialization and not without some soul searching. Nevertheless, I think it would be worth the effort.

One strong cross-disciplinary linkage for MDC is fractal 1/fa slopes in power spectra of time series, which illustrate the dynamic, non-linear, and emergent complex behaviours of full-scale minesite components (e.g., Morin, 2015a, 2016a, and 2016b). These slopes cannot be estimated, explored, or explained by the common scales of testwork currently used for MDC. Additionally, detections and delineations of these slopes are often precluded by typical monitoring activities such as:
- Occasional synoptic sampling, providing a "snapshot" in time of drainage chemistry around and downstream of a minesite or one of its components.
- Collection, analysis, and reporting in annual reports of water samples collected at relatively long frequencies, such as monthly and quarterly.
- Intensive high-frequency (e.g., daily) sampling for a few days or weeks.

Instead, 1/fα slopes in power spectra can only be reliably detected by sampling programs that span at least two orders of magnitude relative to the frequency of sampling collection. Some examples are:
1) sampling daily or hourly for a few years.
2) sampling monthly for decades.
These two examples provide the orders-of-magnitude ranges needed to identify 1/fα slopes, but differ in the information they provide about the physical, geochemical, and biological cycles affecting and determining the aqueous variability.

From the perspective of 1/fα slopes in time-series spectra, a minesite component can be thought of in one or two ways: as a signal filter or as a signal generator.

As an example of a signal filter, precipitation may have a random time series ("white noise"), but the drainage coming from the base of the component shows a non-random pattern. In this case, the component is "filtering" and changing the input, which reflects one or more of the many physical, geochemical, and biological processes operating within it. If the component does not filter the signal at all, but provides the same trends as the input, then non-dispersive convective flow ("plug flow") is likely occurring.

As a real, full-scale example of signal filtering, Figure 1 shows the input signal of rain + snow in the upper left corner (click on the figure to enlarge it).  The remaining power spectra in Figure 1 show how the virtually random input signal was filtered and affected after the water drained from waste-rock dumps.  This drainage then flowed downstream through ditches that also collected more diffuse drainage, with the signal filtered and altered even further.

MDAG Figure 1 - 1/f slopes in flows
Figure 1 (rain+snow as the input to the "signal filter" shown in the upper left)

As an example of a signal generator, precipitation may carry a non-detectable level of a particular chemical element into a component, but the drainage coming from the base contains detectable levels. The pattern of that now-detectable element says something about one or more of the many physical, geochemical, and biological processes operating within it. Furthermore, along long drainage ditches and groundwater flowpaths, the evolution of the power spectrum from point to point represents signal filters.

As real, full-scale examples of signal generators, the power spectra in Figures 2 to 4 show how signals were generated within waste-rock dumps for pH, zinc, and sulphate, respectively (click on the figures to enlarge them).  These signals were then filtered and altered as the drainage flowed downstream through ditches that also collected more diffuse drainage.

MDAG Figure 2 - 1/f slopes in pH MDAG Figure 3 - 1/f slopes in zinc MDAG Figure 1 - 1/f slopes in sulphate
Figure 2                Figure 3                Figure 4


MDAG is currently producing case studies and publications of 1/fα slopes from full-scale minesite components, including both physical flow and geochemical aqueous concentrations. These documents will be listed here as they are released.


RECENT MDAG DOCUMENTS RELATED TO 1/fα SLOPES AND POWER LAWS

- Morin, K.A., and N.M. Hutt. 2007. Scaling and Equilibrium Concentrations in Minesite-Drainage Chemistry. MDAG Internet Case Study #26, www.mdag.com/case_studies/cs26.html

- Morin, K.A. 2015. Fractal and Lognormal Characteristics, Short-Term Maximum Concentrations, and Appropriate Time Discretization of Minesite-Drainage Chemistry. MDAG Internet Case Study #40, www.mdag.com/case_studies/cs40.html

- Morin, K.A. 2016. Fractal 1/f temporal trends in minesite drainage from waste-rock dumps. IN: 14th Experimental Chaos and Complexity Conference, May 16-19, Banff Center, Banff, Canada [M0081]

- Morin, K.A. 2016. Dynamic Geochemical Tension (DGT) in Multi-Mineral-Water Systems - Origin, Characterization, and Role in Fractal 1-over-f Slopes in Minesite-Drainage Chemistry. MDAG Internet Case Study #42, www.mdag.com/case_studies/cs42.html

- Morin, K.A.  2016. Spectral Analysis of Drainage from Highly Reactive Geologic Materials.  MDAG Book, www.mdag.com/spectral-book.html

- Morin, K.A. 2016. Effects of Water-Retention Structures on Temporal Power Spectra for Drainage Waters. MDAG Internet Case Study #43, www.mdag.com/case_studies/cs43.html

- Morin, K.A. 2016. Geochemical Dynamics and Complexities of 1-kg Humidity Cells: Potentials for Geochemical Signal Generation, Phase Transitions, Harmonic Oscillations, and Conceptual Stacking for Large-Scale Predictions. MDAG Internet Case Study #44, www.mdag.com/case_studies/cs44.html


REFERENCES

Bak, P. 1996. How Nature Works: the Science of Self-Organized Criticality. Springer Science+Media, LLC. ISBN 978-0-387-98738-5.

Morin, K.A. 2016. Fractal 1/f temporal trends in minesite drainage from waste-rock dumps. IN: 14th Experimental Chaos and Complexity Conference, May 16-19, Banff Center, Banff, Canada [M0081]

Morin, K.A. 2015a. Nonlinear Science of Minesite-Drainage Chemistry. 1 - Scaling and Buffering, MDAG Internet Case Study #41, www.mdag.com/case_studies/cs41.html

Morin, K.A. 2015b. Fractal and Lognormal Characteristics, Short-Term Maximum Concentrations, and Appropriate Time Discretization of Minesite-Drainage Chemistry. MDAG Internet Case Study #40, www.mdag.com/case_studies/cs40.html

Morin, K.A. 2014. Applicability of scaling factors to humidity-cell kinetic rates for larger-scale predictions. IN: 21st Annual BC/MEND Metal Leaching/Acid Rock Drainage Workshop, Challenges and Best Practices in Metal Leaching and Acid Rock Drainage December 3-4, 2014, Simon Fraser University Harbour Centre, Vancouver, British Columbia, Canada [M0077]

Morin, K.A. 2013. Scaling Factors of Humidity-Cell Kinetic Rates for Larger-Scale Predictions. MDAG Internet Case Study #38, www.mdag.com/case_studies/cs38.html

Morin, K.A., and N.M. Hutt. 2007. Scaling and Equilibrium Concentrations in Minesite-Drainage Chemistry. MDAG Internet Case Study #26, www.mdag.com/case_studies/cs26.html

Morin, K.A., and N.M. Hutt. 2001a. Environmental Geochemistry of Minesite Drainage: Practical Theory and Case Studies, Digital Edition. MDAG Publishing, Vancouver, Canada. ISBN 0-9682039-1-4

Morin, K.A., and N.M. Hutt. 2001b. The Gaia Theorem and minesite-drainage chemistry: implications and observations. IN: Proceedings of Securing the Future, International Conference on Mining and the Environment, Skellefteċ, Sweden, June 25-July 1, Volume 2, p. 586-593. The Swedish Mining Association. [M0056]

Morin, K.A., and N.M. Hutt. 1999. Prediction of Minesite-Drainage Chemistry Using the "Wheel" Approach. MDAG Internet Case Study #15, http://www.mdag.com/case_studies/MDAG%20Case%20Study%2015.pdf

Morin, K.A., and N.M. Hutt. 1998. Minesites Are Made of Distinct Components. MDAG Internet Case Study #5, http://www.mdag.com/case_studies/cs3-98.html

Morin, K.A., and N.M. Hutt. 1997. Environmental Geochemistry of Minesite Drainage: Practical Theory and Case Studies. MDAG Publishing, Vancouver, British Columbia. ISBN 0-9682039-0-6.



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