History of Nonlinear Geophysics

Review Article 
Open Access

A History of the Nonlinear Geophysics Section of the American Geophysical Union

First published: 09 July 2019


The Nonlinear Geophysics Technical Committee was formed in 1998 by a small group of AGU members to meet a growing interest in the analysis, modeling, and prediction of nonlinear behavior in geophysical processes. This paper provides a history as a technical committee evolved into a focus group, and into a section, including officers, awards, prizes, named lectures, standing committees, and books written or edited by members on the subject of nonlinear geophysical patterns and processes.

1 Inception of Nonlinear Geophysics at AGU

The Nonlinear Geophysics (NG) section began as the Technical Committee on NG, 1998–2002, evolved into a focus group in 2002, with elected officers beginning in 2008, and into a section in 2017. NG was formed by a small group of AGU members to meet a growing interest in the analysis, modeling, and prediction of nonlinear behavior in geophysical processes. Its members focus on quantitative nonlinear behavior through analysis of geophysical data and modeling using the mathematical tools and approaches of fractals, chaos theory, scaling, critical phenomenon, cellular automata, self‐organization, and the emergent behavior of complex systems.

In 1997 a group of AGU members met at the Fall Meeting to prepare a letter to formally request the creation of a Technical Committee on NG. Those present included Donald L. Turcotte, Cornell University; John Rundle, U.C. Boulder; Christopher C. Barton, USGS; and Bruce Malamud, Cornell University. The name NG was chosen by this group of AGU members, who had been conducting research in a broad range of disciplines. The founding members of the NG community used the mathematical tools of fractals, chaos theory, scaling, critical phenomenon, cellular automata, self‐organization, and the emergent behavior of complex systems to quantify and model spatial and temporal patterns in the solid earth, oceans, atmosphere, and space physics. Benoit Mandelbrot, an AGU member since 1968 and a fellow since 1986, was a strong supporter of the effort to found the Technical Committee.

John Rundle served as the chair of the Technical Committee and in 1998 wrote the following, setting out the potential role of NG within AGU:

Much of the present AGU structure and modes of operation are driven by disciplinary objectives, even though it is increasingly recognized that the Earth System should be studied with interdisciplinary and transdisciplinary approaches. Moreover, funding agencies are increasingly promoting modes of science that emphasize information technology, numerical simulations to develop models for understanding incomplete observations, and the understanding of the complex, nonlinear systems that surround us. Earth System science must make the transition from a descriptive activity to a fundamentally predictive science. Therefore, AGU needs to begin a process of evolution towards a structure whose organization, goals, and objectives reflect these realities.

At the time that the NG Technical Committee was created, scientific organizations were moving toward management structures that de‐emphasized disciplinary foci and emphasized systems approaches. Within AGU, this resulted in the initiation of joint activities among sections and the initiation of focus groups to promote the transdisciplinary and interdisciplinary character of geophysics. NG was and is a part of this shift. A list of the technical committee membership in 1998 is given in Table 1.

Table 1. List of Nonlinear Geophysics Technical Committee Membership in 1998
John Rundle, Chair
Robert Axtell
Christopher Barton
Charles Bufe
Antoni Correig
John Cushman
Anthony Davis
Vijay Gupta
Klaus Holliger
Louise Kellogg
Susan Kieffer
Peter Mora
Tom Russell
Riccardo Rigon
Garrison Sposito
Donald Turcotte
John Wettlaufer

2 Emergence of Chaos Theory and Fractals

The founding of the NG Technical Committee was preceded by three decades of a growing body of research in the areas of chaos theory and fractals, by research papers published in AGU and other geoscience journals, by AGU meeting sessions and abstracts, and by international meetings. The first fractals session at an AGU meeting was a Union session on Fractals in 1982, cochaired by Leon Knopoff and Benoit Mandelbrot, followed by a Union session on Fractals in Geophysics in 1987, cochaired by Christopher Scholz and Benoit Mandelbrot and by sporadic sessions on chaos and fractals in 1988. In 1991 the European Geophysical Society created an Interdisciplinary working group on Nonlinear Processes in Geophysics (NPG), which had participation by AGU members and which became a Division of the European Geophysical Society, then of the European Geosciences, Union after 2003.

There were many precursors outside of AGU to the founding of the NG Technical Committee. Most of the founding members and early members of NG‐AGU had visited or had extended stays at the Santa Fe Institute, an independent, nonprofit theoretical research institute founded in 1984, located in Santa Fe, NM and dedicated to the multidisciplinary study of the principles of complex adaptive systems, including physical, computational, biological, and social systems. All of the founding members and early members had been participants in the Fractals Gordon Conferences where they met one another and later coalesced into the group that founded NG at AGU. The Gordon Conferences were highly interdisciplinary and enlivened and enriched by the presence of Benoit Mandelbrot, who took a personal interest in the application of fractals to a wide range of scientific disciplines and was himself highly interdisciplinary and transdisciplinary. A listing of the Fractals Gordon Conferences is given in Table 2. Other significant early conferences are listed in Table 3.

Table 2. List of the Year and Location of all the Fractals Gordon Conferences
1985 Hawthorne College in Antrim, NH
1986 Colby‐Sawyer College, New London, NH
1988 Tilton School, Tilton, NH
1990 Plymouth State College, Plymouth, NH
1992 Plymouth State College, Plymouth, NH
1994 San Miniato, Italy
1996 New England College, Henniker, NH
1998 Renaissance Tuscany II Ciocco, Lucia (Barga), Italy
Table 3. A List of Other Significant Early Conferences Attended by the Founders and Early Members of NG
Scaling, Fractals and Nonlinear Variability in Geophysics, Nonlinear Variability in Geophysics Conference, McGill U., Montreal (August 1986)
Scaling, Fractals and Nonlinear Variability in Geophysics, Nonlinear Variability in Geophysics Conference, Ecole Polytechnique, Paris (July 1988)
Scaling, Fractals and Nonlinear Variability in Geophysics, Nonlinear Variability in Geophysics Conference, Cargese, France (August 1993)
International conference on Fractals in the Natural Sciences, Budapest (August 1993)
Santa Fe Institute workshop on Complex Systems in the Earth Sciences: Predictability, Mitigation, and Reduction of Natural Hazards (January 1994)
International Symposium on Fractal Geometry and Self‐Similar Phenomena, Curaçao (February 1995)
International Conference on Mathematical Geophysics ‐ Complex Systems in the Earth Sciences, Santa Fe Institute (1996)
Scaling, Fractals and Nonlinear Variability in Geophysics and Astrophysics (NVAGA4) Conference, Roscoff, France (August 1998)
Modeling Complex Systems: From Fractal Measurements to Modeling, Reno, NV (November 2002)
European Turbulence Conferences (1985‐present)
Large Scale Structures in Nonlinear Physics, Villefranche‐sur‐Mer (1991)
Short Course on Multifractals in Geophysics at the AGU Spring meeting in Montreal given by Shaun Lovejoy and Daniel Schertzer (1992)
Advances in Turbulence Research, Beer‐Sheva (1993)
NPG, Villefranche‐sur‐Mer (1994)
Small–scale structures in fluids and MHD, Nice (1995)
NSF director Rita Colwell delivered an AGU‐wide lecture at the Fall Meeting, entitled: “Complexity and Connectivity: A New Cartography for Science and Engineering.” Colwell had sounded the theme of Complexity at NSF, and her talk explored connections to the geophysical sciences (1999)
The U.S. National Academy of Sciences Arthur M. Sackler Colloquium on “Self‐organized complexity in the physical, biological, and social sciences” was convened at the NAS Beckman Center, Irvine, CA. by Donald Turcotte, John Rundle, and Hans Frauenfelder (2001)
An Aegean Conference on “20 Years of Nonlinear Dynamics in Geosciences,” in Rhodes Greece was convened by J.B. Elsner, and A.A. Tsonis (2006)
Workshop on Geocomplexity in conjunction with the AGU spring meeting in Toronto, Canada (2009)
An AGU Chapman Conference on “Complexity and Extreme Events in Geosciences” in Hydrabad, India, convened by A. Surjalal Sharma, Vijay P. Dimri, and Armin Bunde (2010)
An Aegean Conference on “30 Years of Nonlinear Dynamics in Geosciences” in Rhodes Greece, was convened by A.A. Tsonis (2016)

3 First Year of AGU NG

In 1998 the NG Technical Committee issued its first report, authored by John Rundle, the committee chair. The report included a mission statement:

The NG Committee has the responsibility to foster a focus within the AGU on the general area of nonlinear Earth Systems, including the areas of mathematical and theoretical geophysics, complex adaptive systems, and nonlinear processes in the geophysical sciences. The committee is charged with building strong transdisciplinary interactions, as well as educating AGU members about the nature and importance of problems and issues including fractals, multifractals, temporal, spatial, and magnitude power scaling, chaos, nonlinear waves, solitons, turbulence, earthquake and other threshold system dynamics, critical phenomena and nucleation, and space‐time correlations in a wide variety of data.

The committee is quite new, and we are still in the organizational stages. However, to date we have had 3 formal meetings. The first was held during April, 1998 in Nice, France, in association with the EGS meeting there. The second was during the Spring 1998 AGU meeting in Boston. The third was during the Fall 1998 AGU meeting in San Francisco. The next meeting will be held at the Birmingham IUGG meeting in July, 1999, if possible, then there will be a meeting at the Fall 1999 AGU meeting. End of minutes, taken and compiled by Seth Veitzer.

4 Journal

Nonlinear Processes in Geophysics was founded in 1994 by EGS and soon after became a joint journal of AGU and EGS, and successively an open‐access journal, then an open access discussion journal. With the externalization of the AGU press, it became an AGU partner journal. It is an international, interdisciplinary journal for the publication of original research furthering knowledge on nonlinear processes in all branches of Earth, planetary, and solar system sciences that apply nonlinear analysis methods to both models and data. NG members have been active as members of the editorial board, as authors, and as referees. The editors are selected by its Executive Board, which itself is nominated by the EGU Publications Committee.


NG is a member of the Editorial Advisory Board at EOS, Transactions, American Geophysical Union, a weekly magazine of Earth science with peer‐reviewed articles on current research, member forums, and employment advertisements. The NG member of the Editorial Advisory Board at EOS is appointed to a 2‐year term by the president of NG.

6 Lectureship, Prizes, and Awards

6.1 Edward N. Lorenz Lecture

The Edward N. Lorenz lecture honors the life and work of the renowned MIT mathematician, meteorologist, father of Chaos Theory, and a member of the U.S. National Academy of Science, and who was the first to be awarded the Roger Revelle Medal by the American Geophysical Union in 1991 for his outstanding contributions in atmospheric sciences and his pioneering work in NG. As well as can be determined, Lorenz was never a member or a fellow of AGU. This lecture is presented annually at the AGU Fall Meeting. The Lorenz Lecture is webcast and made available as an archived presentation on the AGU website. The Lorenz lecturer is selected by a committee of NG members in recognition of original contributions to the field of NG. The lectureship includes Lecture certificate, announcement in Eos, invitation to present the Lorenz Lecture at the AGU Fall Meeting during the lecture presentation year, and recognition at the AGU Fall Meeting during the lecture presentation year. The deadline for nominations is 15 April. The chair and members of the Lorenz Lecture selection committee are appointed to a 2‐year term by the president of NG and represent the broad range of disciplines in NG and based on their knowledge of and contributions to research in the subject area with consideration for gender and ethnic balance. The Lorenz lecturers and their titles for 2001–2018 are listed in Table 4.

Table 4. List of Lorenz Lecturers and Their Lecture Titles
2001 Benoit B. Mandelbrot Fractals as a Measure of Roughness in Earth Sciences
2002 Donald L. Turcotte Self‐Organized Complexity in Geophysics
2003 Rafael Bras Wonders of Planet Earth: Complexity and Order in Earth Systems
2004 John Rundle Process, Pattern, Prediction: Understanding Complexity in Driven Earth Systems
2005 Michael Ghil The Earth as a complex system, and a simple way of looking at it
2006 Bach L. Hua Nonlinear Dynamics of Zonal Jets in Planetary Atmospheres and Oceans
2007 Vijay Prasad Dimri Role of Fractals in Solid Earth Geophysics
2008 Daniel Schertzer Predictability and Uncertainties in Geophysics: from the Butterfly Effect to Ensemble Predictions, Multifractal Predictability and the Anthropocene
2009 A. Surjalal Sharma Complexity of Earth's Magnetosphere: Coherence in a Multiscale Open System
2010 Didier Sornette Dragon‐Kings, Black‐Swans and Prediction
2011 Alvaro Corral Criticality and Self‐Organization in Atmospheric Processes
2012 Eugenia Kalnay Fighting Chaos: Applications of Breeding
2013 Daniel Lathrop Linear and nonlinear dynamics of liquid planetary cores
2014 Demetris Koutsoyiannis Random musings on stochastics
2015 Shaun Lovejoy Why the warming cant be natural: the nonlinear geophysics of climate closure
2016 Vladimir Zakharov Analytic theory of wind‐driven seas
2017 William Klein Ergodicity and Phase Transitions and Their Implications for Earthquake Forecasting
2018 Venkat Krishnamurthy Predictability Beyond Weather

6.2 Donald L. Turcotte Award

The award is named in honor of Donald L. Turcotte, a professor at Cornell University for 50 years and later a professor at U.C. Davis. His research interest turned to Fractals and Chaos in the late 1980s. He is the author of many papers and a book on Fractals Applied in the Geosciences, a founding member of NG, and a member of the National Academy of Sciences. The award is given annually to one honoree in recognition of outstanding PhD dissertation research that contributes directly to NG. The awardee delivers an invited talk on his/her dissertation topic at the AGU Fall Meeting. Eligible candidates have completed the degree requirements for a PhD (or highest equivalent terminal degree) up to 24 months prior to the nomination deadline, 15 April. The primary criteria for evaluation is the impact or potential impact of the research on the field of NG. The award includes $200 monetary prize, an award certificate, an announcement in Eos, an invitation to present a talk on the dissertation topic at the AGU Fall Meeting during the award presentation year, and recognition at the AGU Fall Meeting during the award presentation. The chair of the Turcotte Award selection committee is the immediate past president of NG who serves a 2‐year term and who appoints committee members representing the broad range of disciplines in NG and their knowledge of and contributions to research in the subject area with consideration for gender and ethnic balance. The Turcotte awardees and their institutions are listed in Table 5.

Table 5. List of Donald L. Turcotte Awardees
2008 Irina Rypina, Nizhny Novgorod State University, Russia
2009 Jerome A. Neufeld, Yale University, USA
2010 Sabine Lennartz, Justus Liebig University,Germany
2011 Ian Grooms, University of Colorado at Boulder, USA.
2012 Asim Biswas, U Saskatchewan, Canada
2013 Jonathan Donges, Humboldt University, Germany
2014 Woosok Moon, Yale University, USA
2015 Behzad Ghanbarian‐Alavijeh, Wright State University, USA
2015 Jezabel Curbelo, Laboratoire de Géologie de Lyon, France
2016 Yavor Kamer, ETH Zurich, Switzerland
2017 Prachanda Subedi, University of Delaware, USA
2018 Meredith Plumley, University of Colorado, USA

6.3 Space Weather and Nonlinear Waves and Processes Prize

The Space Weather and Nonlinear Waves and Processes Prize was created in 2011 and is given to one honoree, likely in the middle to advanced career range, in recognition of cutting‐edge work in the fields of space weather and nonlinear waves and processes. This prize is jointly presented by the Space Physics and Aeronomy section and the NG section with the nomination cycle alternating between the two focus areas: space weather in odd years and nonlinear waves and processes in even years. The award includes a $10,000.00 monetary prize, an award plaque, an announcement in Eos, recognition at the AGU Fall Meeting, and a complimentary ticket to the hosting section's ticketed event at the AGU Fall Meeting. Funding of the prize is made possible by a contribution from AGU members and from Bruce Tsurutani and Olga Verkhoglyadova, scientists at the National Aeronautics and Space Administration Jet Propulsion Laboratory California Institute of Technology. Initially, the prize was awarded every other year. Beginning in 2020 and in even years thereafter, NG will participate in award selection for research involving nonlinear waves and processes. The selection committee is composed of eight members, with Bruce Tsurutani being a member. In odd years, the committee is chosen and chaired by the Space Physics section. In even years, four members of the committee are chosen by Space Physics and four, including the chair, are appointed by the President of NG. Committee members are selected on the basis of their knowledge of and contributions to research in the subject area with consideration for gender and ethnic balance. The Space Weather and Nonlinear Waves and Processes Prize recipients are listed in Table 6.

Table 6. List of Space Weather and Nonlinear Waves and Processes Prize Awardees
2013 Tamas I. Gombosi, University of Michigan, USA (Space Weather)
2015 Gurbax S. Lakhina, IIG, Navi Mumbai, India (Space Weather)
2017 Walter Gonzalez INPE, Brazil, (Space Weather)
2018 Roberto Bruno, IAPS‐INAF, Rome, Italy (Space Physics)

7 Officers

7.1 Officers, Elected and Appointed, and Length of Term

The officers of NG are as follows: President (2‐year term, elected), President‐Elect (2‐year term followed by a 2‐year term as President), Secretary (2‐year term, elected), and Meeting Program Committee Representative (2‐year term appointed by the President). Past officers are listed in Table 7.

Table 7. Listing of Past Officers of Nonlinear Geophysics
Nonlinear Geophysics Chairs Vice‐Chair Secretary Meeting Program Committee Representative
1998‐2002 John Rundle none Seth Veitzer Bruce Malamud
2002‐2004 Christopher Barton A. Surjalal Sharma Bruce Malamud Sarah Tebbens
2004‐2008 A. Surjalal Sharma Shaun Lovejoy Alin Carsteanu
2008‐2012 Shaun Lovejoy A. Brad Murray James Wanliss J. Johnson & Alin Carsteanu
2012‐2014 Daniel Schertzer Andrea Donnellan Alin Carsteanu Steven Fletcher
2014‐2016 Andrea Donnellan Annick Pouquet Joern Davidsen Steven Fletcher
2016‐2018 Annick Pouquet Sarah Tebbens Joern Davidsen Steven Fletcher
2019‐2021 Sarah Tebbens Juan Restrepo Raffaele Marino Steven Fletcher
  • First Elected Officers, 2‐year terms, began in 2012, then Chair and Vice‐Chair became President and President‐elect in 2016.

7.2 Executive Committee

The Executive Committee is composed of the current elected and appointed officers and past presidents/chairs of NG. The committee advises the current elected and appointed officers concerning all matters of the section. Members can take on tasks on behalf of the president.

8 NG Nominations Committee for AGU Fellows

The Nominations Committee accepts nominations from members and canvases for qualified candidates for AGU Fellow and other Union Honors. The chair and two NG Nominations Committee members are appointed for a term of 2 years by the president of NG. At present, all nominations are passed forward to a Joint Nominations Committee composed of one member from each of the sections as grouped by AGU. The Joint Nominations Committee ranks the nominations from the member sections based on criteria set out by AGU. The Joint Nominations Committee may choose to eliminate a nomination that clearly does not meet the AGU Fellow criteria. The ranked nominations are forwarded to the Union Fellows Committee for selection of Fellows.

9 NG Sessions, Conferences, Short Courses, and Workshops

The first session on Fractals was a union session in 1982, cochaired by Leon Knopoff and Benoit Mandelbrot.

The first session after the formation of the NG Technical Committee was a union session in 1998 titled Frontiers of Nonlinear Geophysics, cochaired by John Rundle and Raymond Jeanloz and cosponsored by the Technical Committee on NG and the Technical Committee on Mineral Physics. The session description was as follows:

The past two decades have witnessed the development of important, general, and effective new techniques for the analysis and understanding of nonlinear, chaotic, and complex dynamical systems. Rather than view these systems as merely the sum of the constituent parts, it is now known that a number of their most important features are emergent properties of the entire system, and cannot be understood from a purely reductionist viewpoint. Many of these developments grew out of, or were associated with, the analysis of geophysical systems: The Lorenz equations, fractals, and pattern formation studies. Subjects will include fractals, multifractals, chaos, nonlinear waves including shock waves, solitons, turbulence, cascades and vortex dynamics, scaling critical phenomena and nucleation, time series analysis and prediction, numerical simulations of nonlinear phenomena, deterministic and stochastic modeling, and correlations of a wide variety of data. Examples of fields of interest include weather and climate, earthquakes, landslides, phase transitions in mantle minerals, landform dynamics, nonlinear data inversion techniques, the analysis of river basin networks, and hazard assessment, forecasting, and predictability.

10 NG Focus Group and Section

From 2002 to 2018 NG was a Focus Group within AGU. Focus groups were interdisciplinary, cutting across the sections, which are disciplinary. NG is very much interdisciplinary, so that at the Fall Meeting there are presentations in virtually all of the sections using the data analysis and modeling methods associated with NG. Members of NG have been instrumental in the founding of new sections within AGU, including the Earth and Planetary Surface Processes section, the Natural Hazards section, and the Earth and Space Sciences Informatics section. NG members continue to be active, providing many sessions and abstracts for the AGU Fall Meetings. In 2018, NG has 171 members with primary affiliation, of which 34 are students and 2,217 are secondary members, with 17% female membership.

11 Books on NG Topics Authored or Edited by NG AGU Members

A list of books authored or edited by NG AGU members is given in Table 8.

Table 8. List of Nonlinear Geophysics Books Authored or Edited by NG‐AGU Members
Barton, C. C., & LaPointe, P. R. (Eds.). (1995). Fractals in the Earth Sciences (p. 284). Springer‐Verlag.
Barton, C. C., & LaPointe, P. R. (Eds.). (1995). Fractals in Petroleum Geology and Earth Processes (p. 317). Springer‐Verlag.
Bernardara, P., Lang, M., Sauquet, E., Schertzer, D., & Tchiguirinskaia, I. (2007). Multifractal Analysis in Hydrology. Application to Time Series, (QUAE Editions, p. 57).
Bunde, A., & Havlin, S. (Eds.). (1994). Fractals in Science (p. 300). Berlin Heidelberg: Springer‐Verlag.
Bunde, A., & Havlin, S. (Eds.). (1996). Fractals and Disordered Systems (p. 408). Berlin Heidelberg: Springer‐Verlag.
Bunde, A., Caro, J., Kärger, J., & Vogl, G. (2018). Diffusive Spreading in Nature, Technology and Society (p. 418). Springer International Publishing.
Elsner, J. B. & Tsonis, A. A. (2007). Nonlinear Dynamics in Geosciences (p. 640). Springer.
Dimri, V. P. (2015). Fractal Solutions for Understanding Complex Systems in Earth Sciences (p. 159). Springer.
Lorenz, E. N. (1993). The Essence of Chaos (p. 227). University of Washington Press.
Lovejoy, S., & Schertzer, D. (2013). The Weather and Climate: Emergent Laws and Multifractal Cascades (p. 475). Cambridge University Press.
Lovejoy, S. (2019). Weather, Macroweather and Climate: Our Random yet Predictable Atmosphere, Oxford University Press (to appear in April 2019, ISBN 978– 0– 19– 086421– 7)
Mandelbrot, B. B. (1977). Title: Fractals: Form, Chance, and Dimension (p. 365). W. H. Freeman.
Mandelbrot, B. B. (2004). Fractals and Chaos: The Mandelbrot Set and Beyond (p. 299). Springer‐Verlag..
Mandelbrot, B. B. (1983) The Fractal Geometry of Nature (p. 261). Freeman.
Meneguzzi, M., Pouquet, A., & Sulem, P. L.(Eds.). (1989). International Workshop on MHD flows (p. 288). Cargèse: North–Holland International.
Meneguzzi, M., Pouquet, A., & Sulem, P. L. (Eds.). (1995), Small–scale structures in fluids and MHD, Lecture Notes in Physics 462, International Workshop (p. 415). Nice: Springer–Verlag.
Rundle, J. B., Turcotte, D. L., & Klein, W. (Eds.). (2013). Geocomplexity and the Physics of Earthquakes. Book Series: Geophysical Monograph Series. (Vol. 120, p. 284). American Geophysical Union.
Schertzer, D., & Lovejoy, S. (Eds.). (1991). Nonlinear Variability, Scaling and Fractals (p. 318). Springer.
Scholz, C. H., & Mandelbrot, B. B. (1989). Fractals in Geophysics (p. 314). Birkhäuser.
Sharma, A. S., Bunde, A., Baker, D. N. & Dimri, V. P. (Eds.). (2012). Extreme Events and Natural Hazards: The Complexity Perspective, Geophysics Monograph Series. (Vol. 196, p. 380). American Geophysical Union.
Tsonis, A. A. (Ed.). (2018). Advances in Nonlinear Geosciences (p. 707). Springer.
Turcotte, D. L. (1992, 1997). Fractals and Chaos in Geology and Geophysics (p. 385). Cambridge University Press.


The authors thank the past NG officers for their input to this paper.