Stochastic Transport and
Emergent Scaling
in Earth-surface Processes
A working group co-sponsored by:
National Center for Earth-surface Dynamics (NCED),
University of Illinois, Hydrologic Synthesis Activities,
and The Desert Research Institute (DRI)
Tahoe Center for Environmental Research
Incline Village, NV
Nov 4-7 2007
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Conference Objectives Participants Presentations
Location and Accommodations Travel Reimbursement
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Conference Objectives
Many of the classical differential equations used to describe physical phenomena arise as the scaling limits of stochastic models. These models use probability theory to predict the outcome of physical processes that contain random elements. If the random components of a physical process are characterized by frequent extreme events and best fit by a power-law distribution, then classical stochastic theory does not apply. The inclusion of heavy-tailed distributions in a stochastic model requires a generalization of the limit theorems used to obtain long time governing distributions. Similarly, equations governing scaling limits of heavy-tailed stochastic processes are a generalization of classical PDEs they include fractional derivatives. These non-integer order derivatives acting on equation parameters, are useful tools for treating seemingly scale-dependent physical processes. For example, fractional advection-dispersion equations have been used to model super- and sub-diffusive contaminant transport in both aquifers and rivers. In these applications, the scale dependence of dispersivity was eliminated because fractional derivatives can scale the dispersion coefficient appropriately.
Power-laws and scaling are frequently observed in Earth surface morphology suggesting that heavy-tailed stochastic models and fractional PDEs may be powerful tools for describing processes and transport laws that take place on the Earth’s surface from the hillslope to the whole river network. We propose to create a working group to explore ideas, in research and applications, in the area of stochastic transport and emergent scaling in earth-surface processes. By convening experts in Earth-surface processes and mathematicians and scientists who have successfully applied heavy-tailed stochastic theory and fractional differential equations in other disciplines, we will identify:
- Geomorphic and hydrologic transport laws to which existing heavy-tailed stochastic theories and fractional calculus tools can be immediately applied
- Outstanding theory required for the development of novel scale-invariant models for Earth surface processes
Participant List
| Foufoula-Georgiou, Efi (co-organizer) Department of Civil Engineering University of Minnesota 2 - 3rd Ave SE Minneapolis, MN 55414 Tel: +1.612.626.0369 Email: efi@umn.edu |
Schumer, Rina (co-organizer) Division of Hydraulic Sciences Desert Research Institute 2215 Raggio Parkway Reno, NV 89512 Tel: +1.775.673.7414 Email: rina.schumer@dri.edu |
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| Ancey, Christophe Environmental Hydraulics Laboratory EPF Lausanne Station 18 CH - 1015 Lausanne Switzerland Tel: +41.21.693.32.87 Email: christophe.ancey@epfl.ch |
Baumer, Boris Department of Mathematics and Statistics University of Otago Science III Building 730 Cumberland St. Dunedin, New Zealand Tel: +03.479.7763 Email: bbaeumer@maths.otago.ac.nz |
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| Benson, David Department of Geology and Geological Engineering Colorado School of Mines Golden, CO 80401 Tel: +1.303.273.3806 Email: dbenson@mines.edu |
Bradley, Nate Department of Geological Sciences University of Colorado, Boulder Campus Box 399 Boulder, CO 80309 Email: nate.bradley@colorado.edu |
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| Chen, Dong Division of Hydrologic Sciences Desert Research Institute 755 E. Flamingo Rd. Las Vegas, NV 89119 Tel: +1.702.862.5541 Email: cong.chen@dri.edu |
Cushman, John Center for Applied Mathematics Purdue University 550 Stadium Mall Drive West Lafayette, IN 47907-2051 Tel: +1.765.494.8040 Email: jcushman@math.purdue.edu |
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| Ganti, Vamsi National Center for Earth-surface Dynamics University of Minnesota 2 - 3rd Ave SE Minneapolis, MN 55414 Tel: +1.612.624.4629 Email: ganti001@umn.edu |
Harman, Ciaran Department of Geography University of Illinois, Urbana/Champaign 607 South Mathews Avenue Urbana, IL 61801-3671 Tel: +1.217.721.8381 Email: charman2@uiuc.edu |
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| Jerolmack, Douglas Department of Earth and Environmental Science University of Pennsylvania 240 S. 33rd Street Hayden Hall Philadelphia, PA 19104-6316 Tel: +1.215.746.2823 Email: sediment@sas.upenn.edu |
Hill, Kimberly Department of Civil Engineering University of Minnesota 2 - 3rd Ave SE Minneapolis, MN 55414 Tel: +1.612-626-0311 Email: kmhill@umn.edu |
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| Kumar, Praveen Department of Civil and Environmental Engineering University of Illinois, Urbana/Champaign 205 N. Mathews Avenue Urbana, IL 61801 Tel: +1.217.333.4688 Email: kumar1@uiuc.edu |
Mantha, Satish Dept of Civil and Environmental Engineering University of Illinois, Urbana/Champaign 205 N. Mathews Avenue Urbana, IL 61801 Tel: +1.504.452.7560 Email: smantha2@uiuc.edu |
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| Meerschaert, Mark Department of Statistics and Probability Michigan State University A416 Wells Hall Michigan State University East Lansing, MI 48823 Tel: +1.517.432.7097 Email: mcubed@stt.msu.edu |
Packman, Aaron Department of Civil and Environmental Engineering Northwestern University A314 Technological Institute 2145 Sheridan Road Evanston, IL 60208-3109 Tel: +1.847.4912.9902 Email: a-packman@northwestern.edu |
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| Passalacqua, Paola National Center for Earth-surface Dynamics University of Minnesota 2 - 3rd Ave SE Minneapolis, MN 55414 Tel: +1.612.624.4675 Email: paolapassalacqua@gmail.com |
Reeves, Matt Division of Hydrologic Sciences Desert Research Institute 2215 Raggio Parkway Reno, NV 89512 Tel: +1.775.673.7605 Email: matt.reeves@dri.edu |
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| Rentschler, Martin Environmental Hydraulics Lab EPF Lausanne Station 18 CH - 1015 Lausanne Switzerland Tel: +41.21.693.23.84 Email: martin.rentschler@epfl.ch |
Schmeeckle, Mark Department of Geography Arizona State University P.O. Box 870104 Tempe, AZ 85287-0104 Tel: +1.480.965.7246 Email: schmeeckle@asu.edu |
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| Sivapalan, Siva Department of Geography Department of Civil and Environmental Engineering University of Illinois, Urbana/Champaign 607 South Mathews Avenue Urbana, IL 61801-3671 Tel: +1.217.333.2675 Email: sivapala@uiuc.edu |
Stark, Colin Lamont-Doherty Earth Observatory Columbia University 305A Oceanography 61 Route 9W - PO Box 1000 Palisades, NY 10964 Tel: +1.845.365.8742 Email: cstark@ldeo.columbia.edu |
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| Tucker, Greg Department of Geological Sciences University of Colorado, Boulder 2200 Colorado Ave. Boulder, CO 80309-0399 Tel: +1.303.492.6985 Email: gtucker@cires.colorado.edu |
Zhang, Yong Division of Hydrologic Sciences Desert Research Institute 775 E. Flamingo Rd. Las Vegas, NV 89119 Tel: +1.702.862.5314 Email: yong.zhang@dri.edu |
Presentations
Christophe Ancey: Intermittent motion and sediment transport -- experimental and theoretical insight (presentation, A(lisse).avi, B(nobed).avi, C(couches).avi, D(sotelem).avi)
Boris Baeumer: Scaling limits and subordination (presentation, corner1_1.avi, MATLAB FILES: randomwalk.m, randomwalk.fig)
David Benson: Fractional Calculus in (underneath) Our Backyard - An Abstracted Introductory Overview Summary Résumé (presentation)
John Cushman: A universal field equation for dispersion: turbulence, porous media, nano-films and microbial dynamics (presentation)
Efi Foufoula-Georgiou: 1) Stochastic transport on the Earth's surface: new physical-statistical formalisms? (presentation1), 2) Experimental evidence for intermittency and scaling in sediment transport (presentation2)
Kimberly Hill: Particle size dependence of bedload transport of gravel particles
Douglas Jerolmack: Thresholds and heavy tails in sediment-transporting systems (presentation)
Praveen Kumar: Emergence of binary tree networks and their inevitable self-similar topology (presentation, 06025Movie1.mpeg, 06025Movie3.mpeg)
Mark Meerschaert: 1) Scaling limits and governing equations (presentation 1), 2)Tail Estimation (presentation 2)
Aaron Packman: Linking surface topography, subsurface structure, and solute transport in rivers (presentation)
Matt Reeves: - Operator-stable densities and solute transport in fractured media (presentation)
Mark Schmeeckle: A Fokker-Planck model of bedload transport and morphodynamics (presentation, comb_link.avi, r1ss.avi, r3ss.avi, r5ss.avi, r7.avi, r7n.avi, rip1.avi, rip11.avi, rip12.avi, ript3.avi, setl_1feb2006.avi)
Rina Schumer: Extreme value models for processes with heavy-tailed interarrivals (presentation)
Siva Sivapalan and Ciaran Harman: The closure problem in watershed hydrology (presentation)
Colin Stark: A review of some outstanding problems in mountain geomorphology and their possible treatment with fractional calculus and similar tools (presentation)
Gregory Tucker and Nathan Bradley: Landscape evolution models and challenges in formulating earth-surface transport laws (presentation)
Location and Accommodations
Daily meetings will be held at the Tahoe Environmental Research Center (TERC) in Incline Village, Nevada.
The Hyatt Regency Lake Tahoe is located on the east shore of Lake Tahoe, a five-minute walk from the TERC. Hotel reservations under each invited participant’s name from Sunday November 4 through Wednesday November 7 will be paid in advance. A map and directions to the hotel can be found here. Please send us your arrival/departure information so we can arrange transportation from the Reno-Tahoe airport to the Hyatt on Sunday and back to the airport on Wednesday.
Travel Reimbursement
Travel expenses can be reimbursed up to $800 for international and $500 for domestic air travel. To obtain travel reimbursement, send receipts and a Participant Expense Worksheet to:
National Center for Earth-surface Dynamics
Attn: David Olsen
2 - 3rd Ave SE RM 379
Minneapolis, MN 55414