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Connecting Process and Form: New Results on Scaling and Implications for Modeling and Prediction in Ungauged Basins Efi Foufoula-Georgiou University of Minnesota Grenoble November, 2006

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HYDROLOGY AND EARTH-SURFACE DYNAMICS RESEARCH @ SAFL and NCED Efi Foufoula-Georgiou St. Anthony Falls Laboratory (SAFL) National Center for Earth-Surface Dynamics (NCED) Department of Civil Engineering University of Minnesota

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SAFL’s goal is to advance the knowledge of environmental hydrology and hydraulics, turbulence, earthscape evolution, and climate/ ecosystem dynamics via high quality experimental, theoretical and computational research. Transfer this knowledge to the engineering community and to the public through applied research and outreach activities St. Anthony Falls Laboratory University of Minnesota (1938-present)

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St. Anthony Falls Laboratory University of Minnesota (1938-present) 5000 m2 of flumes, basins, tanks and offices Main channel (84 x 2.7m, 300 cfs) Recirculating turbidity-current flume Boundary layer wind tunnel (16x1.5x2.5m) 3m deep aquarium-grade tank with suspended inner channel for subaqueous flow experiments Environmental and Sediment laboratories Jurassic Tank (XES - eXperimental EarthScape basin)

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Experimental EarthScapes in “Jurassic Tank” This surface remains near its initial level, while… …this surface subsides… …via these cells 13 x 6.5m; 432 subsidence cells

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Experimental EarthScapes in “Jurassic Tank” Stratigraphy, Morphodynamics, Continental Margins

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ENVIRONMENTAL AND GEOPHYSICAL FLUID DYNAMICS SAFL

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The St. Anthony Falls Laboratory is involved in a wide variety of APPLIED RESEARCH AND ENGINEERING projects commissioned by government agencies, private companies, and consultants. These projects span the areas of river modeling for environmental protection and restoration; water and wastewater treatment; water quality of lakes, rivers and reservoirs; hydropower plants and hydraulic structures; wind engineering; and various performance and calibration testing. WATER AND WASTEWATER TREATMENT AERATION TECHNIQUES HYDROPOWER ENGINEERING HYDRAULIC STRUCTURES SURFACE WATER QUALITY RIVER ENGINEERING WIND ENGINEERING CALIBRATION AND PERFORMANCE TESTING SAFL

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sedimentology ecology hydrology geomorphology sediment transport scaling National Center for Earth-surface Dynamics (NCED) A NSF Science and Technology Center Established at U of M in 2002 NCED's purpose is to catalyze the development of an integrated predictive science of the processes shaping the surface of the Earth, in order to transform management of ecosystems, resources, and land use

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GCMs predict a reduction of precipitation here. How will the system respond (sediment yield, hydrology, ecosystem, landsliding…)? Landscape and ecosystem response to extreme stress

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View downstream from Santa Teresa bridge (courtesy Matt Kondolf, UC Berkeley) Jan 1996 Sustainable solutions to stream restoration

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Jan 1996 July 1997 – After flood of Feb 1996 Could this have been prevented? View downstream from Santa Teresa bridge (courtesy Matt Kondolf, UC Berkeley) Sustainable solutions to stream restoration

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Can climatic variations be inferred from this deposit? Is there recoverable oil in this deposit? Can the history of the channel be used for landscape prediction? Exploration of natural resources

Participating Institutions : 

University of Minnesota (SAFL) University of California, Berkeley University of Colorado, Boulder Fond du Lac Tribal and Community College University of Illinois, Urbana/Champaign Johns Hopkins University Massachusetts Institute of Technology Princeton University Science Museum of Minnesota Participating Institutions

Research Focus of my group : 

Research Focus of my group Hydrology/Geomorphology with emphasis on quantifying the space-time organization and interactions of precipitation, landforms and streamflow over a range of scales For the purpose of: Subgrid-scale parameterizations of predictive models, including downscaling Upscaling of flux laws (water and sediment) in view of small-scale variability Statistical prediction of “extremes” (precipitation depth, floods, large scour in a channelized system, large migration of a channel in a braided river system, etc.) based on observations of more common events

Current Research : 

Current Research Precipitation (NASA, NSF) Multiscale characterization and downscaling methodologies Multisensor estimation NWP model verification and quantification of forecast prediction uncertainty via ensembles Hydro-geomorphology (NSF) Evolution of braided river systems Channel/floodplain dynamics and effect on hydrologic response Process signatures in high resolution topography Atmospheric boundary layer turbulence (NASA, NSF) Subgrid-scale parameterizations and LES closures Stable boundary layer

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Connecting Process and Form: New Results on Scaling and Implications for Modeling and Prediction in Ungauged Basins Efi Foufoula-Georgiou SAFL, NCED University of Minnesota Grenoble November, 2006

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How much of the physical/mechanistic behavior of the coupled hydrologic/geomorphologic system is reflected in the observed statistical patterns of landscapes and streamflows? Are statistical patterns distinct across physical boundaries and how can they be used in assisting modeling, prediction and observatory design across scales and across environments? Where/what to sample to get the most out of a limited number of observations? Overarching Questions

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MAIN MESSAGES Physical processes do leave important signatures on the statistics of landscapes and streamflows and thus provide a powerful means of inference [to guide modeling and observatory design, to further pose and test hypotheses, etc . . .] 2. High resolution topography offers new opportunities for connecting process and form at an ever increasing range of scales [hillslope to watershed scales, explicit extraction of channel heads, verification of mechanistic transport laws, spatially-distributed hydrologic modeling, etc…]

Examples to discuss: 

Examples to discuss The scaling break in floods reflects important fluvial regime transitions and a channel-floodplain exchange process that is scale & frequency dependent. [Implications for modeling and prediction] High-resolution DEMs offer new opportunities, e.g., objective and explicit identification of the hillslope-to-valley-to-channel transition. [Implications for modeling and subgrid-scale parameterizations] Bedload size distributions and mass flux along river networks are less controlled by the flow pathways and more by the sediment production at the hillslope. [Implications for monitoring, theories of scale-dependent channel formation] New ways of looking at landscapes, e.g., river corridor width functions, highlight the ability to depict important physical boundaries in valley forming processes from the presence of statistical boundaries. [Implications for spatially-distributed modeling]

Related Publications: 

Related Publications Dodov B., E. Foufoula-Georgiou, Fluvial processes and streamflow variability: Interplay in the scale-frequency continuum and implications for scaling, Water Resources Research, 41, W05005, doi:10.1029/2004WR003408, 2005 Theodoratos, N., I. Iorgulescu, E. Foufoula-Georgiou, A geomorphologic interpretation of the statistical scaling in floods, Water Resources Research, under review, 2006. Passalacqua P., F. Porté-Agel, E. Foufoula-Georgiou, C. Paola, Application of dynamic subgrid-scale concepts from large-eddy simulation to modeling landscape evolution, Water Resources Research, 42, W06D11, doi:10.1029/2006WR004879, 2006 Sklar L. S., W. E. Dietrich, E. Foufoula-Georgiou, B. Lashermes, D. Bellugi, Do gravel bed river size distributions record channel network structure?, Water Resources Research, 42, W06D18, doi:10.1029/2006WR005035, 2006 Lashermes, B., E. Foufoula-Georgiou, and W. Dietrich, Objective delineation of valleys in canyon systems: a methodology based on wavelets and high resolution DEMs, in preparation, 2006. Lashermes, B. and E. Foufoula-Georgiou, Area and width functions of river networks: new results on multifractal properties, Water Resources Research, under review, 2006 Gangodagamage C., E. Barnes, and E. Foufoula-Georgiou, Anomalous scaling in river corridor widths reflects localized nonlinearities in valley forming processes, under review, 2006.

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1. SCALING BREAK IN FLOODS Multiscaling theory of flood peaks, Gupta et al. [1994]: (reproduced from Smith, 1992) Q(A) =d G() Q(A) CV(A)

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99 stations for HG (100’s of measurements for different Q/ station) 72 stations for max annual flows (>15 yrs) 70 stations for daily flows (>10 yrs) 72 stations for hourly flows (>5 yrs) High resolution hydrography data for Osage and Neosho basins, KS Stratigraphic logs for 420 water wells 115 stations of suspended sediment (100’s measurements for different Q/station) Midwest Region

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Scaling of Maximum Annual Floods Scaling of Daily Discharges What controls the scaling break?

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(2) From maximum annual discharges 10 days/yr 1 day/yr 2 years From daily/hourly time-series

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The scaling break in floods is controlled by the channel/floodplain geometry and interactions

Implications for Flood Prediction: 

Implications for Flood Prediction Hydrologic transitions are imprinted in geomorphologic transitions High resolution DEMs offer potential to explicitly extract channel-floodplain morphometry which can: (a) guide hydrologic predictions over a range of scales, and (b) guide spatially-distributed modeling over large domains

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Implications for Suspended Sediment Loads

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or smooth local Ñh, Ñ2h by spatial averaging. Ref: Lashermes, Foufoula-Georgiou, Dietrich (2006) Computation of local slope and curvature Typically, smooth topography and then take Ñh, Ñ2h Propose a wavelet-based formalism (compute attributes at a range of scales): 2. Objective Extraction of Hillslope-to-Valley Transition from High Resolution DEMs (LIDAR)?

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a ~ 71.1m 35.5m 26.7m 17.8m 11.6m slope = -0.82

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MR1 Whole basin

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MR3 whole basin MR1 MR4 0.04 0.03 0.02 0.04

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MR3 whole basin MR1 MR4 0.04 0.03 0.02 0.04

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Ref: Sklar L. S., W. E. Dietrich, E. Foufoula-Georgiou, B. Lashermes, D. Bellugi, Do gravel bed river size distributions record channel network structure?, Water Resources Research, 42, W06D18, doi:10.1029/2006WR005035, 2006. 3. Bedload size distributions: Importance of hillslope sediment production Do gravel bed size distributions record channel network structure?

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Pdfs of entering sediment

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Pdfs of entering sediment & steady-state bedload sediment As variance of entering sediment distribution increases, bedload steady-state pdf approaches entering pdf

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Bedload mass flux equilibrates with supply over length scale of 1/alpha, and then it becomes independent of drainage area How do channel cross sections develop under flow which scales with area but bedload mass flux that is constant? The bedload steady-state grain size distribution differs little from the hillslope supply distribution in the case of poorly sorted hillslope sediments Large-scale variability in bed material is due primarily to spatial gradients in hillslope sediment production and transport characteristics Need theory and data to predict the grain size distribution supplied to channels by hillslopes Conclusions and Implications

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Ref: Gangodagomage, Bamer, Foufoula-Georgiou, et al. River Corridor Geometry: Can statistics reveal the underlying physics?

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Ref: Gangodagomage, Bamer, Foufoula-Georgiou, et al. River Corridor Geometry: Can statistics reveal the underlying physics? Do differences in mechanistic laws governing valley-forming processes leave their signature on the statistical properties of valley geometry? Are statistically-distinct regimes the result of physically-distinct valley-forming processes?

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River Corridor Width Functions

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Area = 351 km2 South Fork Eel River, CA

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River Corridor Width Function (D=5m)

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89 tributaries: (1 km2 – 150 km2) River Corridor Width Function: South Fork Eel River 6 km 14 km 20 km 28 km 35 km

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River Reach: 0-6 Km

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• Characterize a signal f(x) in terms of its local singularities Ex: h(x0) = 0.3 implies f(x) is very rough around x0. h(x0) = 0.7 implies a “smoother” function around xo. MULTIFRACTAL FORMALISM

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• Spectrum of singularities D(h) • D(h) can be estimated from the statistical moments of the fluctuations. Legendre Transform Multifractal Formalism h D(h)

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Multifractal Formalism • Spectrum of scaling exponents t(q) monofractal multifractal h h

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Implications of Multifractality Normalized moments depend on scale Statistical moments of fluctuations increase faster as scale decreases (at very small scales, pdfs have heavy tails) Chance of getting very high fluctuations locally, although sparsely. More than one degree of singularities is present. These singularities are spread throughout the signal intermittently

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CV of River Corridor Widths Suggests multifractality

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River Reach: 0-6 km

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Summary of Results Right-Left asymmetry

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Physical interpretation of statistical signatures? More localized transport mechanism More localized on R than L side? Smoother overall valleys? Presence of more terraces in R than L?

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How much of the physical/mechanistic behavior of the coupled hydrologic/geomorphologic system is reflected in the observed statistical patterns? Are statistical patterns distinct across physical boundaries and how can they be used in assisting modeling, prediction and observatory design across scales and across environments? Where/what to sample to get the most out of a limited number of observations? Summary of Overarching Questions

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