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NSF Workshop on Environmental Observatory Operations, October 22-23, 2007

Hydro-Kansas Project: Multi-scale Dynamics of Statistical Scaling in Floods & Riparian Evapotranspiration in River Networks. Vijay K. Gupta Lead PI. NSF Workshop on Environmental Observatory Operations, October 22-23, 2007.

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NSF Workshop on Environmental Observatory Operations, October 22-23, 2007

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  1. Hydro-Kansas Project: Multi-scale Dynamics of Statistical Scaling in Floods & Riparian Evapotranspiration in River Networks Vijay K. Gupta Lead PI NSF Workshop on Environmental Observatory Operations, October 22-23, 2007

  2. Hydro-Kansas Project: Names, Affiliations and Disciplines of Senior Investigators Senior Investigator (**) Institution Expertise Vijay K. Gupta Univ, of Colorado, Boulder Hydrology, nonlinear geophysics Hari Rajaram Univ, of Colorado, Boulder Fluid mech., subsurface hydrology Ben Balsley Univ, of Colorado, Boulder Boundary layer meteorology Robert Grossman North-West Research Assoc. Land-atmosphere interactions Bruce T. Milne Univ. of New Mexico Landscape ecology, scaling Witold Krajewski Univ. of Iowa Hydrometeorology, radar Anton Kruger Univ. of Iowa Instrumentation, IT William Eichinger Univ. of Iowa Remote sensing, evapotranspiration Brent Troutman USGS, Denver Applied mathematics, probability Jim Butler KSGS, Lawrence, Kansas Subsurface hydrology, riparian ET David Dawdy Hydrology Consultant, SF Stream flow gauging, hydrology (**) Many graduate students and recent post-docs not listed here played a critical role in HK research

  3. WEB Implementation CUAHSI, 2001 Hydro-Kansas Project: Historical Background Opportunities in Hydrologic Sciences (OHS), NRC, 1987-1991 NSF: HS Program Established, 1992 Water Earth Biota (WEB): Implementation Plan for OHS, 1998-2000 http://cires.colorado.edu/hydrology HK Project: An illustrative example of a Natural Laboratory, WEB

  4. HK Project: Four WEB Pathways • Scaling: Floods & Riparian Evapotranspiration (RET) • Coupling: Biophysical Processes governing Floods & RET • Diagnosing: Core data, Whitewater Basin, KS (Poster) • Modeling:Digital Watershed as a Diagnostic Tool (Poster) Illustrate Four WEB Pathways Through an Example HK Project is an Example of Transformative Science

  5. Digital Watershed: Hillslope-Link Decomposition of a Basin (Poster) CUENCAS: A 30 m resolution DEM retains the natural hillslope-link partioning of a terrain Hillslope Link

  6. Digital Watershed: Nonlinear Dynamical Equations Governing Flow in a River Basin (Poster) (i) Consider a basin partitioned into a collection of hillslope-link pairs, n=1,2,… (ii) Mass and momentum conservation produce a set of nonlinear, non-homogeneous dynamical eqs. governing flow rate, q(n,t), n=1,2,… (iii) Let R(n,t) be the flow rate from adjacent hillslopes into a link, n (iv) Let K(q(n,t)) be a nonlinear function of flow rate, q(n,t) Link-Based Mass conservation equation (Gupta & Waymire, SDSI hydrology, Cambridge, 1998) Mass Conservation for hillslope runoff generation (Duffy, WRR, 1996) Momentum conservation equation for a link (Regianni et al., PRSL-A, 2001)

  7. (HG variable) HG variables NDOF in a 1 km2basin = 10 (links) * 3 + 20 (hillslopes)* 4 = 110 Ex: 110 * (A=1,100 km2)=121,000 values of dynamic parameters in the Whitewater basin to solve dynamical equations of flow (Gupta, Chaos Solitons Fractals, 19(2), 2004) Digital Watershed: Parametric Complexity in Hillslope-Link scale Dynamics (Poster) Simplified set of dynamic parameters for specifying R(n,t) and K(q(n,t)) on a collection of hillslope-Link pairs (n=1,2,…) Spatial variability produces a large number of non-measurable values of 8 dynamical parameter (No. Deg. of Freedom (NDOF))

  8. 150 sq. km. Walnut Gulch Basin: 18 streamflow gauges (red) and 85 rainfall gauges (white) An Illustrative Example of Four WEB Pathways: Walnut Gulch Basin, AZ

  9. Diagnosing Scaling in Floods via Multi-scale Dynamics, Walnut Gulch Basin, AZ (i) Scaling (log-log linearity) between peak flows & areas (ii) Change of scaling exponents in events at (0.1-1 km2) (iii) Different values of scaling exponents in two events (iv) Fluctuations about log-log linearity Diagnosing = 0.53 & 0.63 on the r.h.s

  10. Illustration of Digital Watershed as a Diagnostic Framework to Test Three Sets of Assumptions Example 1: Cons. flow velocity, instant. Input, predicts scaling in floods (=0.55)(Mantilla, Gupta and Mesa, J. Hydro., 322, 2006) Horton Law for Mean floods Statistical Self-similarity for rescaled floods

  11. Illustration of Digital Watershed as a Diagnostic Framework to Test Three Sets of Assumptions Example 2: Constant friction, inst. Input, violates scaling in floods SSS for rescaled floods

  12. Illustration of Digital Watershed as a Diagnostic Framework to Test Three Sets of Assumptions Example 3: Spatially variable friction, , instantaneous input, predicts scaling in floods (=0.50) Statistical Self-Similarity for rescaled floods Horton Law for Mean floods

  13. Multi-scale Dynamics of Statistical Scaling in Floods: An Example of a Science Challenge • Link-hillslope scale dynamic complexity is formally similar to molecular dynamics with a large NDOF involving non-measurable dynamical parameters • NDOF increases linearly with the scale (area) of a basin (NDOF=110A) • Simplifying parametric assumptions are needed to solve the dynamical equations • Tests of these assumptions requires presence of macroscopic scaling relations • Macroscopic scaling relations are not built into the dynamical equations • The science goal is to understand and predict how observable statistical scaling in floods in channel networks arises from unobservable link-hillslope scale dynamics • Many topics in Nonlinear Geophysics encounter similar challenges

  14. Broad Impacts of HK Science • A new scientific framework to make risk assessments for floods under non-stationary climate and landforms (natural and anthropogenic) • The existing engineering approaches use historic data, which is inadequate to predict floods under non-stationary climate and landforms • Prediction in Ungauged Basins (PUB)

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