Effect of Flow-Induced Exchange in Hyporheic Zones on Longitudinal Transport of Solutes in Streams and Rivers (2002) Anders Worman, Aaron Packman, Hakan Johansson, and Karin Jonsson Daniel Kramer

(2) I NTRODUCTION T ERMS F OR D ISCUSSION  Solute (uptake, residence time, longitudinal transport, and spatial variation)  Moment Methods  Solute Break-through Curves  PDF – Probability Density Function  Log Normal Probability  Closed Form Solutions

(3) P URPOSE OF S TUDY  Evaluation of Hyporheic Exchange Using Solutes  To Better Understand Transport and Storage of Solutes in Stream Compare to a theoretical solute model (i.e. Transient Storage Model) Coupled with a physically based flow-induced uptake model (i.e. Pumping Exchange) Compare against real measurement data as obtained for a 30 km reach of stream (Sava Brook) in Uppland County, Sweden

(4) E VALUATION S TEPS  Review Previous Model Approaches (Diffusive and First Order Exchange)  Couple these solute mass flux assumptions with a Hyporheic exchange flux assumption  This combination allows for a solute break-through curve to be developed.  This can then give various residence times depending on mathematical approach for comparison “couple a physically based representation of flow- induced uptake in the Hyporheic zone with a model for the longitudinal in-stream solute transport.”

(5) T HEORY E XCHANGE M ODELS  First order mass transfer relationships Parameterization of all mechanisms governing mixing. VS.  Diffusive process Does not have a hydro mechanical mechanism – entirely non-mechancial

(6) T HEORY T RANSPORT OF S OLUTES  Controlled by: Exchange with neighboring Hyporheic zone/wetlands Sorption on to particle matter Biogeochemical reactions  Must understand these interactions for overall understanding of the transport and fate of nutrient, chemicals, contaminants, etc.

(7) T HEORY - T RANSIENT S TORAGE M ODEL (TSM)  Theory of Transport in Streams with Hyporheic Exchange include  Formulated as first order mass transfer and is defined by: Exchange coefficient Storage zone depth  Yields - Residence Time of Solute Flow Direction (GW versus River) Slope Gradient Diffusion Problems include unrealistic/over-simplified: cannot account for natural variability and must use multiple exchange rates.

(8) T HEORY B ENEFIT OF M ODELS  Provide a simplified model with a mathematical framework.

(9) T HEORY P ROBLEMS WITH M ODELS  Diffusion Model - Includes the order of magnitude differences between effective diffusive coefficients and molecular diffusion coefficients.  Both models are crude representations – oversimplified.  Require reach specific data to be obtained – costly and timely

(10) H YPORHEIC E XCHANGE – A DVECTION P UMPING

(11) H YPORHEIC E XCHANGE – S OLUTE M ASS F LUX & H YPORHEIC E XCHANGE F LUX Equation 1 = Solute Mass Flux Equation 2 = Hyporheic Exchange Flux Equation 1 + Equation 2 = allow for solute breakthrough curves to be Calc’d per input data of in-stream transport parameters and residence times THIS IS THE ADVECTION STORAGE PATH MODEL or ASP Model

(12) R ESIDENCE T IME PDF S  Pumping Exchange Models – Advection Storage Path Model (ASP)  Approximate of flat surface and sinusoidal pressure variation. Mean Depth Hyporheic Zone and Wavelength

(13) R ESIDENCE T IME PDF Log Normal Exponential Simulated ALL Are Close to the Same General Time Pump Model TSM Model Advection Pump Model

(14) R ESIDENCE T IME PDF Single Flow Path Model Different Models Can Be used to predict Different Transports

(15) C LOSED F ORM S OLUTIONS  Derivation revealed that T and F are controlling Factors (Eq 7 through 10)

(16) C LOSED F ORM S OLUTIONS

(17) C LOSED F ORM S OLUTIONS Temporal Moments can be expressed as co-efficients to T(Eq 12 through 15)

(18) SAVA BROOK EXPERIMENT  Tritium as main tracer  Injected for 5.3 hours (how not really discussed?)  Measured at 8 stations along 30 km stretch (no spatial indication?)  Discharge increased along stretch by factor of 4.85  Water depth and discharge – fairly constant  Took hydraulic conductivity measurements along river to provide plus minus 20% accuracy at a 95% confidence interval

(19) SAVA BROOK EXPERIMENT  85 cross sections geometries defined  Slug test at 3 and 7 cm along 4 to 5 verticals lines/locations  Performed weighted average on these tests to get permeability

(20) SAVA BROOK EXPERIMENT

(21) SAVA BROOK EXPERIMENT

(22) S AVA B ROOK E XPERIMENT

(23) SAVA BROOK EXPERIMENT Once water enters it is retained in the hyporheic zone for a relatively long time

(24) M ODEL V ERSUS D ATA P OINTS

(25) M ODEL V ERSUS D ATA P OINTS

(26) E QUATING TO STATE VARIABLES Review of land type per state variables of a stream showed land use may control Hyporheic exchange - (through differences in channel morphology etc.)

(27) C ONCLUSIONS  The ASP model which is transient combined with advection pumping predicted correctly when compared to Sava Brook  Transient systems best generally analyzed by exponential PDF’s  Advection flows tend to dominates Sava Brook and match well with Log-normal PDF’s so best for streams with pump exchange  Based on Froude number you could potentially analyze other streams - exchange rate increase and residence time decrease with decreasing Froude number.

(28) V ARIABLES  I am not sure if they ran monte-carlo simulations or just solved for the equations to find probability factors?  Log normal vs exponential – Why, is it because K is generally on a log scale and that is a major factor. Or because co-efficients of diffusion are exponential?

(29) Q UESTIONS & M ISSING D ATA ?  Missing area description  No real talk of geology, or location images and figures  Specific maps of reach also missing, no spatial image of where measurements were taken  Looking at graphs they need some legend work so I can identify what is what