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) INTRODUCTIONTERMS FOR
DISCUSSION
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) PURPOSE OF STUDY
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) EVALUATION STEPS
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) THEORYEXCHANGE MODELS
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) THEORYTRANSPORT OF
SOLUTES
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) THEORY -TRANSIENT STORAGE
MODEL (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) THEORYBENEFIT OF MODELS
Provide a simplified model with a mathematical framework.
(9) THEORYPROBLEMS WITH
MODELS
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) HYPORHEIC EXCHANGE –
ADVECTION PUMPING
(11) HYPORHEIC EXCHANGE – SOLUTE MASS FLUX & HYPORHEIC
EXCHANGE FLUX
Equation 1 = Solute Mass Flux
Equation 2 = Hyporheic Exchange Flux
Equation 1 + Equation 2 = allow for solute breakthrough curves to beCalc’d per input data of in-stream transport parameters and residence times
THIS IS THE ADVECTION STORAGE PATH MODEL or ASP Model
(12) RESIDENCE TIME PDFS
Pumping Exchange Models – Advection Storage Path Model (ASP)
Approximate of flat surface and sinusoidal pressure variation.
Mean Depth Hyporheic Zone and Wavelength
(13) RESIDENCE TIME PDF
Log Normal
Exponential
Simulated
ALL Are Close to the Same General Time
Pump Model
TSM Model
Advection Pump Model
(14) RESIDENCE TIME PDF
Single Flow Path Model
Different ModelsCan Be used to predict Different Transports
(15) CLOSED FORM SOLUTIONS
Derivation revealed that T and F are controlling Factors (Eq 7 through 10)
(16) CLOSED FORM SOLUTIONS
(17) CLOSED FORM SOLUTIONS
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) SAVA BROOK EXPERIMENT
(23) SAVA BROOK EXPERIMENT
Once water enters it is retained in the hyporheic zone for a relatively long time
(24) MODEL VERSUS DATA POINTS
(25) MODEL VERSUS DATA POINTS
(26) EQUATING 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) CONCLUSIONS
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) VARIABLES
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) QUESTIONS & MISSING DATA?
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