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