5. Sediment transport models

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5. Sediment transport models
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Settling velocity (vf) Stokes equation

• Assumption spherical particles
• Gravity force drag force
• Particle reaches a constant settling velocity
• This velocituy is dependent on fluid viscosity
  (?), density difference between the particle and
  water (?s-?) and particle diameter (d),
• ggravity constant 9,81 m/s2
• Velocity range From 0.07 m/d (clay, d1.2 ?m) to
  710 m/d (sand, d200?m), density2.5 gcm-3

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Settling speed in nature

• Particles are seldom spherical clay particles
  are like plates
• Aggregation of particles happens due to the
  electromagnetic forces ? cohesive soils (clays,
  mud)
• Organic compounds like humic substances have a
  very fragile structure ? changes even in water
  column
• ? velocity from Stokes equation has to be
  corrected with empirical relations
• Baba Komar, 1981 vreal0.761vf
• In sediment transport models vf is calculated
  using the median particle size from a surface
  sediment sample

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Erosion or resuspension from bottom

• Acting forces on a particle laying on the bottom
• difference between gravity on buoyancy
• drag force by the current
• lifting force due to the pressure differences as
  caused by water flowing between particles
• electromagnetic forces causing aggregation
• Term 1. ? density difference and particle
  (diameter)3
• Terms 2 and 3. ? shear force caused by current
  and particle (diameter)2
• Shieldss empirical curve for erosion ? in design
  of structures
• A simplified erosion curve by Hjulström (erosion
  vs. current velocity)
• In models we use most often the critical shear
  concept

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Hjulströms curve for erosion
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Critical shear

• Total shear (?) on the lake bottom
• shear by orbital movements of waves f(wind
  fetch over lake, lake mean depth, wind velocity
  and duration)Materials\Lake Säkylän Pyhäjärvi.pdf
• shear by currents
• ? gt critical shear (?cr), erosion happens with
  a rate ?a(excess shear)b
• ?cr, a and b are experimental values, which we
  calibrate during model application
• values for ?cr 0.0081 Nm-2, b1..3, a depends
  on sediment
• In this formulation there is no consolidation
  effects and bottom morphology included

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Calculation of sediment transport

• Simple screening toolshttp//el.erdc.usace.army.m
  il/dots/doer/tools.html
• Using numerical flow models for predicting the
  horizontal current field
• Suspended solids concentration is calculated with
  concentration equation
• Following terms in concentration equation
• advection with settling speed in vertical
  dimension
• turbulence
• mass flow from tributaries and to out flowing
  river
• settling and deposition to bottom
• erosion or resuspension from bottom

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Example from Mänttä
2DH flow model with BOD7 water quality
compartment Sediment was light organic
fibre Short term regulation at hydropower plant
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Example from Karhijärvi

• Three different models were tested 2DH, 2DV and
  3D model
• Models were tested in an runoff case in Oct 1992,
  when heavy rains caused erosion from watershed
  and a heavy suspended solids load to lake
• Data winds on the lake, water current
  observations, turbidity observations
• ? 3D model gave best results

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Mänttä Transport model resultSediment fibrous
material
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Sediment transport in Tanganyika

• Model simulation
• lake wide circulation model ?boundary values
  (current velocity) for high resolution model at
  river mouths
• flow model and suspended sediment transport
  models
• SS input was estimated from historical data
• real winds from atmospheric model HIRLAM (this
  model was used first time in tropics)

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3D FLOW MODEL
Calculated depth-averaged flow on 24.08.97
0400.
Calculated depth-averaged flow on 24.08.97 2000
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3D SEDIMENT TRANSPORT MODEL
(A), 1200 24.08.97
(B) 000 28.08.97
(C) after 22, 82 and 166 hours after the
simulation start respectively.
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6. Water quality models
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Concentration equation

• where,
• c concentration, qL amount of loading release
  , n length measure against release, u,v,w x-,
  y- ja z- advective velocities in x-, y- ja z-
  directions, Dx, Dy, Dz dispersion coefficients,
  R(T,c) biogeochemical changes in concentration

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Application of WQ-models

• We include
• Advection
• Dispersion
• Settling on the bottom
• Bio- chemical processes
• Decomposition, respiration, aeration, anaerobic
  release of P from the bottom
• Select the most important variables concerning
  the problem
• Oxygen, nutrients (like P,N), chlorophyll-a and
  some conservative substance (like Na)
• Limiting factors (light, nutrients, ) must be
  included. Check!
• Temperature corrections must be included. Check!

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Lake Lappajärvi WQ-model

• PROBE temperature model
• Materials\Effects of Climate Change....pdf
• PROBE-WQ model
• Materials\Lappajarvi_WQ.pdf

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Oxygen model
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Phytoplankton biomass and ToTP
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Interactions in EIA-SYKE-model
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Other WQ-model applications

• Several case studies Materials\Flow_and_WQ_Models
  _Sarkkula.pdf
• Lake Pyhäselkä
• Materials\Pyhaselka.pdf
• What happened to WQ after real reduction of
  loads?
• Materials\IAWQ99.pdf

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Summary of WQ-model calculations

• Check that you have data to describe WQ in
  variable discharge and loading conditions
• Select those properties (variables), which
  describe best the effects of loading and
  concentrate calibration on them
• Use most simple parameterization of the variables
  
• First coefficient values from literature and by
  experience
• Compare the calculated and observed values
• Select the conditions (weather, discharge and
  loading) during which the effects are described
  .and run the model!!