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					Hydroclimatological variability and
channel migration rates on a large,
monsoonal, river: Insights from
physically-based bank erosion
simulations on the Lower Mekong River

Professor Stephen Darby
• Simulating hydraulic bank erosion using a physically-based
  excess shear stress model
    – Partitioning the shear stress into form and skin drag components
    – Parameterising the bank material erodibility
• Application to the Lower Mekong River: Reconstructing high
  resolution (daily time step), multi-decadal, time series of river bank
    – Hydro-climatological controls
    – ENSO influences river bank erosion?

Hydraulic (Fluvial) Bank
Erosion Model
• A widely accepted model of fluvial bank erosion for fine-
  grained (cohesive) materials already exists:

   –  = k (tSF – tc)

    = erosion rate (m/s)
   tSF = skin drag component of applied fluid shear stress
   tc = critical shear stress to initiate erosion (Pa)
   k = erodibility coefficient (m2s/kg)

Shear Stress Partitioning:
The role of bank form roughness
• Kean and Smith (2006, JGR)
  developed an analytical model to
  partition the form and skin drag
  components of boundary shear
  stress on river banks:
                   1   H 2
t   u*IBL   2
                   CD uref
                   2   
• The form drag is induced by
  macro-scale roughness elements     Mekong River near Pakse, October 2006
  characteristic of eroding banks

• These bank topographic
  elements are modelled as
  Gaussian shaped ‘bumps’
Input Data Requirements

• Kean and Smith’s model requires three main groups of
   – Parameters describing the form roughness
     (morphology) of the bank profile: H, , s
   – The skin roughness height of the bank surface (ZoSF)
   – An estimate of the flow velocity (at distance Z from the
     boundary) in the outer region unaffected by wakes

The Lower Mekong Basin

Form Roughness Estimation

                       2. Transect

  1. Field survey

     4. Provides a                              3. Model bank
   statistical model                         roughness elements
of bank roughness in                     H   as Gaussian shapes
        terms of
         H, , Cd

Estimating ZoSF

                  ZoSF = 0.1 s(Hfit - H)
Estimating Uout
                                       PAKSE: Q = 15130 m3/s
 Depth-Averaged Flow Velocity, U (m)

                                                                         d2U/dZ2 (m-1s-1)
                                               U = 0.0746 LN(Z) + 0.73
                                                     (r2 = 0.364)

                                       Distance from Right Bank, Z (m)                      9
Bank Material Erodibility

• Estimation of the bank material
  erodibility parameters (k and tc)
  has, in the past, often simply
  been undertaken via model

• Direct measurement using jet-
  testing devices (e.g. Hanson and
  Simon, 2001, Hyd. Processes) or
  portable flumes is possible, but
  there are limitations
    – Deployment is logistically
    – Slow test speeds

Cohesive Strength Meter
• (Tolhurst et al., 1999, Est.
  Coastal & Shelf Sci., 49, 281-
  294): used in studies of sediment
  stability on inter-tidal flats, but
  not previously on rivers

CSM Data Analysis

Site        Material         tc            n

Ang Nyay    Silt             0.83  0.57   6

Ban Hom     Silt             0.84  1.16   19

F. Bridge   Very fine sand   0.56  0.20   8

Pakse       Fine silt        0.88  0.47   9

Kean and Smith Model
Results for Pakse
                                PAKSE              Mean Qpeak
 Shear Stress, t (Pa)


                        Flow Discharge, Q (m3/s)
Simulation Data: Pakse, Laos
 = k (tSF – tc)

                              Reconstructing Historical
                              (1923-2007) Bank Erosion at Pakse
                                                           Pakse Fluvial Erosion 1923-2007                                                                        Pakse Fluvial Erosion 1923-2007 (Detrended)

                              0.90                                                                                                             1.00

                              0.80                                                                                                             0.90

Fluvial Erosion Rate (m/yr)


                                                                                                                         Detrended FE (m/yr)
                              0.30             y = -0.0016x + 3.5984
                                                    R2 = 0.0682                                                                                0.30

                              0.10                                                                                                             0.10

                              0.00                                                                                                             0.00
                                 1920   1930    1940         1950      1960          1970    1980   1990   2000   2010                            1920   1930   1940     1950      1960          1970   1980    1990   2000    2010
                                                                              Date                                                                                                        Date

1) The long term average rate of fluvial erosion is 0.55 ± 0.15 m/yr
2) There is a very slight (~0.002 m/yr) but statistically significant (at
                                     95%, Mann Kendal test) long term downwards trend in simulated erosion
3) There appear to be quasi-periodic oscillations about the long term trend

 Hydrological Controls on
 Bank Erosion
• The annual rate of bank erosion is a linear function of the
  accumulated runoff over a threshold, S(Q - Qc)

• Inter-annual variability in S(Q - Qc) is likely controlled by:
    – Peak flow discharge (monsoon intensity)
    – Duration over threshold (glacier and snow melt,
      monsoon duration)
    – Shape of annual hydrograph (shape of rising/falling
      limbs, multi-peaks over threshold, etc – timing of
      monsoon onset, incidence of typhoons)

ENSO and Accumulated Runoff

             PAKSE: 1923-2007 FLOW DATA

CWT Analysis

XWT and Wavelet Coherence

1) XWT: Discriminates common high power (between ENSO and bank
   erosion series) in the ~4 to 8 yr band, especially during c.1980-2000.
2) WTC: Confirms coherence between the ENSO and bank erosion series
   in the ~5 yr band, but again only since about 1980
3) The relative phase relationship is shown by arrows (in-phase pointing
   right, anti-phase pointing left, and FE leading ENSO by 90°
   (unrealistic!) pointing straight down).
•   New analytical modelling and field measurement techniques are employed to
    enhance the parameterisation of an excess shear stress model of bank erosion
    for fine-grained bank materials
•   The new model is the first hydraulic bank erosion model that does
    not include any calibration coefficients (Darby et al., 2010, JGR-ES)
•   The form drag imparted by bank topographic elements must be included if the
    applied fluid shear stress is to be estimated accurately
•   By linking Uout to Q, a parsimonious (requires only Q(t), tc and k), but
    physically-based, predictor of bank erosion is developed
•   We have thus far undertaken high-resolution, multi-decadal, simulations of
    bank erosion that are being analysed to explore the role of large-scale climate
    controls (e.g. ENSO) on hydrological variability and thus bank erosion
•   On the Mekong we plan to extend the work to look at future climate scenarios,
    as well as to segregate the respective roles of glacier melt, monsoon dynamics,
    and tropical cyclone strikes on bank erosion

Assumptions & Limitations

• Hydraulic erosion at the toe controls long term retreat of
  bank (top)

• Thresholds for onset and cessation of erosion are identical;
  temporal variations (e.g. due to weathering) in erodibility
  are ignored

• No hysteresis in the relationship between t and Q

• Bank roughness and Uout parameters remain time-
  invariant (even during erosion)

Wavelet Analysis
•   Wavelet analysis is employed to explore the possible links between ENSO (as a
    postulated factor controlling monsoon intensity and typhoon frequency) and
    simulated fluvial erosion at Pakse
•   Three types of analysis are undertaken:
     – Continuous wavelet transform (CWT). Expands a time series into
       time-frequency space
     – Cross-wavelet transform (XWT). Finds regions in the time-frequency
       space where two time series show a high common power
     – Wavelet coherence (WTC). Finds regions in the time-frequency space
       where two time series co-vary
•   Details of the methods used are available at


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