Professor Stephen Darby S.E.Darby@soton.ac.uk

1. 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 S.E.Darby@soton.ac.uk

2. Overview • 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 theLower Mekong River: Reconstructing high resolution (daily time step), multi-decadal, time series of river bank erosion • Hydro-climatological controls • ENSO influences river bank erosion?

3. Hydraulic (Fluvial) BankErosion Model • A widely accepted model of fluvial bank erosion for fine-grained (cohesive) materials already exists: •  = k (tSF – tc) e = erosion rate (m/s) tSF = skin drag component of applied fluid shear stress (Pa) tc = critical shear stress to initiate erosion (Pa) k = erodibility coefficient (m2s/kg)

4. 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: • The form drag is induced by macro-scale roughness elements characteristic of eroding banks • These bank topographic elements are modelled as Gaussian shaped ‘bumps’ Mekong River near Pakse, October 2006

5. Input Data Requirements • Kean and Smith’s model requires three main groups of data: • Parameters describing the form roughness (morphology) of the bank profile: H, l, 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 (Uout)

6. The Lower Mekong Basin

7. Form Roughness Estimation 2. Transect 1. Field survey l 4. Provides a statistical model of bank roughness in terms of H, l, Cd 3. Model bank roughness elements as Gaussian shapes H

8. Estimating ZoSF ZoSF = 0.1 s(Hfit - H)

9. Estimating Uout PAKSE: Q = 15130 m3/s d2U/dZ2 (m-1s-1) Depth-Averaged Flow Velocity, U (m) Depth-Averaged Flow Velocity, U (m) U = 0.0746 LN(Z) + 0.73 (r2 = 0.364) Distance from Right Bank, Z (m)

10. Estimation of the bank material erodibility parameters (k and tc) has, in the past, often simply been undertaken via model calibration. 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 challenging Slow test speeds Bank Material Erodibility

11. 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

12. CSM Data Analysis

13. Kean and Smith ModelResults for Pakse Mean Qpeak PAKSE Shear Stress, t (Pa) tc Flow Discharge, Q (m3/s)

14. Simulation Data: Pakse, Laos = k (tSF – tc)

15. Reconstructing Historical (1923-2007) Bank Erosion at Pakse • The long term average rate of fluvial erosion is 0.55 ± 0.15 m/yr • There is a very slight (~0.002 m/yr) but statistically significant (at 95%, Mann Kendal test) long term downwards trend in simulated erosion • There appear to be quasi-periodic oscillations about the long term trend

16. 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)

17. ENSO and Accumulated Runoff PAKSE: 1923-2007 FLOW DATA

18. CWT Analysis

19. XWT and Wavelet CoherenceAnalyses • XWT: Discriminates common high power (between ENSO and bank erosion series) in the ~4 to 8 yr band, especially during c.1980-2000. • WTC: Confirms coherence between the ENSO and bank erosion series in the ~5 yr band, but again only since about 1980 • 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).

20. Conclusions • 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

21. 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)

23. 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 • http://www.pol.ac.uk/home/research/waveletcoherence/