1D SEDIMENT TRANSPORT MORPHODYNAMICS with applications to RIVERS AND TURBIDITY CURRENTS © Gary Parker November, CHAPTER 31: EROSIONAL NARROWING AND WIDENING OF A CHANNEL AFTER DAM REMOVAL This chapter was written by Gary Parker, Alessandro Cantelli and Miguel Wong View of a sediment control dam on the Amahata River, Japan. Image courtesy H. Ikeda.

1D SEDIMENT TRANSPORT MORPHODYNAMICS with applications to RIVERS AND TURBIDITY CURRENTS © Gary Parker November, CONSIDER THE CASE OF THE SUDDEN REMOVAL, BY DESIGN OR ACCIDENT, OF A DAM FILLED WITH SEDIMENT Before removal

1D SEDIMENT TRANSPORT MORPHODYNAMICS with applications to RIVERS AND TURBIDITY CURRENTS © Gary Parker November, REMOVAL OF THE DAM CAUSES A CHANNEL TO INCISE INTO THE DEPOSIT After removal

1D SEDIMENT TRANSPORT MORPHODYNAMICS with applications to RIVERS AND TURBIDITY CURRENTS © Gary Parker November, AS THE CHANNEL INCISES, IT ALSO REMOVES SIDEWALL MATERIAL A first treatment of the morphodynamics of this process was given in Chapter 15.

1D SEDIMENT TRANSPORT MORPHODYNAMICS with applications to RIVERS AND TURBIDITY CURRENTS © Gary Parker November, EXNER EQUATION OF SEDIMENT CONTINUITY WITH SIDEWALL EROSION The formulation of Chapter 15 is reviewed here. B b = channel bottom width, here assumed constant  b = bed elevation  t = elevation of top of bank Q b = volume bedload transport rate S s = sidewall slope (constant) p = porosity of the bed deposit s = streamwise distance t = time B s = width of sidewall zone  s = volume rate of input per unit length of sediment from sidewalls  s > 0 for a degrading channel, i.e.  b /  t < 0

1D SEDIMENT TRANSPORT MORPHODYNAMICS with applications to RIVERS AND TURBIDITY CURRENTS © Gary Parker November, EXNER EQUATION OF SEDIMENT CONTINUITY INCLUDING SIDEWALL EROSION contd. In Chapter 15, the relations of the previous slide were reduced to obtain the relation: or That is, when sidewall erosion accompanies degradation, the sidewall erosion suppresses (but does not stop) degradation and augments the downstream rate of increase of bed material load.

1D SEDIMENT TRANSPORT MORPHODYNAMICS with applications to RIVERS AND TURBIDITY CURRENTS © Gary Parker November, ADAPTATION TO THE PROBLEM OF CHANNEL INCISION SUBSEQUENT TO DAM REMOVAL: THE DREAM MODELS Saeltzer Dam, California before its removal in Cui et al. (in press-a, in press-b) have adapted the formulation of the previous two slides to describe the morphodynamics of dam removal. These are embodied in the DREAM numerical models. These models have been used to simulate the morphodynamics subsequent to the removal of Saeltzer Dam, shown below.

1D SEDIMENT TRANSPORT MORPHODYNAMICS with applications to RIVERS AND TURBIDITY CURRENTS © Gary Parker November, THE DREAM MODELS Specify an initial top width B bt and a minimum bottom width B bm. If B b > B bm, the channel degrades and narrows without eroding its banks. If B b = B bm the channel degrades and erodes its sidewalls without further narrowing. But B bm must be user-specified.

1D SEDIMENT TRANSPORT MORPHODYNAMICS with applications to RIVERS AND TURBIDITY CURRENTS © Gary Parker November, SUMMARY OF THE DREAM FORMULATION But how does the process really work? Some results from the experiments of Cantelli et al. (2004) follow.

1D SEDIMENT TRANSPORT MORPHODYNAMICS with applications to RIVERS AND TURBIDITY CURRENTS © Gary Parker November, EROSION PROCESS VIEWED FROM DOWNSTREAM rte-bookdamremfrontview.mpg: to run without relinking, download to same folder as PowerPoint presentations. Double-click on the image to see the video clip.

1D SEDIMENT TRANSPORT MORPHODYNAMICS with applications to RIVERS AND TURBIDITY CURRENTS © Gary Parker November, NOTE THE TRANSIENT PHENOMENON OF EROSIONAL NARROWING

1D SEDIMENT TRANSPORT MORPHODYNAMICS with applications to RIVERS AND TURBIDITY CURRENTS © Gary Parker November, EROSION PROCESS VIEWED FROM ABOVE Double-click on the image to see the video clip. rte-bookdamremtopview.mpg: to run without relinking, download to same folder as PowerPoint presentations.

1D SEDIMENT TRANSPORT MORPHODYNAMICS with applications to RIVERS AND TURBIDITY CURRENTS © Gary Parker November, EVOLUTION OF CENTERLINE PROFILE UPSTREAM (x 9 m) OF THE DAM Upstream degradation Downstream aggradation Former dam location

1D SEDIMENT TRANSPORT MORPHODYNAMICS with applications to RIVERS AND TURBIDITY CURRENTS © Gary Parker November, CHANNEL WIDTH EVOLUTION UPSTREAM OF THE DAM The dam is at x = 9 m downstream of sediment feed point. Note the pattern of rapid channel narrowing and degradation, followed by slow channel widening and degradation. The pattern is strongest near the dam.

1D SEDIMENT TRANSPORT MORPHODYNAMICS with applications to RIVERS AND TURBIDITY CURRENTS © Gary Parker November, REGIMES OF EROSIONAL NARROWING AND EROSIONAL WIDENING The dam is at x = 9 m downstream of sediment feed point. The cross-section is at x = 8.2 m downstream of the sediment feed point, or 0.8 m upstream of the dam.

1D SEDIMENT TRANSPORT MORPHODYNAMICS with applications to RIVERS AND TURBIDITY CURRENTS © Gary Parker November, SUMMARY OF THE PROCESS OF INCISION INTO A RESERVOIR DEPOSIT

1D SEDIMENT TRANSPORT MORPHODYNAMICS with applications to RIVERS AND TURBIDITY CURRENTS © Gary Parker November, CAN WE DESCRIBE THE MORPHODYNAMICS OF RAPID EROSIONAL NARROWING, FOLLOWED BY SLOW EROSIONAL WIDENING?

1D SEDIMENT TRANSPORT MORPHODYNAMICS with applications to RIVERS AND TURBIDITY CURRENTS © Gary Parker November, The earthflow is caused by the dumping of large amounts of waste rock from the Porgera Gold Mine, Papua New Guinea. PART OF THE ANSWER COMES FROM ANOTHER SEEMINGLY UNRELATED SOURCE: AN EARTHFLOW IN PAPUA NEW GUINEA

1D SEDIMENT TRANSPORT MORPHODYNAMICS with applications to RIVERS AND TURBIDITY CURRENTS © Gary Parker November, THE EARTHFLOW CONSTRICTS THE KAIYA RIVER AGAINST A VALLEY WALL Kaiya River earthflow The Kaiya River must somehow “eat” all the sediment delivered to it by the earthflow.

1D SEDIMENT TRANSPORT MORPHODYNAMICS with applications to RIVERS AND TURBIDITY CURRENTS © Gary Parker November, THE DELTA OF THE UPSTREAM KAIYA RIVER IS DAMMED BY THE EARTHFLOW earthflow The delta captures all of the load from upstream, so downstream the Kaiya River eats only earthflow sediment

1D SEDIMENT TRANSPORT MORPHODYNAMICS with applications to RIVERS AND TURBIDITY CURRENTS © Gary Parker November, THE EARTHFLOW ELONGATES ALONG THE KAIYA RIVER, SO MAXIMIZING “DIGESTION” OF ITS SEDIMENT A downstream constriction (temporarily?) limits the propagation of the earthflow.

1D SEDIMENT TRANSPORT MORPHODYNAMICS with applications to RIVERS AND TURBIDITY CURRENTS © Gary Parker November, THE VIEW FROM THE AIR Kaiya River The earthflow encroaches on the river, reducing width, increasing bed shear stress and increasing the ability of the river to eat sediment!

1D SEDIMENT TRANSPORT MORPHODYNAMICS with applications to RIVERS AND TURBIDITY CURRENTS © Gary Parker November, THE BASIS FOR THE SEDIMENT DIGESTER MODEL (Parker, 2004) The earthflow narrows the channel, so increasing the sidewall shear stress and the ability of the river flow to erode away the delivered material. The earthflow elongates parallel to the channel until it is of sufficient length to be “digested” completely by the river. This is a case of depositional narrowing!!!

1D SEDIMENT TRANSPORT MORPHODYNAMICS with applications to RIVERS AND TURBIDITY CURRENTS © Gary Parker November, GEOMETRY H = flow depth n = transverse coordinate n b = B b = position of bank toe B w = width of wetted bank n w = B b + B w = position of top of wetted bank S s = slope of sidewall (const.)  b = elevation of bed = volume sediment input per unit streamwise width from earthflow The river flow is into the page. The channel cross-section is assumed to be trapezoidal. H/B b << 1. Streamwise shear stress on the bed region =  bsb = constant in n Streamwise shear stress on the submerged bank region =  bss =  bsb = constant in n,  < 1. The flow is approximated using the normal flow assumption.

1D SEDIMENT TRANSPORT MORPHODYNAMICS with applications to RIVERS AND TURBIDITY CURRENTS © Gary Parker November, EXNER EQUATION OF SEDIMENT BALANCE ON THE BED REGION Local form of Exner: where q bs and q bn are the streamwise and transverse volume bedload transport rates per unit width. Integrate on bed region with q bs = q bss, q bn = 0;  /  t(sediment in bed region) differential steamwise transport transverse input from wetted bank region

1D SEDIMENT TRANSPORT MORPHODYNAMICS with applications to RIVERS AND TURBIDITY CURRENTS © Gary Parker November, EXNER EQUATION OF SEDIMENT BALANCE ON WETTED BANK REGION Integrate local form of Exner on wetted bank region with region with: q bs = q bss for n b < n < n b + B w q bn = - at n = n t where q denotes the volume rate of supply of sediment per unit length from the earthflow Geometric relation: Result:  /  t(sediment in wetted bank region) differential steamwise transport transverse output to bed region transverse input from earthflow

1D SEDIMENT TRANSPORT MORPHODYNAMICS with applications to RIVERS AND TURBIDITY CURRENTS © Gary Parker November, EQUATION FOR EVOLUTION OF BOTTOM WIDTH Eliminate  b /  t between Note that there are two evolution equations for two quantities, channel bottom elevation  b and channel bottom width B b. To close the relations we need to have forms for q bsb, q bss and. The parameter is specified by the motion of the earthflow. and to obtain

1D SEDIMENT TRANSPORT MORPHODYNAMICS with applications to RIVERS AND TURBIDITY CURRENTS © Gary Parker November, FLOW HYDRAULICS Flow momentum balance: where S = streamwise slope and B w = H/S s, Flow mass balance Manning-Strickler resistance relation Here k s = roughness height, D = grain size, n k = o(1) constant. Reduce under the condition H/B s << 1 to get:

1D SEDIMENT TRANSPORT MORPHODYNAMICS with applications to RIVERS AND TURBIDITY CURRENTS © Gary Parker November, BEDLOAD TRANSPORT CLOSURE RELATIONS Shields number on bed region: where R = (  s /  - 1)  Shields number on bank region: Streamwise volume bedload transport rate per unit width on bed and bank regions is q bsb and q bss, respectively: where  s = 11.2 and  c * denotes a critical Shields stress, (Parker, 1979 fit to relation of Einstein, 1950). Transverse volume bedload transport rate per unit width on the sidewall region is q bns, where  n is an order- one constant and from Parker and Andrews (1986),

1D SEDIMENT TRANSPORT MORPHODYNAMICS with applications to RIVERS AND TURBIDITY CURRENTS © Gary Parker November, SUMMARY OF THE SEDIMENT DIGESTER Equation for evolution of bed elevation Equation for evolution of bottom width Hydraulic relations Sediment transport relations As the channel narrows the Shields number increases Higher local streamwise and transverse sediment transport rates counteract channel narrowing A higher Shields number gives higher local streamwise and transverse sediment transport rates. The earthflow encroaches on the channel

1D SEDIMENT TRANSPORT MORPHODYNAMICS with applications to RIVERS AND TURBIDITY CURRENTS © Gary Parker November, EQUILIBRIUM CHANNEL Equilibrium channels that transport bedload without eroding their banks can be created in the laboratory (Parker, 1979). The image below shows such a channel (after the water has been turned off). The image is from experiments conducted by J. Pitlick and J. Marr at St. Anthony Falls Laboratoty, University of Minnesota.

1D SEDIMENT TRANSPORT MORPHODYNAMICS with applications to RIVERS AND TURBIDITY CURRENTS © Gary Parker November, EQUILIBRIUM CHANNEL SOLUTION As long as  < 1, the formulation allows for an equilibrium channel without widening or narrowing as a special case (without input from an earthflow). Choose bed shear stress so that bank shear stress = critical value Streamwise sediment transport on wetted bank region = 0 Transverse sediment transport on wetted bank region = 0 Total bedload transport rate Three equations; if any two of Q w, S, H, Q b and B b are specified, the other three can be computed!!

1D SEDIMENT TRANSPORT MORPHODYNAMICS with applications to RIVERS AND TURBIDITY CURRENTS © Gary Parker November, ADAPTATION OF THE SEDIMENT DIGESTER FOR EROSIONAL NARROWING As the channel incises, it leaves exposed sidewalls below a top surface  t. Sidewall sediment is eroded freely into the channel, without the external forcing of the sediment digester. B b now denotes channel bottom half-width B s denotes the sidewall width of one side from channel bottom to top surface. The channel is assumed to be symmetric, as illustrated below.

1D SEDIMENT TRANSPORT MORPHODYNAMICS with applications to RIVERS AND TURBIDITY CURRENTS © Gary Parker November, INTEGRAL SEDIMENT BALANCE FOR THE BED AND SIDEWALL REGIONS On the bed region, integrate Exner from n = 0 to n = n b = B b to get On the sidewall region, integrate Exner from n = n b to n = n t under the conditions that streamwise sediment transport vanishes over any region not covered with water, and transverse sediment transport vanishes at n = n t

1D SEDIMENT TRANSPORT MORPHODYNAMICS with applications to RIVERS AND TURBIDITY CURRENTS © Gary Parker November, INTEGRATION FOR SIDEWALL REGION Upon integration it is found that or reducing with sediment balance for the bed region,

1D SEDIMENT TRANSPORT MORPHODYNAMICS with applications to RIVERS AND TURBIDITY CURRENTS © Gary Parker November, INTEGRAL SEDIMENT BALANCE: SIDEWALL REGION For the minute neglect the indicated terms: The equation can then be rewritten in the form: As the channel degrades i.e.  b /  t < 0, sidewall material is delivered to the channel. Erosional narrowing, i.e.  B b /  t < 0 suppresses the delivery of sidewall material to the channel.

1D SEDIMENT TRANSPORT MORPHODYNAMICS with applications to RIVERS AND TURBIDITY CURRENTS © Gary Parker November, INTEGRAL SEDIMENT BALANCE: SIDEWALL REGION contd.

1D SEDIMENT TRANSPORT MORPHODYNAMICS with applications to RIVERS AND TURBIDITY CURRENTS © Gary Parker November, INTERPRETATION OF TERMS IN RELATION FOR EVOLUTION OF HALF- WIDTH This term always causes widening whenever it is nonzero. Auxiliary streamwise terms This term causes narrowing whenever sediment transport is increasing in the streamwise direction. But this is exactly what we expect immediately upstream of a dam just after removal: downward concave long profile!

1D SEDIMENT TRANSPORT MORPHODYNAMICS with applications to RIVERS AND TURBIDITY CURRENTS © Gary Parker November, REDUCTION FOR CRITICAL CONDITION FOR INCEPTION OF EROSIONAL NARROWING Narrows if slope increases downstream WidensEither way Where N S and N B are order-one parameters, At point of width minimum  B b /  s = 0

1D SEDIMENT TRANSPORT MORPHODYNAMICS with applications to RIVERS AND TURBIDITY CURRENTS © Gary Parker November, REDUCTION FOR CRITICAL CONDITION FOR INCEPTION OF EROSIONAL NARROWING contd. Where N s and N b are order-one parameters, After some reduction, where M is another order-one parameter. That is, erosional narrowing can be expected if the long profile of the river is sufficiently downward concave, precisely the condition to be expected immediately after dam removal!

1D SEDIMENT TRANSPORT MORPHODYNAMICS with applications to RIVERS AND TURBIDITY CURRENTS © Gary Parker November, NUMERICAL MODELING OF THE MORPHODYNAMICS OF EROSIONAL NARROWING AND WIDENING Wong et al. (2004) used the formulation given in this chapter to numerically model one of the experiments of Cantelli et al. (2004). The code will eventually be made available in this e-book. Meanwhile, some numerical results are given in the next two slides. The reasonable agreement was obtained with a minimum of parameter fitting.

1D SEDIMENT TRANSPORT MORPHODYNAMICS with applications to RIVERS AND TURBIDITY CURRENTS © Gary Parker November, COMPARISON OF NUMERICAL MODEL WITH EXP. 5 OF CANTELLI et al. (2004): EVOLUTION OF LONG PROFILE Calculated and measured long profile 1200 seconds after commencement of experiment.

1D SEDIMENT TRANSPORT MORPHODYNAMICS with applications to RIVERS AND TURBIDITY CURRENTS © Gary Parker November, COMPARISON OF NUMERICAL MODEL WITH EXP. 5 OF CANTELLI et al. (2004): EVOLUTION OF CHANNEL WIDTH Calculated and measured water surface width 0.9 m upstream of original position of dam.

1D SEDIMENT TRANSPORT MORPHODYNAMICS with applications to RIVERS AND TURBIDITY CURRENTS © Gary Parker November, REFERENCES FOR CHAPTER 31 Cantelli, C. Paola and G. Parker, 2004, Experiments on upstream-migrating erosional narrowing and widening of an incisional channel caused by dam removal, Water Resources Research, 40(3), doi: /2003WR Cui,,Y., Parker, G., Braudrick, C., Dietrich, W. E. and Cluer, B., in press-a, Dam Removal Express Assessment Models (DREAM). Part 1: Model development and validation, Journal of Hydraulic Research, preprint downloadable at: Cui, Y., Braudrick, C., Dietrich, W.E., Cluer, B., and Parker, G, in press-b, Dam Removal Express Assessment Models (DREAM). Part 2: Sample runs/sensitivity tests, Journal of Hydraulic Research, preprint downloadable at: Einstein, H. A., 1950, The Bed-load Function for Sediment Transportation in Open Channel Flows, Technical Bulletin 1026, U.S. Dept. of the Army, Soil Conservation Service. Parker, G., 1979, Hydraulic geometry of active gravel rivers, Journal of Hydraulic Engineering, 105(9), 1185 ‑ Parker, G., 2004, The sediment digester, Internal Memorandum 117, St. Anthony Falls Laboratory, University of Minnesota, 17 p, downloadable at: Wong, M., Cantelli, A., Paola, C. and Parker, G., 2004, Erosional narrowing after dam removal: theory and numerical model, Proceedings, ASCE World Water and Environmental Resources 2004 Congress, Salt Lake City, June 27-July 1, 10 p., reprint available at: 1D SEDIMENT TRANSPORT MORPHODYNAMICS with applications to RIVERS AND TURBIDITY CURRENTS