excercise 2

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Climatic Geomorphology Exercise #2 – River Adjustments, Discharge, and Hydraulic Geometry

Purpose: This exercise explores more deeply some of the concepts we discussed on rivers. In Part (A) we will make observations and answer some questions. Parts (B) and (C) explore more deeply some of quantitative aspects of river discharge and hydraulic geometry.

Part A (40 Points) - Channel Adjustments and Vegetation:

Background Information. The Colorado Piedmont section of the Great Plains is a semiarid region with periodic floods occurring between mid-May and late September as a result of local thunderstorms. Floods were reported in the West Bijou Creek, a tributary to the South Platte River, in 1935, 1951, and 1965. The largest known flood occurred in 1965. The floodplain lies within a broad (>0.5 km wide) valley consisting of Aeolian deposits, generally dry Pleistocene alluvial terraces, and frequently inundated alluvial deposits overlying a lithology of sandstone. The Upper West Bijou (Figures 1 and 2) flows intermittently in the spring. Subsurface flow sustains the bottomland forests, which are comprised mainly of cottonwood. During floods the stream channels are adjusted either through channel migration or channel widening. Cottonwood seedlings begin to grow on eroded sites within 1-3 years following the flood, and are sustained by moderate base flows. Over periods of decades the channels narrow and the bottomland forests become established. If the bottomlands experience no significant flooding for 150-200 years then the forests are replaced with grasslands (Friedman and Lee, 2002).

Figure 1. Location of study site in eastern Colorado.

Figure 2. Aerial photographs taken four years (August, 1969) and 28 years (June, 1993) following a flood event.

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Questions: a) What evidence do you see of channel widening and narrowing? b) What evidence do you see of channel migration? c) How do you know there was channel migration pre-dating the 1965 flood? d) Can you think of ways you might date past floods in this region? e) Can you identify and explain a link between vegetation establishment and channel narrowing? f) With respect to reaction times and relaxation times how do these systems exhibit complex geomorphic response? g) Are these systems in steady state or non-steady state? h) How might these systems be affected by changes in climate or changes in land use?

Reference: Friedman, J.M. and Lee, V.J., 2002. Extreme floods, channel change, and riparian forests along

ephemeral streams. Ecological Monographs, 72(3), 409-425. (Posted on UBlearns)

Part B (30 Points) - Estimates of Bankfull Discharge:

Table 1 shows basic survey data required to make discharge estimates, from the Ashnola and upper Similkameen Rivers in central British Columbia, Canada. This area has a semi-arid climate and so streams are bedload dominated.

Table 1. Hydraulic geometry data for Ashnola and Similkameen Rivers. Source: J.R. Desloges.

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1. a) Using Manning’s Equation, estimate bankfull mean velocity of flow at each survey cross- section in Table 1. Then, use the continuity equation to estimate bankfull discharge for each cross- section. Report your numbers in a table that resembles Table 1. Note that you can do this manually or use Microsoft Excel software and the spreadsheet provided on UBlearns.

Manning’s Equation: , where d is mean depth (m) and S is slope.

Continuity Equation: , where Q is discharge (m3 s-1) and w is width.

b) Measured bankfull discharge at the gauging station on the Ashnola River (drainage area, Ad = 1040 km2) is 86 m3 s-1. How does this compare with the estimate made using the Manning type equation? If there is a difference what might account for it?

2. Examine the graph in Figure 3, which uses log scales for both x- and y-axis, of bankfull discharge, Q, versus drainage area, Ad, using the data in Table 1. The straight line through the scatter of points yields the equation of the form,

, where a is the intercept at Ad = 1 and b is the slope of the line (see Appendix A). Values for a and b can be determined by either making measurements directly from the graph and using Appendix A, or rather easily by fitting a power function to the scatter points using computer software, which has been done here for you. Note the equation for the straight line.

a) Flows measured in other tributaries to the Similkameen are as follows:

Ad Q Tulameen R. 1,760 201 Otter R. 673 85 Pasayten R. 562 67 Shatford Cr. 101 10

b) How similar are the predicted flows in these tributaries (using the relationship developed above) to the actual measurements? If differences occur what might explain them?

n Sdv

2132

=

vdwQ ××=

b daAQ =

Ashnola River

Figure 3. Bankfull discharge versus drainage basin area for the Ashnola River, British Columbia, Canada.

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Part C (30 Points) - Hydraulic Geometry

1. Examine the plots of width, w, mean depth, d, and bankfull mean velocity, v, against bankfull discharge, Q, in Figure 4. The fitted functions are:

a) Confirm that b + f + m = 1 and a× c × k = 1.

b) What is the significance of the constants b, f, and m of this cobble-gravel river system?

c) Compute b, f, and m for the Brandywine Creek of eastern Pennsylvania (a silt and clay stream with a lower stream gradient) using the plots given in Figure 5B (downstream locations). [Hint: Use Appendix A]

Compare these results with those for the Ashnola/Similkameen system and explain any differences.

2. a) Is there a strong relationship between mean grain size, D50, and channel slope, S? Explain.

b) What happens to D50 with Distance from the source, notably at the 25-28 km distance? What physical cause could explain what you see?

[Hint: You can quickly plot D50 versus S and D50 versus Distance from source in Excel. You do not need to include these plots with your answers]

3. Is there a consistent relationship between bankfull mean velocity and channel slope? Explain your answer.

baQw = fcQd = mkQv =

Ashnola River

Figure 4. Width, depth, and velocity versis bankfull discharge.

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Figure 5. A. Relation of width, mean depth, mean velocity, water surface slope and roughness parameter (n’) to changing discharge at-a-station from Brandywine Creek at Cornog, Pennsylvania. B. Relation of width, mean depth, mean velocity and water surface slope to bankfull discharge along a 40-km stretch of Brandywine Creek, Pennsylvania. Source: Wolman, 1955, figures 10 and 29, pp. 11 and 31, as reproduced in Chorley et al. (1984), Geomorphology, Methuen, London.

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Appendix A If y is a power law function of x, it will plot as a straight line on log-log paper or when using log-log axes in any graphing software (Figure A-1). For example, y=x3. Common applications are in hydrology and fluvial geomorphology. The slope of the line on the log-log paper is:

.

If a is the intercept at x=1, then the equation of the line is: .

Figure A-1. Illustration of a power law function drawn as a straight line on log-log axes.

b = log y2( )− log y1( ) log x2( )− log x1( )

y = ax b