USGS Home
Contact USGS
Search USGS

U.S. GEOLOGICAL SURVEY
Scientific Investigations Report 2007–5159

Back to Table of Contents

Calculated Water-Surface Slope for the 2006 Flood and the n Value for the 2003 Flood

Information from the 2003 and 2006 floods was combined to re-evaluate the n value for the reach. The 2003 flood survey provided detailed channel geometry and HWMs on both sides of the river, but had a poorly defined water-surface slope due to the wide scatter of HWMs at XS3. The 2006 flood survey accurately measured the water-surface slope, but it did not include a survey of the cross sections or left-bank HWMs. If the slope estimated for the 2006 flood is substituted into the two-section equation for a slope-area measurement using the geometry surveyed for the 2003 flood, and utilizing the peak discharge for the 2003 flood, the n value for this reach for the 2003 flood can be calculated.

Water-Surface Slope for the 2006 Flood

Figure 2 shows a profile of the HWMs from the peak of November 6, 2006, with the location of the cross sections and a straight line approximating the water surface at the peak. As a peak recedes, it may leave additional HWMs that are identified in the field. As a result, it is common to identify HWMs lower than nearby marks. A peak water surface generally is drawn with a bias to be nearest the highest water marks. Additional weight is given to water marks with the highest quality ratings. Despite having some scatter in the 2006 HWMs, the scatter of the HWMs is considerably less than the scatter of HWMs from the 2003 flood at XS3. Instead of providing a possible range in water-surface slopes as was done with the 2003 flood data, a single peak water-surface profile can be drawn for the 2006 flood that closely aligns with several HWMs at XS3 and several excellent HWMs just upstream of XS3. The water surface approximated in figure 2 has a slope of 0.00114. This slope is in the range of values estimated from the survey of the HWMs from the 2003 flood, 0.00064 to 0.00124, and it is very close to the slope of 0.00120 calculated by Stewart in 1923 for the 1921 flood (James Stewart, U.S. Geological Survey, written commun., November 1923).

Two recent medium-to-high discharge measurements plot close to the current rating without applying shifts. A discharge measurement made from a cableway on November 9, 2006, measured 53,000 ft³/s and plotted +7.1 percent off the current rating without shifts. A discharge measurement of 138,000 ft³/s on October 21, 2003, plotted +1.5 percent off the same rating without shifts. These discharge measurements indicate that the hydraulics of the reach have changed little between the 2003 and 2006 floods. We, therefore, expect that the slope for the 2006 flood should be similar to the slope of the 2003 flood.

n-Value for the 2003 Flood

Initially, the surveyed cross section points for XS2 and XS3 for the 2003 flood were entered into the computer program Slope Area Computation, v97-01 (SAC, Fulford, 1994). The elevation of the water surface for XS2 was held to an elevation of 37.50 ft, a relatively accurate water-surface elevation determined from the survey of HWMs from the 2003 flood. The elevation of XS3 was set to 34.82 ft, the calculated elevation from applying a slope of 0.00114 to the reach length. As was done by Stewart in his 1923 calculation of the 1921 flood, no subdivision of the cross sections was made and n values were held the same for both cross sections. By trial and error with the SAC program, the estimated n value for the 2003 flood using the water-surface slope from the 2006 flood that resulted in a discharge of 166,000 ft³/s (the peak discharge for the 2003 flood) was calculated to be 0.0306. Calculated velocities were 11.1 and 12.1 ft/s and Froude numbers 0.43 and 0.46 for XS2 and XS3, respectively. This n value is at the high end of the range of n values calculated earlier by Mastin and Kresch (2005)—0.024 for the flattest estimated water-surface slope and 0.032 for the steepest water-surface slope. James Stewart used the Chezy and Kutter equations (Corbett, 1962, p. 81-83) along with an n value of 0.033. Stewart, however, used the water-surface slope in his calculations rather than the energy slope that is used today, which results in slightly different peak-discharge values for the same n values.

A close examination of the shape of XS2 indicated that a subdivision of the cross section should be done when performing one-dimensional hydraulic computations. The decision to subdivide follows guidelines outlined by Davidian (1984, p. 21) for “bench panhandle shapes” of cross sections. Davidian’s guidelines state that cross sections should be subdivided when the ratio of the length of the panhandle to its depth is 5 or greater. In the case of XS2, the ratio is roughly 15. A second n-verification computation was made with XS2 subdivided into two subareas, a main channel on the left half of the cross section and a high-water bench on the right half of the cross section containing the forested island/bar. The plot of XS2 from the 2004 survey indicates that three subareas may be warranted (left main channel, high-water bench, and right main channel). However, because the plot of XS2 from the 1923 survey shows only two subareas (on main channel and one panhandle area) only two subareas for the 2004-surveyed XS2 were used for consistency between the two calculations. No distinct panhandle shape is found in cross section XS3 so no subdivision of XS3 was used in the calculations. XS2 was subdivided at station 346 (fig. 3) for the cross section data surveyed in 2004. Using a weighted-wetted perimeter technique (Arcement and Schneider, 1989) for the panhandle portion of XS2, the n value of the right subarea was calculated to be 0.066 based on an estimated n value of 0.120 for the forested island/bar portion (station 346 to 486, wetted perimeter = 140 ft) and 0.033 for the remainder of the subarea (wetted perimeter = 231 ft). Therefore; 0.066 = ((0.120 * 140) + (0.033 * 231)) / 371. The n value for the forested island (0.120) was estimated from photographs of verified n values for floodplain reaches (Arcement and Schneider, 1989). The n value of the remainder of the right subarea of XS2 was set to Stewart’s original n value for the reach, 0.033.

Several trial-and-error runs of the SAC program were performed to determine the n value for the left subarea of XS2 and all of XS3, which are considered to be the main channel in this reach of the Skagit River. Running the SAC program to produce a discharge as close to the 2003 flood peak as possible (166,000 ft³/s), an n value of 0.033 was calculated for the main channel areas (a discharge of 168,000 ft³/s resulted in an n value of 0.033, and a discharge of 163,000 ft³/s resulted in an n value of 0.034).

Back to Table of Contents