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Stream Gradient and Bankfull Discharge Correlations at San Clemente, California State Beach

by Betsy Murphy


        Field research has shown a “ consistency with which rivers of various sizes in various physiographic settings make… adjustments to increasing discharge downstream,” suggesting that “there is a common tendency or physical principal governing these adjustments" (Leopold 1964, 248).   Understanding this common response, physical geographers have conducted numerous studies on the importance of discharge on the morphology of stream channels, and have found that longitudinal stream profiles are largely determined during times of moderate or high discharge (Butzer 1976).  One common adjustment found to occur during periods of high discharge is a general decrease in the stream gradient in relation to increases in stream discharge as one moves downstream.  The most meaningful discharge for any discussion of channel morphology is bankfull discharge, for it is the main catalyst in stream gradient adjustments.  Bankfull discharge occurs when the stream is at the brink of overflowing its banks, an event which has an average recurrence interval of about 1.5 years (Summerfield).

        Geologists and geomorphologists have been especially concerned with stream gradient because it is the stream gradient which is most impressed upon or revealed in the landscape.  Although ancient rocks or alluvial terrace deposits occasionally preserve channel form, more often it is the stream gradient which can be inferred from terrace remnants.  Remains of longitudinal profiles of past epochs have at times helped researchers uncover past geological activity. Through understanding the factors and processes related to the formation of a stream profile, some idea of previous climates, river discharge, sediment load, drainage basin characteristics, and vegetation may be constructed (Leopold 1964).
The purpose of the paper is to review field research conducted to test the relationship between bankfull discharge and stream gradient in the channels present along the coast of San Clemente State Beach.   Assuming a pattern similar to the findings of other related field work, a general hypothesis was formulated that a downstream increase in bankfull discharge will be accompanied by a corresponding decrease in stream gradient.   A graphic representation of this hypothesis, based on a study conducted in the Yellowstone River Basin, is shown below.

(graph of Yellowstone River Basin to be loaded soon)

Study area and method
        Research was conducted along a half-mile stretch of San Clemente State Beach.  Four stream channels were selected for the study based on their comparatively well-defined stream channels.  In total, measurements for eighteen sampling sites were collected.  Among the channels there exists a great deal of variation.  For example, the vegetation cover ranged from thick ice-plant along stream number three to bare, exposed bedrock along stream number four.  Related studies have shown that the presence of vegetation along a stream channel has been found to have significant impacts on the morphology of the stream (Karlinger 1983; Benson 1967).

        A standard methodology, well-used in the literature, was employed in this study.  At each sampling site, stream gradient was measured by differential leveling.  Maintaining balanced elevations throughout the survey, horizontal distances, or runs, were plotted in 20 feet increments with a level tape.  A leveled hand level and a measurement rod were then used to calculate the rate of elevation change per run.  Foresight readings were subtracted from ‘height of instrument’ figures in order to ascertain the difference in elevation. Since the study was conducted at a time of low flow, hydraulic radius was used as a surrogate for bankfull discharge. To calculate the hydraulic radius, the width and depth of each run were first measured with a tape and multiplied to get the area (A).  The wetted perimeter (WP) was then determined by adding the width to twice the depth (width + 2 x depth).  This number was then divided into the area to get the hydraulic radius (A/WP).  This method of determining peak discharge through the application of hydraulic equations is a standard, well-known technique used to relate the discharge of the water to the geometry of the channel (Benson 1967).  (Please see Appendix A for a table of individual values for sites.)

        The results of this study have been plotted on a scatter graph in Figure 1.  When comparing the findings of this field project (in Figure 1) with the results of the hypothesis-supporting Yellowstone study presented earlier (Graph A), it is immediately clear that the findings of this study do not support the hypothesis.  In fact, the positive regression slop of .0034 could be interpreted as indicating that there could be a weak positive relationship between increasing stream radius and increasing hydraulic radius.  This is in stark contrast to the inverse relationship postulated in the hypothesis.  However, the flatness of the slope and the high degree of scatter around the regression line show that the correlation between the two variables is very weak. (With a r2 value of .0013, less than 1% of the variation in stream gradient can be "explained" by variations in bankfull discharge.)  Hence, while the results most certainly reject the hypothesis, they do not provide strong evidence that an opposite relationship may exist. When analyzed independently, two of the four stream channels have negative regression slopes which do support the hypothesis (see Figure 2).  However, the flat slopes and high degree of scatter around the regression lines show that these two channels (one and three) have very weak correlations between the variables.

(Figure 2 to will be scanned in soon)

Summary and Conclusions
        The results of this field research conducted along a segment of the San Clemente State Beach do not support the original hypothesis.  Stream gradient did not decrease as bankfull discharge increased as one moves down the stream.  Hence, the hypothesis must be rejected for this data set based on the findings of this study.

        There are a number of problems that may have caused errors significant enough to require the results to be abandoned.  Observer error due to lack of experience in locating bankfull discharge marks is probably the most consequential inaccuracy in this study.  According to Benson, the “proper identification of the bankfull discharge marks is the part of the work that requires the most experience (Benson 1967, 11).”  Likewise, Leopold et. al. state that “at times of low flow, the determination of bankfull stage or flood stage is not in itself a simple matter.  As everyone who has tried to make this determination has discovered, the difficulty lies…in deciding in the field exactly what to call bankfull (Leopold 1964, 321)."  Because ascertaining the accurate location of bankfull discharge is critical to the success of this research, errors in this area could negate all findings, both positive and negative.  The physically disparate environments of the four streams most likely exacerbated the problem of locating the bankfull discharge level, as the lack of experience was not overcome with successive measurements.  Streams one and three, both with negative regression slopes that support the hypothesis, had vegetation cover and had moderately well-defined banks.  However, the two stream channels with the positive regression slopes, numbers two and four, were dry, deep cut channels with no vegetation and no clear high water markings.  The probability of observer error in locating the bankfull level in these two streams is much greater than in streams one and three.  Therefore, the possibility that observer error in these two streams skewed the overall results of the study toward a rejection of the hypothesis must be acknowledged. Also important to the validity of the findings is the small sample size.  With only 18 sites measured, the results contained in this study are not considered “statistically significant”  by usual field research standards.  Without a statistically significant sample size, it is possible that the data presented in this study is not representative of the population, and could therefore be erroneously skewed by an ‘outlier.’

        However, a high degree of care was taken in the field to avoid all errors in measurement and calculations.  Therefore, a second trip to the study site would help confirm or reject these findings.  Additionally, the use of different measurement techniques could decrease the chance of observer error.  According to Benson, the transit-stadia method is best suited for this type of field work, for the “problem with level-and-tape is that it does not provide the exact locations of high-water marks and channel features that are necessary” (Benson 1967, 3).  While the results of this study do not support the hypothesis or provide a significant reason to reject it, the findings do help illustrate the likelihood that the connection between decreasing stream gradient and increasing bankfull discharge should not be considered a direct cause-effect relationship.  Though situations do exist with strong correlations between these two variables (such as in the Yellowstone case), this study reflects the fact that such correlations often must interact with other complex processes of nature in creating the physical environments in which we live.

*This paper was prepared for a California State University Fullerton Graduate Seminar in Physical Geography.


Works Cited
Benson, M.A. and T. Dalrymple.  1967.  "General Field and Office Procedures for Indirect Discharge
      Measurements."  In Techniques of Water-Resources Investigations of the United States  Geological 
      Survey. Washington, DC: U.S. Government Printing Office.
Butzer, K.W.  1976.  Geomorphology From the Earth.  New York: Harper & Roe.
Karliner, M.R., Eschner, T.R., Hadley, R.F., and J.E. Kircher.  1983.  "Relation of Channel-Width Maintenance 
     to Sediment Transport and River Morphology: Platte River, South-Central Nebraska." Geological Survey 
     Professional Paper 1277-E: E1-E18. 
Leopold, L.B., Wolman, M.G. and J.P. Miller. 1964.  Fluvial Processes in Geomorphology. San Francisco:
      W. H. Freeman and Company.
Summerfield, M.A.  1991.  Global Geomorphology.  New York: John Wiley & Sons Inc. 


Appendix A:  Measurement table

to be loaded soon