Annual and Storm Analysis, Turbidity Threshold Sampling (TTS)

The purpose of this analysis was to estimate sediment loads using the relations between suspended sediment concentration, turbidity and discharge in Freshwater Creek.  The analysis as presented below was carried out at RSL on a Unix operating system using S-Plus and Perl.  The majority of the analysis tools and plotting routines were written in S-Plus because of its powerful ability to manipulate and graphically represent the data.

Instrumentation included a Campbell data logger, a pressure transducer for recording stage height (water depth), an ISCO sampler to extract pumped sediment samples from the stream, and an infrared turbidity probe.  The pressure transducer was calibrated in the field, and the electronic measurements were adjusted to observations made systematically in the field when appropriate.  Stage height and turbidity were recorded at 15-minute intervals.  Manual discharge measurements were made in the field to develop a relationship between stage height and discharge.  Pumped samples were collected automatically at pre-determined turbidity thresholds according to a program loaded in the data logger.  These sample bottles were analyzed for sediment concentration at RSL and the Salmon Forever Sunnybrae Sediment Lab using methods described in Standard Methods for the Examination of Water and Wastewater.  The turbidity measurements recorded by the Campbell data logger were converted to suspended sediment concentrations using regressions based on the pumped sample concentrations.  The regression methodology is described in following sections of the web page.

Depth-integrated water/sediment samples were also collected at various stages so that the point samples taken by the ISCO sampler could be adjusted to account for sediment delivered across the entire cross section.  However due to an insufficient number of depth-integrated samples, this portion of the analysis was not carried out.  Thus all load estimates presented are based on the point samples taken by the ISCO sampler.  If an adjustment based on an adequate number of samples were to be carried out, it is likely that it would result in higher sediment loads than those presented below, because sediment concentrations are expected to be greater near the stream bed.

A linear equation seemed to do a poor job in fitting the lower portion of the data set. A quadratic, a cubic polynomial, and a smooth loess were also fit to the data set. "Loess", short for LOcal regrESSion, is flexible tool for fitting almost any shape curve. There is a good description of loess in William S. Cleveland's book "Visualizing Data" (Hobart Press, 1993). The loess fit was determined to give the best fit to the data set. The results of the linear and the loess fit are given below including the annual load predictions. Notice that the linear fit gives a fairly good R-SQUARED value and that the linear and loess predictions are very close.
 

Plot 2 (shown below) summarizes the entire data set for hydrologic year 1999 at Freshwater (January 13, 1999 to August 1, 1999). The upper plot is the sedigraph and the lower plot is the hydrograph. The sedigraph is based on the linear regression model presented above where suspended sediment concentration is assumed to be a linear function of turbidity. The suspended sediment concentration is shown on the upper left axis (in mg/L) and the turbidity scale is on the right axis (in NTU). For the entire period, the load estimate (shown below the legend) matches the prediction made by the linear model presented above. The sedigraph peaks tended to occur before the hydrograph peaks.

How well does the loess regression predict the load delivered by individual storms? Eight storms were selected for analysis (these storms are numbered 1-8 on plot 2 above). Each storm period was first designated. Then a linear regression was carried out on the samples analyzed under the dump(s) that corresponded to the designated storms. In some cases a rating curve relating discharge and suspended sediment was used where the linear regression between suspended sediment and turbidity predicted negative values. This was often at the very beginning or end of the storm. As an example, we shall select Storm 3 (start:02/06/99, 0300 hrs; end:02/08/99, 1315 hrs). The initial regression using all ISCO sample bottles taken during the storm was carried out and is shown below in plot 3.

However, this linear regression model predicted negative values at the very beginning and end of the storm. A power relationship between discharge and suspended sediment was then determined using the samples taken for Storm 3. This plot is shown below as plot 4. The plot shows a characteristic hysteresis loop in the suspended sediment - discharge rating curves. This can be seen by tracing the bottle numbers in plot 4 for either dump.

Notice the hysteresis loop is formed because a greater suspended sediment concentration was observed on the rising limb of the hydrograph, while the suspended sediment concentration was lower for a given discharge on the falling limb of the hydrograph.  Because the objective was to correct the negative predictions at the front end of the storm, another rating curve was developed using only the first three sample bottles taken. This rating curve is shown below in plot 5.

Finally, a regression using suspended sediment concentration and turbidity values from the last three sample bottles were used to remove the negative predictions at the end of the storm given by the original regression (refer to plot 3 above). This final regression is shown below as plot 6.

All three of these relationships are then pieced together to form the final estimate for the storm. Plot 7 (below) shows the resulting sedigraph and hydrograph for Storm 3. Notice the load estimate for the storm is given under the legend.

The table below shows each storm estimate compared to an estimate computed from the annual loess fit. Notice that all eight storms accounted for 86% of the total annual load estimate. As shown in the table below, the loess fit gave fairly good estimates for individual storms with the largest deviation observed to be 28%. The deviations are explained by observing the distribution of points in plot 1. By observing how the dumps (i.e. ISCO sample bottles) corresponding to a given storm fall in relation to the loess curve, one can predict whether the loess model will under- or over-estimate the sediment load delivered by the storm event. The bias in using an annual relationship to estimate individual storms was limited in this example because there was relatively little scatter in the annual data set.
 

LOESS LOAD ESTIMATE OF ANNUAL LOAD: 2845365kg
TOTAL ESTIMATED STORM LOAD AS A PERCENTAGE OF ESTIMATED ANNUAL LOAD: 85.8%


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Freshwater // Last updated on October 19, 2000, by Ben Bray