prepared by Dr. Andre Lehre, Dept. of Geology, Humboldt State University http://sorrel.humboldt.edu/~geodept/geology550/550_handouts/suspended_load_computation.pdf COMPUTATION OF SUSPENDED–LOAD DISCHARGE

GENERAL COMMENTS

The primary data collected to determine the suspended-sediment discharge of a stream are: Q, the instantaneous water discharge in ft3/sec or m3/sec. This quantity is either measured with a current meter or taken from a stage-discharge curve for the station. C, the instantaneous suspended-sediment concentration in parts of sediment per million parts of water (ppm) or milligrams of sediment per liter of water (mg/l). Concentration is measured by analysis of water samples. For low sediment concentrations (< 15,000 ppm) the concentration in mg/l is the same as that in ppm. For concentrations greater than 15,000 ppm the conversion factors in "Table 2 -- Conversion factors" below can be used to turn ppm into mg/l.

Qs, the instantaneous suspended-sediment discharge in tons/day (English or metric) is computed as: Qs = k Q C where k is a conversion factor appropriate to the units used for Q, C, and Qs (see table below)

Values of k for Qs, Q, and C in units indicated Qs QC k English tons/day ft3/sec mg/l 0.0027 metric tons/day ft3/sec mg/l 0.0024 metric tons/day m3/sec mg/l 0.0864 1 English ton = 2000 lb 1 metric ton = 1000 kg = 9810 N Given values of Q and C, two techniques are available for computation of suspended-sediment discharge: the concentration graph – hydrograph method and the duration curve – sediment rating curve method. Both are described below. CONCENTRATION GRAPH – HYDROGRAPH METHOD This is the most accurate method of computing suspended-sediment load, but it is also the most laborious and requires the most complete and detailed discharge and sediment data. It is especially appropriate for computing the sediment discharge during individual storms where there has been extensive sampling over the entire hydrograph. It is difficult or impossible to use if sediment data on the stream are sparse. Analogous procedures can be used for computing bedload or dissolved-solids discharge. The procedure below, called the mean-interval method, is adapted from USGS Techniques of Water Resources Investigations, Book 3, Chapter C1, p. 49-50 (1972). a. Plot the stream hydrograph for the storms of interest. Use a time base and discharge scale that allows reasonable definition of the storm. A time base of 1/20 in = 1 hr or 2 hr is often about right for small streams. b. Plot the sediment concentration-graph for the same time period. This is simply a graph of the variation of sediment concentration C, with time. Use the same time scale as for the hydrograph and a reasonable scale for concentration. I usually plot both the hydrograph and the concentration-graph on top of one another, showing the concentration-graph with a colored line. Be sure that your discharge and concentration data points are evident on the plots. Note that defining the concentration-graph adequately requires a fair number of measurements during the storm. c. If there has been sufficient change in sediment concentration and water discharge during the storm period, the hydrograph will have to be subdivided into shorter time intervals before computing the sediment discharge. The diagram below ("Fig. 36") is the standard USGS guide as to whether subdivision is necessary. Its use is described on the next page. 1. Divide the hydrograph tentatively into time intervals. I typically start by drawing vertical lines through the troughs and peaks of the hydrograph and concentration graph-- these define the beginning and end of my time intervals. 2. For each time interval determine Qmin/Qmax, the ratio of minimum water discharge to maximum water discharge, and Cmin/Cmax, the ratio of minimum sediment concentration to maximum sediment concentration. 3. Mentally plot these ratios against each other on the subdivision graph. If the point falls to the right of the heavy line, the period should be subdivided into smaller time intervals. You don't have to be real picky in subdivision, but the hydrograph should be divided into enough time periods so that in each period the ratios fall to the left of the heavy line. d. For each time interval ti, determine the mean water discharge Qi from the hydrograph and the mean sediment concentration Ci from the concentration-graph. (If the hydrograph and concentration graph are single straight lines throughout the period, the mean values correspond to the midpoints of the respective lines.) e. Sediment discharge for each time interval ti is computed as: = k Qs Ci Qi ti where i 24 Q sediment discharge in time interval i (English or metric tons) si

Ci mean sediment concentration for time interval i (mg/l) 3 3 Qi mean water discharge for time interval i (ft /sec or m /sec) ti duration of time interval i (hours) k appropriate conversion factor for units used (from table on previous page) f. The total sediment discharge Qs over the time span of the hydrograph is: n = Qs ∑ Qsi where the hydrograph has been divided into n time intervals i =1 If the hydrograph did not need to be subdivided, then it can be treated as a single interval, and the formula above used with ti equal to the time base of the hydrograph. g. To get the sediment discharge for a year, this procedure must be carried out for each day, i.e., for all flows, and the results summed.

These calculations are most easily carried out using a table. A spreadsheet is ideal.

DURATION CURVE – SEDIMENT RATING CURVE METHOD

This is a speedier but less accurate method for estimating sediment discharge on a stream. It is particularly useful where we have only scattered water and sediment data, i.e., where we have irregular or discontinuous sampling. The technique can be used to calculated suspended-sediment, bedload, or dissolved-solids discharges. The flow- duration curve (or simply duration curve) at a measurement site is a plot of the percent of time any given mean daily discharge is equalled or exceeded there. It is typically plotted on log-probability paper. A suspended-sediment rating curve is a plot of instantaneous suspended-sediment discharge Qs vs. instantaneous water discharge Q for a measurement site. It is typically plotted on log-log paper. Similarly, we can create bedload and dissolved-solids rating curves if instantaneous data on them are available. The calculations below are best done using a table. Again a spreadsheet is ideal. An example table follows the procedure description below. Procedure: a. Plot the flow-duration curve for the stream at your site; in some cases this may need to be synthesized from regional relations. Use log-probability paper. b. Plot a sediment rating curve for your site using whatever water and sediment discharge data are available there. Fit the data with a straight line or a smooth curve, whichever appears more appropriate. c. Column 1: Divide the flow-duration curve into about 20 percent-of-time intervals. I suggest using the following class boundaries: 0.02, 0.10, 0.20, 0.50, 1, 2, 3, 5, 9, 15, 25, 35, 45, 55, 65, 75, 85, 95, 99, 99.8% d. For each percent-of-time increment determine: Column 2: duration of increment (∆ % of time) Column 3: median time % of increment e. Column 4: From the duration curve, determine the Q corresponding to each median time % f. Column 5: From the sediment rating curve determine the instantaneous Qs corresponding to each Q in column 4. g. Column 6: Determine the contribution of each time increment to the mean daily sediment discharge by multiplying each Qs (column 5) by the % time in the corresponding increment (column 2) and dividing by 100. h. Determine the mean daily suspended-sediment discharge (in tons/day) by summing column 6. This is the average daily sediment discharge for the period of time represented in the duration curve. i. Determine total suspended-sediment discharge (in tons for the period of interest by multiplying the mean daily suspended-sediment discharge (from step h) by the total number of days in the period.

Example: Suspended-sediment discharge for Main Lone Tree Creek (1) (2) (3) (4) (5) (6) lower bound time in median of mean daily instantaneous mean sediment of % time increment time Q Qs discharge for increment increment time increment ∆% % ft3/sec tons/day tons 0.02 0.02 0.01 39.2 292 0.0584 0.10 0.08 0.06 34.5 200 0.1600 0.20 0.10 0.15 29.1 123 0.1230 0.50 0.30 0.40 21.8 52 0.1560 1.0 0.50 0.75 16.5 23.5 0.1175 2.0 1.0 1.5 11.8 9.20 0.0920 3.0 1.0 2.5 9.0 4.45 0.0445 5.0 2.0 4.0 5.85 1.54 0.0308 9.0 4.0 7.0 4.60 0.89 0.0356 15.0 6.0 12.0 2.97 0.33 0.0198 25.0 10.0 20.0 1.41 0.059 0.0059 35.0 10.0 30.0 0.74 0.014 0.0014 45.0 10.0 40.0 0.43 0.005 0.0005 55.0 10.0 50.0 0.19 0.002 0.0002 65.0 10.0 60.0 0.093 0.00083 0.00008 75.0 10.0 70.0 0.051 0.00041 0.00004 85.0 10.0 80.0 0.031 0.00023 0.00002 95.0 10.0 90.0 0.018 – – 99.0 4.0 97.5 0.012 – – 99.8 0.8 99.4 0.010 – – TOTAL 99.8 – – – 0.846 Mean daily suspended sediment discharge: 0.846 tons/day Annual suspended sediment discharge: (0.846 t/day)(365 day/yr) = 309 tons/yr