Logarithmic plots of daily mean stream discharge versus daily mean concentration were drawn for seven gaging stations for the period 1982-90 (figs. 53 , 54 , 55 , 56 , 57 , 58 , 59 ). The scatter in the plots results from measurement and estimation error, from the nonlinear relation between stream discharge and sediment concentration, and from random changes in the sediment-transport process. Although mean concentration can be calculated for a day, the nonlinear relation with stream discharge will cause a range of concentrations to be associated with a single discharge. Random changes occur because sediment concentration will vary with tributary contribution, sporadic mass wasting, changes in sediment size, and reentrainment of sediments deposited by preceding streamflows. Storm-flow hysteresis and sediment lag can contribute scatter to plots of daily mean concentration versus stream discharge.
To detect coarse adjustments in the discharge/concentration relation, the mean values within an arbitrary period of one water year were used for sequences of statistical regressions. Daily mean sediment concentration was related to daily mean stream discharge by the equation,
where C is daily mean concentration in milligrams per liter, Q is daily mean stream discharge in cubic feet per second, and a and b are coefficients. Logarithmic transformation gives
which transforms the sediment data for a least-squares linear regression where log a is the axis intercept and b is the slope of the regression line. In the daily tables of sediment data, mean concentration was not recorded for days without sediment samples. If a mean concentration was not recorded, an estimated daily mean concentration was computed by equation 1 from mean stream discharge and the estimated sediment discharge. The a and b values for annual regressions are listed in tables 10a , 10b . Also listed are the coefficients of determination (r2) and the standard errors of estimate (Se). Standard error of estimate was computed by
where SSE is the sum of squares for error and n is the number of observations. Values of standard error are in log units. The zone equal to log C + 2Se above and below the regression line will include about 95 percent of the points.
In figures 53 through 59, the bottom graph includes regression lines for selected years during the study period. For each station, regression lines for the initial year, the final year, and an intermediate year (usually 1986) are plotted. A downward shift in the discharge-concentration relation is apparent at all stations. Other regression lines follow the overall trend, as documented in table 10. The downward shift corresponds with decreased mean sediment concentrations at given mean stream discharges. The separation of two distinct regions of points in the scatter plots for the North Fork Toutle River at Kid Valley and the Toutle River at Tower Road is attributable to sediment deposition behind the SRS, which was closed near the beginning of water year 1988.
Common discharges (the discharge value exceeded on 50 percent of the days of the period of record) and high discharges (the discharge value exceeded on 1 percent of the days) were used to illustrate long-term changes in sediment concentration at similar discharges. The distribution of stream discharge was calculated for the period of sediment- discharge records, and the 1- and 50-percent exceedance values were derived ( table 11 ). Concentrations at the discharge values exceeded on 1 percent and on 50 percent of days in the record period were then computed from the regression equation (table 10).
The relation between stream discharge and sediment concentration is obscured by sudden inputs of sediment produced by occasional rains in drier periods and by "first flushes." The phrase "first flush" is typically applied to storm flows that occur at the start of the rainy season after a long period of low flow. At that time, sediment concentrations are higher than measured at similar discharges later in the rainy season. Anomalously high concentrations at lower discharges also are measured during sporadic rains in late spring and summer. To separate the effects of sudden sediment inputs at lower discharges from the functional relation between sediment concentration and higher discharges, daily values between April 1 and October 31 were eliminated from the daily data. A separate set of regression equations was then derived for the remaining days (tables 12a , 12b ). The period analyzed, November 1 to March 31, has 151 days in non-leap years, and the resulting regressions are called "seasonal." In many cases, standard errors of estimate, Se, of the seasonal regressions were lower than those of the annual regressions in table 10.
The seasonal regression equations for November 1 to March 31 (table 12) were used to compute concentrations for common and high discharges. Two sediment concentrations for each regression equation were plotted by year in figures 60 and 61 . At the high discharges, all stations except the South Fork Toutle River at Camp 12 showed a decrease in concentration from 1982 to 1990 of 80 percent or greater. The non-parametric Kendall tau analysis was applied to concentrations for both the common and high discharges to detect any significant, monotonic correlation with time in years. Concentrations for common and high discharges at the Green River, the North Fork Toutle River, and the Toutle River at Tower Road were significantly correlated with time at the 95-percent confidence level ( table 13 ). Sediment concentrations for high discharges at the Muddy River were significantly correlated with time at the 95-percent confidence interval (table 13). Sediment concentrations at common and high discharges for Clearwater Creek and the South Fork Toutle River did not show significant correlations with time at a high confidence level.
