Sediment and the Environment (Proceedings of the Baltimore Symposium, May 1989) IAHS Publ. no. 184, 1989. Hysteresis and nonlinearity of discharge-sediment relationships in the Atchafalaya and lower Mississippi rivers Joann Mossa Coastal Geology Section, Louisiana Geological Survey, Box G, Uni­ versity Station, Baton Rouge, Louisiana 70893 ABSTRACT The Atchafalaya and lower Mississippi rivers in south Louisiana show the following characteristics: 1) Hysteresis effects are pronounced, especially during high discharge years where the sediment concentration and load maxima precede discharge maxima by several months and show decreased sediment concentra­ tions by the time discharge peaks; 2) The silt-clay and sand com­ ponents of the suspended sediment operate distinctively; 3) The total suspended-sediment concentration and the suspended silt-clay concentration follow quadratic power relationships; 4) Downstream differences in discharge-sediment relationships are apparent. INTRODUCTION The Atchafalaya and lower Mississippi rivers in south-central and southeastern Louisiana are two of the largest rivers in the United States and are an important source of fresh water and sedi­ ment for the Louisiana coastal zone. The drainage area of the Atchafalaya River at Simmesport, just downstream of the head and confluence of the Red River and Old River, is approximately 228,410 km2, not including the Mississippi River area. The Mis­ sissippi River is the largest river on the North American conti­ nent, draining approximately 3,224,000 km2. The Atchafalaya's flow consists of that from the Red River and controlled diversion at all stages from the Mississippi through the Old River Outflow Channel. Use of the Old River Control Structure, completed in 1963, and the Auxiliary Structure, com­ pleted in 1987, has increased flow in the Atchafalaya and decreased flow in the Mississippi. Flow is also diverted from the Mississippi to the Atchafalaya basin through the Morganza Floodway and to the Pontchartrain basin through the Bonnet Carre Spillway during floods. The Atchafalaya is approximately one-third the length and one- half the width of the Mississippi. In both rivers, bed material size decreases downstream; in the lower Mississippi it decreases from about 99% fine and medium sand near Old River to about 20% fine sand and 80% silt and clay at the Head of Passes (Keown, 1981; 1986). Suspended sediment in the lower Mississippi River also varies with depth; higher concentrations occur near the river bottom, primarily because of variations in sand concentration (Fisk, 1952; Wells, 1980). Other studies suggest that the suspended-sediment concentration and load in the lower Mississippi River are both discharge-depen­ dent (Jordan, 1965; Robbins, 1977; Sedimentation Seminar, 1977) and location-dependent (Everett, 1971; Wells, 1980; Meade, 1985). Studies of discharge-dependent behavior generally show linearity, because concentration being statistically independent from 105 Joann Mossa 106 discharge, was not examined in detail as was load, a dependent variable. Robbins (1977), in contrast, found that a linear power function did not represent the relationship between concentration and discharge for the 1973 water year. However, he did not attempt to apply a nonlinear relationship. Studies of location- dependent behavior are based on short-term data sets, and may be inadequate to characterize river behavior. The timing of sediment transport, statistical relationships in the Atchafalaya, and the differences in behavior between the two rivers have not been examined in detail previously. This investigation examines some of the physical relationships between discharge and sediment in the Atchafalaya and lower Missi­ ssippi rivers. The objectives are: 1) examining temporal variations in sediment transport to identify the physical factors that contribute to these variations between both rivers and downstream along these rivers; and 2) assessing the statistical relationships between discharge, sediment concentration and its components, and sediment load so that these interactions can be better understood. DATA BASE AND APPROACH The data base consisted of several instantaneous measurements of discharge, suspended sediment concentration, suspended sediment load, and percentage sand in the suspended load; they were col­ lected periodically between 1972 and 1986 on the Atchafalaya River at Simmesport (n = 438), the Lower Atchafalaya River at Morgan City (n = 174), and on the lower Mississippi River at Tarbert Landing (n = 460) and at Belle Chasse (n = 93) by the U.S. Geological Survey and the U.S. Army Corps of Engineers. The com­ posite suspended sediment samples consist of 15 and 40 point-inte­ grated samples (Federal Inter-Agency Sedimentation Project, 1963; Guy and Norman, 1970) on the Atchafalaya and lower Mississippi, respectively (Keown et al., 1977). Time series were plotted for each water year. Statistical relationships between discharge and sediment characteristics in the Atchafalaya and lower Mississippi River were examined using a linear least-squares regression, or power relationship, with dis­ charge (log10) as the independent variable, and concentration (log10), sand concentration (log10), silt-clay concentration (log10), suspended sediment load (log10), and the percentage sand as dependent variables. It was determined that a quadratic power function should also be applied once the suspended sediment data were plotted. The quadratic and linear statistical models were compared by means of a test of the full and reduced regression (Neter et al., 1983). This test was attempted to determine whether the addi­ tional parameters in the quadratic model substantially reduce the variance of the observations around the fitted regression line. The test statistic, F*, is a function of the error sum of squares of the reduced model SSE(R), and the error sum of squares of the full model SSE(F), namely: SSE(R) - SSE(F) - SSE(F) F* = dfR - dfF dfF 107 Hysteresis and nonlinearity of discharge-sediment relationships where dfR and dfF are the degrees of freedom for the reduced and full models. TEMPORAL VARIATIONS AND HYSTERESIS During high discharge years, the sediment concentration and load maxima may precede discharge maxima by several months, show­ ing a deficit in sediment supply by the time discharge peaks (Fig. 1). The hydrographs in both rivers show similar patterns, but in some years the sediment time series are very different. In high- discharge years, the highest suspended-sediment loads generally occur in the winter and early spring. During low discharge years, sediment maxima occur only shortly before or coincide with discharge maxima (Fig. 2). Most of the maxima are associated with pronounced increases in discharge. In low- and average-discharge years, the sediment load shows stronger seasonal relationships, and the highest loads occur during the spring and early summer. Extreme short-term variations in sediment concentration and load during both falling and rising stages are common. These variations occur in both rivers but are more frequent in the Atchafalaya. Some possible causes of these variations are bank failures, turbulent fluctuations of stream velocity, local dredging, and measurement and other errors. STATISTICAL RELATIONSHIPS AND NONLINEARITY Upstream, at Simmesport and Tarbert Landing, the relationship between discharge and silt-clay concentration in both rivers is nonlinear (Fig. 3; Table 1). The silt-clay component of the sus­ pended load increases at first, then levels, and may then decrease as discharge increases. Downstream, at Morgan City and Belle Chasse, the quadratic pattern is less well-defined but nonetheless evident. Correlation coefficients for the linear least-squares relationship between the silt-clay component and discharge range from r = 0.30 to 0.54 for the Atchafalaya and r = 0.12 to 0.68 for the Mississippi, increasing downstream; quadratic correlation coeffients range from r = 0.60 to 0.65 and r = 0.58 to 0.72. The sand concentration is more nearly linear, with correlation coeffi­ cients of r = 0.72 to 0.88 and r = 0.73 to 0.83, also increasing downstream. The relationship between total suspended concentration and dis­ charge also showed nonlinearity, because the silt-clay component is the larger proportion of the total concentration. The dis­ charges with highest sediment concentrations range from 5,000 to 15,000 m3 s"1 in the Atchafalaya and 10,000 to 30,000 m3 s"1 in the lower Mississippi rivers. The discharges below and above these ranges show lower concentrations. Linear correlation coefficients of r = 0.48 to 0.62 and r = 0.39 to 0.77, and quadratic correlation coefficients of r = 0.66 to 0.72 and r = 0.65 to 0.78 were computed. Quadratic power functions produced better correlations than linear power functions in all cases. The comparative test of the models using the F* statistic shows that, overall, the quadratic power model produces a better fit. 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