Turbidity (T) is the most ubiquitous of surrogate technologies used to estimate suspended-sediment concentration (SSC). The effects of sediment size on turbidity are well documented; however, effects from changes in particle size distributions (PSD) are rarely evaluated. Hysteresis in relations of SSC-to-turbidity (SSC∼T) for single stormflow events was observed and quantified for a dataset of 195 concurrent measurements of SSC, turbidity, discharge, velocity, and volumetric PSD collected during five stormflows in 2009–2010 on Yellow River at Gees Mill Road in metropolitan Atlanta, Georgia. Regressions of SSC-normalized turbidity (T/SSC) on concurrently measured PSD percentiles show an inverse, exponential influence of particle size on turbidity that is not constant across the size range of the PSD. The majority of the influence of PSD on T/SSC is from particles of fine silt and smaller sizes (finer than 16 µm). This study shows that small changes in the often assumed stability of the PSD are significant to SSC∼T relations. Changes of only 5 µm in the fine silt and smaller size fractions of suspended sediment PSD can produce hysteresis in the SSC∼T rating that can increase error and produce bias. Observed SSC∼T hysteresis may be an indicator of changes in sediment properties during stormflows and of potential changes in sediment sources. Trends in the PSD time series indicate that sediment transport is capacity limited for sand-sized sediment in the channel and supply limited for fine silt and smaller sediment from the hillslope.
 Surrogate metrics are increasingly used to provide suspended-sediment concentration (SSC) and load estimates that are critical to many engineering, ecological, and agricultural issues. SSC and load estimates from continuously monitored surrogate metrics typically provide greater accuracy, much higher temporal resolution, and potentially lower cost than traditional SSC-to-water discharge rating curve methods [Landers et al., 2012; Gray and Gartner, 2009, 2010; Selker and Ferre, 2009; Jastram et al., 2010]. Turbidity is the most ubiquitous of sediment-surrogate technologies used to estimate SSC and load and has been endorsed for sediment-monitoring programs by the U.S. Geological Survey, Federal Interagency Sedimentation Project, and others [Gray and Gartner, 2009; Rasmussen et al., 2009]. Turbidity is measured at a point and must be calibrated to average cross-section SSC using depth-integrated and width-integrated physical SSC samples collected using isokinetic samplers [Davis, 2005; Rasmussen et al., 2009]. Turbidity is known to be affected by several parameters, particularly sediment size, in addition to SSC; but those parameters are typically assumed to be stable for SSC-to-turbidity (SSC∼T) rating curves developed for a specific site using a specific turbidity meter [Lewis, 1996; Loperfido et al., 2010].
 Hysteresis in the relation of SSC to fluvial discharge (Q) for single stormflow events is a well-documented source of uncertainty in SSC-to-Q (SSC∼Q) rating curves and has been used to infer changing sediment sources during stormflows [Walling, 1977; Wood, 1977; Williams, 1989; Evans and Davies, 1998]. Hysteresis in SSC∼T relations for single stormflow events is often considered to be negligible and has received almost no discussion, although it has been observed by a few authors [Gilvear and Petts, 1985; Lewis, 1996; Lenzi and Lorenzo, 2000; Minella et al., 2008]. Hysteresis in SSC∼T relations is caused by factors distinct from SSC∼Q hysteresis and may contain distinctly valuable information on rise-to-recession changes in physical and/or optical sediment characteristics. Evaluation of SSC∼T hysteresis and isolation, to the extent possible, of its causes may explain uncertainty in SSC∼T ratings, suggest sampling strategies to reduce uncertainty, and provide qualitative or quantitative information on changing sediment sources.
 Hysteresis is evidenced graphically as a difference in the timing and/or shape of the time series response of two variables, such as SSC and Q. In a bivariate plot, hysteresis is indicated by a loop in the chronologically ordered data, as shown in Figure 1. If two variables have a similarly shaped, but nonsynchronous time series, then a “leading,” clockwise, or “trailing,” counterclockwise hysteresis will result. For example, in Figure 1, the SSC peak leads the discharge peak, producing clockwise SSC∼Q hysteresis. Williams  identified five classes of hysteresis in SSC∼Q relations and described how clockwise or counterclockwise hysteresis can occur where two variables have synchronous peaks, but different rise or recession slopes. Turbidity and SSC generally have near-synchronous peaks but may exhibit different relative slopes on the rise versus the recession. This difference in slopes can be quantified as a change in the ratio of turbidity to SSC. Turbidity and SSC will exhibit hysteresis if there is a consistent difference in the turbidity to SSC ratio between the SSC rise and the SSC recession. For example, in Figure 1, the turbidity per unit SSC is consistently higher on the recession than on the rise, producing clockwise SSC∼T hysteresis. The terminology in this paper for hysteresis of SSC∼T will be consistent with traditional usage in reference to SSC∼Q hysteresis. Thus, if the turbidity to SSC ratio is consistently larger on the recession than on the rise, we refer to this as clockwise SSC∼T hysteresis.
 Analysis of SSC∼Q hysteresis has been used to evaluate uncertainty in SSC∼Q rating curves and to evaluate watershed sediment transport characteristics [Walling, 1977; Wood, 1977; Lawler et al., 2006]. The SSC∼Q relation is determined by the sediment supply and the transport capacity of discharge; thus SSC∼Q hysteresis provides information on these processes. Causes of SSC∼Q hysteresis have been identified as early suspension of material from the stream channel, the timing of material transported from hillslope erosion, changing groundwater and throughflow hydrograph contributions, and the effects of main-stem backwater on tributary sediment flux [Wood, 1977; Williams, 1989; Horowitz., 2008]. The SSC∼Q relation typically exhibits leading, clockwise hysteresis (Figure 1) which is often ascribed to resuspension of sediment from the stream channel at the initiation of storm runoff and to relatively limited sediment supply on the stormflow recession. Lagging counter clockwise SSC∼Q hysteresis may indicate an influx of sediment on the discharge recession from an upstream tributary or mass wasting of stream banks on stormflow recessions [Lawler et al., 2006]. Characteristics of SSC∼Q hysteresis may change seasonally due to changing antecedent and erosion characteristics and over multiple years due to changing land use and climate [Wood, 1977].
 The SSC∼T relation for a given turbidity meter is directly determined by the effect on light scattering of suspended sediment particle concentration, physical properties, and optical properties [Downing et al., 1981; Lewis, 1996; International Organization for Standardization (ISO), 1999; Davies-Colley and Smith, 2001; Boss et al., 2009] and is not directly determined by changes in Q or velocity. Thus, hysteresis in SSC∼T may contain information on changing sediment characteristics that could not be interpreted from SSC or T independently or from SSC∼Q hysteresis. Lewis  observed SSC∼T hysteresis in more than half of sampled stormflows in a 3.83 km2 (1.48 mi2) forested watershed in coastal northern California. The hysteresis was clockwise and turbidity and SSC peaked synchronously for stormflows shown by Lewis , but potential causes of the hysteresis were not discussed. At a monitoring station downstream from the confluence of a reservoir and an unregulated tributary in Wales, U. K., Gilvear and Petts  found counterclockwise SSC∼T hysteresis for a stormflow dominated by tributary runoff and clockwise SSC∼T hysteresis for a stormflow dominated by reservoir release flow. The authors concluded the reversal in hysteresis implied changes in the sediment particle size distribution (PSD) or density between the two flows. The authors recommended sampling during the rise and recession of stormflows to reduce uncertainty and bias in load estimation if SSC∼T hysteresis is observed. In a 267 km2 (103 mi2) watershed in east central Iowa, Loperfido et al.  used high-frequency turbidity data to identify diel turbidity cycles during base flow conditions, attributed to nocturnal bioturbation, which had a substantial impact on sediment and nutrient transport during base flow. They also noted the implications for sampling strategies, because sampling during daytime only could lead to underestimates of sediment and nutrient flux for the studied watersheds. Gillain  likewise identified diel turbidity cycles in base flow in 11 watersheds in metropolitan Atlanta, Georgia, including the watershed used for this study, and showed significant correlation with dissolved oxygen from which bioturbation was inferred as the cause.
 This study describes the measured occurrence, causes, and effects of SSC∼T hysteresis on computed SSC and load for five stormflows measured in 2009–2010 on the Yellow River at Gees Mill Road in metropolitan Atlanta, Georgia. The data set includes continuous, concurrent measurements of precipitation, discharge, turbidity, temperature, velocity, and laser-diffraction-based volumetric particle concentration (VPC) and PSD. Concurrent physical samples were collected for mass SSC analysis every 1–2 h throughout each monitored stormflow event. These data are used here for the first time to show consistent, significant occurrence of SSC∼T hysteresis caused by measured small changes in suspended sediment PSD during storm runoff. From these results changes in sediment sources during stormflows are inferred, and sampling strategies to minimize bias and error in computed SSC and loads are identified.
2. Materials and Methods
 The Yellow River at Gees Mill Road streamgage (U.S. Geological Survey station 02207335, data available through waterdata.usgs.gov) is located in metropolitan Atlanta, Georgia in the southeastern United States (Figure 2). The monitoring site has a 673 km2 (260 mi2) watershed in the Piedmont physiographic province. Early in the 20th century, clear cut forestry in the Piedmont physiographic province was followed by row-crop agriculture, then abandonment of land management, leading to large-scale erosion. Abundant sand supply in channels and flood plains for many watersheds of this region is generally regarded as a legacy of those land use practices [Ruhlman and Nutter, 1999]. In the last half century, urbanization is the primary land use change that has affected soil erosion in this watershed [Landers et al., 2007]. Principal land uses in the study watershed in 2009 were residential (56%), commercial and industrial (15%), and forest (14%), with only 2% in agriculture [Atlanta Regional Commission, 2009]. The flows are well mixed in the main channel, which contains most runoff less than the mean annual peak. The median bed material size is about 0.5 mm in pools and 1–2 mm (coarse sand) in riffle areas, with less than 1% of the bed material composed of silt and clay (<0.063 mm). There are abundant supplies of sand-size material stored in the channel, banks, and flood plain. For example, a 0.5% annual exceedance probability flood in 2009 (not sampled for this study) deposited about 0.3–0.6 m (1–2 ft) of sand across the flood plain at this site.
 The Yellow River at Gees Mill Road streamgage is operated by the U.S. Geological Survey to collect continuous stage, discharge, and rainfall. During 2008–2010, the site was also equipped to measure continuous turbidity, specific conductance, temperature, velocity, laser-diffraction-based VPC and PSD, and with a fixed-point pumping sampler for collection of SSC samples. The multiparameter water-quality sonde, stage sensor, intake for the physical pumping sampler, and intake for the laser-diffraction VPC and PSD analyzer were all colocated and mounted 0.15–0.30 m (0.5–1 ft) above a large sloping granite ledge at a well-mixed location on the eastern bank of the stream. Velocity was measured with a side looking, 1.5 megahertz acoustic Doppler current profiler mounted on the downstream side of a bridge pier located 30.5 m (100 ft) downstream of the other instruments. Streamflow, turbidity, and velocity were measured and recorded every 15 min. VPC and PSD were measured and recorded every 1–2 h depending on stormflow duration.
 Physical SSC samples (251 samples) were obtained at the location of the turbidity meter using a fixed-point pumping sampler with 24 bottles of 1 L each, collecting samples every 1–2 h, depending on stormflow duration. Physical SSC samples were also collected 30.5 m (100 ft) downstream from the streamgage at the Gees Mill Road bridge cross section using equal-width-integrated (EWI) methods (24 samples) and single vertical methods (nine samples) that were calibrated to EWI concentrations. An isokinetic US DH-95 sediment sampler [Davis, 2005] was used for all samples collected from the bridge cross section. Standard sampling procedures were followed [Edwards and Glysson, 1999; Diplas et al., 2008]. All samples were analyzed in U.S. Geological Survey sediment laboratories for mass SSC and percent finer than 63 µm; and 13 samples were analyzed for mass PSD. The time assigned to the SSC samples was the beginning of sample collection for the fixed-point samples (sample duration was about 7 min) and the midpoint of sample collection for EWI samples.
 The SSC∼T hysteresis was evaluated in this study using 251 concurrent measurements of turbidity and fixed-point SSC samples (SSCPOINT), unadjusted to the cross-section average. The unadjusted SSCPOINT was used to obtain a direct comparison with the collocated turbidity meter, fixed-point sample intake, and laser-diffraction analyzer intake. Fluvial sediment load was computed by using the 33 channel cross-section samples (SSCXSEC) to calibrate the SSCPOINT samples to representative cross-section conditions using linear regression in logarithmic space. The SSCPOINT to SSCXSEC model calibration has a R2 of 0.96, a model standard error of 1.2 mg/L and is significant at a p-value of 5%. The model was used to compute the time series of SSCXSEC for computation of sediment loads for each stormflow as further described in Landers .
 Turbidity was measured using a nephelometric turbidity meter that measures light scattering using a light detector 90° from the incident light [ISO, 1999]. Nephelometric turbidity measurements quantify the optical properties that cause light to be scattered or attenuated rather than transmitted in straight lines through the measured solution. The turbidity meter used in this study is manufactured by YSI Incorporated (ysi.com) as model number 6136 and conforms to the ISO Method 7027 [ISO, 1999] measurement standards. The meter was calibrated following manufacturer recommendations using styrene formazin nephelometric unit (FNU) standard solutions at 0 and 1000 FNUs. Throughout the study period, the meter performed well and was regularly cleaned, compared with an independent turbidity meter, and verified against calibration standards.
 Laser-diffraction instruments characterize VPC and PSD by measuring the forward scattering angles produced by a laser striking small particles [Agrawal and Pottsmith, 2000]. Development of this technology for in situ deployment has provided major advances in environmental particle size measurement [Andrews et al., 2011]. The PSD is highly relevant to many facets of engineering and ecosystem issues, yet it is rarely measured in field studies [Reynolds et al., 2010]. In this study, a LISST-Streamside laser-diffraction instrument manufactured by Sequoia Scientific, Inc. (seqouiasci.com) measured VPC and PSD in 32 logarithmically spaced size classes from 2 to 381 µm. Stream water conveyed to the LISST-Streamside instrument via submersible pump is analyzed for PSD and VPC in a flow-through sample chamber. The unit was programmed to obtain a 120 s reading during which 4677 volumetric measurements are averaged. Stream water was cycled through the unit for 270 s before readings began, and clean water was pumped from a vessel into the unit between each measurement cycle to rinse the sample chamber and to provide a calibration check. Field operation of the laser-diffraction analyzer required much more field maintenance than the other instruments used in this study and it was not operational during brief periods of the data collection. Additional information on the site, materials, and methods is provided in Landers .
3.1. Hydrologic and Sediment Data Summary
 Comprehensive, concurrent hydrologic, sediment, and multiparameter surrogate measurements were obtained at Yellow River at Gees Mill Road in metropolitan Atlanta, Georgia during five stormflows that began in August 2009, and March, April, May, and September 2010. The sampled stormflows cover a range of typical stormflow runoff events from just above base flow to bank full, as indicated in Figure 3. The channel cross section is stable and did not change substantially over the study period. The smallest sampled storm began on 27 September 2010, rose only 0.49 m (1.6 ft) above seasonal base flow, and peaked at 10.4 m3/s (368 ft3/s). The largest sampled storm began on 3 May 2010, rose 2.86 m (9.4 ft) above seasonal base flow to approximately bank-full stage, and peaked at 144 m3/s (5070 ft3/s) with an annual exceedence probability of about 50% (2 year flood).
 The hydrologic and velocity characteristics of the five measured stormflows are summarized in Table 1. The reported precipitation was measured at the streamgage and is an inconsistent indicator of the total precipitation over the 673 km2 watershed, depending on the spatial uniformity of the precipitation. The total runoff is an indicator of the watershed precipitation, the antecedent conditions, and the seasonal variation in evapotranspiration. The approximate number of prior days since runoff-producing rainfall indicates antecedent hydrologic conditions and the supply of recently stored channel sediment available for suspension and transport. The reference velocity location is 43.77 m (143.6 ft) from the east bridge abutment and 0.71 m (2.34 ft) above the channel bed. The time series of discharge, turbidity, and fixed-point SSC are shown for each of the stormflows in Figure 4.
Table 1. Summary of Hydrologic and Reference Velocity Characteristics of Measured Storms
Event Begin Date
Reference velocity location is 43.77 m from east bridge abutment and 0.71 m above channel bed.
 Table 2 summarizes the average and maximum SSCPOINT, SSCXSEC, turbidity, VPC, and average volumetric PSD for each of the five measured stormflows. The maximum measured SSCXSEC for the five stormflows is 648 mg/L. The maximum measured SSCPOINT and turbidity for the five stormflows is 508 mg/L and 286 FNU, respectively. The volumetric PSD values are representative only for the measureable size range (2–381 µm) of the laser-diffraction analyzer and will differ from mass PSD because of different analytical methods as discussed in Landers . More than 30% of the mass SSC is less than 2 µm based on 13 mass PSD samples collected and analyzed during these stormflows. Nonetheless, the laser-diffraction analyzer provides a quantitative and highly informative time series of volumetric PSD within its measured range. The average size of sediments in the D10 and D16 fractions are all in the very fine silt size range (4–8 µm). Sediments in the D50 fraction are in the medium silt size range (16–31 µm) and in the D84 fraction are in the coarse silt to very fine sand ranges (31–125 µm). The laser-diffraction analyzer was operational to measure VPC and PSD for 195 of the 251 concurrent measurement time steps during the five stormflows, as indicated in Table 2.
Table 2. Average and Maximum SSC (Cross Section and Fixed Point), Turbidity, VPC, and Average Volumetric PSD for the Five Measured Stormflow Events
Stormflow Begin Date
Average SSCXSEC (mg/L)
Maximum SSCXSEC (mg/L)
SSCXSEC <63 µm (% by mass)
Average SSCPOINT (mg/L)
Maximum SSCPOINT (mg/L)
Number of SSC samples
Average turbidity (FNU)
Maximum turbidity (FNU)
Average fixed-point VPC (µL/L)
Maximum fixed-point VPC (µL/L)
Average volumetric D10 (µm)
Average volumetric D16 (µm)
Average volumetric D50 (µm)
Average volumetric D84 (µm)
Number of VPC measurements
3.2. Occurrence of Measured SSC∼Q and SSC∼T Hysteresis
 Hysteresis in the SSC∼Q and SSC∼T relations are indicated graphically in the time series and bivariate plots of Figure 4. The SSC∼Q hysteresis is clockwise for all five stormflows, but its shape and magnitude vary significantly with changing antecedent conditions and storm characteristics. Clockwise SSC∼Q hysteresis due to sediment stored in the channel between storms is indicated in Figure 4 by lower magnitude SSC∼Q hysteresis for secondary within-event rises in August 2009 and September 2010. The hydrograph shape of the May 2010 stormflow has a distinctive gradual rise, later peak, and more rapid recession than other observed events. This hydrograph shape likely indicates larger rainfall amounts in the upper watershed and contributes to the SSC∼Q hysteresis of this stormflow.
 If hysteresis in SSC∼Q and SSC∼T for single stormflow events is evident graphically, then it can be evaluated quantitatively in the range and coefficient of variation of the ratios of Q/SSC and T/SSC, respectively (Table 3). Where hysteresis is occurring, the magnitude of hysteresis (the nonlinearity in the bivariate plot) increases with increasing range and coefficient of variation in these ratios. The minimum and maximum Q/SSC ratios are 14 and 241% of the mean, respectively, and the standard deviation ranges from 21 to 74% of the mean Q/SSC ratio (Table 3). The magnitude of SSC∼Q hysteresis observed for these storms is not unexpected and causes uncertainty in the SSC∼Q rating that is strong motivation for using surrogate metrics other than discharge to estimate SSC and load.
Table 3. Statistical Characteristics of Ratio of Water Discharge to SSC (Q/SSC) and Turbidity to SSC (T/SSC)
Event Begin Date
Maximum Q/SSC (% of mean)
Minimum Q/SSC (% of mean)
Coefficient of variation Q/SSC (%)
Maximum T/SSC (% of mean)
Minimum T/SSC (% of mean)
Coefficient of variation T/SSC (%)
 The SSC∼T hysteresis for these five stormflows is much less pronounced than SSC∼Q hysteresis but is consistent in its occurrence and clockwise direction as shown in the bivariate plots of Figure 4. The peaks of the SSC and turbidity time series are nearly synchronous for all stormflows, and the SSC∼T hysteresis is evident graphically as a consistently higher T/SSC ratio on the receding SSC limb versus the rising SSC limb (Figure 4). The minimum and maximum T/SSC ratios are 56 and 139% of the mean, respectively, and the standard deviation ranges from 12 to 23% of the mean T/SSC ratio (Table 3). The significant magnitude and consistency of the SSC∼T hysteresis observed in these data prove rise-to-recession changes in the SSC∼T relation and indicate dynamic driving mechanisms.
 The occurrence of SSC∼T hysteresis also was evaluated in this study for the first time in four other urban watersheds in the metropolitan Atlanta area, where discrete SSC samples were collected during storm hydrographs between 2003 and 2007 (fluxes evaluated in Horowitz et al. ). The samples were from fixed-point pumping samplers calibrated to cross-section concentrations. The watersheds are located in the same physiographic province as Yellow River at Gees Mill, but are smaller with sizes ranging from 58.3 to 225 km2 (22.5–86.8 mi2) and are generally more urbanized. Hysteresis was evaluated for all sampled stormflows having at least five discrete SSC samples and with at least two samples collected during each rising and falling limb of the SSC time series. These criteria were met for 24 sampled stormflows that occurred in 2003–2007 in the four watersheds; 23 of these had clockwise SSC∼T hysteresis, while the 24th had no SSC∼T hysteresis. The samples were not analyzed for sediment size.
3.3. Potential Causes of SSC∼T Hysteresis
 Hysteresis in the SSC∼T relation for a single stormflow can be caused by a rise-to-recession change in sediment physical properties (size, shape, and density), optical properties (color), artifacts introduced by instrument performance (such as fouling), or SSC sample bias [Downing et al., 1981; Lewis, 1996; ISO, 1999; Davies-Colley and Smith, 2001; Boss et al., 2009]. SSC is the primary variable affecting turbidity [Downing, 2006], and SSC typically has much higher variance than other factors affecting turbidity for a specific turbidity sensor and stream site. Potential causes of SSC∼T hysteresis are evaluated here in the variation of SSC-normalized turbidity computed as T/SSC. This section discusses potential causes of SSC∼T hysteresis that were determined to be of insignificant or minor impact, followed by sections on changing PSD characteristics and how these affect SSC∼T hysteresis.
 The same turbidity meter was used throughout the study and was not affected by performance problems or fouling, as verified by regular verification of calibration against standards and onsite comparisons with independent, manually deployed turbidity meters. Thus, the turbidity meter was not the cause of observed SSC∼T hysteresis. A rise to recession bias in sampling errors associated with fixed-point pumping samplers [Edwards and Glysson, 1999] could manifest as SSC∼T hysteresis. This potential bias was evaluated by comparing residuals of regression of concurrently measured SSCPOINT and SSCXSEC collected during rising and falling conditions. Residuals from rising (20 samples) versus falling (13 samples) stormflow conditions are not statistically significantly different (t test, p = 0.64), thus this is not a significant cause of observed SSC∼T hysteresis. Flow velocity is highly correlated with SSC as a measure of the erosion and transport capacity of the main channel flow. If the SSC to velocity relation was significantly different for rising versus falling SSC, then this could be a spurious source of observed hysteresis in other relations. However, for these data, and employing the techniques that were used to analyze Q and T hysteresis, there was no hysteresis between SSC and velocity, and velocity was not a significant explanatory variable for T/SSC.
 Hysteresis of SSC∼T could be produced by substantial changes in sediment density during stormflow events. Any changes in sediment density would have an equal linear effect on T/SSC and VPC/SSC, and thus be evidenced in a positive correlation between these two ratios. The correlation between T/SSC and VPC/SSC for these data is actually weakly negative (r = −0.45 at p value < 1%) indicating that any effects from changing sediment density during the measured stormflows is overwhelmed by other factors. Sediment particle albedo (whiteness) affects light scattering, as discussed by Sutherland et al. , and changes in particle albedo over storm events could cause SSC∼T hysteresis. The sediment data were not analyzed for sediment albedo in this study, however, visual evaluation of sequential SSC sample bottles and (after analysis) dried sediment indicated no qualitative changes in sediment color or lightness. Because all of these potential causes of SSC∼T hysteresis were determined to be of insignificant or minor impact, changes in sediment PSD are likely to be the primary determinants of SSC∼T hysteresis in this study.
3.4. Particle Size Distribution Trends in Stormflow Events
 The high-resolution time series of volumetric PSD measured by the laser-diffraction analyzer provide valuable data to evaluate changing sediment sources during stormflows and the effects of particle size on SSC∼T hysteresis. Trends in PSD in single stormflow events were evaluated in the time series of sediment diameters for the 10th, 16th, median, 60th, and 84th percentiles of the volumetric PSD (D10, D16, D50, D60, and D84). For all five stormflows, the sizes of the D10 and D16 have decreasing trends during the rising streamflow hydrograph with a flat or increasing trend on the hydrograph recession. This descending trend is illustrated in Figure 5 which summarizes data measured using four independent technologies for the stormflow of 3–6 May 2010. Except for an initial increase, the D50 and larger size fractions do not have a significant trend during the stormflows and have much higher variance than the finer fractions of the PSD. Measured trends in the D10 and D16 of the PSD cover a very narrow size range, from 2 to 9 µm; however, they are well defined and correlate well with the independently measured ratio of turbidity to SSC as discussed further below.
 The trends in the D10 and D16 of the PSD time series indicate that the source of sediment is changing during stormflow events at this site. As D10 and D16 of the SSC decrease, the concentration of fine silt and clay size particles increases relative to the total SSC. If the source sediment PSD was unchanging in a transport-capacity-limited system, then all fractions of the suspended sediment PSD would become coarser on the stormflow rise with the increased capacity to entrain increasingly larger particles. If the source sediment PSD was unchanging in a sediment-supply-limited system, then the suspended sediment PSD also would become coarser over the event due to winnowing of the fines. The consistent trend during stormflow rises of decreasing size for the D10 and D16, and thus increasing relative concentration of these fine silt and clay sizes, indicates that the source sediment is changing during stormflow events.
 The increase in the relative SSC of fine silt and clay size particles during stormflow rises is likely due to a limited supply in the channel bed and banks of these size sediments; and to their abundant supply and transport from hill slope sources affected by rainfall impact, rill, and gully erosion. The watersheds in the study region contain abundant fine silt and clay-sized particles, primarily bound by cohesive forces and/or protected from erosive forces by vegetative land cover. The supply of these sediments for transport is controlled by detachment processes such as rainfall impact or rill and gully erosion, which is driven by climate, geology, land cover and use, and watershed management practices. Urbanization leads to increased exposure of fine sediments to rainfall impact erosion due to land disturbance for construction and increased rill and gully erosion due to greater frequency and energy of runoff events from impervious surfaces and developed drainage networks. Erosion control management regulations have a mitigating influence on these factors. Although urbanization is causing increased erosion in the watershed, the data indicate that the flux of fine silt and clay size particles remains supply limited.
 These smaller particles may not be stored in the streambed between stormflows because even lower stream velocities are adequate to transport them. For example, base flow velocity prior to each of the measured stormflows was greater than the computed critical velocity of 0.15 m/s (0.48 ft/s) for incipient motion of 8 µm sediment at the channel bed at the velocity reference location. The limited availability of small size particles in the channel is further indicated by the difference between the percent of the material smaller than 63 µm in the sampled bed-material sediment (less than 1%) versus that of the SSC samples (62–92%, Table 2). These data also indicate the interesting condition in which suspended-sediment transport is capacity limited for coarser fractions of sediment sourced in the channel and supply limited for finer fractions delivered from the hillslope.
 Prior studies have reported an increase in the percent of very fine material with discharge for some watersheds and have cited similar causes [Slattery and Burt, 1997; Lawler et al., 2006]. For a 4.90 km2 (1.89 mi2) alpine watershed in northeastern Italy, Lenzi and Lorenzo  found that the SSC∼T relation is affected by changing PSDs due both to changing entrainment velocities and changing influx of silty material eroded from failed channel banks and from hillslopes. They developed separate SSC∼T rating curves for changing particle sizes but did not assess SSC∼T hysteresis.
3.5. Changing Sediment Size Effects on SSC∼T Hysteresis
 The effect of sediment size on turbidity creates a size-concentration ambiguity that has been widely noted [Lewis, 1996; Gray and Gartner, 2009]. In Mie scattering theory, if the effects on light scattering of sediment concentration, density, color, and shape are unchanging, or if the effects can be normalized for, then the amount of light scattered by homogenous spheres is a function of the scattering surface area [van de Hulst, 1981; Sutherland et al., 2000; Clavano et al., 2007; Boss et al., 2009]. Summarizing data for particles between about 30 and 1000 µm from previous studies, Downing  and Sutherland et al.  showed an inverse relation between particle size and SSC-normalized optical backscatter, after adjusting for other factors affecting light scattering. Although the effect of sediment size on turbidity is a known factor of turbidity as a SSC surrogate, stability of PSD during stormflow events is generally assumed and corrections for SSC∼T hysteresis have not been attempted in prior studies.
 The correlation of SSC-normalized turbidity (T/SSC) and the D10 and D16 sediment sizes is evident in the time series data shown for the 3–6 May 2010 stormflow in Figure 5. This relation is summarized for 195 samples from all five stormflows in Figure 6 in which the data are from three independently measured metrics: mass SSC, turbidity, and laser-diffraction-based volumetric D10 and D16. The regression lines in Figure 6 are statistically significant at p-values of 5%, and scatter around the lines may be due to effects of particle shape, other size fractions, and (or) measurement errors. The slope of the least squares fit in logarithmic space is −0.76 for D10 and −0.66 for D16, compared with the slope of −1.0 reported by Downing . The results of log-transformed least squares regressions of (T/SSC) and sediment size for the 10th, 16th, 50th, 60th, and 84th PSD percentiles are given in Table 4 and shown in Figure 7 (in which the sediment size data were centered for graphical comparison). The relation of normalized turbidity to D84 is not statistically significant for these data in which the average D84 is 67 µm and the range is 25–58 µm.
Table 4. Results of Regression of Log-Transformed, SSC-Normalized Turbidity on Volumetric, Laser-Diffraction-Based Sediment Diameter (D) for 10th, 16th, 50th, 60th, and 84th Percentiles of Particle Size Distribution (PSD) for Yellow River at Gees Mill Road in Metropolitan Atlanta, Georgia
Average diameter (µm)
Logarithmic slope with T/SSC
p-Value less than
 The magnitude of the regression slope and the R2 (the influence and the percent of variance explained) increase with decreasing PSD percentile and size range. The influence on T/SSC of D10 is more than double that of D50; and D10 explains 44% of the variance in T/SSC compared with 14% for D50 (Table 4). These results show that the inverse, exponential influence of particle size on turbidity is not constant across the PSD but increases for the finer fractions of the PSD for these data. These results are in agreement with the theoretical results of Clavano et al.  who found that for modeled PSDs of nonspherical shapes with particle sizes ranging from 0.2 to 200 µm, at least 50% of the contribution to light scattering, attenuation, and absorption comes from particles smaller than 10 µm. For these data, changes of only a few microns in the fractions of the PSD less than about 10 µm significantly affect turbidity and explain observed SSC∼T hysteresis.
 These findings show that for the many studies where turbidity is being used to compute SSC, the assumed stability of the PSD is highly significant, particularly for fine silt and smaller sizes (16 µm and smaller). Even small changes of about 5 µm in the fine silt and smaller size fractions of suspended sediment PSD will create changes in the SSC∼T rating that can increase error and produce bias. Turbidity provides a sensitive indicator of suspended fine silt and smaller size particles and associated constituents, while suspended sand information from turbidity may be an extrapolation from the effects of smaller sizes of the PSD. Thus, SSC∼T hysteresis should be regularly evaluated where turbidity is used as a SSC surrogate.
 Concurrent turbidity and SSC samples during single stormflow events can be used to evaluate SSC∼T hysteresis and to indicate relative stability of factors, including PSD, that are deterministic to the SSC∼T rating. Observed SSC∼T hysteresis may be used to identify changes in sediment properties during stormflow events, in some cases without high-resolution PSD data, if other potential causes can be evaluated as negligible. SSC∼T hysteresis for single events may indicate a transition from channel to hillslope sediment sources as discussed previously. Trends in magnitude of SSC∼T hysteresis between events may indicate changing initial conditions related to hillslope erodibility or bank stability. Sampling to develop SSC∼T rating curves should cover the range of potential changes in PSD, including rise to recession changes, to avoid bias errors resulting from SSC∼T hysteresis.
3.6. Effects of Hysteresis on Sediment Load Computations
 Suspended sediment load is a key indicator of many cumulative watershed processes. Computation of suspended sediment load often is the primary purpose of SSC sampling and monitoring streamflow and turbidity as a sediment surrogate. The effect of SSC∼Q hysteresis on the SSC∼Q rating is evident in Figure 8, particularly in the pattern of points for specific stormflow events. Event-to-event changes in the magnitude of SSC∼Q hysteresis and slope of the SSC∼Q rating indicated in Figure 8 may reflect changes in sediment supply and transport capacity. The least-squares regression for the SSC∼Q rating curve has an R2 of 0.57, and the error of prediction ranges from −48 to +58% for individual stormflows and is 21% overall (Table 5). Compared with the SSC∼Q rating, the effect of SSC∼T hysteresis is much smaller and the SSC∼T rating has a much better fit as shown in Figure 9. The least-squares regression for the SSC∼T rating curve has an R2 of 0.90, and the error of prediction ranges from −23 to 12% for individual stormflows and is only 1.6% overall (Table 5). This comparison clearly demonstrates the advantages of using turbidity instead of, or in addition to discharge as a surrogate measure of SSC and for computation of sediment load [Rasmussen et al., 2009].
Table 5. Measured and Estimated Sediment Load for Yellow River at Gees Mill Road in Metropolitan Atlanta, Georgiaa
 The observed SSC∼T hysteresis would produce biased computed sediment loads if the collection of samples were substantially biased to the rising or falling limb of the SSC time series. For example, if samples were collected only on the falling hydrograph due to logistical challenges at a site with clockwise SSC∼T hysteresis, then the SSC∼T rating curve would be biased low and SSC would be underestimated by T on the rising limbs of runoff. In this study, the average effect of SSC∼T hysteresis on computed load was minimized by collecting samples on the rising and falling SSC limbs and using a best fit modeling approach. The effect of SSC∼T hysteresis can be partially accounted for in this study by including D10 in the regression model because changes in D10 explain the SSC∼T hysteresis as discussed previously. For the model of SSC as a function of both turbidity and D10, the error of prediction in Table 5 is based on the comparison with the measured load where D10 was successfully measured (195 of the 251 total measurements). For this model results for individual events are notably more accurate (Table 5), the explanation of variance improved slightly from a R2 of 0.90–0.94, however the change in the overall error of prediction is negligible. These errors for specific stormflow events would be particularly important in a study of event mean SSCs or event loads.
 The concurrent time series data used in this analysis exhibit positive first-order autoregression at a 1% significance level, based on the Durbin-Watson test statistic. To evaluate the effects of this autocorrelation, the regression models were run using maximum likelihood estimation in a generalized least squares model for each regression model between SSC and explanatory variables. The explanatory variables remained significant at p values of 1% and the model standard error was not greater than that computed using ordinary least squares, within reported significant digits.
4. Summary and Conclusions
 Turbidity is widely used as a surrogate to estimate SSC and load with typically greater accuracy, much higher temporal resolution, and potentially lower cost than traditional SSC∼Q rating curve methods. Turbidity is known to be affected by several parameters, particularly sediment size, in addition to SSC; but those parameters are typically assumed to be stable or proportional during stormflows and for a site specific SSC∼T rating. Hysteresis in the SSC∼T relation for single stormflows has been observed in this study for a concurrent dataset of 251 SSC, turbidity, discharge, velocity, and temperature measurements and 195 volumetric concentration and PSD measurements collected during five stormflow events in 2009 and 2010 on Yellow River at Gees Mill Road in metropolitan Atlanta, Georgia. Hysteresis was also observed in the SSC∼T relation for 23 of 24 stormflows sampled from 2003 to 2007 at four additional sites in metropolitan Atlanta, indicating the possibility of common driving mechanisms for the SSC∼T relations for watersheds of this region. Hysteresis in SSC∼T relations for single stormflow events has received almost no discussion previously and has not previously been quantitatively related to changing PSD. The data collected in this study are used here for the first time to compare SSC∼Q and SSC∼T hysteresis, to characterize observed SSC∼T hysteresis, isolate its causes, relate those causes to changing PSD and potential watershed sediment processes, and to evaluate the effects of SSC∼T hysteresis on sampling plans and computed sediment load.
 The SSC∼Q hysteresis is clockwise for all of the five stormflows with the SSC peak leading the discharge peak, primarily due to sediment stored in the channels being entrained and transported at the beginning of runoff. The standard deviation of Q/SSC ranges from 21 to 74% of the mean Q/SSC ratio (Table 3). The observed SSC∼Q hysteresis is a source of significant uncertainty in the SSC∼Q rating curve but also is a source of information about the relative magnitude of total sediment coming from resuspension on the stormflow rise of sediment stored in the stream channel. The SSC∼T hysteresis for these five stormflows is much less pronounced than SSC∼Q hysteresis but is consistent in its occurrence and clockwise direction. The SSC and turbidity time series peaks are nearly synchronous, but the T/SSC ratio is consistently higher on the receding SSC limb versus the rising SSC limb. The standard deviation of T/SSC ranges from 12 to 23% of the mean T/SSC ratio (Table 3).
 The significant magnitude and consistency of the SSC∼T hysteresis observed in these data show rise-to-recession changes in the SSC∼T relation that can be caused by changes in sediment physical properties, optical properties, instrument performance, or SSC sample bias. These potential causes of SSC∼T hysteresis were each evaluated and, for these data, changing sediment size characteristics were isolated as the primary cause. Data for all five stormflows show sizes of the D10 and D16 to be decreasing during the rising streamflow hydrograph and stable or increasing on the hydrograph recession. Observed trends in the D10 and D16 of the PSD time series indicate that the source of suspended sediments is changing during stormflow events at this site. The increased relative concentration of fine silt and clay size particles during stormflow rises is likely due to a limited supply of these size sediments in the channel bed and banks and to their availability and transport from hill slope sources affected by rainfall impact, rill, and gully erosion. The results indicate that sediment transport is capacity limited for sand-sized sediment sourced in the channel; and supply limited for fine silt and smaller sediment delivered from the hillslope.
 Results of regression of log-transformed (T/SSC) and sediment size for the 10th, 16th, 50th, and 60th PSD percentiles show an inverse, exponential influence of particle size on turbidity that is not constant across the PSD. The majority of the influence of PSD on T/SSC and of the amount of T/SSC variance explained by PSD is from particles in the fine silt and smaller size range. Changes of only a few microns in the fine silt and smaller size fractions of the PSD significantly affect turbidity and explain observed SSC∼T hysteresis. These results are in agreement with the theoretical results of Clavano et al.  who found that at least 50% of the contribution to light scattering, attenuation, and absorption comes from particles smaller than 10 µm for modeled PSDs.
 Turbidity should provide a sensitive indicator of suspended fine silt and smaller size particles and associated constituents and may be particularly valuable for studies focused on small particle sizes. In studies of systems where most of the suspended sediment is sand sized, the SSC∼T relation may be dependent on a relatively small fraction of the PSD, and minor changes in the PSD could have a large influence on the SSC∼T relation. In any case, turbidity is only a bulk optical indicator and quantitative information on changes in the PSD and how these may affect the SSC∼T relation and the fluvial system will require independent measurements.
 This study shows that the often assumed stability of sediment PSD is highly significant to SSC∼T rating curves, particularly for fine silt and smaller sizes. Small changes of less than 5 µm in the fine silt and smaller size fractions of suspended sediment PSD will create changes in the SSC∼T rating that can increase error and produce bias. Thus, the stability of the PSD should be evaluated where turbidity is used as a SSC surrogate. Most sediment studies do not collect high-resolution time series of PSD. However, concurrent turbidity and SSC samples for single stormflow events can be used to evaluate SSC∼T hysteresis and to indicate relative stability of factors, including PSD, that are deterministic to the SSC∼T rating. Observed SSC∼T hysteresis may be used to identify changes in sediment properties during stormflow events and potential changes in sediment sources, even without high-resolution PSD data, if other potential causes can be evaluated as negligible.
 Sampling to develop SSC∼T rating curves should cover the range of potential changes in PSD, including rise to recession, seasonal, and (or) long-term changes, to avoid bias errors in computed loads resulting from SSC∼T hysteresis. This may be particularly important where individual stormflow results are being studied, as for computation of stormflow mean concentrations of sediment and sediment-associated constituents. Use of a best fit modeling approach is also advisable to minimize the effect of SSC∼T hysteresis on the SSC∼T model.
 The results of this study demonstrate the value of detailed physical sampling, monitoring using multiple sensor technologies and metrics, and the importance of metadata about instruments, environmental sample material, environmental conditions, and methods. Multiple continuous data streams with associated metadata can produce understanding that is not redundant, but synergistic. The physical samples for SSC and PSD, together with streamflow discharge were the foundation data of this study. Detailed, discrete SSC and PSD data can yield improved understanding and methods for use of sediment surrogates including turbidity, laser-diffraction, and acoustic metrics. These methods, in turn, can lead to improved solutions to the many important sediment-related environmental and engineering problems.
 The financial and collegial support of the U.S. Geological Survey for this work is gratefully acknowledged.