Hysteresis in suspended sediment to turbidity relations due to changing particle size distributions

Hysteresis in suspended sediment to turbidity relations due tochanging particle size distributions

Mark N. Landers1 and Terry W. Sturm2

Received 1 March 2013; revised 24 June 2013; accepted 27 June 2013; published 9 September 2013.

[1] Turbidity (T) is the most ubiquitous of surrogate technologies used to estimatesuspended-sediment concentration (SSC). The effects of sediment size on turbidity are welldocumented; however, effects from changes in particle size distributions (PSD) are rarelyevaluated. Hysteresis in relations of SSC-to-turbidity (SSC�T) for single stormflow eventswas observed and quantified for a dataset of 195 concurrent measurements of SSC,turbidity, discharge, velocity, and volumetric PSD collected during five stormflows in2009–2010 on Yellow River at Gees Mill Road in metropolitan Atlanta, Georgia.Regressions of SSC-normalized turbidity (T/SSC) on concurrently measured PSDpercentiles show an inverse, exponential influence of particle size on turbidity that is notconstant across the size range of the PSD. The majority of the influence of PSD on T/SSC isfrom particles of fine silt and smaller sizes (finer than 16 mm). This study shows that smallchanges in the often assumed stability of the PSD are significant to SSC�T relations.Changes of only 5 mm in the fine silt and smaller size fractions of suspended sediment PSDcan 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 duringstormflows and of potential changes in sediment sources. Trends in the PSD time seriesindicate that sediment transport is capacity limited for sand-sized sediment in the channeland supply limited for fine silt and smaller sediment from the hillslope.

Citation: Landers, M. N., and T. W. Sturm (2013), Hysteresis in suspended sediment to turbidity relations due to changing particlesize distributions, Water Resour. Res., 49, 5487–5500, doi:10.1002/wrcr.20394.

1. Introduction

[2] Surrogate metrics are increasingly used to providesuspended-sediment concentration (SSC) and load esti-mates that are critical to many engineering, ecological, andagricultural issues. SSC and load estimates from continu-ously monitored surrogate metrics typically provide greateraccuracy, much higher temporal resolution, and potentiallylower cost than traditional SSC-to-water discharge ratingcurve 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-surrogatetechnologies used to estimate SSC and load and has beenendorsed for sediment-monitoring programs by the U.S.Geological Survey, Federal Interagency Sedimentation Pro-ject, and others [Gray and Gartner, 2009; Rasmussen etal., 2009]. Turbidity is measured at a point and must becalibrated to average cross-section SSC using depth-

integrated and width-integrated physical SSC samples col-lected using isokinetic samplers [Davis, 2005; Rasmussenet al., 2009]. Turbidity is known to be affected by severalparameters, particularly sediment size, in addition to SSC;but those parameters are typically assumed to be stable forSSC-to-turbidity (SSC�T) rating curves developed for aspecific site using a specific turbidity meter [Lewis, 1996;Loperfido et al., 2010].

[3] Hysteresis in the relation of SSC to fluvial discharge(Q) for single stormflow events is a well-documented sourceof uncertainty in SSC-to-Q (SSC�Q) rating curves and hasbeen used to infer changing sediment sources during storm-flows [Walling, 1977; Wood, 1977; Williams, 1989; Evansand Davies, 1998]. Hysteresis in SSC�T relations for singlestormflow events is often considered to be negligible and hasreceived almost no discussion, although it has been observedby a few authors [Gilvear and Petts, 1985; Lewis, 1996;Lenzi and Lorenzo, 2000; Minella et al., 2008]. Hysteresisin SSC�T relations is caused by factors distinct fromSSC�Q hysteresis and may contain distinctly valuable infor-mation on rise-to-recession changes in physical and/or opti-cal sediment characteristics. Evaluation of SSC�Thysteresis and isolation, to the extent possible, of its causesmay explain uncertainty in SSC�T ratings, suggest sam-pling strategies to reduce uncertainty, and provide qualitativeor quantitative information on changing sediment sources.

[4] Hysteresis is evidenced graphically as a difference inthe timing and/or shape of the time series response of two

1Office of Surface Water, U.S. Geological Survey, Norcross, Georgia,USA.

2School of Civil and Environmental Engineering, Georgia Institute ofTechnology, Atlanta, Georgia, USA.

Corresponding author: M. N. Landers, Office of Surface Water, U.S.Geological Survey, 1770 Corporate Drive, Suite 500, Norcross, GA 30093,USA. ([email protected])

©2013. American Geophysical Union. All Rights Reserved.0043-1397/13/10.1002/wrcr.20394

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WATER RESOURCES RESEARCH, VOL. 49, 5487–5500, doi:10.1002/wrcr.20394, 2013

variables, such as SSC and Q. In a bivariate plot, hysteresisis indicated by a loop in the chronologically ordered data,as shown in Figure 1. If two variables have a similarlyshaped, but nonsynchronous time series, then a ‘‘leading,’’clockwise, or ‘‘trailing,’’ counterclockwise hysteresis willresult. For example, in Figure 1, the SSC peak leads thedischarge peak, producing clockwise SSC�Q hysteresis.Williams [1989] identified five classes of hysteresis inSSC�Q relations and described how clockwise or counter-clockwise hysteresis can occur where two variables havesynchronous peaks, but different rise or recession slopes.Turbidity and SSC generally have near-synchronous peaksbut may exhibit different relative slopes on the rise versusthe recession. This difference in slopes can be quantified asa change in the ratio of turbidity to SSC. Turbidity andSSC will exhibit hysteresis if there is a consistent differ-ence in the turbidity to SSC ratio between the SSC rise andthe SSC recession. For example, in Figure 1, the turbidityper unit SSC is consistently higher on the recession than onthe rise, producing clockwise SSC�T hysteresis. The ter-minology in this paper for hysteresis of SSC�T will beconsistent with traditional usage in reference to SSC�Qhysteresis. Thus, if the turbidity to SSC ratio is consistentlylarger on the recession than on the rise, we refer to this asclockwise SSC�T hysteresis.

[5] Analysis of SSC�Q hysteresis has been used to eval-uate uncertainty in SSC�Q rating curves and to evaluatewatershed sediment transport characteristics [Walling,1977; Wood, 1977; Lawler et al., 2006]. The SSC�Q rela-tion is determined by the sediment supply and the transportcapacity of discharge; thus SSC�Q hysteresis provides in-formation on these processes. Causes of SSC�Q hysteresishave been identified as early suspension of material fromthe stream channel, the timing of material transported fromhillslope erosion, changing groundwater and throughflowhydrograph contributions, and the effects of main-stembackwater on tributary sediment flux [Wood, 1977; Wil-liams, 1989; Horowitz., 2008]. The SSC�Q relation typi-cally exhibits leading, clockwise hysteresis (Figure 1)which is often ascribed to resuspension of sediment fromthe stream channel at the initiation of storm runoff and torelatively limited sediment supply on the stormflow reces-sion. Lagging counter clockwise SSC�Q hysteresis mayindicate an influx of sediment on the discharge recessionfrom an upstream tributary or mass wasting of streambanks on stormflow recessions [Lawler et al., 2006]. Char-acteristics of SSC�Q hysteresis may change seasonally

due to changing antecedent and erosion characteristics andover multiple years due to changing land use and climate[Wood, 1977].

[6] The SSC�T relation for a given turbidity meter isdirectly determined by the effect on light scattering of sus-pended sediment particle concentration, physical proper-ties, 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 ve-locity. Thus, hysteresis in SSC�T may contain informationon changing sediment characteristics that could not beinterpreted from SSC or T independently or from SSC�Qhysteresis. Lewis [1996] observed SSC�T hysteresis inmore than half of sampled stormflows in a 3.83 km2 (1.48mi2) forested watershed in coastal northern California. Thehysteresis was clockwise and turbidity and SSC peakedsynchronously for stormflows shown by Lewis [1996], butpotential causes of the hysteresis were not discussed. At amonitoring station downstream from the confluence of areservoir and an unregulated tributary in Wales, U. K., Gil-vear and Petts [1985] found counterclockwise SSC�T hys-teresis for a stormflow dominated by tributary runoff andclockwise SSC�T hysteresis for a stormflow dominated byreservoir release flow. The authors concluded the reversalin hysteresis implied changes in the sediment particle sizedistribution (PSD) or density between the two flows. Theauthors recommended sampling during the rise and reces-sion of stormflows to reduce uncertainty and bias in loadestimation if SSC�T hysteresis is observed. In a 267 km2

(103 mi2) watershed in east central Iowa, Loperfido et al.[2010] used high-frequency turbidity data to identify dielturbidity cycles during base flow conditions, attributed tonocturnal bioturbation, which had a substantial impact onsediment and nutrient transport during base flow. They alsonoted the implications for sampling strategies, becausesampling during daytime only could lead to underestimatesof sediment and nutrient flux for the studied watersheds.Gillain [2005] likewise identified diel turbidity cycles inbase flow in 11 watersheds in metropolitan Atlanta, Geor-gia, including the watershed used for this study, andshowed significant correlation with dissolved oxygen fromwhich bioturbation was inferred as the cause.

[7] This study describes the measured occurrence,causes, and effects of SSC�T hysteresis on computed SSCand load for five stormflows measured in 2009–2010 on theYellow River at Gees Mill Road in metropolitan Atlanta,

Figure 1. Conceptual hysteresis due to differences in timing or shape of time series data. (Note turbid-ity and suspended sediment concentration (SSC) are shown on separate axes.)

LANDERS AND STURM: HYSTERESIS SUSPENDED SEDIMENT-TURBIDITY WITH PARTICLE SIZE

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Georgia. The data set includes continuous, concurrentmeasurements of precipitation, discharge, turbidity, tem-perature, velocity, and laser-diffraction-based volumetricparticle concentration (VPC) and PSD. Concurrent physicalsamples were collected for mass SSC analysis every 1–2 hthroughout each monitored stormflow event. These data areused here for the first time to show consistent, significantoccurrence of SSC�T hysteresis caused by measured smallchanges in suspended sediment PSD during storm runoff.From these results changes in sediment sources duringstormflows are inferred, and sampling strategies to mini-mize bias and error in computed SSC and loads areidentified.

2. Materials and Methods

[8] The Yellow River at Gees Mill Road streamgage(U.S. Geological Survey station 02207335, data available

through waterdata.usgs.gov) is located in metropolitanAtlanta, Georgia in the southeastern United States (Figure2). The monitoring site has a 673 km2 (260 mi2) watershedin the Piedmont physiographic province. Early in the 20thcentury, clear cut forestry in the Piedmont physiographicprovince was followed by row-crop agriculture, then aban-donment of land management, leading to large-scale ero-sion. Abundant sand supply in channels and flood plains formany watersheds of this region is generally regarded as alegacy of those land use practices [Ruhlman and Nutter,1999]. In the last half century, urbanization is the primaryland use change that has affected soil erosion in this water-shed [Landers et al., 2007]. Principal land uses in the studywatershed in 2009 were residential (56%), commercial andindustrial (15%), and forest (14%), with only 2% in agri-culture [Atlanta Regional Commission, 2009]. The flowsare well mixed in the main channel, which contains mostrunoff less than the mean annual peak. The median bed

Figure 2. Location map for study watershed, Yellow River near Atlanta, Georgia.


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material size is about 0.5 mm in pools and 1–2 mm (coarsesand) in riffle areas, with less than 1% of the bed materialcomposed of silt and clay (<0.063 mm). There are abun-dant supplies of sand-size material stored in the channel,banks, and flood plain. For example, a 0.5% annual exceed-ance probability flood in 2009 (not sampled for this study)deposited about 0.3–0.6 m (1–2 ft) of sand across the floodplain at this site.

[9] The Yellow River at Gees Mill Road streamgage isoperated by the U.S. Geological Survey to collect continu-ous stage, discharge, and rainfall. During 2008–2010, thesite was also equipped to measure continuous turbidity,specific conductance, temperature, velocity, laser-diffraction-based VPC and PSD, and with a fixed-pointpumping sampler for collection of SSC samples. The multi-parameter water-quality sonde, stage sensor, intake for thephysical pumping sampler, and intake for the laser-diffraction VPC and PSD analyzer were all colocated andmounted 0.15–0.30 m (0.5–1 ft) above a large sloping gran-ite ledge at a well-mixed location on the eastern bank ofthe stream. Velocity was measured with a side looking, 1.5megahertz acoustic Doppler current profiler mounted onthe downstream side of a bridge pier located 30.5 m (100ft) downstream of the other instruments. Streamflow, tur-bidity, and velocity were measured and recorded every 15min. VPC and PSD were measured and recorded every 1–2h depending on stormflow duration.

[10] Physical SSC samples (251 samples) were obtainedat the location of the turbidity meter using a fixed-pointpumping sampler with 24 bottles of 1 L each, collectingsamples 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 Roadbridge cross section using equal-width-integrated (EWI)methods (24 samples) and single vertical methods (ninesamples) that were calibrated to EWI concentrations. Anisokinetic US DH-95 sediment sampler [Davis, 2005] wasused for all samples collected from the bridge cross section.Standard sampling procedures were followed [Edwardsand Glysson, 1999; Diplas et al., 2008]. All samples wereanalyzed in U.S. Geological Survey sediment laboratoriesfor mass SSC and percent finer than 63 mm; and 13 sampleswere analyzed for mass PSD. The time assigned to the SSCsamples was the beginning of sample collection for thefixed-point samples (sample duration was about 7 min) andthe midpoint of sample collection for EWI samples.

[11] The SSC�T hysteresis was evaluated in this studyusing 251 concurrent measurements of turbidity and fixed-point SSC samples (SSCPOINT), unadjusted to the cross-section average. The unadjusted SSCPOINT was used toobtain a direct comparison with the collocated turbiditymeter, fixed-point sample intake, and laser-diffraction ana-lyzer intake. Fluvial sediment load was computed by usingthe 33 channel cross-section samples (SSCXSEC) to cali-brate the SSCPOINT samples to representative cross-sectionconditions using linear regression in logarithmic space. TheSSCPOINT to SSCXSEC model calibration has a R2 of 0.96, amodel standard error of 1.2 mg/L and is significant at a p-value of 5%. The model was used to compute the time se-ries of SSCXSEC for computation of sediment loads foreach stormflow as further described in Landers [2011].

[12] Turbidity was measured using a nephelometric tur-bidity meter that measures light scattering using a light de-tector 90� from the incident light [ISO, 1999].Nephelometric turbidity measurements quantify the opticalproperties that cause light to be scattered or attenuatedrather than transmitted in straight lines through the meas-ured solution. The turbidity meter used in this study is man-ufactured by YSI Incorporated (ysi.com) as model number6136 and conforms to the ISO Method 7027 [ISO, 1999]measurement standards. The meter was calibrated follow-ing manufacturer recommendations using styrene formazinnephelometric unit (FNU) standard solutions at 0 and 1000FNUs. Throughout the study period, the meter performedwell and was regularly cleaned, compared with an inde-pendent turbidity meter, and verified against calibrationstandards.

[13] Laser-diffraction instruments characterize VPC andPSD by measuring the forward scattering angles producedby a laser striking small particles [Agrawal and Pottsmith,2000]. Development of this technology for in situ deploy-ment has provided major advances in environmental parti-cle size measurement [Andrews et al., 2011]. The PSD ishighly relevant to many facets of engineering and ecosys-tem issues, yet it is rarely measured in field studies [Reyn-olds 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 loga-rithmically spaced size classes from 2 to 381 mm. Streamwater conveyed to the LISST-Streamside instrument viasubmersible pump is analyzed for PSD and VPC in a flow-through sample chamber. The unit was programmed toobtain a 120 s reading during which 4677 volumetric meas-urements are averaged. Stream water was cycled throughthe unit for 270 s before readings began, and clean waterwas pumped from a vessel into the unit between each mea-surement cycle to rinse the sample chamber and to providea calibration check. Field operation of the laser-diffractionanalyzer required much more field maintenance than theother instruments used in this study and it was not opera-tional during brief periods of the data collection. Additionalinformation on the site, materials, and methods is providedin Landers [2011].

3. Results

3.1. Hydrologic and Sediment Data Summary

[14] Comprehensive, concurrent hydrologic, sediment,and multiparameter surrogate measurements were obtainedat 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 sampledstormflows cover a range of typical stormflow runoff eventsfrom just above base flow to bank full, as indicated in Fig-ure 3. The channel cross section is stable and did notchange substantially over the study period. The smallestsampled storm began on 27 September 2010, rose only0.49 m (1.6 ft) above seasonal base flow, and peaked at10.4 m3/s (368 ft3/s). The largest sampled storm began on 3May 2010, rose 2.86 m (9.4 ft) above seasonal base flow toapproximately bank-full stage, and peaked at 144 m3/s(5070 ft3/s) with an annual exceedence probability of about50% (2 year flood).


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[15] The hydrologic and velocity characteristics of thefive measured stormflows are summarized in Table 1. Thereported precipitation was measured at the streamgage andis an inconsistent indicator of the total precipitation overthe 673 km2 watershed, depending on the spatial uniformityof the precipitation. The total runoff is an indicator of thewatershed precipitation, the antecedent conditions, and theseasonal variation in evapotranspiration. The approximatenumber of prior days since runoff-producing rainfall indi-cates antecedent hydrologic conditions and the supply ofrecently stored channel sediment available for suspensionand transport. The reference velocity location is 43.77 m(143.6 ft) from the east bridge abutment and 0.71 m (2.34ft) above the channel bed. The time series of discharge, tur-bidity, and fixed-point SSC are shown for each of thestormflows in Figure 4.

[16] Table 2 summarizes the average and maximumSSCPOINT, SSCXSEC, turbidity, VPC, and average volumet-ric PSD for each of the five measured stormflows. Themaximum measured SSCXSEC for the five stormflows is648 mg/L. The maximum measured SSCPOINT and turbidityfor the five stormflows is 508 mg/L and 286 FNU, respec-tively. The volumetric PSD values are representative onlyfor the measureable size range (2–381 mm) of the laser-diffraction analyzer and will differ from mass PSD becauseof different analytical methods as discussed in Landers[2011]. More than 30% of the mass SSC is less than 2 mm

based on 13 mass PSD samples collected and analyzed dur-ing these stormflows. Nonetheless, the laser-diffraction an-alyzer provides a quantitative and highly informative timeseries of volumetric PSD within its measured range. Theaverage size of sediments in the D10 and D16 fractions areall in the very fine silt size range (4–8 mm). Sediments inthe D50 fraction are in the medium silt size range (16–31mm) and in the D84 fraction are in the coarse silt to veryfine sand ranges (31–125 mm). The laser-diffraction ana-lyzer was operational to measure VPC and PSD for 195 ofthe 251 concurrent measurement time steps during the fivestormflows, as indicated in Table 2.

3.2. Occurrence of Measured SSC�Q and SSC�THysteresis

[17] Hysteresis in the SSC�Q and SSC�T relations areindicated graphically in the time series and bivariate plotsof Figure 4. The SSC�Q hysteresis is clockwise for all fivestormflows, but its shape and magnitude vary significantlywith changing antecedent conditions and storm characteris-tics. Clockwise SSC�Q hysteresis due to sediment storedin the channel between storms is indicated in Figure 4 bylower magnitude SSC�Q hysteresis for secondary within-event rises in August 2009 and September 2010. Thehydrograph shape of the May 2010 stormflow has a distinc-tive gradual rise, later peak, and more rapid recession thanother observed events. This hydrograph shape likely

Figure 3. Cross section at downstream side of bridge, reference velocity location, and measured flowstages for Yellow River at Gees Mill Road in metropolitan Atlanta, Georgia.

Table 1. Summary of Hydrologic and Reference Velocity Characteristics of Measured Storms

Event Begin Date

28/8/2009 10/3/2010 24/4/2010 3/5/2010 27/9/2010

Peak flow (m3/s) 51.0 74.8 36.0 143.6 10.4Peak stage (m) 2.61 2.85 1.96 3.92 1.19Total precipitation (mm) 68 59 38 57 55Total runoff (mm) 15 22 7 29 4Event duration (days) 5.5 4.0 2.6 2.8 3.9Dry antecedent (days) 23 5 14 7 14Peak reference velocitya (m/s) 1.38 1.25 1.58 0.98Peak cross section velocity (m/s) 0.76 0.96 0.80 1.13 0.44Peak section Froude number 0.19 0.23 0.21 0.25 0.14Average water temperature (�C) 22.9 11.1 18.8 21.2 21.2

aReference velocity location is 43.77 m from east bridge abutment and 0.71 m above channel bed.


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indicates larger rainfall amounts in the upper watershedand contributes to the SSC�Q hysteresis of this stormflow.

[18] If hysteresis in SSC�Q and SSC�T for singlestormflow events is evident graphically, then it can be eval-uated quantitatively in the range and coefficient of variationof 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 withincreasing range and coefficient of variation in these ratios.The minimum and maximum Q/SSC ratios are 14 and241% of the mean, respectively, and the standard deviationranges from 21 to 74% of the mean Q/SSC ratio (Table 3).The magnitude of SSC�Q hysteresis observed for thesestorms is not unexpected and causes uncertainty in the

Figure 4. Time series of streamflow discharge, turbidity, and mass suspended sediment concentration(SSC), and bivariate scatter plots of concentration and discharge, and concentration and turbidity, forfive stormflows in 2009 and 2010 on Yellow River at Gees Mill Road in metropolitan Atlanta, Georgia.


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SSC�Q rating that is strong motivation for using surrogatemetrics other than discharge to estimate SSC and load.

[19] The SSC�T hysteresis for these five stormflows ismuch less pronounced than SSC�Q hysteresis but is con-sistent in its occurrence and clockwise direction as shownin the bivariate plots of Figure 4. The peaks of the SSC andturbidity time series are nearly synchronous for all storm-flows, and the SSC�T hysteresis is evident graphically as aconsistently higher T/SSC ratio on the receding SSC limbversus the rising SSC limb (Figure 4). The minimum andmaximum T/SSC ratios are 56 and 139% of the mean,respectively, and the standard deviation ranges from 12 to23% of the mean T/SSC ratio (Table 3). The significantmagnitude and consistency of the SSC�T hysteresisobserved in these data prove rise-to-recession changes inthe SSC�T relation and indicate dynamic drivingmechanisms.

[20] The occurrence of SSC�T hysteresis also was eval-uated in this study for the first time in four other urbanwatersheds in the metropolitan Atlanta area, where discreteSSC samples were collected during storm hydrographsbetween 2003 and 2007 (fluxes evaluated in Horowitz et al.[2008]). The samples were from fixed-point pumping sam-plers calibrated to cross-section concentrations. The water-sheds are located in the same physiographic province asYellow River at Gees Mill, but are smaller with sizes rang-ing from 58.3 to 225 km2 (22.5–86.8 mi2) and are generallymore urbanized. Hysteresis was evaluated for all sampled

stormflows having at least five discrete SSC samples andwith at least two samples collected during each rising andfalling limb of the SSC time series. These criteria were metfor 24 sampled stormflows that occurred in 2003–2007 inthe four watersheds; 23 of these had clockwise SSC�Thysteresis, while the 24th had no SSC�T hysteresis. Thesamples were not analyzed for sediment size.

3.3. Potential Causes of SSC�T Hysteresis

[21] Hysteresis in the SSC�T relation for a single storm-flow can be caused by a rise-to-recession change in sedi-ment physical properties (size, shape, and density), opticalproperties (color), artifacts introduced by instrument per-formance (such as fouling), or SSC sample bias [Downinget al., 1981; Lewis, 1996; ISO, 1999; Davies-Colley andSmith, 2001; Boss et al., 2009]. SSC is the primary variableaffecting turbidity [Downing, 2006], and SSC typically hasmuch higher variance than other factors affecting turbidityfor a specific turbidity sensor and stream site. Potentialcauses of SSC�T hysteresis are evaluated here in the varia-tion of SSC-normalized turbidity computed as T/SSC. Thissection discusses potential causes of SSC�T hysteresis thatwere determined to be of insignificant or minor impact, fol-lowed by sections on changing PSD characteristics andhow these affect SSC�T hysteresis.

[22] The same turbidity meter was used throughout thestudy and was not affected by performance problems orfouling, as verified by regular verification of calibration

Table 3. Statistical Characteristics of Ratio of Water Discharge to SSC (Q/SSC) and Turbidity to SSC (T/SSC)

Event Begin Date

28/8/2009 10/3/2010 24/4/2010 3/5/2010 27/9/2010

Average Q/SSC 0.19 0.64 0.25 0.77 0.25Maximum Q/SSC (% of mean) 183 159 152 241 149Minimum Q/SSC (% of mean) 19 34 41 14 41Coefficient of variation Q/SSC (%) 31 31 25 74 21Average T/SSC 0.82 0.8 0.51 0.8 0.7Maximum T/SSC (% of mean) 129 119 127 128 139Minimum T/SSC (% of mean) 61 61 57 56 60Coefficient of variation T/SSC (%) 17 12 17 23 13

Table 2. Average and Maximum SSC (Cross Section and Fixed Point), Turbidity, VPC, and Average Volumetric PSD for the FiveMeasured Stormflow Events

Stormflow Begin Date

28/8/2009 10/3/2010 24/4/2010 3/5/2010 27/9/2010

Average SSCXSEC (mg/L) 146 84 99 157 33Maximum SSCXSEC (mg/L) 648 198 190 496 93SSCXSEC <63 mm (% by mass) 92 62 73 66 85Average SSCPOINT (mg/L) 120 71 83 130 29Maximum SSCPOINT (mg/L) 508 163 157 393 79Number of SSC samples 64 49 32 34 72Average turbidity (FNU) 89 55 44 99 20Maximum turbidity (FNU) 286 129 93 274 74Average fixed-point VPC (mL/L) 188 54 89 110 30Maximum fixed-point VPC (mL/L) 596 143 201 369 56Average volumetric D10 (mm) 6 4 6 4 5Average volumetric D16 (mm) 8 6 7 5 6Average volumetric D50 (mm) 23 17 21 16 15Average volumetric D84 (mm) 83 69 61 76 57Number of VPC measurements 27 48 30 30 60


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against standards and onsite comparisons with independent,manually deployed turbidity meters. Thus, the turbiditymeter was not the cause of observed SSC�T hysteresis. Arise to recession bias in sampling errors associated withfixed-point pumping samplers [Edwards and Glysson,1999] could manifest as SSC�T hysteresis. This potentialbias was evaluated by comparing residuals of regression ofconcurrently measured SSCPOINT and SSCXSEC collectedduring rising and falling conditions. Residuals from rising(20 samples) versus falling (13 samples) stormflow condi-tions are not statistically significantly different (t test,p¼ 0.64), thus this is not a significant cause of observedSSC�T hysteresis. Flow velocity is highly correlated withSSC as a measure of the erosion and transport capacity ofthe main channel flow. If the SSC to velocity relation wassignificantly different for rising versus falling SSC, thenthis could be a spurious source of observed hysteresis inother relations. However, for these data, and employing thetechniques that were used to analyze Q and T hysteresis,there was no hysteresis between SSC and velocity, and ve-locity was not a significant explanatory variable for T/SSC.

[23] Hysteresis of SSC�T could be produced by substan-tial changes in sediment density during stormflow events.Any changes in sediment density would have an equal lin-ear effect on T/SSC and VPC/SSC, and thus be evidencedin a positive correlation between these two ratios. The cor-relation between T/SSC and VPC/SSC for these data isactually weakly negative (r¼�0.45 at p value< 1%) indi-cating that any effects from changing sediment density dur-ing the measured stormflows is overwhelmed by other

factors. Sediment particle albedo (whiteness) affects lightscattering, as discussed by Sutherland et al. [2000], andchanges in particle albedo over storm events could causeSSC�T hysteresis. The sediment data were not analyzedfor sediment albedo in this study, however, visual evalua-tion of sequential SSC sample bottles and (after analysis)dried sediment indicated no qualitative changes in sedimentcolor or lightness. Because all of these potential causes ofSSC�T hysteresis were determined to be of insignificant orminor impact, changes in sediment PSD are likely to be theprimary determinants of SSC�T hysteresis in this study.

3.4. Particle Size Distribution Trends in StormflowEvents

[24] The high-resolution time series of volumetric PSDmeasured by the laser-diffraction analyzer provide valuabledata to evaluate changing sediment sources during storm-flows and the effects of particle size on SSC�T hysteresis.Trends in PSD in single stormflow events were evaluatedin 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, thesizes of the D10 and D16 have decreasing trends during therising streamflow hydrograph with a flat or increasing trendon the hydrograph recession. This descending trend is illus-trated in Figure 5 which summarizes data measured usingfour independent technologies for the stormflow of 3–6May 2010. Except for an initial increase, the D50 and largersize fractions do not have a significant trend during thestormflows and have much higher variance than the finer

Figure 5. Time series of discharge, ratio of turbidity to mass suspended sediment concentration (SSC),and sediment diameter for (a) 10th and (b) 16th percentiles of volumetric particle size distribution forevent of 3–6 May 2010 on Yellow River at Gees Mill Road in metropolitan Atlanta, Georgia.


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fractions of the PSD. Measured trends in the D10 and D16

of the PSD cover a very narrow size range, from 2 to 9 mm;however, they are well defined and correlate well with theindependently measured ratio of turbidity to SSC as dis-cussed further below.

[25] The trends in the D10 and D16 of the PSD time seriesindicate that the source of sediment is changing duringstormflow events at this site. As D10 and D16 of the SSCdecrease, the concentration of fine silt and clay size par-ticles increases relative to the total SSC. If the source sedi-ment PSD was unchanging in a transport-capacity-limitedsystem, then all fractions of the suspended sediment PSDwould become coarser on the stormflow rise with theincreased capacity to entrain increasingly larger particles.If the source sediment PSD was unchanging in a sediment-supply-limited system, then the suspended sediment PSDalso would become coarser over the event due to winnow-ing of the fines. The consistent trend during stormflow risesof decreasing size for the D10 and D16, and thus increasingrelative concentration of these fine silt and clay sizes, indi-cates that the source sediment is changing during stormflowevents.

[26] The increase in the relative SSC of fine silt and claysize particles during stormflow rises is likely due to a lim-ited supply in the channel bed and banks of these size sedi-ments; and to their abundant supply and transport from hillslope sources affected by rainfall impact, rill, and gully ero-sion. The watersheds in the study region contain abundantfine silt and clay-sized particles, primarily bound by cohe-sive forces and/or protected from erosive forces by vegeta-tive land cover. The supply of these sediments for transportis controlled by detachment processes such as rainfallimpact or rill and gully erosion, which is driven by climate,geology, land cover and use, and watershed managementpractices. Urbanization leads to increased exposure of finesediments to rainfall impact erosion due to land disturbancefor construction and increased rill and gully erosion due togreater frequency and energy of runoff events from imper-vious surfaces and developed drainage networks. Erosioncontrol management regulations have a mitigating influ-ence on these factors. Although urbanization is causingincreased erosion in the watershed, the data indicate thatthe flux of fine silt and clay size particles remains supplylimited.

[27] These smaller particles may not be stored in thestreambed between stormflows because even lower streamvelocities are adequate to transport them. For example,base flow velocity prior to each of the measured stormflowswas greater than the computed critical velocity of 0.15 m/s(0.48 ft/s) for incipient motion of 8 mm sediment at thechannel bed at the velocity reference location. The limitedavailability of small size particles in the channel is furtherindicated by the difference between the percent of the ma-terial smaller than 63 mm in the sampled bed-material sedi-ment (less than 1%) versus that of the SSC samples (62–92%, Table 2). These data also indicate the interesting con-dition in which suspended-sediment transport is capacitylimited for coarser fractions of sediment sourced in thechannel and supply limited for finer fractions deliveredfrom the hillslope.

[28] Prior studies have reported an increase in thepercent of very fine material with discharge for some

watersheds and have cited similar causes [Slattery andBurt, 1997; Lawler et al., 2006]. For a 4.90 km2 (1.89 mi2)alpine watershed in northeastern Italy, Lenzi and Lorenzo[2000] found that the SSC�T relation is affected by chang-ing PSDs due both to changing entrainment velocities andchanging influx of silty material eroded from failed channelbanks and from hillslopes. They developed separateSSC�T rating curves for changing particle sizes but didnot assess SSC�T hysteresis.

3.5. Changing Sediment Size Effects on SSC�THysteresis

[29] The effect of sediment size on turbidity creates asize-concentration ambiguity that has been widely noted[Lewis, 1996; Gray and Gartner, 2009]. In Mie scatteringtheory, if the effects on light scattering of sediment concen-tration, density, color, and shape are unchanging, or if theeffects can be normalized for, then the amount of light scat-tered by homogenous spheres is a function of the scatteringsurface area [van de Hulst, 1981; Sutherland et al., 2000;Clavano et al., 2007; Boss et al., 2009]. Summarizing datafor particles between about 30 and 1000 mm from previousstudies, Downing [2006] and Sutherland et al. [2000]showed an inverse relation between particle size and SSC-normalized optical backscatter, after adjusting for otherfactors affecting light scattering. Although the effect ofsediment size on turbidity is a known factor of turbidity asa SSC surrogate, stability of PSD during stormflow eventsis generally assumed and corrections for SSC�T hysteresishave not been attempted in prior studies.

[30] The correlation of SSC-normalized turbidity (T/SSC) and the D10 and D16 sediment sizes is evident in thetime series data shown for the 3–6 May 2010 stormflow inFigure 5. This relation is summarized for 195 samples fromall five stormflows in Figure 6 in which the data are fromthree independently measured metrics : mass SSC, turbid-ity, and laser-diffraction-based volumetric D10 and D16.The regression lines in Figure 6 are statistically significantat p-values of 5%, and scatter around the lines may be dueto effects of particle shape, other size fractions, and (or)measurement errors. The slope of the least squares fit inlogarithmic space is �0.76 for D10 and �0.66 for D16,compared with the slope of �1.0 reported by Downing[2006]. The results of log-transformed least squares regres-sions of (T/SSC) and sediment size for the 10th, 16th, 50th,60th, and 84th PSD percentiles are given in Table 4 andshown in Figure 7 (in which the sediment size data werecentered for graphical comparison). The relation of normal-ized turbidity to D84 is not statistically significant for thesedata in which the average D84 is 67 mm and the range is25–58 mm.

[31] 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 ofD50; and D10 explains 44% of the variance in T/SSC com-pared with 14% for D50 (Table 4). These results show thatthe inverse, exponential influence of particle size on turbid-ity is not constant across the PSD but increases for the finerfractions of the PSD for these data. These results are inagreement with the theoretical results of Clavano et al.[2007] who found that for modeled PSDs of nonspherical


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shapes with particle sizes ranging from 0.2 to 200 mm, atleast 50% of the contribution to light scattering, attenua-tion, and absorption comes from particles smaller than 10mm. For these data, changes of only a few microns in thefractions of the PSD less than about 10 mm significantlyaffect turbidity and explain observed SSC�T hysteresis.

[32] These findings show that for the many studies whereturbidity is being used to compute SSC, the assumed stabil-ity of the PSD is highly significant, particularly for fine siltand smaller sizes (16 mm and smaller). Even small changesof about 5 mm in the fine silt and smaller size fractions ofsuspended sediment PSD will create changes in the SSC�Trating that can increase error and produce bias. Turbidityprovides a sensitive indicator of suspended fine silt andsmaller size particles and associated constituents, whilesuspended sand information from turbidity may be anextrapolation from the effects of smaller sizes of the PSD.Thus, SSC�T hysteresis should be regularly evaluatedwhere turbidity is used as a SSC surrogate.

[33] Concurrent turbidity and SSC samples during singlestormflow events can be used to evaluate SSC�T hysteresisand to indicate relative stability of factors, including PSD,that are deterministic to the SSC�T rating. ObservedSSC�T hysteresis may be used to identify changes in sedi-ment properties during stormflow events, in some caseswithout high-resolution PSD data, if other potential causes

can be evaluated as negligible. SSC�T hysteresis for singleevents may indicate a transition from channel to hillslopesediment sources as discussed previously. Trends in magni-tude of SSC�T hysteresis between events may indicatechanging initial conditions related to hillslope erodibility orbank stability. Sampling to develop SSC�T rating curvesshould cover the range of potential changes in PSD, includ-ing rise to recession changes, to avoid bias errors resultingfrom SSC�T hysteresis.

3.6. Effects of Hysteresis on Sediment LoadComputations

[34] Suspended sediment load is a key indicator of manycumulative watershed processes. Computation of sus-pended sediment load often is the primary purpose of SSCsampling and monitoring streamflow and turbidity as asediment surrogate. The effect of SSC�Q hysteresis on the

Table 4. Results of Regression of Log-Transformed, SSC-Nor-malized Turbidity on Volumetric, Laser-Diffraction-Based Sedi-ment Diameter (D) for 10th, 16th, 50th, 60th, and 84th Percentilesof Particle Size Distribution (PSD) for Yellow River at Gees MillRoad in Metropolitan Atlanta, Georgia

PSD Percentile

D10 D16 D50 D60 D84

Average diameter (mm) 4.7 6.1 18 24 67Logarithmic slope

with T/SSC�0.76 �0.66 �0.35 �0.24 0.07

R2 0.44 0.32 0.14 0.07 0.02p-Value less than 0.0001 0.0001 0.0001 0.0004 0.08

Figure 7. Regression curves for ratio of turbidity to SSCand centered volumetric sediment size for four percentilesof PSD from 195 measurements.

Figure 6. Sediment diameter for tenth (D10) and sixteenth (D16) percentile of volumetric size distribu-tion and ratio of turbidity to mass suspended sediment concentration (SSC).


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SSC�Q rating is evident in Figure 8, particularly in thepattern of points for specific stormflow events. Event-to-event changes in the magnitude of SSC�Q hysteresis andslope of the SSC�Q rating indicated in Figure 8 mayreflect changes in sediment supply and transport capacity.The least-squares regression for the SSC�Q rating curvehas an R2 of 0.57, and the error of prediction ranges from�48 to þ58% for individual stormflows and is 21% overall(Table 5). Compared with the SSC�Q rating, the effect ofSSC�T hysteresis is much smaller and the SSC�T ratinghas a much better fit as shown in Figure 9. The least-squares regression for the SSC�T rating curve has an R2 of0.90, and the error of prediction ranges from �23 to 12%for individual stormflows and is only 1.6% overall (Table5). This comparison clearly demonstrates the advantages ofusing turbidity instead of, or in addition to discharge as asurrogate measure of SSC and for computation of sedimentload [Rasmussen et al., 2009].

[35] The observed SSC�T hysteresis would produce bi-ased computed sediment loads if the collection of sampleswere substantially biased to the rising or falling limb of the

SSC time series. For example, if samples were collectedonly on the falling hydrograph due to logistical challengesat a site with clockwise SSC�T hysteresis, then theSSC�T rating curve would be biased low and SSC wouldbe underestimated by T on the rising limbs of runoff. Inthis study, the average effect of SSC�T hysteresis on com-puted load was minimized by collecting samples on the ris-ing and falling SSC limbs and using a best fit modelingapproach. The effect of SSC�T hysteresis can be partiallyaccounted for in this study by including D10 in the regres-sion model because changes in D10 explain the SSC�Thysteresis as discussed previously. For the model of SSC asa function of both turbidity and D10, the error of predictionin Table 5 is based on the comparison with the measuredload where D10 was successfully measured (195 of the 251total measurements). For this model results for individualevents are notably more accurate (Table 5), the explanationof variance improved slightly from a R2 of 0.90–0.94, how-ever the change in the overall error of prediction is negligi-ble. These errors for specific stormflow events would beparticularly important in a study of event mean SSCs orevent loads.

Figure 8. Observed cross section SSC, streamflow dis-charge, and regression model curve.

Table 5. Measured and Estimated Sediment Load for Yellow River at Gees Mill Road in Metropolitan Atlanta, Georgiaa

Discharge Surrogate Turbidity Surrogate Turbidity and D10 Surrogate

EventMeasured Load

(Tons)bEstimated

Load (Tons)b

Error ofPrediction

(%)Estimated

Load (Tonsb)

Error ofPrediction

(%)Estimated

Load (Tonsb)

Error ofPrediction

(%)

August 2009 2609 1361 �47.8 2391 �8.4 2232 7.7a

March 2010 1757 2760 57.1 1908 8.6 1829 4.1a

April 2010 651 515 �21.0 498 �23.4 579 �8.2a

May 2010 3893 6155 58.1 4244 9.0 3081 �9.8a

September 2010 98 127 29.5 110 12.2 91 4.9a

Samples 251 251 251 195Total/mean 9008 10,918 21 9151 1.6 7812 �1.9a

aThese error estimates are based on the concurrent measured load for which D10 is available (195 samples with total measured load of 7964 metrictons).

bLoad is shown in metric tons.

Figure 9. Observed cross section SSC, turbidity, andregression model curve.


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[36] The concurrent time series data used in this analysisexhibit positive first-order autoregression at a 1% signifi-cance level, based on the Durbin-Watson test statistic. Toevaluate the effects of this autocorrelation, the regressionmodels were run using maximum likelihood estimation in ageneralized least squares model for each regression modelbetween SSC and explanatory variables. The explanatoryvariables remained significant at p values of 1% and themodel standard error was not greater than that computedusing ordinary least squares, within reported significantdigits.

4. Summary and Conclusions

[37] Turbidity is widely used as a surrogate to esti-mate SSC and load with typically greater accuracy,much higher temporal resolution, and potentially lowercost than traditional SSC�Q rating curve methods. Tur-bidity is known to be affected by several parameters,particularly sediment size, in addition to SSC; but thoseparameters are typically assumed to be stable or propor-tional during stormflows and for a site specific SSC�Trating. Hysteresis in the SSC�T relation for singlestormflows has been observed in this study for a concur-rent dataset of 251 SSC, turbidity, discharge, velocity,and temperature measurements and 195 volumetric con-centration and PSD measurements collected during fivestormflow events in 2009 and 2010 on Yellow River atGees Mill Road in metropolitan Atlanta, Georgia. Hys-teresis was also observed in the SSC�T relation for 23of 24 stormflows sampled from 2003 to 2007 at fouradditional sites in metropolitan Atlanta, indicating thepossibility of common driving mechanisms for theSSC�T relations for watersheds of this region. Hystere-sis in SSC�T relations for single stormflow events hasreceived almost no discussion previously and has notpreviously been quantitatively related to changing PSD.The data collected in this study are used here for thefirst time to compare SSC�Q and SSC�T hysteresis, tocharacterize observed SSC�T hysteresis, isolate itscauses, relate those causes to changing PSD and poten-tial watershed sediment processes, and to evaluate theeffects of SSC�T hysteresis on sampling plans andcomputed sediment load.

[38] The SSC�Q hysteresis is clockwise for all of thefive stormflows with the SSC peak leading the dischargepeak, primarily due to sediment stored in the channelsbeing entrained and transported at the beginning of runoff.The standard deviation of Q/SSC ranges from 21 to 74% ofthe mean Q/SSC ratio (Table 3). The observed SSC�Qhysteresis is a source of significant uncertainty in theSSC�Q rating curve but also is a source of informationabout the relative magnitude of total sediment coming fromresuspension on the stormflow rise of sediment stored inthe stream channel. The SSC�T hysteresis for these fivestormflows is much less pronounced than SSC�Q hystere-sis but is consistent in its occurrence and clockwise direc-tion. The SSC and turbidity time series peaks are nearlysynchronous, but the T/SSC ratio is consistently higher onthe receding SSC limb versus the rising SSC limb. Thestandard deviation of T/SSC ranges from 12 to 23% of themean T/SSC ratio (Table 3).

[39] The significant magnitude and consistency of theSSC�T hysteresis observed in these data show rise-to-recession changes in the SSC�T relation that can be causedby changes in sediment physical properties, optical proper-ties, instrument performance, or SSC sample bias. Thesepotential causes of SSC�T hysteresis were each evaluatedand, for these data, changing sediment size characteristicswere isolated as the primary cause. Data for all five storm-flows show sizes of the D10 and D16 to be decreasing duringthe rising streamflow hydrograph and stable or increasingon the hydrograph recession. Observed trends in the D10

and D16 of the PSD time series indicate that the source ofsuspended sediments is changing during stormflow eventsat this site. The increased relative concentration of fine siltand clay size particles during stormflow rises is likely dueto a limited supply of these size sediments in the channelbed and banks and to their availability and transport fromhill slope sources affected by rainfall impact, rill, and gullyerosion. The results indicate that sediment transport iscapacity limited for sand-sized sediment sourced in thechannel ; and supply limited for fine silt and smaller sedi-ment delivered from the hillslope.

[40] Results of regression of log-transformed (T/SSC)and sediment size for the 10th, 16th, 50th, and 60th PSDpercentiles show an inverse, exponential influence of parti-cle size on turbidity that is not constant across the PSD.The majority of the influence of PSD on T/SSC and of theamount of T/SSC variance explained by PSD is from par-ticles in the fine silt and smaller size range. Changes ofonly a few microns in the fine silt and smaller size fractionsof the PSD significantly affect turbidity and explainobserved SSC�T hysteresis. These results are in agreementwith the theoretical results of Clavano et al. [2007] whofound that at least 50% of the contribution to light scatter-ing, attenuation, and absorption comes from particlessmaller than 10 mm for modeled PSDs.

[41] Turbidity should provide a sensitive indicator ofsuspended fine silt and smaller size particles and associatedconstituents and may be particularly valuable for studiesfocused on small particle sizes. In studies of systems wheremost of the suspended sediment is sand sized, the SSC�Trelation may be dependent on a relatively small fraction ofthe PSD, and minor changes in the PSD could have a largeinfluence on the SSC�T relation. In any case, turbidity isonly a bulk optical indicator and quantitative informationon changes in the PSD and how these may affect theSSC�T relation and the fluvial system will require inde-pendent measurements.

[42] This study shows that the often assumed stability ofsediment PSD is highly significant to SSC�T rating curves,particularly for fine silt and smaller sizes. Small changes ofless than 5 mm in the fine silt and smaller size fractions ofsuspended sediment PSD will create changes in the SSC�Trating that can increase error and produce bias. Thus, thestability of the PSD should be evaluated where turbidity isused as a SSC surrogate. Most sediment studies do not col-lect high-resolution time series of PSD. However, concur-rent turbidity and SSC samples for single stormflow eventscan be used to evaluate SSC�T hysteresis and to indicaterelative stability of factors, including PSD, that are deter-ministic to the SSC�T rating. Observed SSC�T hysteresismay be used to identify changes in sediment properties


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during stormflow events and potential changes in sedimentsources, even without high-resolution PSD data, if otherpotential causes can be evaluated as negligible.

[43] Sampling to develop SSC�T rating curves shouldcover the range of potential changes in PSD, including riseto recession, seasonal, and (or) long-term changes, to avoidbias errors in computed loads resulting from SSC�T hys-teresis. This may be particularly important where individ-ual stormflow results are being studied, as for computationof stormflow mean concentrations of sediment andsediment-associated constituents. Use of a best fit modelingapproach is also advisable to minimize the effect ofSSC�T hysteresis on the SSC�T model.

[44] The results of this study demonstrate the value ofdetailed physical sampling, monitoring using multiple sen-sor technologies and metrics, and the importance of meta-data about instruments, environmental sample material,environmental conditions, and methods. Multiple continu-ous data streams with associated metadata can produceunderstanding that is not redundant, but synergistic. Thephysical samples for SSC and PSD, together with stream-flow discharge were the foundation data of this study.Detailed, discrete SSC and PSD data can yield improvedunderstanding and methods for use of sediment surrogatesincluding turbidity, laser-diffraction, and acoustic metrics.These methods, in turn, can lead to improved solutions tothe many important sediment-related environmental andengineering problems.

[45] Acknowledgment. The financial and collegial support of theU.S. Geological Survey for this work is gratefully acknowledged.

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Hysteresis in suspended sediment to turbidity relations due to changing particle size distributions