The Effect of Sand Content on Sediment Transport, Deposition, and Bar Morphology

By John Kemper

Advisor: Dr. Karen Prestegaard

April 26th, 2012

GEOL394H

Abstract

Studies of stream adjustment to urbanization have focused primarily on the geomorphic consequences of increases in discharge, such as channel widening (e.g. Hammer, 1972, Pizutto et al., 2000). Urbanization can also affect sediment supply, grain size, or sediment transport mechanics, which can alter channel stability and morphology. Sediment deposition can initiate feedbacks among geomorphic and hydraulic variables leading to significant alterations of stream morphology. This has been documented in lower Little Paint Branch Creek by Blanchet [2009], although the underlying mechanics for these changes were not fully investigated. In summer 2012, simple alternate bars in the channel at Cherry Hill Road were replaced by large diagonal bars with very sharp bar fronts. These elevations of these bars changed were reduced during floods associated with Hurricane Sandy. These changes occurred over short timescales (< 6 months) and coincide with an increase in upstream sand supply associated with major road construction (of the Inter-County Connector or ICC) in the watershed (Blanchet, 2009). This research is designed to test the hypothesis that changes in bar morphology were caused by varying amounts of sand in the bedload, which reduces the critical dimensionless shear stress of the gravel, thus increasing sediment transport and deposition rates. (Wilcock and Crowe, 2003). Test of this hypothesis were based on field data collection and modeling of the sediment transport conditions before and after the Hurricane Sandy flood. Data collection included field measurements of channel morphology, water surface gradient, and grain size analysis of surface and subsurface material. Field data show that dimensionless shear stress for Hurricane Sandy was well below the * τ crit for homogenous gravel, indicating that sand content is responsible for lowering the critical dimensionless shear stress, leading to the substantial sediment transport observed. Using time series of important flow parameters a model for sediment transport in lower Little Paint Branch Creek was created. Suspended sediment profiles indicate that 500 µm and larger sand is not suspended at significant heights above the bed. Rouse number calculations indicate that sand is accumulated during small events and winnowed during large events. The model shows that a substantial number a small events occurred in the months prior to Hurricane Sandy, leading to the lowering of the critical dimensionless shear stress. This suggests that sand content, and the small flow events that lead to the accumulation of sand, have a significant impact on bar morphology and channel morphology for systems experiencing a sudden influx of sand sized sediment.

Introduction

Stream channel morphology results from the deposition and erosion of sediment in alluvial channels. Although streams indicate a wide range of morphology, the location of sediment deposition generates three main planform patterns: straight, braided, and meandering (Leopold and Wolman, 1957). Even straight channels indicate patterns of sediment deposition either as riffle-pool sequences, which are vertical accumulations of gravel spaced along the channel bed, or as alternate bars that are deposited along alternating banks. The spacing of riffle- pool sequences and alternate bars are about 5-7 times the width of the channel (Leopold and Wolman, 1957). The alternate bars accompany a wandering thalweg, or line of greatest depth, which alternates from bank to bank as well. There is a continuum in channel form between channels with alternate bars and those with meander bends. The wavelength of the meander is 10-14 times the width of the channel; a meander wavelength contains 2 alternate bar sequences (Leopold and Wolman, 1957). In braided streams, sediment is initially deposited near the channel center, which is usually the location of highest bedload transport. Diversion of flow around the central bar forms two or more anastomosing channels and a resulting channel morphology that is wider and shallower than straight and meandering streams for equivalent discharges. Braided channels occur on steeper slopes than meandering channels with similar discharge. This makes sense because braided channel streams are generally mostly gravel and, for the same bankfull discharge, it requires a greater shear stress to transport gravel than sand. (Leopold and Wolman, 1957). In addition, sand is more easily suspended and thus swept to the channel edges by secondary currents (Dietrich and Smith, 1979). Channel morphology develops due to the interactions between flow and sediment transport in stream channels. Pioneering researchers identified systematic downstream changes in average channel morphology (termed hydraulic geometry) in most river systems (Leopold and Maddock, 1953). Average downstream hydraulic geometry relationships indicate that bankfull width is proportional to the square root of the discharge (w  Q0.5). In a given stretch of river, Q is mostly constant, but width exhibits systematic changes between riffles and pools (Andrews, 1980) or between reaches with and without channel bars (Ferguson et al., 1993). To explain downstream hydraulic geometry, Parker (1979) hypothesized that most channels were “threshold channels” that moved sediment when the critical dimensionless shear stress was exceeded and that this threshold was achieved at the bankfull stage. Therefore, for a given energy gradient, the channel adjusts width until the channel depth generates a bankfull shear stress (~gdS, with  = fluid density, g = gravitational constant, d = depth, S = water surface gradient) that is near the threshold of motion for the bed material size. Parker [1979] explained threshold channels by comparing the distributions of bankfull shear stress ( = gdS) and channel depth within a river cross section. If average bankfull shear stress is near critical, the distribution of shear stress indicates higher bankfull shear stress values ~ 20% above critical in the center of the channel, whereas shear stresses on the channel banks are below critical. In other words,  is variable across the channel, and is above crit (shear stress required for incipient motion) for gravel in the center of the channel. This allows channels to transport sediment while maintaining stable channel banks. Therefore, for a threshold gravel bed stream (with a given gradient), grain size determines the threshold (bankfull) depth which, in turn, influences velocity. The threshold channel maintains itself through varying discharge events through positive and negative feedbacks and the importance of the adjacent floodplain in

carrying discharge through the width of the floodplain, which limits the rate at which depth increases in the channel. The original theory for threshold channel morphology assumed a constant critical dimensionless shear stress for a channel. Dimensionless shear stress is the ratio between fluid shear stresses and grain resisting forces (Shields, 1938): ∗ 1 where  is shear stress, s is the ratio of sediment density s to water density , g is gravity, and * D50 is median grain size (measured as intermediate axis of a particle).  is therefore the ratio of * fluid shear stress to grain resisting forces and  crit is the dimensionless shear stress required for incipient motion (critical dimensionless shear stress). The original work on critical dimensionless shear stress was conducted on homogeneous sediment in flumes (Shields, 1936). Since that time, investigators have determined that the size distribution of surface particles (Parker and Klingeman, 1982; Wilcock, 1986) and the influences of sand on gravel transport (Ferguson et al, 1992; Wilcock and Crowe 2003) both significantly lower the critical dimensionless shear stress for gravel transport. The increase in sand content lowers the friction angle of the gravel, causing a decrease in dimensionless shear stress required for incipient motion. The increase in sand content causes the gravel sized particles (2-256 mm) to roll across the smaller sand particles ( mm to 2 mm) or, in other words, ride on a carpet of sand, thus lowering critical dimensionless shear stress. Thus, in gravel bed streams, changes in the supply of sand or the sorting of bed material can result in changes in sediment transport mechanics and thus sediment transport rates. These changes in transport can result in changes in sediment deposition and channel morphology. * Due to the dependence of  crit (for gravel) on sand content, it introduces another parameter into the mechanics of gravel bar formation that has been largely ignored by previous studies. By combining the observations of Leopold and Maddock [1953], Leopold and Wolman [1957], Parker [1978], and Wilcock and Crowe [2003], we find that sand content could be an important parameter for gravel bar formation that has not been previously investigated.

Partitioning of Shear Stress

It is also important, when studying the effects of shear stress on sediment transport and gravel bar formation, to separate the shear stress into two components: the mean boundary shear stress exerted on bed surface particles and mean boundary shear stress exerted on form roughness of bars which, when summed together, equal the total mean boundary shear stress (Lisle et al., 1993). Surface particle shear stress can be calculated by where is fluid density, Ur is a reference velocity, and Cg is a resistance coefficient calculated by 1 5.62log 4 th where D84 is the 84 percentile of surface grain size. is the shear stress component responsible for the initiation of motion of bed surface particles. Bar resistance can be calculated by 1 2

where CD is drag coefficient for form roughness, is fluid density, Ax is the cross sectional area of the bar at its maximum, and Ab is the area of the channel occupied by the bar. Lisle et al. [1993], in a studying examining channel responses to a decrease in sediment supply, found that reduction in sediment supply leads to an coarsening of the bed surface, a reduction in bar roughness, and a decrease in sediment transport, despite having little to no impact on boundary shear stress on the bed surface. This decrease in sediment transport despite a constant is thus a result of the coarsening of the bed, which could stabilize the channel. Therefore, a coarsening of the bed surface in a channel led to an increase in inactive areas at bar heads (i.e. bar growth) and that bed coarsening was due to the winnowing of finer particles from inactive areas of the bed. This winnowing of the finer particles from inactive areas of the bed and the bar fronts lowers the * sand content, thus increasing  crit, which will likely stabilize the thalweg.

Sediment Transport Modeling

Critical dimensionless shear stress and bedload transport rate are parameters that are highly sensitive to available grain sizes and bed conditions at the time of the storm event. In order to model sediment transport at the study site, two approaches were used in order to attempt to account for the sensitivity of suspended load to sand size and bed load to the amount of sand. Church [2006] uses the settling velocity to shear velocity ratio to predict at what point sand becomes suspended and transitions from bed load to suspended load. This approach can be used to define suspension versus bedload at different points of the channel for different flood stages and can also identify the flow depths at which different grain sizes transition from bed load to suspended load. Settling velocity, or fall velocity, is the velocity at which a particle descends through a fluid and is defined as

where Rf is the dimensionless fall velocity calculated from the particle Reynolds number, g is gravity, R is the submerged specific gravity of the sediment, and D is the grain size of the particle in question. Shear velocity is defined as ∗ where τ is shear stress and ρ is fluid density (Church, 2006). The ratio of the settling velocity to shear velocity can be used to examine the effects of a variety of depth and grain size combinations, which can be used model sediment transport for different flood stages and for different locations in the stream channel. If upstream sand were to be deposited by smaller storm events, then it would affect the critical dimensionless shear stress of the gravel. Rouse [1939] developed the Rouse-Vanoni profile for suspended sediment which is defined as ̅ 1 ϛ/ϛ ∗ 1 ϛ/ϛ and represents the concentration of sediment of a certain grain size at any percentage ϛ of the water column (Rouse, 1939). It is dependent on the Rouse number which is defined as

P ∗ and is unitless. For P > 2.5, sediment is transported as bed load, for P > 1.2 and < 2.5, sediment is transported as 50% suspended load, for P > 0.8 and < 1.2, sediment is transported as 100% suspended load, and for P < 0.8 sediment is transported as wash load. Using the method described in Parker [2007] suspended sediment concentration profiles can be created for different grain sizes and different flow depths, and can also be used to model the transport of sediment for different storm events and at different locations in the channel (Parker, 2007). The second approach used was following the method of Wilcock and Crowe [2003] who developed a bed load transport equation that can be used to calculate bed load transport rate for * various grain sizes. Dimensionless bed load transport rate, or Wi , is dependent upon transport stage ϕ and is defined as ∗ . 0.002ϕ 1.35 and 0.894 . ∗ 141 1.35 . where ϕ and τ and τcrit are shear stress and critical shear stress, respectively (Wilcock and Crowe, 2003). Given the known relationship between discharge and τ, various scenarios of Q can be run to define the flow conditions (u*) and the change in bed state (% sand).

Significance

Understanding the adjustments of stream channels to changes in both discharge and sediment supply is important. Furthermore, understanding where and why channel bars form is important for human habitation along stream channels. Gravel bars formation is usually accompanied by channel widening at the location of the bar, which leads to potential issues for structures built along the channel. An example of this has occurred along Route 1 at the housing complex called the University View. This apartment building is built in the floodplain of Paint Branch Creek, and an expensive channel engineering project was undertaken to remove a gravel bar due to the perceived risk that the channel would widen. The modified channel, however, now contains very high and fast flows within the channel right at the site of a pedestrian bridge. Therefore, it would be highly useful for planning decisions if we were able to predict where gravel bars would form and how they would change with subsequent high flow events. Gravel bar formation is also a natural process of channel adjustment, as discussed in Leopold and Wolman [1957] and Leopold and Maddock [1953]. One of the primary results of gravel bar formation is that it can turn an incised channel (eroded channel) back into a bank full channel (stable channel). This transformation allows the channel to reconnect with its floodplain, which can improve surface-groundwater exchanges as well as a variety of other ecologically useful processes (Blanchet, 2009). Therefore, the ability to promote gravel bar formation in desired places would be a useful one. This study is significant because it seeks to examine sand content as an important parameter of gravel bar formation, which would lead to an enhanced ability to predict and promote gravel bar formation, as discussed above

Hypotheses

* 1. Evidence of gravel mobility at low τ crit is associated with locally high (> ~10%) sand content, which enables gravel sized sediment to be transported onto the stream banks during bankfull flows. 2. 1-2 mm sand is not suspended at heights significantly above the bed at less than bankfull events. 3. Subsequent bankfull events should entrain surface sand, and decrease subsurface sand content, thereby increasing *crit and re-establishing initial alternate bar morphology.

Study Site

The study site is Lower Paint Branch Creek located off of Cherry Hill Road in the Cherry Hill Road Recreation Center in College Park, MD (figure 1). The site has a drainage area of 25.9 square miles and is located approximately a quarter of a mile downstream from the Beltway and approximately 5.5 miles downstream from the Inter-County Connector (ICC). Much of the Little Paint Branch creek is channelized or regulated, and thus the study site is one of the first available locations for sediment deposition in the channel (Blanchet, 2009). The channel is a natural channel that has a recognizable floodplain and has not been channelized or altered in any way. Larger sediment grains are mostly rounded, quartz dominated particles, and smaller sediment tends to have a large amount of mica flakes (visible to the naked eye) transported from upstream schist (Hankin, 2009). The site is easily accessible by car and has been monitored over more than 15 years by Dr. Karen Prestegaard and various students. Therefore, a significant amount of data is available for the site which allows for the comparison of present observations and data with the past, thus allowing us to form a more complete picture of the evolution of the site over time. Because this project seeks to evaluate changes in bar morphology and sediment transport, this ability to compare and contrast past data is very important.

Figure 1: Map of Little Paint Branch Creek watershed, from Blanchet [2009]

Figure 2: Sketch map of the study site at lower Little Paint Branch Creek. Red lines indicate the location of cross sections. Photo to the right is taken from the right bank looking at the cross channel diagonal bar.

Methods

Channel cross section measurements

Bankfull cross section morphology is measured by surveying with a surveyor’s level or total geodetic station or by measurement of flow depth below a known datum (bankfull elevation). Bankfull datum is identified for each cross section. Rebar is installed at both ends of the cross section and then carpenters string and a line-level is used to establish a horizontal bankfull datum. A tape measure is also attached to the rebar to obtain horizontal distance across the channel. Depth is measured at the three foot (0.91 m) intervals across the stream channel. Depth is measured using stainless steel wading rod marked in 0.05m increments and is recorded to the nearest cm. Depth is measured for shorter intervals where morphology changes rapidly and measurements are obtained for the right and left edges of water. Where water is present, water depth measurements are also taken. In this way, we are able to construct a cross section of the bankfull flow and the flow in the channel. The error on the depth measurements is ~1 cm and the error on the width measurements is ~10 cm. Four cross sections were taken along the length of each major bar. In addition to the bankfull channel measurements, surveying techniques were used to measure channel elevations. The survey measurements can be repeated to provide changes in bed elevation.

Subsurface Grain Size Sampling and sieving

Subsurface grain size is sampled in cross sections, with bulk samples taken over regions with similar surface size distributions. Subsurface samples were taken at two of the measured cross sections, at initial intervals of 20 ft. Subsurface samples were also taken at two different locations on the bar front. Subsurface samples were gathered and then placed into plastic bags, and then transported to the lab for sieve analysis. Sieve analysis was conducted on each of the subsurface samples in order to determine percent sand by weight. Because this study seeks to correlate bar formation as a function of sand content, percent sand measurements are extremely important. Subsurface samples for various locations across both cross sections were sieved to determine percent sand content. Samples were weighed and then sieved through a 2 mm sieve in order to determine the percent sand by weight. The sand portion of the sample was then put through a full sand sieve stack (63 µm – 180 µm – 250 µm – 500 µm – 707 µm – 850 µm – 1 mm – 2mm) to determine the grain size distribution. Using the theory discussed above, the grain size distributions will then be used to calculate * Rouse numbers for different flow de model crit and  crit for each location, and deduce the effect on sand on these parameters.

Hydraulic variables during flood events.

The site is gauged, therefore discharge is known for each measured high flow event. For each flood event the following hydraulic variables can be calculated for each cross section: flood width, flood datum, average cross sectional depth, cross sectional area, average shear stress, shear stress distribution across channel, and flood *. Flood width can be measured by flagging the width of each flow during an event and then measuring the distance Figure 3: Relationship between Q at Lower Little Paint Branch between the flags across the Creek at Cherry Hill Road and Q at USGS gauge site on the NE channel with a tape measure. Flood Branch of the Anacostia datum can be measured by flagging to denote the edge of the channel during the event and then following the methods above. Average cross sectional depth and cross sectional area can be obtained with the same procedures described in the previous sections. Average shear stress and shear stress distribution across the channel can be calculated by creating a longitudinal profile for the flow related to a flood event, obtaining the gradient from this profile, and following the formula for . Flood * can be calculated in using the surface gradient combined with grain size measurements. Because the site is gauged, we can associate these variables with a measured

10 discharge, and thus we can evaluate which events move sediment and thus affect bar morphology.

Flood Frequency Curves and Discharge Relationships

The USGS gauge for the Northeast Branch of the Anacostia is located downstream of the study site. Discharge was measured at the Northeast Branch gauge by Blanchet, 2009, which is located just downstream of the study site. High flow discharges associated with the 2012 floods at the study site were calculated using the slope-area method, and the combined results are shown in figure 3. These data indicate that peak discharge at L. Paint Branch is 27% of the peak Q at the NEB gauge. Using this relationship, discharges for the study can be calculated for any discharge recorded at the USGS gauge. From this data a flood frequency curve can be constructed, again using the discharge data available from the downstream gauge. This information can then be evaluated in order to determine which flow events cause morphological changes seen at the study site, and how often these morphological changes could be expected to occur. This relationship can also be used to create flow duration curves, shear stress versus time distributions, and a variety of other parameters. Knowing this relationship is extremely useful, because discharge can be now calculated for the study site for any flow, which will allow for a better understanding of the observed changes at the study site.

Time series of main sediment transport parameters

Time series of the main sediment transport variables (shear velocity, shear stress, Rouse number, dimensionless shear stress) were constructed using the time series of discharge, depth, in order to evaluate the constraints on sediment transport mechanics. Using the approach discussed in Church [2006], the ratio of shear velocity to settling velocity was calculated for different grain size and flow combinations. This was then plotted in order to determine what was moved as suspended load and what was moved as bed load. This provides constraints on the mode of sediment transport at different locations in the channel and at different flood stages. Suspended sediment concentration profiles were created for different flow depths and grain sizes after the method of Parker [2007]. The profiles were used to complement the Church [2006] approach, and to identify whether sand was suspended significantly above the bed for different flow depths. In this way, and using the discharge relationships discussed above, discharges associated with the differing modes of sediment transport were identified. Using the approach outlined in Wilcock and Crowe [2003], as well as discharge relationships discussed above, bed load transport rate was calculated for various discharges. Combined with the shear stress time series, the bed load transport rate at the study site was modeled for the previous water year. Different possible values of dimensionless shear stress were used to model sediment transport at the site. The use of different values of critical dimensionless shear stress allow the examination of the effect of sand content on the various parameters of the * * model. For example, using a τ crit of 0.045 – τ crit for homogenous gravel – sediment transport can be modeled and compared to field observations to determine the accuracy of the assumed * * value of τ crit. This will allow for an estimation of τ crit over time. Using the Rouse-Vanoni profile, and the morphology of the channel, sediment transport can be modeled in order to determine which discharges move sand as suspended load and

remove it from the site, and which discharges move sand as bed load and lead to a build-up of sand at the study site. In this way, the flux of sand through the study site can be examined. The flow events that do not suspend the sand significantly above the bed will contribute to the buildup of sand at the study site, and those that do will remove it from the study site. In this way, * the change in τ crit over time can also be estimated.

Error

Much of the error in this study is built into the assumptions made in the construction of the model. Because the relationships between grain size and shear stress are complex, simplifying assumptions must be made in order to construct a workable model. In this model, it was assumed that sand accumulates when the Rouse number for 500 µm sand is above 2.5 and that sand is winnowed from the site when the Rouse number for 1 mm is below 2.5. These reasonable assumptions were made in order to construct a straightforward model. Furthermore, because relationships among the various parameters outlined in this study are complex and build upon one another, there is an unavoidable small amount of error inherent in the model, as in any model. However, assumptions have been kept to a minimum and those assumptions that were made were based upon field observations so as to minimize error while creating a straightforward at workable model. Furthermore, as in any geomorphic model, this model likely will only apply to similar situations to that for which it was designed. Error in cross section surveying is smaller than the data points, and error in sieving is also negligible. Error for surface grain size measurements is evaluated using standard deviation to identify D50 and D84.

Hydraulic and sediment conditions associated with Hurricane Sandy

Channel cross sectional changes with Sandy

Cross sections for two locations were measured pre- and post- Hurricane Sandy. Figure 4a is the cross section for site one, located 119 ft upstream from the diagonal bar front. Figure 4a shows that post-Sandy, the bankfull channel is shallow near the east (left) bank, deeper in the center and, the same on the west (right) bank. The observed bed surface is also much coarser in the post-Sandy cross section than in the pre-Sandy cross section. Also, the deepening of Figure 4b: Pre- and post-Sandy cross sections for site 3 the channel follows the Lisle et al. [1993] hypothesis that channels will initially deepen and coarsen as fine particles are winnowed away, before widening and shallowing. Therefore, this shows that the sand is being winnowed away and that the channel is coarsening, result in a deepening in the center of the channel, and accretion on the banks, as inactive areas grow. Gravel sized particles were also found distributed across the channel, including at very low flow depths, in both pre- and post- Sandy cross sections (figure 4a). The fact that particles this size (along with sand) were found at low flow depths supports the hypothesis that an increase in sand content is allowing the transportation of these grain sizes at very low shear stresses. The cross section for site three, located 162 feet downstream of cross section one, is shown in figure 4b. As can be seen, there is deepening in the center of the channel, while the banks remain stationary. This further supports the hypothesis that the bed surface is coarsening (i.e. the sand is being winnowed away) and that bed surface coarsening causes an initial deepening of the channel. Sand contents and coarseness for each of these sites will be measured over the upcoming months, using both repeated cross sections at millimeter scales and repeated sampling to evaluate the hypothesis of bar formation and growth as a function of increasing sand content.

Water surface gradient during Sandy

Water surface gradient for two high flows associated with Hurricane Sandy Figure 5: Water surface gradient for Hurricane Sandy flow was measured in order to evaluate shear event stress. During Hurricane Sandy, flags were placed along the channel for two Figure 4a: Pre- and post-Sandy cross sections for site 1 flows, the absolute peak flow, which will be referred to as the high peak flow, and a lower peak flow, which will referred to as the low peak flow. The flags denote the edge of the flow for

13 each and were surveyed subsequent to the end of the storm with a surveyor’s level or total geodetic station. Each flag was surveyed to obtain the elevation, and then the distance downstream was measured using a tape measuring stretching from the first flag to the last flag. A longitudinal profile was created, from which water surface gradient for each flow was obtained (figure 5).

Grain Size distribution of surface sediment

Surface grain size measurements were taken using the Wolman pebble count method (Wolman, 1955) and can be seen in figure 6. 106 measurements were taken for cross section one and 128 measurements Figure 6: surface grain size distribution for Little Paint Branch Creek were taken for cross section 3. The size of each particle was estimated by measuring the intermediate access (width) of each particle using a ruler, with an estimated erro r of 2-3 mm. D50 for cross section one is 15 mm and D50 for cross section 3 is 23.5 mm, both of which are large gravel-sized particles. A summary of calculated values can be seen in figure 7. This shows that the bed surface of the channel in areas of bar formation is very coarse and, therefore, that bed coarseness is a parameter affecting bar formation and that bars tend to form in areas with coarse bed surfaces. Furthermore, as can be seen by the values in figure 7, gravel sized particles are found all across the channel, even at very low flow depths. This indicates that the high sand content found in the subsurface is responsible for the lowering of the critical dimensionless shear stress required to move these particle sizes, and that thus sand content is an important parameter of bar formation.

Changes in dimensionless shear stress associated with Sandy

The longitudinal profile of two peak flows, the high peak flow and the low peak, flow were measured in order to determine the water surface gradient of each flow. The values are for the high peak flow and are summarized in table 1 in the appendix. Using the gradient calculated from the longitudinal profile, as

Figure 7a: 7a shows the calculated * from surface grain size measurements for cross section one. well as surface grain size measurements, the dimensionless shear stress that occurs as a result of the peak flow event can be estimated by the equation for * for various locations across the channel at cross section sites one and three (table 2 in appendix). The critical dimensionless shear stress required for the transport of gravel is 0.045. As you can see in table 2, as well as figure 7a, dimensionless shear stress at low depths is below what is required for the initial of motion for gravel sized particles. Furthermore, for Figure 7b: 7b shows the calculated * from surface grain cross section three (figure 7b), the size measurements for cross section one. * dimensionless shear stress is below  crit for gravel across entire channel. However, pre- and post-Sandy observations show that sediment transport occurred and that sediment was mobilized across the entire channel. Gravel sized sediment was mobilized at low flow depths for cross section one, and was deposited on the banks along with a significant amount of sand (figure 8). Gravel sized sediment was also mobilized across the entire channel for cross section three. Therefore, sand content must lower the critical dimensionless shear stress, or no sediment transport would occur at all, thus reinforcing the hypothesis that sand content is an important parameter for gravel bar formation and sediment transport.

% subsurface sand

The core questions this study seeks to address are a) what is the critical dimensionless shear stress and b) what is the bed load transport Figure 8: Gravel sized particles deposited at low flow depths for cross rate. Due to the sensitivity of the section one, pre-Sandy (left) and post-Sandy (right). The size of the suspended sediment load to sand particles coupled with amount of sand present indicates high sand size and the bedload to the * content lowered  crit well below 0.045 amount of sand, these questions are very dependent upon the grain sizes available for transport and the bed condition prior to flood events. The knowledge of the grain size distribution, coupled with the known flow depth shear stress should allow for a forensic analysis of the flood events associated with Hurricane Sandy. Grain size distributions were calculated from three samples taken at different locations across cross section one - 12 ft, 18 ft, and 30 ft. These locations represent different flow depths of the stream. As you can see from figures 9 and 10, most of the sand (~75%) at each location is medium sand between 250 µm and 500 µm or coarse 1mm sand. The median grain size falls somewhere between 250 µm and 500 µm, and most sand larger than 500 µm is 1 mm sand. Sand of this size is likely not suspended significantly above the bed for flows less than bankfull. This indicates that a majority

15 of the sand is not being removed from the study site for less than bank full flows, which suggests that the critical dimensionless shear stress is not increased by these smaller flow events.

Grain Size Distribution 120

100

80 than 60 12 ft finer 18 ft % 40 30 ft 20

0 < 63 µm 63 µm 180 µm 250 µm 500 µm 707 µm 850 µm 1 mm 2 mm Grain Size

Figure 9: Cumulative distribution for sand grain sizes at cross section one

Grain Size Distribution 40

% 20 12 ft

15 18 ft 30 ft 10

0 < 63 µm 63 µm 180 µm 250 µm 500 µm 707 µm 850 µm 1 mm 2 mm Grain Size

Figure 10: Histogram for sand grain sizes at cross section one

* * Predicted τ crit versus observed τ for Hurricane Sandy

* Predicted τ crit was calculated following the equation ∗ 0.021 0.015 , where Fs represents sand content (Wilcock and Crowe, 2003). * Predicted τ crit (dotted black line) and observed τ* are shown in figure 11. Although values of observed τ* do not fit the predicted line perfectly, the same trend of decreasing τ* with increasing sand content is followed. Observed τ* decreases with sand content much steeper than predicted. Figure 11: The variation of T* with % sand content. Red Wilcock and Crowe [2003] developed triangles indicate the observed values and the dotted black line * the relationship between τ crit and sand indicates the predicted values from Wilcock and Crowe [2003]. content based on several flume studies, so the variance between observed τ* and their model is not unexpected. Most specific geomorphic equations can only be applied to the specific situations for which they were designed. It is likely that the difference in values for the predicted versus the observed can be explained by the expected difference from site to site. Although observed τ* at the study site may follow a different equation than the literature, the overall trend remains the same. Figure 11 shows that τ* decreases with an increase in sand content, which is consistent with literature conclusions and consistent with the hypotheses of this study.

Time series of morphological and hydraulic parameters for Little Paint Branch Creek

Discharge (Q) and depth for Little Paint Branch Creek

Little Paint Branch Creek at Cherry Hill Road 1000

100

10 /s) 3 (m 1 Q

0.1

0.01 ND J FMAMJ J ASOND J Month

Figure 12: hydrograph for Little Paint Branch Creek at Cherry Hill Road from Novermber 2011 – January 2013

Using the slope-area method discussed previously, discharge for the Little Paint Branch Creek study site can be calculated for discharges measured at the USGS downstream gauge at the Northeast Branch of the Anacostia. The hydrograph for the previous water year, which includes Hurricane Sandy, can be seen in figure 12, and includes all time between November 2011 and January 2013. Peaks represent storm events, with the largest peak in late October 2012 representing Figure 13: Relationship between Q and depth at the study Hurricane Sandy. site With a known relationship between discharge (Q) and depth (figure 13) calculated from surveyed cross sections, a time series of depth at the study site can be calculated (figure 14). The large peak in late October 2012 is Hurricane Sandy. It is more evident in the depth time series that Hurricane Sandy is of a much larger magnitude than the other storm events during the displayed time period. The time series of depth at the study site is an important parameter in the modeling of sediment transport. Events of a greater magnitude have a greater depth, and thus have a greater capacity to transport sediment. Rouse calculations are dependent upon depth, so, by modeling depth, the variation of Rouse number with time can be modeled as well. This variation will indicate the sediment transport mechanism (suspended load vs. bed load) during the indicated months.

Little Paint Branch Creek at Cherry Hill Road

1.01

0.81 (m) 0.61

Dpeth 0.41

0.21

0.01 ND J FMAMJ J ASOND J Month

Figure 14: depth time series for Little Paint Branch Creek at Cherry Hill Road from Novermber 2011 – January 2013

u* for Paint Branch (u* time series)

A time series of shear velocity (u*) can be constructed from the time series of depth. Shear velocity varies as a function of depth in the form of ∗ and therefore will correlate with the depth time series. As can be seen in figure 15, the peaks of the depth time series correspond with the peaks of the shear velocity time series. Again, the large peak seen in late October 2012 represents Hurricane Sandy. Shear velocity varies with the magnitude of flow in the channel. Larger flow events have a greater u* and thus have a greater ability to entrain sediment and transport it as bed load. Smaller events will transport all but the finest grain sizes as bed load, where larger events will have the ability to entrain and transport larger grain sizes as suspended load. The grain size able to be transported by suspended load by any given flow event is dependent upon the shear velocity. If sediment is suspended significant heights above the bed during a bank full or greater flow event, it will be removed from the site and deposited overbank. Therefore, the relationship of shear velocity to particle velocity is an important parameter in modeling sediment transport, and thus the time series of u* is essential in modeling the transport of sediment at Little Paint Branch Creek. Little Paint Branch Creek at Cherry Hill Road 0.3 0.25 0.2

u* 0.15 0.1 0.05 0 ND J FMAMJ J ASOND J Month

Figure 15: shear velocity (u*) time series for Little Paint Branch Creek at Cherry Hill Road from Novermber 2011 – January 2013

Shear stress

Much like shear velocity, the time series of shear stress is constructed from the time series of depth. Shear stress varies as a function of depth, and thus the peaks of the depth time series will correspond with the peaks of the shear stress time series. Shear stress, like shear velocity, is higher for storm events, which indicates the enhanced ability of larger flow events to move sediment. Shear stress does not take into account grain size and thus is not a very reliable indicator of sediment transport thresholds, but can be used in concert with grain size data to construct a time series of dimensionless shear stress. Given a constant grain size distribution, increases in shear stress will lead to an increase in sediment transport, and higher shear stresses will transport larger sediment loads. However, an increase in supply of fine grained sediment (and thus sand content) will have a significant impact on the relationship between shear stress

19 and sediment transport thresholds, as is the case with this study. Figure 16 shows the shear stress time series for the study site at Little Paint Branch, with the peak in late October 2012 representing Hurricane Sandy.

Little Paint Branch Creek 100

τ 10

1 ND J FMAMJ J ASOND J Month

Figure 16: shear stress (τ) time series for Little Paint Branch Creek at Cherry Hill Road from Novermber 2011 – January 2013 Dimensionless shear stress The time series of dimensionless stress is constructed from the above time series of shear

Little Paint Branch Creek 1 *

τ 0.1

0.01 ND J FMAMJ J ASOND J Month

Figure 17: dimensionless shear stress (τ*) time series for Little Paint Branch Creek at Cherry Hill Road from Novermber 2011 – January 2013. Dotted black indicates critical dimensionless shear stress for gravel (0.045)

20 stress. Dimensionless shear stress is the ratio of grain resisting forces to fluid shear stresses and thus is a function both of depth and grain size. As in the previously discussed time series, dimensionless shear stress is higher for larger flow events, which thus have an increased capacity to transport sediment (figure 17). Dimensionless shear stress varies with the magnitude of the flow events. In general, the dimensionless shear stress remains below 0.045 (dotted black line) expect for a few peaks during storm events. Figure X shows the time series of dimensionless shear stress, but does not indicate the critical dimensionless shear stress. Critical dimensionless shear stress is a complex relationship between bed grain size distributions and sediment supply, and requires the consideration of multiple parameters that are discussed later in this study. The variation of dimensionless shear stress over time can be combined with sediment transport thresholds and conditions to fully model sediment transport at the study site. Sediment transport thresholds and conditions will be modeled in the subsequent sections of this study.

* Vs/u The ratio of settling velocity to shear velocity can be used to predict when sand of a certain grain size is suspended (Church, 2006), as outlined above. Settling velocity varies with particle size and is calculated for the four major sand grain sizes at the study site – 250 µm, 500 µm, 1 mm, and 2 mm. Settling velocity calculations are combined with the time series of shear * velocity (figure 15) to determine the time series of Vs/u (figure A1). Generally, the peaks of the * Vs/u time series correspond with the low points of the shear velocity series, meaning that the ratio is highest for low flows. The time series varies widely for larger the larger grain sizes (1-2 mm sand) than for the smaller grain sizes (250 µm – 500 µm), which can be explained by their respective settling velocities. Because the settling velocity is small fluctuations in shear velocity have less of an effect on sand of 250 µm, as it is likely suspended for all but the smallest flows. * Fluctuations for 500 µm are somewhat more noticeable, but the largest variance of Vs/u is for 1 mm and 2 mm sand. Due to the large settling velocity for sand of this grain size (1 mm and especially 2 mm), fluctuations in shear velocity will have a large effect and on the ratio of settling velocity to shear velocity. In other words, large grain sizes will be transported as bed load for small flows and suspended into the water column for large flows. This time series can be

21 Figure 18: variation of Rouse number with depth. Solid black line indicates P = 2.5, which is the threshold between suspended load transport and bedload transport used in Rouse calculations in order to determine the location of sediment transport (suspended load versus bed load) which is a very important parameter in the evolution of critical dimensionless shear stress and the proposed sediment transport model.

Calculation of sediment transport thresholds and conditions

Rouse calculations and suspended sediment profiles

Rouse number calculations are made using the equations discussed in the previous sections. The Rouse number is simply the ratio of settling velocity to shear velocity divided by von Karman’s constant κ and determines the mode of sediment transport (suspended load versus bedload). Rouse number varies inversely with depth (figure 18) and indicates the mode of transport both for varying locations in the channel and flow events of varying magnitude. As a general rule, larger flow events will move larger sediment as suspended, while smaller events will move most of the sediment as bed load. The solid black line in figure 18 indicates the transition between suspended load and bedload (P = 2.5), which is an important parameter in the sediment transport model outlined in this study. For P > 2.5, sand is moved as bedload and is added to the bed at the site. For P < 2.5, sand is moved as suspended load and can be removed from the site and deposited overbank for flow events of large magnitude. 2 mm sand (a small fraction of sand sized sediment at the study site) is moved as suspended load for a flow depth of > 1.2 m, which is about 0.5 m deeper than Hurricane Sandy related flows (1.05 m). Therefore, no sand of 2 mm size was suspended and removed from the study site during Hurricane Sandy. The transition from bedload to suspended load occurs at depths of 0.36 m, 0.08 m, and < 0.02 m for 1 mm, 500 µm, and 250 µm sand, respectively. This means that sand of these sizes are suspended at bankfull flow depth (0.78 m), as well as Hurricane Sandy-magnitude flow depths (1.05 m). Suspended sediment profiles can be used to fully analyze sediment transport as a function of depth. Rouse-Vanoni suspended sediment profiles are calculated using the method discussed above. A profile is created for three different flow depths of 2.0 m, 1.0 m and 0.5 m. Average bankfull flow depth is 0.78 m, so 0.5 m represents a flow depth that is less than bankfull. 1.0 m represents the flow depth during Hurricane Sandy and 2.0 m represents a large flood event. Flow depths of 0.5 m, 1.0 m, and 2.0 m represent discharges of 14.2, 47.3, and 157.0 m3/s, which have a recurrence interval of < 1 year, 3 years, and > 50 years (figure X). These recurrence intervals represent the expected recurrence interval of each flood event, meaning that flows of 14.2 m3/s can be expected occur about once a year, and flows of 47.3 m3/s can be expected to occur once every three years, but can also occur more often than that. Put another way, there is a 33% chance a flow event of 47.3 m3/s will occur in a given year. Suspended sediment profiles can be for 0.5 m and 1.0 m can be seen in figure 19a and 18b. 1.0 m flow depth (figure 19a) suspends ~40% of 500 µm sand, the median sand distribution for the study site. Much of the sand available for suspension is suspended less than 40% above the bed, and about 60% of the sand (10% of that available for suspension) is suspended only 20% above the bed. The average depth for bankfull flow is 0.78 m so for a flow of Hurricane Sandy magnitude (1.0 m depth) sediment must be suspended 78% above the bed to be deposited over bank and removed from the site. About 5% of available 500 µm sand is suspended at an overbank height, while about 28% of 250 µm sand is suspended at an overbank height. This means that for a Hurricane Sandy magnitude flow, 5% of 500 µm sand and about 28% of 250 µm sand is removed from the site. Median grain

size (D50) is somewhere between 250 µm and 500 µm for the study so the Hurricane Sandy event represents the loss of a significant amount of sand sized particles from the site. Specifically, given D50 slightly less than 500 µm, 13% of sand content is removed from the study site during a Hurricane Sandy magnitude flow. This correlates well with the down cutting seen after the hurricane; loss of sand content from the study site caused the deepening of the channel at the monitored locations. A flow depth of 0.5 m represents less than bankfull flow and has a recurrence interval of less than one year (figure 19b). For this magnitude, 500 µm sand is not suspended at any significant height above the bed, meaning that sand of that grain size and larger is moved as bed load. This means that flow events of the magnitude of 0.5 m depth move 500 µm sand and larger as bed load and increase the sand content of the study site.

Periods of bedload transport

The previously discussed time series of discharge, depth, and shear velocity are combined to create a time series of Rouse number (figure 20). As mentioned above, the Rouse number identifies the mode of sediment transport for particles of a given grain size. For P < 2.5, sediment is transported suspended load and for P > 2.5 sediment is transported as suspended load. Periods of bed load transport are clearly defined by the dotted black line, which represents a Rouse number of 2.5. Periods of bedload transport indicate sediment deposition, therefore periods of bed load transport represent periods of sand accumulation at the study site. Because the accumulation of sand directly influences the critical dimensionless shear stress of the site, it is * important to identify periods of transport in order to determine the evolution of τ crit over time, which is the primary goal of this sediment transport model. 500 µm sized sand (~ D50) is moved mostly as suspended load until late-April/early-May, after which bedload transport events occur more frequently. This noticeably correlates with an increase in events with relatively larger Q, d, and u*. It is likely that these were events of sufficient magnitude to move the sand as bed load, but small enough to not suspend 500 µm sand. This is in contrast to late winter/early spring, where flow events were either too small to move sand of this size, or of sufficient magnitude to move 500 µm sand as suspended load. Periods of clear bed load transport occur with regularity from May to October leading up to Hurricane Sandy, after which they become less clearly defined. Although several events with a Rouse number near 2.5 occur subsequent to Hurricane Sandy, they are not clear cut and likely represent periods of slight bed load transport. 1 mm sand is transported as bed load for much of the water year except for briefs periods of suspension associated with storm events. 250 µm sand is never transported fully as bed load, but several events from May to October have a Rouse number above 1.2, indicating that 250 µm is moved as 50% suspended load for these events, meaning that there was some deposition of 250 µm sand during this time period. 2 mm sand is moved as bed load for the entire water year except for Hurricane Sandy. By defining periods of bed load transport versus periods of suspended load * transport the evolution of τ crit can be modeled.

z/H vs. C/Cb 63 micron 1 125 micron 0.9 180 micron 0.8 250 micron 0.7 420 micron 0.6 500 micron 0.5

z/H 707 micron 0.4 850 micron 0.3 1 mm 0.2 2 mm 0.1 4 mm 0 0.0000 0.5000 1.0000 1.5000 C/Cb

Figure 19a: Rouse-Vanoni suspended sediment profile for 1.0 m flow depth.

z/H vs. C/Cb 63 micron 1.2 125 micron 180 micron 1 250 micron 420 micron 0.8 500 micron

z/H 0.6 707 micron 850 micron 0.4 1 mm 2 mm 0.2 4 mm

0 0.0000 0.5000 1.0000 1.5000 C/Cb

Figure 19b: Rouse-Vanoni suspended sediment profile for 0.5 m flow depth..

Figure 20: Rouse number time series for Little Paint Branch Creek at Cherry Hill Road from Novermber 2011 – January 2013. Dotted black indicates threshold between suspended sediment transport and bedload transport (P = 2.5)

* Accumulation of sand and change in τ crit for gravel

Periods of bed load transport for 500 µm represent periods of sand accumulation, while periods of suspended load transport for 1 mm represent periods of sand removal. These are * simplifying assumptions made in order to model the evolution of τ crit with time. Generally, flow events that suspend 1 mm sand are of sufficient magnitude to suspend 500 µm – the median grain size – at significant heights above the bed so that it is lost to overbank deposition. Events that suspened only 500 µm sand generally do not suspend it at heights above the bed that allow for overbank deposition (see suspended sediment profiles). Therefore, it is a safe assumption that events that suspend 1 mm sand are removing 500 µm (and potentially 1 mm sand) from the study site. The periods for sand accumulation and sand removal at the study site were then identified using these criteria. Periods of sand removal cause an increase in critical dimensionless shear stress for gravel transport and periods of sand accumulation lead to a decrease in critical dimensionless shear stress for gravel, per the theory discussed previously. Because critical dimensionless shear stress is a complex relationship between sediment supply and grain size, the * relative change of τ crit over time is recorded, as the exact impact of each accumulation and winnowing affect cannot be known without comprehensive field measurements. For each event * with a Rouse number above 2.5, τ crit was increased, and for each event with a Rouse number * * below 2.5 τ crit was decreased. As can be seen in figure 21, τ crit remained mostly steady throughout the late winter and early spring, with a few incremental increases. Around late- * April/early-May τ crit begins to decrease and continues to constantly decreases until Hurricane Sandy in late October. At this point there is an increase in critical dimensionless shear stress as a result of the suspension of sand sized sediment up to 2 mm, which is consistent with the severe * downcutting seen in the field (figure 4a). The model shows that τ crit was constant (likely around 0.045) until early 2012, at which point a rapid decrease began. This decrease occurs parallel to increases in shear velocity and bed load transport events, indicating that it occurs as a result of sand accumulation at the study site. This implies that the critical dimensionless shear stress at the

τ*c over time (Little Paint Branch) c * τ

ND J FMAMJ J ASOND J Month

Figure 21: evolution of critical dimensionless shear stress (τ*) over for Little Paint Branch Creek at Cherry Hill Road from Novermber 2011 – January 2013

study site falls below 0.045 and that critical shear stress is lowered by an increase in sand content, which is consistent with the hypotheses of this study. Therefore, small flow events that transport sand sized sediment as bed load decrease the critical dimensionless shear stress for gravel, which directly influences bar formation and morphology. Small flow events thus have a profound impact on the evolution of channel and bar morphology.

Conclusions

Leopold and Maddock [1953] found that stream channel dimensions adjust to and are defined by changes in width, while Parker [1978] found that stream channel dimensions also adjust to grain size, both of which are affected by gravel bar formation. Wilcock and Crowe [2003] found that sand content has an effect on the dimensionless shear stress required for * * incipient motion ( crit), namely that an increase in sand content causes a decrease in  crit for gravel sized particles. These observations introduce another parameter (sand content) as being possibly important for the formation of gravel bars. Lisle et al. [1993] found that bed coarsening can lead to bar growth and channel stabilization. The winnowing of fine grained sediment from the bed in inactive areas leads to a decrease in sand content and coarsening of the bed. This decrease in sand content would increase the critical dimensionless shear stress, thus stabilizing the channel and causing the growth of gravel bars. Gravel bar formation widens the channel, causing possible problems for nearby structures, and thus it would be highly useful to predict locations at which they would form. Gravel bar formation can also transform an incised channel into a stable channel, which has various ecological and geomorphological benefits. Thus, the ability to promote gravel bar formation in desired location would be useful. Cross sections coupled with water surface gradient measurements and surface grain size measurements indicate the dimensionless shear stresses for Hurricane Sandy high flows fall mostly below 0.045. This suggests that sand content is responsible for lowering critical dimensionless shear stress, thus leading to sediment transport. Therefore, this indicates that sand content is indeed a parameter in the mechanics of gravel bar formation. Data also show that the stream is incising, especially at locations upstream of the large cross channel bar. Using the slope-area method and depth-discharge relationships, time series of depth and discharge are constructed for Little Paint Branch Creek using data from the downstream USGS gauge. From these, time series of shear velocity, settling velocity to shear velocity ratio, and Rouse number are created. These are used to model the mode of sediment transport for sand sized sediment at the study site. Flood frequency curves, flow duration curves, and hydrographs have been developed for Little Paint Branch Creek from calculated relationships between the study site and the downstream USGS gauge at the Northeast Branch of the Anacostia. Data indicate that the Hurricane Sandy discharges are the peak discharges of the year and that stream discharge is often far below the values observed during the storm event. The recurrence interval for Hurricane Sandy related floods was calculated to be about 3 years, indicating that the discharges responsible for the observed changes are fairly common. Suspended sediment concentration profiles have been created for flows depths of 1.0 m and 0.5 m, which represent a Hurricane Sandy-sized event (larger than bankfull) and a slightly less than bankfull magnitude event. The variation of Rouse number with depth for study site was also calculated and plotted. Combined with flood frequency and flow duration curves, sediment transport at the study site was modeled

for November 2011 – January 2013. This model indicates that while large flow events deplete the site of sand sized sediment, small flow events deposit sand at the site and build up the sand content of the reach. It also indicates that for less than bankfull events, sand sized sediment of 500 µm and larger was not suspended significant heights above the bed. * Using suspended sediment profiles and Rouse number time series, the evolution of τ crit was modeled. Flow events that transported sand sized sediment primarily as bedload lead to the accumulation of sand at the study site, and flow events that transported sand sized sediment primarily as suspended load caused the decrease of sand at the study site. This model indicates a temporary increase of critical dimensionless shear stress after large flow events and a steady decrease as small events deposit sand and build up sand content. The profound effect of sand accumulation on critical dimensionless shear stress underlines the importance of small flow events on bar formation and morphology and thus channel morphology. Therefore, small flow events have a previously poorly addressed influence on channel morphology for gravel bed channels experiencing a sudden influx of sand sized sediment. This decrease in critical dimensionless shear stress increases the length of time when gravel can be transported and lead to the development of large ground gravel bars. Therefore, the appearance of large gravel bars is likely not a result of a sudden influx of gravel sized sediment into the system, but rather a sudden increase in sand sized sediment. Therefore, sand content plays a previously underappreciated role in bar formation and sediment transportation. However, it is likely that this variation is episodic and that the channel will become much less dynamic when the fine sediment source is no longer present.

Appendix

Figure A1: Time series of shear stress for Little Paint Branch Creek at Cherry Hill Road from Novermber 2011 – January 2013

Figure 17: flood frequency for Little Paint Branch Creek at Cherry Hill Road from 1970-2012.

Flood Frequency 1970‐2012 100 (m3/s)

10 LPB Discharge

1 110100 Recurrence Interval

Figure A2: flood frequency for Little Paint Branch Creek at Cherry Hill Road from 1970-2012.

Table 2: Dimensionless shear stress values (*) calculated based on surface grain size distributions for cross section one and cross section three.

Downstream Downstream Station # Distance Distance (m) FS BS Height Instrument Elevation (ft) Gradient 0 0 0 0.65 1.635 11.635 10.985 0.006306 1 47.6 14.50848 0.65 1.635 11.635 10.985 2 65 19.812 0.725 1.635 11.635 10.91 3 83.2 25.35936 0.715 1.635 11.635 10.92 4 99.9 30.44952 0.815 1.635 11.635 10.82 5 107.8 32.85744 0.825 1.635 11.635 10.81 6 120.9 36.85032 0.88 1.635 11.635 10.755 7 134.2 40.90416 0.862 1.635 11.635 10.773 8 150.6 45.90288 0.89 1.635 11.635 10.745 9 168.3 51.29784 0.945 1.635 11.635 10.69 10 203.9 62.14872 0.97 1.635 11.635 10.665 11 232.1 70.74408 1.11 1.635 11.635 10.525 12 266.4 81.19872 0.732 1.205 11.205 10.473

Table 1: list of values for longitudinal profile taken for the high peak flow during Hurricane Sandy.

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