Quantification of swash flows using video-based particle image velocimetry

Coastal Engineering 44 (2001) 65 – 77 www.elsevier.com/locate/coastaleng

Quantification of swash flows using video-based particle image velocimetry K.T. Holland *, J.A. Puleo, T.N. Kooney Naval Research Laboratory, Code 7440.3, Stennis Space Center, Mississippi 39529-5004, USA Received 6 September 2000; received in revised form 18 April 2001; accepted 9 July 2001

Abstract Understanding of fluid flows and sediment transport in the foreshore has been severely hampered by the difficulty of obtaining swash flow velocity measurements in this dynamic and extremely shallow region. We present a digital imaging method, known as particle image velocimetry (PIV), to quantify the horizontal flow structure of swash. This technique exploits similar patterns of image intensity in multiple images sampled sequentially to identify spatial offsets corresponding with maximum correlations between image subregions. These offsets are used in conjunction with the sampling interval to derive velocity vectors describing the horizontal flow structure. Pre-processing methods to geo-rectify oblique imagery to a planar surface and post-processing methods of correcting spurious vectors are described. The PIV method overcomes many of the limitations of in situ sampling of swash flows and is shown consistent with results from a previously tested remote sensing technique for measuring swash edge velocities. In general, this technique provides a unique capability for spatially extensive and well-resolved quantification of swash flows. Published by Elsevier Science B.V. Keywords: Swash; Remote sensing; Video; Velocity

1. Introduction The foreshore region (defined as the intermittently wetted, intertidal area of beach in the proximity of the shoreline) acts as a buffer between energetic ocean waves and the back beach and as such serves as the primary region of coastal erosion. Hydrodynamic processes acting in this region are loosely termed swash which can be characterized as thin, fast, spatially variant flows occurring subsequent to bore collapse.

*

Corresponding author. Tel.: +1-228-688-5320; fax: +1-228688-4476. E-mail address: [email protected] (K.T. Holland). 0378-3839/01/$ - see front matter. Published by Elsevier Science B.V. PII: S 0 3 7 8 - 3 8 3 9 ( 0 1 ) 0 0 0 2 2 - 9

Given that the effectiveness of various sediment transport mechanisms is roughly correlated with flow velocity based on energetics modeling approaches (Bagnold, 1966), prediction of erosional events within the foreshore region specifically requires knowledge of swash flow fields. Unfortunately, such a fundamental understanding of foreshore sediment transport is lacking largely due to the extreme difficulty in obtaining swash measurements in this complex, dynamic region. Although the foreshore is readily accessible and the swash signals are large, in situ instrumentation is susceptible to often harsh and rapidly varying conditions. A handful of researchers, however, have had some success in the foreshore with the use of in situ

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instrumentation to measure swash velocities and in some cases suspended sediment concentrations. The types of instrumentation used for measuring velocities include: ducted impeller current meters (DICMs) (Hughes et al., 1997; Masselink and Hughes, 1998; Puleo et al., 2000), electro-magnetic current meters (EMCMs) (Butt and Russell, 1999), and acoustic Doppler velocimeters (ADVs) (Osborne and Rooker, 1999). Yet, each of these instruments has weaknesses when deployed in natural swash. For example, the impeller-based current meters only measure flow velocity in one direction and can have a relatively small maximum measurable velocity. EMCMs lack reliability when deployed in shallow (0 –30 cm) flows because they must be continuously wetted (although they have been successfully used in the deeper depths of the inner surf zone, e.g. Beach and Sternberg, 1988 and further offshore, e.g. Guza et al., 1988). Similarly, Doppler methods require a minimum depth on the order of 10 cm, unless deployed horizontally, and are susceptible to measurement error resulting from bubbles or foam. Given their deployment within the flow field, all of these sensors can serve as efficient traps for floating debris, such as kelp, which will degrade performance. Most importantly, however, these sensors provide only a single spatial measurement, which given the Lagrangian nature of the swash flow makes dense spatial sampling exceedingly costly and logistically difficult. Since the foreshore region often exhibits spatial non-uniformity, a small grid or cross-shore array of instruments will not be adequate for predicting non-localized, larger scale foreshore changes. Recently, video-based techniques have proven useful in the quantification of spatially extensive nearshore information such as morphological patterns and hydrodynamic characteristics (for reviews, see Holland et al., 1997; Holman et al., 1993). In addition, a video method known as particle image velocimetry (PIV) has been successfully used by nearshore scientists to measure two-dimensional cross-sections of flow structure under breaking waves (e.g. Chang and Liu, 1998; Lin and Rockwell, 1995; She et al., 1997) among others uses. The PIV technique relies on images (separated by a short-time interval) of flows tagged with passive tracer particles. The measured particle displacement and the known time interval yield numerous 2D velocity components within the

flow field. In the laboratory, highly resolved fluid flows are obtained by artificial illumination using a pulsed light sheet source and by seeding with neutrally buoyant (and sometimes reflective) particles. For more natural flows, such control is impossible. However, a method similar to PIV has been applied to measure horizontal flows in rivers by relying on variations in image intensity or ‘‘texture’’ rather than tracking seeded particles (Fujita et al., 1998). The swash region contains a great deal of visual texture (namely distinct image intensity patterns resulting from surface foam), so determination of swash flow velocity vectors using PIV techniques is feasible. The purpose of this paper is to develop and validate a PIV technique applicable to natural swash zone flows over a large study region. Section 2 describes the PIV technique, the filtering methods used to reject anomalous signals, and a verification of this technique using synthetic data. Section 3 presents results from the application of the PIV method to a swash zone field study at Duck, NC and discusses the comparison of PIV-based measurements with estimates from both video-based and in situ sensors. Concluding remarks are given in Section 4.

2. Particle image velocimetry Particle image velocimetry is a non-intrusive, remote sensing technique that tracks individual particles or groups of particles (seeded in a fluid flow) over time yielding the associated flow velocity components. Because PIV is generally performed on two photographic or digital images taken very close together in time, the advective velocity of the particles can be taken to be the velocity of the fluid in which they are carried. In laboratory studies, clear water fluid flows are seeded with neutrally buoyant particles and generally illuminated with a laser sheet of light to constrain flow measurements to a known orientation. One type of PIV generally used in laboratory experiments is Particle Tracking Velocimetry, which seeds a flow with a small enough number of particles such that individual particles or particle streaks can be determined as a function of time. Other laboratory experiments may utilize a high particle density and instead track groups of particles. In natural flows, such as the swash zone, artificial seeding is not

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Fig. 1. Schematic of the image comparison used in the PIV method showing the interrogation window, I, the search window, S, and the search region, R. The pixel pattern is shown in gray and solid circles indicate grid points. The offsets from the grid point location (xm,yn) in the horizontal and vertical directions, respectively, are given by a and b.

practical. Instead, image ‘texture’ resulting from naturally occurring foam patterns is tracked with our PIV technique in an analogous way to pattern matching in a densely seeded flow.1 For a more extensive overview of the various methods and techniques associated with PIV, see Adrian (1991), Grant (1997) or Raffel et al. (1998).

the second image, H, and is the same size as I. While I is constrained to its center coordinates, S is offset from the original grid node (xm, yn) by a measurable distance (a, b) about a larger searchable region, R. So for each I, a number of windows, S, within R are searched for the maximum correlation between S and I. The pixel intensities in S are thus defined for each I as

2.1. Area of interest selection

S ¼ Hðxmþaþi ; ynþbþj Þ

In general, PIV relies on a measure of correlation within specified regions of two images (G, H ) having coordinate orientations (x, y) and separated in time by Dt. A grid of nodes is chosen within the images to define the startpoint of estimated velocity vectors (Fig. 1). For each grid location, (xm, yn), a set of pixel intensities of dimension 2s + 1
2s + 1, where s is defined as the half-width of the set of pixels, centered on (xm, yn) is extracted from G (Fig. 1). This collection of pixels, I, known as an interrogation window, is defined by I ¼ Gðxmþi ; ynþj Þ

ð1Þ

where  s  (i, j)  + s. Another collection of pixels, known as the search window, S, is then obtained from

where  s  (i,j)  + s,  Lx  a  Lx,  Ly  b  Ly , and Lx and Ly are the dimensions of R, (Fig. 1). Since the offsets as described are integer values, an interpolation method can be used to optimally determine the peak displacement to sub-pixel accuracy. 2.2. Correlation algorithms A variety of correlation algorithms have been used, with the most common method being cross-correlation calculated in either the spatial or frequency domain (e.g. Stevens and Coates, 1994; Utami et al., 1991). Other methods such as minimum absolute deviation (e.g. Mitchell et al., 1996) or an error correlation function (e.g. Hart, 1998; Roth et al., 1995) are also used. The cross-correlation function is calculated as

1

A more appropriate term for the technique to be described and tested here could be Image Texture Velocimetry, but for clarity, we continue to use the more common term, PIV.

ð2Þ

/a;b ¼

2X sþ1 2X sþ1 1

1


ðI 
IÞ  ðS  SÞ ðr2I þ r2S Þ2

ð3Þ

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where the overbar denotes the mean, r2 is the variance and the subscripts I and S refer to the I and S windows, respectively. The dot operator implies the scalar product of the two matrices. So, the method seeks values of /a,b such that the cross-correlation is maximum and yields the pixel offsets (a, b) in the x and y directions. Note that un-normalized crosscorrelation functions should not be employed because the normalization is very important as it essentially removes the weighting toward higher pixel intensities. The determined offsets when divided by Dt yield velocity components in the x and y directions. For time constraining and computational efficiency, the maximum search distances, Lx and Ly , can be chosen based on the maximum expected velocity, r, such that the maximum offsets can be determined from Lx ; Ly ¼ rpDt

ð4Þ

where p is the scaling ratio of real world distance to pixel distance. The minimum velocity (other than zero) is confined to the ratio of p/Dt. The other variable that can be prescribed is the window size given by 2s + 1. Increasing the value of s will increase the computation time but yield more reliable vectors due to the larger spatial averaging region, while decreasing the value of s does the opposite (Stevens and Coates, 1994). However, increasing the value of s also decreases the spatial resolution of the technique and causes interrogation windows to overlap such that they are not truly independent. So the optimal window size is a trade-off between accuracy and resolution. Cross-correlation, however, may not be the most time efficient or accurate method to use for PIV. The existence of a product term in the numerator of Eq. (3) causes the cross-correlation method to be fairly sensitive to noisy interrogation and search areas. In addition, the calculation of the means and variances in Eq. (3) increases computational time. Therefore, we present (following Hart, 1998) another method for correlating the two windows of interest. The error correlation function is similar to crosscorrelation and has been shown to yield similar PIV results (Roth et al., 1995) while decreasing computational time. Utilizing the interrogation and search

windows defined above, the error correlation function, Ua,b is defined as 2X sþ1 2X sþ1

Ua;b ¼ 1 

1 1 2X sþ1 2X sþ1 1

ðjI  SjÞ :

ð5Þ

ðI þ SÞ

1

Similar to the cross-correlation technique, the Ua,b values range from 0 (no correlation) to 1 for perfect correlation between the two areas. In addition, the error correlation (EC), relying on differences between interrogation and search windows, does not weigh towards higher pixel intensities. So, similar to crosscorrelation, we seek the two windows such that Ua,b is a maximum yielding the required two-dimensional offsets. Since the offsets given by this method are at integer pixel distances, the true EC maximum is obtained by finding the location of the EC maximum of some functional fit to the nearby EC’s (e.g. Gaussian fitting (Huang et al., 1997), parabolic curve fitting (Fujita et al., 1998), or bilinear interpolation (Hart, 1998)). Here, we utilize the Gaussian fit near the maximum as our observations have shown EC values to be similarly shaped, although other interpolation methods yield similar results. Using this procedure, the 2D displacements (a,b) are determined to sub-pixel resolution. Velocity magnitudes in the crossshore and longshore directions are determined as u = ap/Dt and v = bp/Dt, respectively. 2.3. Synthetic data example Fig. 2 shows the flow field corresponding to the synthetic generation of two images (not shown) containing a random pattern of ‘particles’ of intensity 150 (on a 0 to 255 scale). The field corresponds to corner flow such that a largely vertical (down arrows) flow coming from the top of the image is diverted to flow out of the right-hand side. The minimum and maximum total offset magnitudes were 0.8 and 4.9 pixels, respectively. Random, Gaussian distributed noise between 0 and 80 in intensity value was introduced to degrade each image. Eq. (5) was then applied multiple times to each grid point of interest in the two images by varying s from 2 (size of interrogation window is 5
5) to 15 (size of interrogation window

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Fig. 2. Comparison of a prescribed flow field (gray) with PIV-based estimates using two synthetic images. Only deviations between measurements and expectations of more than 17% are shown (bold). The highlighted errors represent approximately 10% of the overall number of vectors.

is 31
31) and a search length Lx, Ly = 6. Results from s = 10 are shown in Fig. 2 for comparison to the prescribed flow field with the 10% largest deviations highlighted. The mean deviation between the PIV estimates and theory was less than 1% and 90% of the estimated vectors had normalized errors (defined as the absolute difference between expectation and observation normalized by expected value) of 0.17 or less (Fig. 3). The root-mean-square normalized error was 0.11, which corresponds to typical errors on the order of 10%. Statistics corresponding to the other simulations are given in Table 1. Because of the nested loops inherent in this PIV method, an important decision besides the amount of acceptable error is to determine an acceptable computation time. The above results required 56 s to process 900 vectors ( 16 vectors/s) on a SUN UltraSPARC30 (code written in MATLAB) with the given window size and search distances. Application of the PIV routine to the same images with varying window sizes shows the computation time versus error reduction benefits (Table 1). It is clear from the table that increasing the window size to more than twice the

maximum expected offset (from 5
5 to 11
11) results in a three-fold decrease in the average absolute and relative error, while only increasing computation time by 10%. In contrast, increasing the window size from 11
11 to 27
27 causes the computation time to increase by nearly 60% while decreasing the RMS error by about only 20%. So, performing PIV is a balancing act of choosing between appropriate window sizes that fit within time constraints and acceptable error. Because PIV experiments differ so widely in flow characteristics and methods used, a universal set of window sizes, time constraints and acceptable errors cannot be prescribed. However, for these simulations, we found an optimum size of interrogation window on the order of five times the maximum expected offset. 2.4. Error detection and correction methods Regardless of the tradeoffs between window size, acceptable error and computation time, application of PIV to natural flows requires post-processing to remove any spurious vectors resulting from incorrect

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Fig. 3. A histogram of normalized errors for the synthetic test case depicted in Fig. 2.

selection from multiple correlation peaks of similar magnitude. Spurious vectors have previously been removed by looking at local continuity of flow (Fujita and Kaizu, 1995; Fujita et al., 1998). The erroneous vectors were removed by setting a threshold value of flow divergence (obtained from discretization of the two dimensional continuity equation), and removing vectors whose local divergence exceeded this threshold. Removed vectors are replaced with an interpolated vector using an inverse-square-distance weighted average of nearby vectors. Utami et al. (1991) used a similar method by analyzing each vector with respect to the local mean velocity of surrounding vectors.

They further constrained their use of local vectors by requiring a cross-correlation coefficient of 0.7 or higher. If a vector differed from the local mean by more than 30%, it was deemed erroneous and replaced with a weighted average of the values of vectors from an elliptical area surrounding the vector in question. Several other similar techniques have been presented which involve more elaborate or multi-step methods for error detection and correction (e.g. Collins and Emery, 1988; Huang et al., 1997; Nogueira et al., 1999; Stevens and Coates, 1994). The disadvantage of these flow continuity approaches is that continuity will smooth strong gra-

Table 1 Statistical errors and timings for various window sizes Window size

RMS error (pixel)

Maximum absolute error (pixel)

RMS normalized error

Maximum normalized error

Computation time (s)

s = 2 (5
5) s = 5 (11
11) s = 7 (15
15) s = 10 (21
21) s = 13 (27
27) s = 15 (31
31)

1.24 0.39 0.30 0.29 0.28 0.28

3.85 2.82 2.30 2.41 0.67 0.68

0.57 0.14 0.12 0.11 0.11 0.11

0.99 0.74 0.62 0.63 0.29 0.27

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dients, which often exist in natural swash flows resulting from convergence of backwash and the subsequent uprush. A post-processing method presented by Raffel et al. (1998) uses the dynamic mean value operator to discard vectors when the absolute difference between the vector magnitude, w, and that of the mean magnitude of the eight surrounding vectors exceeds a certain threshold. The improvement resulting from using the dynamic mean value operator over a standard mean value operator is that the threshold varies based on local velocity gradients that will allow convergence. The mean value, lmag, of the eight vectors surrounding the center vector at a location (xm, yn), is given by lmag ¼

N 1X w2D ðnÞ N n¼1

ð6Þ

where (partially adopting the notation of Raffel et al., 1998) w2D is the array of surrounding vector magnitudes. In the case of vectors near image edges or if a surrounding vector has been removed from a prior correction, the remaining surrounding vectors will be utilized in which case, N < 8. The average magnitude of the difference between lmag and its eight neighbors is also calculated. This value, cmag, analogous to a standard deviation and used to determine flow variability or the degree to which velocity gradients exist, is defined as c2mag ¼

N 1X ðl  w2D ðnÞÞ2 : N n¼1 mag

3. Field data and validation

ð8Þ

where emag = K1 + K2cmag is an error threshold defined by user-supplied constants K1 and K2. Their technique is easily extended to include not only the magnitude, but also the direction, h, (in radians) of the vector using variables ldir, the mean direction of the surrounding vectors, and cdir, the directional variability. These terms are directly analogous to lmag and cmag such that a vector in the post-processing scheme will be rejected if: jlmag  wj > emag or jldir  hj > edir

where edir = K3 + K4cdir, cdir is determined as in Eq. (7) but for direction, and K3 and K4 are constants. Once the locations of all the rejected vectors have been determined, they are replaced using a weighted average of the eight nearest surrounding non-rejected vectors. In the event the eight surrounding vectors were also rejected in a previous step, the last procedure is repeated, as necessary, by expanding the region of surrounding vectors used in the weighted average until no data holes or gaps remain. Applying the post-processing method to the results from the second synthetic case (s = 5) with K1 = 0.3, K2 = 0.1, K3 = 0.3 and K4 = 0.2 corrected 99 of the 900 total vectors. The normalized RMS error before postprocessing (see Table 1) of 0.14 decreased to 0.11 after post-processing. This slight decrease in error implies that the vectors were adjusted by only small amounts (in fact, decreasing the K constants to K1 = 0.1, K2 = 0.05, K3 = 0.1 and K4 = 0.05 did not further change the RMS error). To more strenuously test this post-processing method, 1/10 of the vectors were manually replaced with new vectors of random direction and magnitude (up to the maximum magnitude in the prescribed flow field). After these ‘false’ vectors were implemented, the normalized RMS error was 0.22. Using the first set of K constants above, post-processing adequately corrected all of the vectors and yielded a normalized error of 0.11 which was the same as the error before the ‘false’ vectors were introduced.

ð7Þ

A vector is then rejected if: jlmag  wj > emag ;

71

ð9Þ

PIV-based swash analysis was performed on imagery obtained at the US Army Corps of Engineers’ Field Research Facility (FRF) at Duck, NC. Duck is multi-barred, intermediate to reflective beach with a tidal range of approximately 2 m. This barrier island field site consists of a relatively steep ( 1:10) and straight foreshore and an approximately planar offshore region (bottom slope of 1:500) with no nearby headlands or inlets. A large number of prior swash measurements have been obtained by the authors at this site with many observations indicating infragravity dominated motions at the shoreline, especially during storms and dramatic profile change responses (Holand and Holman, 1999; Holland and Puleo, 2001).

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The data presented here are from a small subset (approximately 80 s) of a 2-h record sampled on October 10, 1997 at 1400 local time. Individual video images were digitized at 2.5 Hz (i.e. every twelfth frame) using frame grabbing software and an Image Technology Inc. (ITI) image processor. The Dt value of 0.4 s was selected to allow a several pixel offset while maintaining sufficient temporal resolution. Once the set of images was collected, each was georectified following the camera model method of Holland et al. (1997) to a nearly horizontal plane along the slope of the beach in the shore-normal (FRF) coordinate system with 10-cm spacing, p = 10 pixels per meter. The cross-shore values range from 90 to 115 m and the alongshore values range from 650 to 690 m, relative to the local coordinate system. Application of the PIV technique required specification of the constant r to restrict the minimum window size. Cross-shore velocities on the order of several meters per second have been reported (Holland et al., 1998; Hughes et al., 1997; Masselink and Hughes, 1998); therefore, we choose a velocity value, r, of 5 m s  1 as a reasonable maximum. Using Eq. (4), and the values for r, p, and Dt yields a search distance Lx, Ly of 20 pixels. Grid points for the velocity vectors were spaced every 0.8 m within the specified cross-shore and alongshore grid. A value of s = 10 was chosen for the interrogation window size (21
21). Because the window size is roughly 2.5 times the grid point spacing, interrogation windows will overlap. This overlapping implies that neighboring velocity estimates are not truly independent, but still represent individual measurements because each window incorporates a different set of image texture. The PIV technique was performed on the entire set of 197 images and subsequently post-processed using K1 = 1.1, K2 = 0.6, K3 = 0.7, and K4 = 0.6 as representative of error thresholds for magnitude and direction of more than 30% from maximum expected values. In Fig. 4, several example swash images representing a complete swash cycle are shown with overlying surface velocity vectors computed using the PIV technique. Fig. 4a depicts uprush shortly after bore collapse at the beach. Here, all the vectors near the swash front are essentially onshore and have a magnitude of nearly 3.5 m s  1. The surface velocities just seaward of the swash front are also directed onshore, but smaller in magnitude (having an average of 1.3 m

s  1 ) and exhibit more longshore variation. As expected, nearly all of the grid nodes on the dry beach portion show little or no velocity, with the average velocity within this region being 0.08 m s  1. Fig. 4b shows the same swash 1.6 s later, just prior to the maximum uprush. Again, the velocities at grid nodes landward of the swash front are small (average of 0.01 m s  1). The vectors within the swash front are still essentially onshore, but their magnitude has decreased considerably to approximately 2.5 m s  1, which is expected as uprush nears flow reversal. The vectors seaward of the swash front have decreased in magnitude as well to around 0.6 m s  1. The ensuing backwash (3.2 s after the maximum uprush) is displayed in Fig. 4c and shows small offshore surface velocities of about 0.5 to 1.2 m s  1 throughout the study region. Finally in Fig. 4d (1.6 s later than 4c), stronger backwash flows with offshore velocities of up to 2 m s  1 have channeled into cusp embayments roughly located at alongshore locations y = 665 and y = 685. Also note the divergent flow between approximately y = 670 and y = 680 where the vectors are directed away from the cusp horn located near y = 675. The ability to measure flows with high spatial gradients is clearly displayed in the lower right corner of Fig. 4c where a strong bore (average velocity of 3 m s  1) is moving in the landward direction in opposition to offshore flow. Alongshore velocities in all cases were typically less than 1 m s  1, but occasionally reached 3 m s  1. These unique observations are clearly consistent with typical flow patterns over a swash cycle. We would liked to have compared these PIV results with independent measurements of swash velocity, unfortunately no in situ current meters were deployed within the foreshore study region during this Duck experiment. Also intricacies of their use in the swash zone (as previously mentioned) complicates quantitative comparison. Holland et al. (1998), however, developed a video-based technique for extracting the cross-shore swash edge velocity (virtual current meter) that is suitable for a qualitative comparison. By utilizing a swash timestack (see Holland et al., 1995 for more information), the velocity of the leading swash edge during uprush and backwash can be derived along a cross-shore transect in a manner quite different from the PIV technique. This method has been shown to closely approximate the temporal phase of swash velocity time series from co-located ADV and DICM

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Fig. 4. Swash flow vectors superimposed over rectified imagery depicting a complete swash cycle. The timings corresponding to each sampled image over the 80-s sampling interval are (a) 10.8 s, (b) 12.4 s, (c) 15.6 s, and (d) 17.2 s. The vector scale located in the upper left-hand corner of the image represents a 5-m s  1 velocity.

sensors, although some discrepancies in measured magnitudes have been observed (Holland et al., 1998). For this Duck experiment, cross-shore velocity measurements estimated by applying the timestack method at three positions separated in the cross-shore compare favorably with corresponding time series derived using the PIV technique (Fig. 5). Essentially, five swash cycles are apparent in both sets of time series with both the magnitude and duration of flow

decreasing in the landward direction. Internal structure is more apparent in the PIV flow measurements as the virtual current meter linearly interpolates the flow between maximum uprush and backwash. In addition, intervals for which the bed is dry, as indicated by zero velocities in the timestack method, have small PIVbased estimates. A more rigorous validation was conducted using ducted-impeller current meter measurements of cross-

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Fig. 5. Comparison of cross-shore velocity time series measured using the PIV (solid) and timestack (dashed) methods. Under the prescribed coordinate system, onshore velocities are negative. Upper, middle and lower panels represent measurements at cross-shore locations 96.5, 98, and 101 m, respectively.

shore swash velocities obtained at Gleneden Beach, OR (for experiment details, see Puleo et al., 2000). These data were compared with PIV-based estimates collected using a processing scheme essentially equivalent to that applied at Duck, with the exception that only a 1.5 by 1.5 m spatial region near the location of the most landward DICM sensor was analyzed. Instrument packages, cabling and other visible structures precluded use of the PIV method over a larger spatial grid. Fig. 6 shows a 6-min subset of the 1-h run for comparison. Both the magnitude and phase of signals are very similar. The only obvious discrepancy is that occasionally the maximum offshore velocity for a particular swash cycle is smaller using the PIV-based estimate. Since the ducted impeller method assumes that all flow is in the cross-shore direction (whereas the PIV method can measure both cross-shore and alongshore velocity components), even small alongshore-oriented swash flows, as often occur during backwash, will artificially increase the DICM estimated velocity. In general, however, maximum onshore and offshore velocities using both methods

were highly correlated over the entire 1-h record (r2 = 0.91 for n = 271). Also note that because the current meter is located roughly 4 cm above the bed and the video effectively records a surface level velocity, deviations in the exact timing of the flow, such as when backwash ceases, will be apparent for thin swashes. For example, in Fig. 6, the DICM velocity at 150 s drops to zero while the PIV-based estimate is positive, indicating that the flow at that time and location was less than 4 cm deep. During uprush where the swash front is relatively steep faced, there will be less of a discrepancy. We maintain, however, that swash measurements obtained using the PIV method should closely approximate those obtained using in situ sensors fully submerged within the flow. Our results support the hypothesis that during uprush and during an early portion of the backwash, a nearly uniform vertical velocity structure exists over most of the water column in typical swash flows, similar to that recently described by Petti and Longo (2001). For developed backwash where significant vertical structure may exist, the shallow

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Fig. 6. Comparison of cross-shore velocity time series measured using the PIV method (solid) and a ducted impeller current meter positioned 4 cm above the bed (dashed). Onshore velocities are negative. Upper and lower panels present continuous observations over two consecutive 3min intervals, respectively.

nature of the flow itself may preclude the simple use of in situ instrumentation.

4. Conclusions A laboratory technique known as particle image velocimetry has been successfully adapted for application in swash zone field studies. This method quantifies swash flow velocities in both alongshore and cross-shore directions at an extremely high spatial and temporal resolution compared to in situ instrumentation such as electromagnetic current meters. We present observations sampled at 2.5 Hz over a 25
40-m region with grid points spaced every 0.8 m in both directions. The results demonstrate that the method is capable of monitoring swash velocity magnitudes of over 4 m s  1 and can reliably monitor flow structures with high spatial gradients. Such measurements will prove useful in the application of sediment transport models that depend upon spatially and temporally variant velocity estimates.

Pre- and post-processing steps are required in the field application of the PIV technique. To restrict flow measurements to a common plane (as done in the laboratory through the use of a laser light sheet), oblique, time-sequenced imagery is first rectified to ground coordinates using a two-stage photogrammetric camera model previously described (Holland et al., 1997). Determination of velocity vectors requires specification of interrogation window and search region sizes, both of which can be related to a maximum expected velocity value. As window size is shown to increase computation time while decreasing noise, up to a point, we found the optimal window size to be approximately five times the maximum expected offset. In addition. interpolation was used to identify the position of the correlation peak to sub-pixel accuracy. A post-processing method to identify vectors significantly different from the surrounding flow field in either magnitude or direction is lastly applied. This step involves the selection of error thresholds that for this study were set to 30% of the expected range. In general, the PIV-based results were consistent with

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expectations for swash behavior on a sloping beach and were similar to estimates derived using a related remote sensing method and to in situ measurements. Quantification of swash flows using video-based particle image velocimetry has several advantages over alternative methods including larger spatial coverage, higher resolution, lower cost, unobtrusiveness to the flow, and essentially automated operation. The largest disadvantage of this method is the processing time required, which for the software-based system used in this study was approximately 16 vectors per second (excluding post-processing). Typical frames representing a study region on the order of 200 m2 may require more than 1000 vectors to be processed. However, a recent translation of the PIV software to take advantage of computer graphics hardware suggests a 10-fold increase in performance is easily achievable. Application of this system should allow substantial advances in our understanding of nearshore processes, especially with respect to sediment transport in the swash zone region and therefore we intend to present more extensive measurements using this technique in future publications.

Acknowledgements This work was supported under base funding to the Naval Research Laboratory from the Office of Naval Research, PE#61153N. We would like to thank Tony Butt for several helpful suggestions for improving the manuscript. We also appreciate the assistance of Rob Holman and Reg Beach in providing the Gleneden Beach current meter data. References Adrian, R.J., 1991. Particle-imaging techniques for experimental fluid mechanics. Annual Review of Fluid Mechanics 23, 261 – 304. Bagnold, R.A., 1966. An Approach to the Sediment Transport Problem from General Physics, 422-I, US Geological Survey, Washington DC. Beach, R.A., Sternberg, R.W., 1988. Suspended sediment transport in the surf zone: response to cross-shore infragravity motion. Marine Geology 80, 61 – 79. Butt, T., Russell, P., 1999. Suspended sediment transport mechanisms in high-energy swash. Marine Geology 161 (2 – 4), 361 – 375.

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