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Journal of Coastal Research 26 2 342–349 West Palm Beach, Florida March 2010 Spatial Trends in Tidal Flat Shape and Associated Environmental Parameters in South San Francisco Bay Joshua A. Bearman†, Carl T. Friedrichs†, Bruce E. Jaffe‡, and Amy C. Foxgrover†,‡ † Virginia Institute of Marine Science Gloucester Point, VA 23062, U.S.A jbearman@vims.edu ‡ U.S. Geological Survey Santa Cruz, CA 95060, U.S.A ABSTRACT BEARMAN, J.A.; FRIEDRICHS, C.T.; JAFFE, B.E., and FOXGROVER, A.C., 2010. Spat
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  Journal of Coastal Research 26 2 342–349 West Palm Beach, Florida March 2010 Spatial Trends in Tidal Flat Shape and AssociatedEnvironmental Parameters in South San Francisco Bay   Joshua A. Bearman † , Carl T. Friedrichs † , Bruce E. Jaffe ‡ , and Amy C. Foxgrover †,‡ †  Virginia Institute of Marine ScienceGloucester Point, VA 23062, U.S.A jbearman@vims.edu ‡ U.S. Geological SurveySanta Cruz, CA 95060, U.S.A  ABSTRACT BEARMAN, J.A.; FRIEDRICHS, C.T.; JAFFE, B.E., and FOXGROVER, A.C., 2010. Spatial trends in tidal flat shapeand associated environmental parameters in South San Francisco Bay. Journal of Coastal Research, 26(2), 342–349.West Palm Beach (Florida), ISSN 0749-0208.Spatial trends in the shape of profiles of South San Francisco Bay (SSFB) tidal flats are examined using bathymetricand lidar data collected in 2004 and 2005. Eigenfunction analysis reveals a dominant mode of morphologic variabilityrelated to the degree of convexity or concavity in the cross-shore profile—indicative of (i) depositional,tidallydominantor (ii) erosional, wave impacted conditions. Two contrasting areas of characteristic shape—north or south of a con-striction in estuary width located near the Dumbarton Bridge—are recognized. This pattern of increasingordecreasingconvexity in the inner or outer estuary is correlated to spatial variability in external and internal environmentalparameters, and observational results are found to be largely consistent with theoretical expectations. Tidal flatconvexity in SSFB is observed to increase (in decreasing order of significance) in response to increased deposition,increased tidal range, decreased fetch length, decreased sediment grain size, and decreased tidal flat width.  ADDITIONAL INDEX WORDS: EOF, eigenfunction analysis, morphodynamics, convexity, concavity, mudflat. INTRODUCTION The shapes of tidal flat profiles have been related to suchfactors as the relative intensity of wave vs. tidal forcing, thesupply and grain size of sediment, and local elevation of theflat with respect to mean sea level. Dieckmann, Osterthun,and Partenscky (1987) and Kirby (2000) presented observa-tional examples from the German Bight and the U.K. sug-gesting that profiles tend to become more strongly convexupward with increased tidal range. Kirby (2000) also ob-served a strong connection between increased tidal range andgreater percentages of flat area found above mean tide level.Several authors have noted that accretionary tidal flats tendto be convex upward, whereas erosional flats tend to be con-cave upward (Dyer, 1998; Kirby, 2000; Le Hir et al., 2000;Mehta, 2002; Van Rijn, 1998). Tidal flat erosion, in turn,tends to be associated with wind wave activity, while depo-sition tends to be associated with tidal currents (  e.g., Allen etal., 1998; Christie, Dyer, and Turner, 1999; Fan et al., 2006;Janssen-Stelder, 2000). Similarly, wave-dominated areashave been associated with coarser, sandier tidal flats, andtidally dominated regimes with finer, muddier flats (  e.g., Wooand Je, 2002; Yang et al., 2008).These trends are, by and large, consistent with the conceptthat the morphodynamics of tidal flats are driven at lowestorder by temporally evolving gradients in hydrodynamic en-ergy and sediment supply. Tidal currents tend to producegreatest bed stresses over lower flats and subtidal areas,driving sediment shoreward, whereas waves produce highest  DOI: 10.2112/08-1094.1 received 11 July 2008; accepted in revision12 November 2008. stresses in the shallowest nearshore regions, driving sedi-ment seaward (  e.g., Fan et al., 2006; Lee, 1995; Ridderinkhof, Van Der Ham, and Van Der Lee, 2000; Yang et al., 2003). Itfollows that a profile with spatially uniform bottom stresswill be more likely to disperse sediment equally everywhere.Friedrichs and Aubrey (1996) showed that a convex profilefavors uniform stress from tidal currents, whereas a concaveprofile favors uniform stress from waves. Simple sedimenttransport models incorporating tides and waves generallysupport these equilibrium trends, such that waves enhanceconcavity and tides enhance convexity (Lee, 1995; Lee andMehta, 1997; Pritchard and Hogg, 2003; Pritchard, Hogg,andRoberts, 2002; Roberts, Le Hir, and Whitehouse, 2000;Waeles, Le Hir, and Jacinto, 2004). Although theoretical and conceptual arguments favorquantitative relationships between tidal flat shape and theimpacts of tides, waves, and recent deposition or erosion, fewobservational studies have incorporated sufficiently largemorphological data sets to adequately test predicted trends.Kirby (2000) visually compared the distribution of surfacearea with height for seven U.K. flat systems as a function of tidal range. Dyer, Christie, and Wright (2000) used clusteranalysis to analyze 20 attributes of 18 mudflats from north-west Europe. Although profile shape was not examined byDyer, Christie, and Wright (2000), waves and tides were stillshown to be the two most significant discriminators amongthe attributes considered. Yamada and Kobayashi (2004)used eigenfunction analysis to examine the temporal evolu-tion of two tidal flat profiles over 2 years but found no cor-relation between profile curvature and changes in environ-mental forcing. Considering the relatively small number of   343Spatial Trends in Tidal Flat Shape in South San Francisco BayJournal of Coastal Research, Vol. 26, No. 2, 2010Figure 1. South San Francisco Bay tidal flat locations. Shown here isthe area extending from mean high water to mean lower low water(MLLW)—0.0 m—and the near subtidal area extending to  0.5 m belowMLLW.Figure 2. Cross-shore profiles drawn in ARCMAP. Of the more than 800srcinally drawn, 766 were used for the spatial analysis. comparative empirical studies that have focused on tidal flatshape, the rich data sets available for the diverse flats sur-rounding South San Francisco Bay provide a unique oppor-tunity to significantly increase the quantitative basis for ourunderstanding of the relationship and feedback betweentidalflat morphology and the impact of tides, waves, and sedimentsupply. SITE DESCRIPTION South San Francisco Bay (SSFB) (Figure 1) is a mesotidal,mixed tide system with semidiurnal tides ranging up to 2.5m (Pestrong, 1972). Because of a contraction in estuary widthand reflection of the tidal wave at the inner end, tidal rangeincreases with distance from the Golden Gate (  1.2 m) to thesouthern head of SSFB (  2.5 m); tidal range on the south-western shore is slightly larger, a result of the Coriolis effect.Wave activity in SSFB is characterized by short period windwaves, rather than ocean swells (Conomos, 1979; PWA,2005). Strong summer winds from the northwest generatewaves with periods on the order of 2–3 seconds and heightsup to 1 m (Conomos, 1979), which act to resuspend sediment,allowing transport to the channels by tidal currents (Cono-mos, 1979, Krone, 1979).Foxgrover et al. (2004) showed that SSFB underwent a netsediment loss from 1858 to 1983. While the loss was not asteady process over the studied period, the system as a wholehas been predominantly erosional. This loss of sediment wasaccompanied by a large loss in tidal flat area in outer SSFB(Jaffe and Foxgrover, 2006a). In contrast, the innermost por-tion of SSFB—the area southeast of the Dumbarton Bridge—has seen a slight increase in sediment volume over the periodstudied (Foxgrover et al., 2004; Jaffe and Foxgrover, 2006b).Sediment in SSFB is derived from two sources: (i) the Sac-ramento–San Joaquin Basin (the Inland Delta) after passingthrough the northern and central Bay, and (ii) the manysmaller tributaries that directly fringe SSFB. TheInlandDel-ta is the commonly, though not universally, accepted sourcefor the majority of sediment influx into SSFB because thelocal tributaries are thought not to have the discharge nec-essary to contribute a substantial portion, except during verywet winters (Jaffe and Foxgrover, 2006b; Krone, 1979;McKee, Ganju, and Schoellhamer 2006; Porterfield, 1980;Schoellhamer, 1996). Sediment exchange between the Cen-tral Bay and Golden Gate generally results in a loss of sedi-ments to the ocean (Krone, 1979). Regardless of their ulti-mate source, suspended sediments are primarily advectedinto SSFB in the deeper channels. Resuspension by tidal cur-rents then moves the sediments up onto tidal flats andmarshes, where they are sometimes deposited, depending ontidal stage, wave conditions, and other hydrodynamic factors(Krone, 1979; Schoellhamer et al., 2005). Significant waveevents presumably favor sediment transport back toward thedeeper channels.Pestrong (1972) examined sedimentation on the tidal flatsof SSFB at Cooley Landing (2 km south of the DumbartonBridge) and determined that sediment is preferentiallymoved across the entire tidal flat on flood tides, with finesediment sequestered on the higher flats because of settlingand scour lag. Highest transport rates occur at the marshedge and in tidal channels, and sediments eroded from theflat on flood tide are deposited in the adjacent marsh. Sig-nificant accretion occurs at the tidal flat–marsh interfacewhen the flood tide has inundated the mudflat and as theebb tide drains the marsh. METHODSExtraction and Normalization Using a combination of bathymetric sounding and lidardata, with a vertical resolution between 15 and 25 cm, gath-ered in 2004–2005 and modeled by Foxgrover et al. (2004)and Foxgrover and Jaffe (2005), multiple cross sections weredrawn with an ARCMAP platform (Figure 2). Spaced atroughly 50-m intervals, the profiles were selected to remainlargely normal both to shore and the predominant contours.Profiles range in length from 120 to 3100 m; this length isnot necessarily indicative of the tidal flat width because lineswere drawn to well exceed the intertidal zone. Once all tran-sects were drawn, horizontal and vertical information wasextracted and normalized to specified upper and lower ver-tical bounds. To perform an eigenfunction analysis, each line  344 Bearman et al. Journal of Coastal Research, Vol. 26, No. 2, 2010Figure 3. Example of the normalization process. Profiles are bound atupper and lower limits (dotted lines) and regridded onto a unitless scaleof 30 points. It is necessary for EOF analysis that all profiles have anequal number of data points. was normalized to the same number of horizontal points. Thenormalization procedure involved replotting the horizontalextent of each profile onto a series of 30 unitless horizontalpoints and then performing a spline interpolation that fit apiecewise polynomial function to the vertical data (Figure 3).In evaluating the morphologic character of the profilelines,we examined four sets of vertical bounds: (i) between meanhigh water (MHW) and mean lower low water (MLLW); (ii)between MHW and 0.5 m below MLLW; (iii) between 1.7 mabove and 0.5 m below MLLW; and (iv) between 1.7 m aboveand 1 m below MLLW. The first set of boundaries representswhat is classically considered to be a tidal flat. Two sets of boundaries below MLLW were also extracted to examine thesensitivity of including the near subtidal areas. A standard-ized upper limit of 1.7 m was also tested (i) to examine thesensitivity of the choice of the upper limit, and (ii) for use ina larger temporal study (see Bearman, 2008) that applied ei-genfunction analysis to SSFB bathymetric data sets collectedin the 1890s, 1930s, 1950s, and 1980s. None of the previoussurveys included lidar or other subaerial topographic data,and 1.7 m above MLLW represented the mean maximum ver-tical datum surveyed by these previous studies.For profiles within the 2004–2005 data set for whichbathy-metric data did not extend all the way to 1.7 m or MHW, theprofiles were extrapolated upward to the desired higherboundary. Any profile with an upper edge of srcinal bathy-metric data less than 1.0 m above MLLW was discarded be-cause the interpolation tended to assign unrealistic upperslopes in such cases. Figure 3 shows an example of a mudflatprofile in its pre- and postnormalization forms. Of the srci-nal 800  profiles, 766 survived the normalization procedure. Eigenfunction Analysis To identify the principal components of variation, we per-formed an eigenfunction analysis, also known as empiricalorthogonal function (EOF) analysis. Empirical orthogonalfunction analysis allows for large quantities of data to becompressed into a few dominant modes without compromis-ing the most significant variability within the data. Becausethe components of variability identified through EOF analy-sis are orthogonal, they are uncorrelated and can be exam-ined individually.Of great use in spatial analysis is the pattern of scores thatpertain to the individual eigenfunctions, or modes of vari-ability. EOF analysis has been used in the examination of morphologic variability of beach profiles (Aubrey, Inman,andWinant, 1980; Winant, Inman, and Nordstrom, 1975), estu-aries (Karunarathna, Reeve, and Spivack, 2008), and mud-flats (Yamada and Kobayashi, 2004), among other environ-ments. When compared with variation in other physical fac-tors, the spatial patterns of the scores can suggest connec-tions between morphology and external forcing. In the caseof this EOF analysis, the profile set was first de-meaned sothat the dominant eigenfunction would identify variabilityamong profiles rather than simply the shape of the mean pro-file.The 766 profiles were broken up into 12 distinctgeographicsections, using for region boundaries such features as tribu-tary mouths and steep intertidal zones wherein no tidal flatwas evident (see Figure 2). To help ensure that the bound-aries of the regions were rigorous in the face of the analysis,we plotted the individual regions against a running cumula-tive sum of the eigenfunction scores. For the most part, theprofiles within a given geographic section showed a consis-tent pattern of morphologic score, and the boundaries werefound to be justifiable. In the few cases where the pattern of cumulative scores reversed directions midregion, the regionboundaries were redefined to produce a more morphologicallydistinct geographic section. As a check on the independenceof the eigenfunction scores between regions, a lagged auto-correlation was run on the scores of all 766 profiles, se-quenced in order of position around the perimeter of SSFB.The r 2 value for an autocorrelation lagged by 64 profiles (theaverage number of profiles in each region) was 0.27, indicat-ing that profile shapes within a given region were reasonablyindependent of those in neighboring regions. Physical Variables Potential fetch lengths for local wave generation were ac-quired from the GIS database by drawing 100 sets of 16 lines,spaced evenly around the shoreline of SSFB, with each set of lines beginning at 0  and progressing by 22.5  intervalsaround a compass rose. Fetch lengths for each of the 16 lineswere logged for all 100 sets, and the mean fetch length foreach set was calculated. Tidal range data was obtained fromNOAA (2008) at all available stations in SSFB and was lin-early interpolated for profile regions that fell between thelocations of the NOAA stations. Surface sediment data wascollected at various locations in SSFB in the fall of 2004 andsummer of 2005 by U.S. Geological Survey (USGS) personnelusing a small van Veen grab sampler. The sediments wereanalyzed for bulk density as well as the Folk and Ward meangrain size.  345Spatial Trends in Tidal Flat Shape in South San Francisco BayJournal of Coastal Research, Vol. 26, No. 2, 2010Figure 4. (a) Dominant mode of morphologic variability determinedthrough EOF analysis of all four boundary scenarios analyzed together;(b) dominant mode of variability determined through EOF analysis of flats bounded by MHW on upper edge and  0.5 m on lower edge.Figure 5. (a) Regionally averaged scores of first eigenfunction for eachboundary scenario when all four boundary scenarios are analyzed togeth-er; (b) regionally averaged scores of first eigenfunction for flats boundedby MHW on upper edge and  0.5 m on lower edge.  Although the 2004–2005 bathymetric data set is the focusof this paper, elevations for these same profiles were alsogathered for the 1980s, 1950s, 1930s, and 1890s by applying ARCMAP to the larger Foxgrover et al. (2004) historical dataset as part of our broader analysis. By comparing profile el-evations from the 1980s and 2004–2005, we were able to es-timate deposition and erosion preceding the 2004–2005 sur-vey. RESULTSComparison of Boundaries Eigenfunction analysis was performed on four sets of nor-malized bathymetric data, each with slightly different upperand lower tidal flat boundaries, 2958 bathymetric profiles inall. For all four data sets, it was found through this analysisthat the profiles vary most intensely in terms of their degreeof concavity or convexity, represented by a negative or posi-tive first eigenfunction (Figure 4a). Figure 5a shows the pri-mary mode of variation (first eigenfunction)—referredtohereas morphologic score—regionally averaged for each of thefour boundary scenarios. While the primary pattern—that of concavity or convexity in the outer or inner estuary flats—remains the same in all scenarios, the values of the scores ineach situation varies. Concavity increases (and the scores be-come more negative) if the lower limit of the flat is extended,while convexity increases (and the scores become more posi-tive) if area is added to the upper flat. The analysis using theboundaries of MHW to MLLW shows the highest scores(greatest convexity), while the analysis of the flats boundedby 1.7 m and 1 m below MLLW is the most negative (mostconcave).In the interest of capturing as full a picture of the profileas possible, while simultaneously not straying too far fromthe classic definition of an ‘‘intertidal’’ flat, the rest of thispaper highlights results using the tidal flat extent fromMHW to 0.5 m below MLLW water. Figures 4b and 5bdisplaythe primary eigenfunction and regionally averaged mode 1scores when the MHW to  0.5-m data set is analyzed alonerather than being combined with all four sets of bathymetry. As can be seen from comparing parts a and b of Figures 4and 5, there is very little difference in the shape of the dom-inant mode or the associated scores for the MHW to  0.5-mdata whether the data set is considered alone or is consideredtogether with the other sets of bathymetry. However,limitingthe analysis to a single set of bathymetric endpoints doesincrease the percent of variance explained by the dominantmode of variability.
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