Source-Transport Inversion: An Application of Geophysical Inverse Theory to Sediment Transport in Monterey Bay, California


James F. Tait
Earth Sciences Department
Southern Connecticut State University
New Haven, CT 06515

Justin Revenaugh
Institute of Tectonics,
Earth Sciences,
University of California,
Santa Cruz, CA 95064

SECTIONS
Abstract Introduction The Physical Setting Methods Results and Discussion Conclusions References Figure Captions
ABSTRACT
Application of forward coastal sediment transport models in situations involving large temporal and spatial scales or topographically complex environments can be highly problematic since the distribution of hydrodynamic parameters is rarely adequately known. Where rocky topography is present, flow patterns may be altered and sediments trapped by topographic barriers. A frequently employed approach to these problems is the application of the statistical technique known as empirical orthogonal functions (EOF). One limitation of EOF analysis of grain size and mineralogical data is that EOF is a purely mathematical/geometric technique which does not allow incorporation of a priori knowledge we may have regarding the physical environment. In fact, there is no guarantee that a meaningful physical interpretation of the results of an EOF analysis actually exists. This is not true of geophysical inverse theory which is capable of incorporating diverse forms of information and is not limited to purely geometric manipulations of data. We have formulated an inverse-theoretical approach to study sediment transport which we call STI, short for Source-Transport Inversion. STI relaxes the non-physical assumption of orthogonal end-members and can handle many forms of a priori information. STI has been developed initially in the context of modeling the sediment supply and dispersal system of Monterey Bay, California. Using the geographical distribution of heavy mineralogy data, significant sources are identified and sediments traced from those sources along transport pathways. Model results are encouraging both in terms of goodness-of-fit between model and data, and in terms of the agreement of model results with the sediment sourcing and dispersal patterns inferred in previous studies. Model results indicate that beach sediments are primarily derived from the open coast north of the bay, that a littoral cell boundary exists in the center of the bay at Moss Landing, and that beach deposits produced by paleo- littoral drift during a sea level low-stand lie along the 100-m isobath.

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INTRODUCTION
Considerable progress has been made in the last two decades in modeling shelf sediment transport. Work on benthic boundary layer physics and the development of wave and current interaction models [e.g., Sternberg, 1972; Smith, 1977; Grant and Madsen, 1979; Glenn and Grant, 1987] has provided the conceptual and quantitative tools for addressing a variety of shelf sediment transport problems. These models have been successful notwithstanding unresolved issues of predicting initial motion and measuring suspended sediment concentrations [Cacchione and Drake, 1990]. Predicting time-integrated fluxes on regional scales, however, remains problematic since knowledge of the temporal and spatial distribution of hydrodynamic parameters is generally inadequate. On rocky coasts, the problem is further complicated by the presence of subaqueous bedrock topography. In particular, topography may steer bottom currents, enhance turbulent shear stress at the bed, trap sediments, and fractionate sediments by grain size during transport [e.g., Tait et al., 1992].

A number of strategies for investigating sediment transport at large temporal and spatial scales have been developed. Most use the characteristics of the sediments to infer dispersal patterns and processes. These include the use of basic statistics such as mean grain size, sorting, and skewness [Krumbein, 1938; Folk and Ward, 1957]; distinguishing subpopulations in the cumulative frequency curve [Visher, 1969; Middleton, 1976]; use of the hyperbolic distribution [Bagnold and Barndorf-Nielsen, 1980]; quantification of grain shape by Fourier analysis [Ehrlich and Weinberg, 1970; Osborne and Yeh, 1991]; and development of sediment transfer functions [McLaren and Bowles, 1985].

Perhaps the most prominent technique is the multivariate statistical approach known as Factor Analysis or Empirical Orthogonal Functions (EOF). This technique partitions sample variance into orthogonal components or factors ranked by the percentage of sample variance they account for, granting insight into the primary shapes or distributions contained in the data. Early application of this technique to sedimentological data includes Krumbein and Aberdeen [1937] and Imbrie and Van Andel [1964]. Applications of EOF to coastal sediments include analysis of shoreface morphology [Dolan et al., 1977, Resio et al., 1977, and Felder et al., 1979], shoreline variability [Hayden et al., 1979], seasonal patterns of cross-shore transport [Winant et al., 1975; Aubrey, 1979; Aubrey et al., 1980; Clarke and Eliot, 1983; Aubrey and Ross, 1985], and alongshore transport patterns [Clarke and Eliot, 1982, Clemens and Komar, 1988]. In a more recent series of papers, Liu and Zarillo [1989, 1990, 1992] have employed factor analysis to study passive margin shoreface dynamics using a set of cross-shore grain size distribution profiles along the south shore of central Long Island.

Although clearly a powerful tool, a major limitation of EOF analysis is that it is a purely mathematical/geometric technique (length-preserving spatial projection). The condition of orthogonality central to EOF limits its ability to resolve physical end-members unless the end-members are themselves orthogonal. Any a priori information we may have, such as source mineralogies or grain size distributions, transport effects, or physical processes, cannot be incorporated into the solution. In the end, the investigator must interpret the significance of the orthogonal components produced by EOF analysis. These limitations do not apply to geophysical inverse theory.

We have developed an inverse technique based on least squares applicable to the study of large-scale sediment transport and sourcing patterns. We are motivated by the desire to model time-integrated regional sediment transport systems. The technique, called source- transport inversion (STI), is applied initially to sediment samples collected on the continental shelf, beaches, and coastal streams of Monterey Bay. The objective is to test STI in a relatively simple topographic environment using heavy mineralogy as the sediment property of interest before progressing to more complex (e.g., rocky open ocean) coastal environments and incorporating more diverse forms of a priori information such as grain size, grain shape, or transport efficiencies.

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THE PHYSICAL SETTING
Monterey Bay is located between 36 30' and 37 degrees north latitude on the central California coast (Figure 1). It has a Mediterranean climate, receiving 90% of its rainfall between November and March. Storms tend to be intense and of short duration. Mean annual rainfall is 45-70 cm along the coast and as much as 150 cm at the crest of the Santa Cruz mountains [Rantz, 1971].

Monterey Bay has a number of distinct sediment sources. The most important are the three rivers that drain into the bay and littoral drift from the north (Figure 1). The Salinas River is the largest of the three major streams with a basin area of 11,137 km2, an average annual stream discharge of 3.9 * 10^7 m^3 [Yancy, 1968], and an average yearly sand and gravel load of 586,000 m^3. The San Lorenzo has the smallest basin with an area of 275 km^2, an average annual stream discharge of 1.3 * 10^7 m^3 [Yancy,1968], and an average yearly sand and gravel load of 51,000 m^3. The Pajaro is intermediate in size with a basin area of 3,626 km^2 and an average annual stream discharge of 1.5 * 10^7 m^3[Yancy, 1968]. Sediment load volumes were estimated from U.S.G.S. Water Resources stream gauging data.

Despite the San Lorenzo's relatively small basin area, it is a fairly prodigious sediment producer. Its basin is steep and it delivers a large amount of coarse-grained sediment due to high erosion rates in the Santa Cruz Mountains. By comparison, the Pajaro and Salinas Rivers are low-gradient streams and have low sediment discharge-to-basin area ratios. A number of smaller creeks also episodically deliver sediments to the bay. The largest of these is Soquel Creek which is an order of magnitude smaller than any of the rivers in basin area and annual discharge.

In northern Monterey Bay, net littoral drift is from north to south and has been estimated as 200,000-250,000 m^3/yr at Santa Cruz Harbor [Best and Griggs, 1991]. In the southern half of the bay, littoral drift is more complicated and poorly understood. The Salinas River delta, covering an area of approximately 72 km^2, bends the isobaths seaward at the coast (Figure 2) and may cause a divergence of littoral drift in the region [Oradiwe, 1986]. In the center of the bay, Monterey Canyon, one of the world's largest submarine canyons, heads directly into shore. It has been suggested by a number of researchers [e.g., Sayles, 1966] that the canyon decouples littoral drift in the northern and southern halves of the bay and separates the bay into two distinct littoral cells, the Santa Cruz Cell to the north and the Monterey Cell to the south.

The predominant direction of wave approach in central California is from the northwest. Occasional cyclonic subtropical storms bring storm waves from the south or west, however, and the beaches are often exposed to southerly swells during the summer months. The wave climate is fairly energetic with significant wave heights of 2-3 meters occurring in fall and winter. Refraction of waves over the complex bathymetry of Monterey Canyon makes the beach between Monterey and Moss Landing particularly susceptible to high waves.

A recent paper [Breaker and Broenkow, 1994] provides a thorough summary of circulation studies in Monterey Bay. The connection between the bay and the open ocean is unconstricted, making circulation within the bay very responsive to open ocean currents. Furthermore, the bay is divided by Monterey Canyon which brings deep water very close to shore. These two factors make surface and subsurface circulation spatially and temporally complex. The bay is susceptible as well to perturbations in circulation during years of strong El Nino events. Due to this complexity, circulation patterns in the bay are not well-understood despite studies going back as far as 1930. Recent studies indicate that surface flow within the bay is typically cyclonic (south to north) with current speeds on the order of 5 to 20 cm/s. The depth of this surface layer is estimated as 25-30 m, although this depth can be variable. At intermediate depths of approximately 25-150 m (in the thermocline), long-term flow patterns are poorly documented. The temperature distribution suggests that geostrophic flow may possibly be anticyclonic (north to south), but the data necessary to substantiate this are not available (William Broenkow, personal communication, 1996). Below this depth is a third circulation regime which affects the canyon interior and the continental slope.

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METHODS
The heavy mineral abundances of surface sediment samples from the continental shelf, beaches, and coastal streams of the Monterey Bay area that we model were collected and analyzed by the Hydraulic Engineering Laboratory (HEL hereafter) at the University of California, Berkeley, in September of 1966 (Figure 2). Heavy mineral analysis was confined to the sand sized-fraction (> 62 microns).

Using the nine most abundant heavy minerals, a simple end-member mixing model was constructed. The end-members correspond to the main sediment contributors to Monterey Bay. These are (1) littoral drift, (2) the Salinas River, (3) Soquel Creek, and (4) a combined end-member, the San Lorenzo-Pajaro Rivers (Figure 3). The reason for combining two streams into the latter end-member is that the two sources are, for the purposes of this study, indistinguishable in terms of mineral percentages.

In other words, nearby samples are constrained to resemble one another in terms of end-member contribution. Since the number of equations (the number of diagnostic minerals) exceeds the number of unknowns (number of end-members), the system in (1) is overdetermined. The addition of (2) results in a much larger system of simultaneous equations, but which remains overdetermined. The combined system is solved using the non-negative least squares approach of Lawson and Hanson [1974, pp. 160-165], avoiding the non-physical situation of a negative contribution. W was chosen to down weight mineralogies whose ensemble distributions departed significantly from normality (i.e., outliers are not allowed to dominate the solution), with the lowest weights assigned garnet and zircon, and to balance the influence of observations and smoothing equations. Smoothing was minor: samples separated by greater than 2.4 km were assumed to be independent and the remaining non-trivial equations were given little weight in the inversion.

The next step is to evaluate how adequately this simple model explains the data, i.e., how well the end-member mixtures reproduce observations. Unlike EOF analysis, we do not expect a one-to-one correspondence. Variability in sampling and errors in sample analysis, random noise in the samples themselves (e.g., small-scale spatial variations), sorting during transport, and other effects, all lead to inconsistency with the simple end- member model. To determine how significant this inconsistency is, a variance reduction analysis is performed, quantifying the differences between the actual mineral abundances and the model estimates. This is discussed at greater length later in the text. The ultimate step in this analysis is to define sediment transport pathways through the system. This is accomplished by defining (mapping) lines of high source contribution through the sampling region.

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RESULTS AND DISCUSSION
Littoral Drift
The littoral drift signature tracks very well along the shoreline of the northern half of the bay and particularly well from the source region to Point Santa Cruz (Figure 4). Its contribution to the southern Monterey Bay shoreline is almost non-existent. The contribution of this source to most of the beach samples along the northern half of the bay is between 60 and 100%. Low contribution percentages for beaches in the northern bay are found primarily where San Lorenzo River and Soquel Creek are located. High sourcing along the shoreline extends as far south as Moss Landing and then ends abruptly. This pattern of high littoral drift sourcing is consistent with the results of previous studies of sediment transport in Monterey Bay [e.g., Sayles, 1966; Oradiwe, 1986; Best and Griggs, 1991; Anima et al., 1993]. Most of the sand transported as littoral drift in the northern portion of the bay appears to come from the open coast to the north. This flux overwhelms sources within the bay. The bottom of the Santa Cruz littoral cell is assumed to be located at Moss Landing where most of the sediment moves offshore and into Monterey Canyon. Southern Monterey Bay receives no significant contribution of beach sand via littoral drift from the north despite a predominant northwesterly direction of wave approach.

Another high-source track of the littoral drift signal is found at the outer edge of the continental shelf along the 100-m isobath. This was unexpected but we now believe that this is a paleo-littoral drift signal from a sea level low stand when the shoreline was located near the shelf break. The cross-shore distribution of the mean grain size of the samples was examined for corroborative evidence (Figure 5). Mean grain size generally decreases seaward, reaching a minimum at a depth of ~70 m, then increases. The samples obtained in the deepest waters of each transect (90 - 100 m) have a uniform mean grain size of 2.75- 3.0 phi. This is an appropriate size for a fine sand beach or for dunes.

Salinas River
The Salinas River signature tracks the shoreline of southern Monterey Bay and dominates the continental shelf, both north and south of the canyon (Figure 4). It is particularly dominant on the shelf in the east-central portion of the bay. It is clearly the only significant source for the southern Monterey Bay shelf. This is to be expected as it is the only major stream discharging into this half of the bay. The Salinas River delta is apparent in the bathymetric contours near the shoreline. It is perplexing, however, that this source should be significant to the sediments of the northern shelf. The heavy mineral analysis used the sand-size fraction exclusively, and transporting this material from the river's mouth across Monterey Canyon in suspension seems implausible.

An explanation can be found in the historical migration of the mouth of the Salinas River. Historical accounts locate the mouth of the Salinas River north of Moss Landing until the winter of 1909 or the spring of 1910 [Gordon, 1979, pp. 230-245]. The present location of the river mouth has been artificially maintained since that time by trenching through low dunes and opening a connection between the channel and the bay during times of high discharge. The purpose of this diversion was the expansion of farming into the lower flood plain of the river. The presence of a large delta, however, argues for the location of the river mouth in its present position over most of its geologic history. The Salinas has the largest coarse-grained sediment load of all streams entering the bay. If the river is in the habit of switching the location of its mouth between south and north of the canyon head, and if the river recently discharged into the northern portion of the bay, it stands to reason the sediments would present a strong signature on the shelf on both sides of the canyon. The dispersal pattern in the northern half of the bay shows high source contribution on the shelf between Moss Landing and the head of Soquel Canyon. The significance of Salinas sediments lessens markedly to the west and to the north. This is consistent with our understanding of Monterey Bay circulation. In particular, cyclonic (northward flowing) circulation during the winter would tend to disperse the heavy minerals in a northwest trending pattern. Minerals which were transported into the region of reverse flow, if such a region exists, would be swept into the canyon. There is no Salinas signature along the shoreline in the north bay, consistent with the notion of a cell boundary at Moss Landing and southward-directed net littoral drift.

San Lorenzo-Pajaro Rivers
The heavy mineralogy of the San Lorenzo and Pajaro Rivers are quite similar and, for the purposes of stability during the inversion, the two were combined as a single end- member (Figure 4). Although the signature of the two rivers is broadly distributed geographically, they nowhere completely dominate the sample compositions. There is a fairly high source contribution (approximately 60%) in the far northwestern portion of the sampling region. This is probably San Lorenzo material which has been swept out onto the mid-shelf then advected in a northwesterly direction by cyclonic circulation. It is notable that this particular signature does not show up on the beaches of the north bay. The rivers of the Monterey Bay region experience highly variable flows, both seasonally and interannually. A characteristic sand bar forms across the mouths of the streams during the spring, summer, and early fall because stream flow is so low. Water ponds behind this bar to form a lagoon. Stream connection to the sea at this time is principally via groundwater seepage through the bar. As a result, the alongshore distribution of heavy mineralogy is time-dependent. If sampling occurs during a time of high winter stream discharge, or after a particularly eventful year, then the source signature of the two rivers should be manifest. The HEL samples were collected in September of 1966. September is typically a dry month with little or no stream flow. Seasonal storm activity does not begin until October or early November. Littoral drift of material originating outside the bay will have gone unmixed with local sources throughout the summer, thus masking the local source signatures.

Soquel Creek
Unlike the San Lorenzo-Pajaro signature, the Soquel Creek signature dominates the beach and offshore in the immediate vicinity of its mouth (Figure 4). This is one of the more vexing results of the inversion. Because Soquel Creek is so much smaller than the San Lorenzo and Pajaro Rivers, this disparity does not seem reasonable. Two immediate possibilities come to mind. One is that the channel mouth bar was broken, or that water was released from the lagoon, intentionally. The other possibility has to do with the inversion. Soquel Creek has a unique mineralogy compared to the other coastal streams. In particular, it is low in green hornblende and high in hypersthene. Even with the smoothing constraints, it stands out in a region dominated by the littoral drift signature. It may be that the San Lorenzo-Pajaro signature can be mimicked by a combination of the other sources and therefore not stand out without additional parameters, such as grain size distribution or transport effects, being included in the inversion. In and of itself, the dispersal pattern of the Soquel Creek is what one might expect of a less important sediment producer. There is high sourcing locally and this signature dies out rapidly with distance.

Variance Reduction

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CONCLUSIONS
What we have gained by developing STI is the ability to include a priori knowledge resulting in a physical model of sediment sourcing and dispersal that is simply interpreted in terms of the hydrodynamics of the bay. In this experiment, the a priori knowledge consists of source identification (and the relative abundances of the nine most common heavy minerals in each source), reasonable expectations of mixing scales (incorporated as smoothing constraints), and relative precision of the heavy mineralogy analysis. Despite significant simplifying assumptions such as linear mixing of end-members without transport-related sorting, the fit of model to data is very good. It should be noted that in obtaining this solution we restricted smoothing to samples with small geographic separation (smoothing decreased linearly with geographic separation, vanishing at 2.4 km), i.e., we imposed very little smoothing. Nonetheless, the solution is visually smooth, as we would expect of any plausible model, and yet marked by a severe discontinuity across Monterey Canyon, also as we would expect, in the case of littoral drift. Model results were consistent with available environmental data (e.g., data on currents), despite their omission in the inversion, a sign of a stable and adequate model. The dispersal pattern of Salinas River sediments, for example, is in keeping with cyclonic circulation in the shallower depths. High discharge occurs during winter storms and this is the time of strongest northerly flow within the bay.

Model results provide new insights into sourcing and dispersal behavior of sediments in Monterey Bay, at least in terms of the available sample data. Salinas River sediments dominate shelf heavy mineralogy except in the northwestern portion of the bay and in the north bay nearshore. Historical switching of the river's mouth between the northern and southern portion of the bay is evident in the inversion results. That the coarse-grained sediment discharge of the Salinas is approximately an order of magnitude greater than the San Lorenzo is also consistent with this pattern. At present, we have no sediment discharge data for the Pajaro River. Inversion results, however, suggest that it is small relative to the Salinas. San Lorenzo sediments tend to dominate offshore in the northwest corner of the bay and on the open coast to the north. This is, again, consistent with a northerly current direction. One of the most intriguing results of the inversion is the indication of a paleo-littoral drift signature on the outer shelf corresponding to a sea level low stand. The results obtained using STI can be compared with the results of Yancy [1968] who, working with the analytic methods available at the time, identified 5 mineral provinces within the bay. One, a garnet- and brown hornblende-rich province, he associated with the mouth of the Salinas River. A second, glaucophane-rich, was tentatively associated with the Pajaro River. The other three provinces were not traceable to any known source and did not correspond to known river mineralogies.

Results of previous studies concerning the nearshore sediment transport regime have also been confirmed by model results. The majority of the sand moving as littoral drift within the northern half of the bay originates outside the bay on the open coast to the north [Best and Griggs, 1991]. The signatures of local sources are largely masked, i.e., overwhelmed by littoral drift from outside the bay, or are at least masked by the end of summer when the samples were collected. The bottom of the Santa Cruz littoral cell is at Moss Landing [Sayles, 1966]. Southern Monterey Bay is decoupled from northern Monterey in beach and nearshore sediment supply. Beach sediments in the southern bay are ultimately derived from the Salinas River. These results are important to those who must make policy and management decisions concerning the coastal environment of Monterey Bay.

STI, as an innovative application of geophysical inverse methods to sedimentological data, has proven useful for investigating sediment sourcing and dispersal in a relatively simple geomorphic setting. Future work will involve adapting the method to include grain size and shape, to include efficiency parameters modeling the effects of changes to the source signature during transport, and application of STI to sediment supply problems on topographically complex coasts. Given its simplicity and adaptability, STI should also be useful in studies of fluvial or eolian environments, and or in paleo-transport problems.

Acknowledgements This work was funded by the Branch of Pacific Marine Geology (now Western Coastal and Marine Geology) United States Geologic Survey, through a cooperative research agreement with the Institute of Marine Sciences, University of California, Santa Cruz. Thanks are also due to Gary Griggs and Robert Anderson for thoughtful reviews.

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REFERENCES
  1. Anima, R. J., J. F. Tait, G. B. Griggs, and K. M. Brown, Nearshore morphology and sedimentation using side-scanning sonar and underwater video along the central California coast (abstract), Eos Trans. AGU, 74, 348, 1993.
  2. Aubrey, D.G. and R.M. Ross, The quantitative description of beach cycles, Mar. Geol, 69, 1-2, 155-170, 1985.
  3. Aubrey, D. G., D. L. Inman, and C. D. Winant, Statistical prediction of beach changes in southern California, J. Geophys. Res., 85, 3264-3276, 1980.
  4. Aubrey, D. G, Seasonal patterns of onshore/offshore sediment movement, J. Geophys. Res., 84, 6347-6354, 1979.
  5. Bagnold, R. A., and O. Barndorff-Nielsen, The pattern of natural size distributions, Sedimentology, 27, 199-207, 1980.
  6. Best, T., and G. B. Griggs, A sediment budget for the Santa Cruz littoral cell, in From Shoreline to Abyss, pp. 35-50, S.E.P.M. Spec. Pub. No. 46, 1991.
  7. Breaker, L. C., and W. W. Broenkow, The circulation of Monterey Bay and related processes, Oceanog. Mar. Biol.: Ann. Rev., 32, 1-64, 1994.
  8. Cacchione, D. A., and D. E. Drake, Shelf sediment transport: an overview with applications to the northern California continental shelf, in The Sea, Ocean Engineering Research, edited by B. LeMehaute and D. Hanes, pp. 729-773, Wiley-Interscience, 1990.
  9. Clarke, D.J., and I. G. Eliot, Description of littoral, alongshore sediment movement from empirical eigen-function analysis, J. Geol. Soc. of Australia, 29, 3, 327-241, 1982.
  10. Clarke, D.J., and I.G. Eliot, Offshore-onshore patterns of sediment exchange in the littoral zone of a sandy beach, J. Geol. Soc. Australia, 30, 3, 341-351, 1983.
  11. Clemens, K.E. and P.D. Komar, Oregon beach-sand compositions produced by mixing of sediments under a transgressing sea, J. Sed. Pet., 58, 3, 519-529, 1988.
  12. Dolan, R., B. P. Hayden, W. Felder, Systematic variations in inshore bathymetry, J. Geol., 85, 2, 129-141, 1977.
  13. Ehrlich, R., and B. Weinberg, An exact method for characterization of grain shape, J. Sed. Pet., 40, 205-212, 1970.
  14. Felder, W., Analysis of inshore and offshore profiles, J. Geol., 87, 4, 455-461, 1979.
  15. Folk, R. L., and W. C. Ward, Brazos River bar: a study in the significance of grain size parameters, J. Sed. Pet., 27, 3-26, 1957.
  16. Glenn, S. M., and W. D. Grant, A suspended sediment stratification for combined wave and current flows, J. Geophys. Res., 92, 8244-8464, 1987.
  17. Gordon, B.L., Monterey Bay Area: Natural History and Cultural Imprints, 2nd ed., 321 pp., The Boxwood Press, Pacific Grove, Ca, 1979.
  18. Grant, W. D., and O. S. Madsen, Combined wave and current interaction with a rough bottom, J. Geophys. Res., 84, 1797-1808, 1979.
  19. Hayden, B., R. Dolan, and W. Felder, Spatial and temporal analyses of shoreline variations, Coast. Eng., 2, 4, 351-361, 1979.
  20. Imbrie, J., and Tj. H. Van Andel, Vector analysis of heavy mineral data, Geol. Soc. Am. Bull., 75, 1131-1156, 1964.
  21. Krumbein, W. C., Size-frequency distributions of sediments and the normal phi curve, J. Sed. Pet., 8, 84-90, 1983.
  22. Krumbein, W. C., and E. Aberdeen, The sediments of Barataria Bay, J. Sed. Pet., 7, 3- 17, 1937.
  23. Lawson, C. L., and R. J. Hanson, Solving Least Squares Problems, 340 pp., Prentice Hall, Englewood Cliffs, NJ, 1974.
  24. Liu, J. T., and G. A. Zarillo, Distribution of grain sizes across a transgressive shoreface, Mar. Geol., 87, 121-136, 1989.
  25. Liu, J. T., and G. A. Zarillo, Shoreface dynamics: evidence from bathymetry and surficial sediments, Mar. Geol., 94, 37-53, 1990.
  26. Liu, J. T., and G. A. Zarillo, Simulation of grain-size abundances on a barred upper shoreface, Mar. Geol., 109, 3-4, 237-251, 1992.
  27. McLaren, R., and D. Bowles, The effects of sediment transport on grain-size distributions, J. Sed. Pet., 55, 4, 457-470, 1985.
  28. Middleton, G. V., Hydraulic interpretation of sand distributions, J. Geol., 84, 405-426, 1976.
  29. Oradiwe, E. N., Sediment budget for Monterey Bay, M. S. thesis, 110p., Naval Postgraduate School, Monterey, California, 1986.
  30. Osborne, R. H., and C.-C. Yeh, Fourier grain-shape analysis of coastal and inner shelf sand samples, Oceanside littoral cell, southern Orange and San Diego counties, southern California, in From Shoreline to Abyss, pp. 51-66, S.E.P.M. Spec. Pub. No. 46, 1991.
  31. Rantz, S. E., Precipitation depth-duration-frequency relations for the San Francisco Bay region, California, U.S. Geologic Survey Basic Data Contribution 25, 23 pp., 1971.
  32. Resio, D. T., R. Dolan, B. P. Hayden, and C. L. Vincent, Systematic variations in offshore bathymetry, J. Geol., 85, 1, 105-113, 1977.
  33. Sayles, F. L., A reconnaissance heavy mineral study of Monterey Bay beach sediment, Report no. HEL 2-16, Hydraulic Engineering Laboratory, University of California, Berkeley, 1966.
  34. Sternberg, R. W., Predicting initial motion and bedload transport of sediment particles in the marine environment, Mar. Geol., 10, 113-119, 1972.
  35. Smith, J. D., Modelling of sediment transport on continental shelves, in The Sea, Vol. 6, edited by E.D. Goldberg et al., pp. 539-577, Wiley-Interscience, New York, 1977.
  36. Tait, J. F., R. J. Anima, and G. B. Griggs, Shoreface storage and transport of littoral sediments along the central California coast (abstract), Eos Trans. AGU, 73, 302, 1992.
  37. Visher, G. S., Grain size distributions and depositional processes, J. Sed. Pet., 39, 655- 744, 1969.
  38. Winant, C. D., D. L. Inman, and C. F. Nordstrom, Description of seasonal beach changes using empirical eigenfunctions, J. Geophys. Res., 80, 15, 1979-1986, 1975.
  39. Yancy, T. E., Recent sediments of Monterey Bay, California, Report no. HEL 2-18, Hydraulic Engineering Laboratory, University of California, Berkeley, 1968.

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FIGURE CAPTIONS
Figure 1. Location map of Monterey Bay.

Figure 2. Location of surface sediment samples collected by the University of California, Berkeley Hydraulics Engineering lab in 1966. Stream samples and samples from the northern-most beaches were averaged to determine end-member mineralogical abundances. Depth contours are at 20, 40, 60, 100, 200, 500 and 1000 meters.

Figure 3. Mineralogic composition of the end-members used in the source decomposition. The mean abundance of each mineral species is subtracted from each end-member.

Figure 4. Results of inversion for sediment sources within Monterey Bay using the heavy mineral data of Yancy [1968]. Four sources were assumed with mineral breakdowns computed from HEL data either within the littoral zone north of Monterey Bay (Littoral Drift), or from riverbed samples (other three sources). The sources are not orthogonal, but are distinct. Smooth, non-negative least squares inversion resulted in excellent fit to data, with variance reduction well in excess of 80% for most sites. Symbol size is keyed to source contribution which ranges from 0 (no contribution) to 1 (sample consists of one source only); see scale in upper right corner of each panel. Note the excellent localization of the Soquel Creek sediments, the deep water line of littoral drift sediments tracing a sea level low stand, and extension of Salinas River sediments north on Monterey Canyon marking sediments introduced prior to the early 1900's when the river mouth was further north. Depth contours are at 20, 40, 60, 100, 200, 500 and 1000 meters.

Figure 5. Median grain size profiles for cross-shore sampling transects in the northwestern part of the bay obtained from HEL grain size analysis. Samples located near the 100-m isobath are consistently in the phi range of fine sand (2 to 3).

Figure 6. Variance reduction for the model. A value of 1 indicates complete agreement between model and data; a value of 0 indicates no improvement in fit relative to the mean heavy mineralogy. Variance reduction is high throughout the sampling region, indicating that the model does a good job of fitting sample mineralogy by linear mixing of 4 non- orthogonal end-members.

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