San Francisco Bay Conservation and Development Commission 

Wave Exposure of Corte Madera Marsh, Marin County, 

California—a Field Investigation 

Open-File Report 2011–1183 

U.S. Department of the Interior 

U.S. Geological Survey 

 
This page intentionally left blank.

 
Wave Exposure of Corte Madera Marsh, Marin County, 

California—a Field Investigation 

By Jessica R. Lacy and Daniel J. Hoover 

Open-File Report 2011–1183 

U.S. Department of the Interior 

U.S. Geological Survey 
U.S. Department of the Interior 

KEN SALAZAR, Secretary 

U.S. Geological Survey 

Marcia K. McNutt, Director 

U.S. Geological Survey, Reston, Virginia 2011 

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Suggested citation: 

Lacy, J.R., and Hoover, D.J., 2011, Wave exposure of Corte Madera Marsh, Marin County, California—a field 

investigation: US Geological Survey Open-File Report 2011-1183, 28 p. [http://pubs.usgs.gov/of/2011/1183/]. 

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iii 

Contents 

Introduction .................................................................................................................................................................... 1

Objectives .................................................................................................................................................................. 1

Methods ......................................................................................................................................................................... 2

Study site ................................................................................................................................................................... 2

Field campaign ........................................................................................................................................................... 4

Wave statistics ........................................................................................................................................................... 6

Bed-sediment grain size............................................................................................................................................. 7

Time and direction conventions ................................................................................................................................. 7

Results ......................................................................................................................................................................... 7

Conditions during deployment .................................................................................................................................... 7

Bed-sediment grain size............................................................................................................................................. 8

Tidal elevations .......................................................................................................................................................... 8

Temperature and salinity ...........................................................................................................................................11

Currents ....................................................................................................................................................................13

Waves .....................................................................................................................................................................13

Ferry wakes ..............................................................................................................................................................23

Summary and Conclusions ...........................................................................................................................................26

Acknowledgments ........................................................................................................................................................27

References Cited ..........................................................................................................................................................27

Appendix .......................................................................................................................................................................28

Figures 

1. San Francisco Bay region. A, location of study area and Richmond meteorological station (RCMC1). B, 

Aerial photograph of marsh with M1 and M2 locations. C,1980 bathymetry and stations.. ............................... 3

2. Approximate bed elevation along study transect .................................................................................................. 4

3. Tripod deployment at station S2.. ........................................................................................................................ 5

4. Tides and Delta outflow for January-March 2010. ................................................................................................ 8

5. Meteorologic conditions at Richmond meteorological station RCMC1 January-March 2010.. ............................. 9

6. Grain-size distribution in top 2 cm of grab samples collected at S1-S3 and DP on January 28 and 

March 18, 2010............... ............................................................................................................................. 10

7. A, Tidal elevations measured at the three ADV stations, M1, and M2, from January 25 to February 8, 

2010. B, Difference in water depth between stations M2 and M1.. ................................................................. 11

8. Time series from January 22 to March 24, 2010 of A, depth at S2 showing tidal fluctuations, and B, 

temperature and C, salinity, 1 m below the water surface and 0.5 m above the bed (mab) at DP, and 

0.5 mab at S2. ................................................................................................................................................ 12

9. Tidal currents at 30-minute intervals from February 1 to February 6, 2010, showing variation from 

spring to neap tides ........................................................................................................................................ 14

10. Current profiles from ADCP at station DP for March 1-7, 2010. ........................................................................ 15

11. Tidally averaged (30-hour lowpass filtered) currents at stations in Corte Madera Bay. ..................................... 16

12. A, Speed and direction of spring-tide tidal currents at stations DP-T (depth averaged), S1, S2, and S3. 

B, Speed and direction of mean tidally averaged currents at DP-T, and at S1, S2, and S3. .......................... 17
iv 

13. Time series of wave statistics and tidal elevations from ADCP at station DP-T. A, Significant wave 

height. B, Peak wave period. C, Wave direction. D, Water depth, and E, Nondirectional spectra of 

wave energy.. ................................................................................................................................................. 18

14. High-frequency water depths from a burst at 0400 February 5, 2010 UTC at stations S3 (A), S2 (B), S1 

(C), and M2 (D). .............................................................................................................................................. 19

15. Spectra of wave height (A,C) and velocity in principal direction (B,D) from two 8-minute bursts, at 

stations S1-S3 and M2.. ................................................................................................................................. 20

16. Wave statistics at all stations for 5-day period including the February 5, 2010 wave event. .............................. 21

17. Wave statistics at all stations for 5-day period including the February 24 and 26-27, 2010 wave 

events............. .............................................................................................................................................. 22

18. Factors influencing wave damping. A, Normalized wave height (ratio of local significant wave height Hs

to Hs at station DP) versus water depth relative to MLLW. B, Normalized wave height versus wave 

direction at DP. C, Normalized wave height versus Hs at DP. ........................................................................ 24

19. Examples of ferry wakes at low tide (A, B), mid tide (C, D) and high tide (E, F). Water depths at S3 

have been offset by -0.5 m to facilitate comparison between stations. ........................................................... 25

Tables 

1. Station locations .................................................................................................................................................. 5

2. Instrumentation and sampling schemes ............................................................................................................... 6

3. Bed sediment grab sample times and locations ................................................................................................... 7
v 

Conversion Factors 

SI to Inch/Pound 

Multiply By To obtain 

Length 

centimeter (cm) 0.3937 inch (in.) 

millimeter (mm) 0.03937 inch (in.) 

micrometer (um) 0.00003937 inch (in.) 

meter (m) 3.281 foot (ft) 

kilometer (km) 0.6214 mile (mi) 

meter (m) 1.094 yard (yd) 

Flow rate 

meter per second (m/s) 3.281 foot per second (ft/s) 

Pressure 

hectopascal (hPa) 0.0009869 atmosphere, standard (atm) 

hectopascal (hPa) 1 millibar (mbar) 

Temperature in degrees Centigrade (°C) is converted to degrees Fahrenheit (°F) as follows: 

°F=(1.8×°C)+32 

Vertical coordinate information is referenced to the North American Vertical Datum of 1988 (NAVD 88). 

Altitude, as used in this report, refers to distance above the vertical datum. 

Pacific Standard Time (PST) = Universal Time, Coordinated (UTC) – 8 hours. 
vi 

Glossary 

Term Definition

Bottom orbital velocity (ub) Maximum near-bed wave velocity during a wave period 

Delta Outflow An estimate of the average daily flow of freshwater from 

the Sacramento-San Joaquin Delta to San Francisco Bay.

Diurnal Recurring daily 

Frequency Inverse of period 

Hertz s-1, unit of frequency 

Mean high water The average of all high water heights over the 

national tidal datum epoch (NTDE) 

Mean Lower-Low Water The average of the lower low water height of each tidal day 

over the NTDE 

Neap tides Tides with the smallest range of the lunar cycle, which occur in 

the first and third quarters of the moon 

Peak wave period (Tp) Period of the highest waves in the sampling interval 

Phi (Φ) Negative of the base-2 logarithm of the grain-size diameter 

in millimeters. Phi units simplify calculation of grain size statistics 

because distributions are typically lognormal. 

Representative bottom orbital Root-mean-square value of ub during the sampling interval 

velocity (ubr) 

Significant wave height (Hs) Average height (trough to crest) of the highest third of 

waves during the sampling interval 

Spring tides Tides with the greatest range of the lunar cycle, which occur 

at the time of the new or full moon 

Tidally-averaged Averaged over a diurnal tidal cycle 
Wave Exposure of Corte Madera Marsh, Marin County, 

California—a Field Investigation 

By Jessica R. Lacy and Daniel J. Hoover 

Introduction 

Tidal wetlands provide valuable habitat, are an important source of primary productivity, and 

can help to protect the shoreline from erosion by attenuating approaching waves. These functions are 

threatened by the loss of tidal marshes, whether due to erosion, sea-level rise, or land-use practices. 

Erosion protection by wetlands is expected to vary geographically, because wave attenuation in marshes 

depends on vegetation type, density, and height (Moller, 2006) and wave attenuation over mudflats 

depends on slope and sediment properties (Le Hir and others, 2000). In macrotidal northern European 

marshes, a 50 percent reduction in wave height within tens of meters of vegetated salt marsh has been 

observed (Moller, 1999; 2006). This study was designed to evaluate the role of mudflats and marshes in 

attenuating waves at a site in San Francisco Bay. 

In prehistoric times, the shoreline of San Francisco Bay was ringed with tidal wetlands, with 

mudflats at lower elevations and marshes above. Most of the marshes around the Bay emerged 2,000-

4,000 years ago, after the rate of sea-level rise slowed to approximately 1 mm/year (Atwater, 1979). 

Approximately 80 percent of the acreage of tidal marsh and 40 percent of the acreage of tidal mudflats 

in San Francisco Bay have been lost to filling and draining since 1800 (Monroe and others, 1999). Tidal 

wetlands are particularly susceptible to impacts from sea-level rise because the vegetation at each 

elevation is adapted to a specific tidal-inundation regime. The maintenance of suitable marsh-plain 

elevations depends on a supply of sediment that can keep up with the rate of sea-level rise (Atwater, 

1979). Sea-level rise, which according to recent projections may reach 75 to 190 cm by the year 2100 

(Vermeer and Rahmstorf, 2009), poses a significant threat to wetlands in San Francisco Bay, where 

landward migration is frequently impossible due to urbanization of the adjacent landscape. 

In this study, we collected data in Corte Madera Bay and Marsh (fig. 1) to determine whether, 

and to what degree, waves are attenuated as they transit the Bay and, during high tides, the marsh. Corte 

Madera Bay was selected as a study site because of its exposure to wind waves, as well as its history of 

shoreline erosion and marsh restoration and monitoring. Data were collected in the winter of 2010, 

along a cross-shore transect extending from offshore of the subtidal mudflats into the tidal marsh. This 

study forms part of the Innovative Wetland Adaptation in the Lower Corte Madera Creek Watershed 

Project initiated by the Bay Conservation and Development Commission (BCDC) 

(http://www.bcdc.ca.gov/planning/climate_change/WetlandAdapt.shtml). 

Objectives 

This study was designed to address the following questions: 

What are the characteristics of waves and currents in the study area, and how do they vary over time? 

Do wave heights or orbital velocities decrease, or wave periods change, as waves pass over the 

mudflats? 

Do wave heights decrease, or wave periods change, as waves pass over the marsh? 
2 

Methods 

Study site 

Corte Madera Bay and Marsh are both in Marin County, California on the west side of Central 

San Francisco Bay. The embayment is north of the Tiburon peninsula and south of the Richmond 

Bridge (fig. 1). Water depths throughout the embayment are less than 2 m relative to mean lower low 

water (MLLW), whereas depths in the adjacent main channel exceed 10 m MLLW. The Larkspur ferry 

landing is in the northwest corner of Corte Madera Bay, and ferries traverse Corte Madera Bay regularly 

through a dredged channel that runs along the north edge of the Bay (fig. 1). 

Central Bay waters are strongly influenced by the Pacific Ocean, with salinities typically greater 

than 20 practical salinity units (psu), except during periods of high freshwater inflow through the 

Sacramento-San Joaquin Delta in winter. Salinities in the shallow embayments of Central Bay may be 

influenced by local watersheds as well: specifically, Corte Madera Creek flows into the northwest 

corner of Corte Madera Bay. Currents in San Francisco Bay are predominantly driven by tides at the 

Golden Gate. In channels, tidal currents exceed 1 m/s and are oriented along channel, whereas in 

shallow areas currents are weaker and their direction varies more, under the influence of local 

bathymetry (Walters and others, 1985). 

In San Francisco Bay, winds and associated waves vary seasonally (Conomos and others, 1985). 

In summer, the daily sea breeze generates westerly afternoon winds as strong as 8 m/s. During winter, 

storms out of the south generate strong winds that can last several days and generate waves with periods 

as long as 5 s in areas with long fetch. Conditions are typically calm between winter storms. 

Corte Madera Marsh consists of three sections: an historical marsh at the north end, adjacent to the 

mouth of Corte Madera Creek; and two formerly diked areas that were restored to tidal action in 1976. 

The southern restored area, which forms the landward edge of the transect for this study, is called Muzzi 

Marsh. In the restored marsh the outboard levee was left partly intact for wave protection. The evolution 

of Muzzi Marsh has been studied extensively since the restoration (Philip Williams & Associates, Ltd. 

and Faber, 2004). Inner and outer Muzzi Marsh initially formed two distinct elevation zones. Inner 

Muzzi Marsh was filled with dredge disposal to an elevation of 2.1 m above MLLW, which is above 

mean higher high water. The elevation of outer Muzzi Marsh ranged from 1.1 m to 1.4 m MLLW, 

below the mean high water (MHW) elevation of 1.58 m MLLW. Tidal channels and a vegetated marsh 

plain developed in this part of the marsh, which is regularly inundated by tides. The landwardmost 

station in our study was located in outer Muzzi Marsh (fig. 1B). 

The shoreline of Corte Madera Marsh is exposed to easterly to southeasterly wind-waves as well 

as wakes from the Larkspur ferry. As a result, the remaining outboard levee and adjacent marsh have 

progressively eroded over the past 25 years (Philip Williams & Associates, Ltd. and Faber, 2004). It 

should be noted that wave attenuation over marshes does not necessarily protect the marsh edge: 

evidence suggests that vegetation does not reduce wave-driven lateral erosion, which is the primary 

erosive mechanism at the marsh edge (Feagin and others, 2009). The marsh plain continues to provide a 

dissipative buffer between waves at the shoreline and the flood-control levee located at the west edge of 

the marsh. 
3 

Figure 1. San Francisco Bay region. A, location of study area and Richmond meteorological station (RCMC1). 

B, Aerial photograph of marsh with M1 and M2 locations. C,1980 bathymetry and stations. Shoreline (black 

outline, fig. 1C) is shown at the mean high water elevation, which is 158 cm above mean lower low water in the 

study area. 
4 

Field campaign 

Instruments were deployed in a cross-shore transect along the axis of Corte Madera Bay, from station 

DP, on the edge of the main channel of San Francisco Bay, to station M1, located approximately 150 m 

shoreward of the marsh edge (fig. 2). Deployment dates were January 22 to March 23, 2010. The 

primary purpose of the deployment was to measure the properties of waves as they propagated from the 

main channel of San Francisco Bay across Corte Madera Bay and, when the tidal elevation was 

sufficiently high, into the marsh. Instrumentation and sampling frequencies for all stations are listed in 

Table 2. The deployment sites can be divided into three categories on the basis of instrumentation and 

water depth: DP, S1-S3, and M1/M2. DP was positioned to measure the properties of waves entering 

Corte Madera Bay. It was located to the north of the transect defined by the rest of the stations to avoid 

the ferry lanes, at a depth of approximately 7 m below MLLW. Instruments at this site were deployed on 

both a tripod (DP-T) and a mooring (DP-M), separated by less than 30 m. At DP-T, wave properties, 

tidal elevations, and current profiles were measured with an acoustic Doppler current profiler (ADCP). 

At the shallow stations within Corte Madera Bay (S1-S3), wave properties, tidal elevations, and currents 

at a single depth were measured with acoustic Doppler velocimeters (ADVs). Finally, at the marsh 

stations (M1 and M2), wave height and period and tidal elevations were measured with pressure 

sensors. M2 was located on the mudflats adjacent to the marsh edge, and M1 was located in a sinuous 

tidal creek within the marsh at an elevation of 0.82 m above MLLW (fig. 1B). The elevation of the 

adjacent marsh plain was 1.6 m MLLW. 

Additional data were collected to characterize environmental conditions during the study and to 

support analysis and numerical modeling of hydrodynamics and sediment transport. Time series of 

salinity and temperature were measured near the surface and near the bed at DP, and 0.5 m above the 

bed (mab) at S3. Optical backscatterance, a surrogate for suspended-sediment concentration (SSC), was 

Figure 2. Approximate bed elevation along study transect (red line, fig. 1C). Station M1 was located in a tidal 

creek channel below the marsh plain. 
5 

measured at S1, S2, S3, and DP. Optical backscatter sensors (OBS) were equipped with mechanical 

wipers to minimize biofouling, and suspended-sediment samples were collected to calibrate OBS 

voltages to SSC. The OBS and SSC data are omitted from this report. 

 At stations S1-S3 and DP, instrument platforms were deployed from the R/V Parke Snavely

(fig. 3). Pressure sensors, mounted on vertical posts attached to 40 lb weights, were deployed at M1 and 

M2 by kayak. M1 was located in a tidal creek within the marsh, whereas M2 was on the intertidal 

mudflats adjacent to (bayward of) the marsh edge. At the end of the deployment, we found the pressure 

sensor at station M2 entangled in debris, tipped over, and buried in the mud, approximately 20 m 

southwest of its initial position. None of the other platforms moved during the deployment, and all 

instruments were recovered in good condition, although some biofouling had occurred. 

Figure 3. Tripod deployment at station S2. ADV, acoustic Doppler velocimeter; OBS, optical backscatter sensor. 

Table 1. Station locations 

Station Longitude, W. Latitude, N. 

Bed depth

(cm relative to 

MLLW) 

M1 122.50582 37.93198 82 

M2 122.50403 37.93163 64 

S1 122.48882 37.92837 -50 

S2 122.48423 37.92782 -86 

S3 122.47967 37.92772 -155 

DP-M 122.46228 37.93118 -727 

DP-T 122.46265 37.93047 -680 
6 

Table 2. Instrumentation and sampling schemes 

Site Platform Instrument Parameters 

measured 

height above 

bed, m 

Sampling frequency

M1 Bursting 

pressure 

sensor 

Tide height, wave 

height, and period. 

0.1 Tides: 60 s average every 15 minutes. 

Waves: 2048 samples at 4 Hz every 

hour. 

M2 Bursting 

pressure 

sensor 

Tide height, wave 

height, and period. 

0.1 Tides: 60 s average every 15 minutes. 

Waves: 2,048 samples at 4 Hz every 

hour. 

S1 Tripod ADV Current and wave 

velocities, distance to 

bed. 

0.2 Currents: 90 s @ 4 Hz every 15 

minutes. Waves: 8 minutes @ 10 Hz 

every hour. 

 Pressure 

sensor 

Tide height, wave 

height, and period. 

0.21 Tides: 90 s @ 4 Hz every 15 minutes. 

Waves: 8 minutes @ 10 Hz every 

hour. 

S2 Tripod ADV Current and wave 

velocities, distance to 

bed. 

0.3 Currents: 90 s @ 4 Hz every 15 

minutes. Waves: 8 minutes @ 10 Hz 

every hour. 

 Pressure 

sensor 

Tide height, wave 

height, and period. 

0.16 Tides: 90 s @ 4 Hz every 15 minutes. 

Waves: 8 minutes @ 10 Hz every 

hour. 

 CT Salinity and 

temperature. 

0.5 10-s average every 5 minutes. 

S3 Tripod ADV Current and wave 

velocities, distance to 

bed. 

0.3 Currents: 90 s @ 4 Hz every 15 

minutes. Waves: 8 minutes @ 10 Hz 

every hour. 

 Pressure 

sensor 

Tide height, wave 

height, and period. 

1.08 Tides: 90 s @ 4 Hz every 15 minutes. 

Waves: 8 minutes @ 10 Hz every 

hour. 

DP Mooring CTD Salinity, temperature, 

and depth. 

1 m below 

surface 

10-s average every 5 minutes 

 Tripod CTD Salinity, temperature, 

and depth. 

0.5 10-s average every 5 minutes 

 ADCP Currents, wave 

parameters, tidal 

height. 

0.75 m to 

surface at 0.5 m 

intervals. 

Currents: 50 pings every 10 minutes. 

Waves: 2,048 samples at 2 Hz every 

hour. 

Wave statistics 

The ADCP software generated wave statistics for station DP-T. Wave statistics for stations S1-

S3, M1, and M2 were calculated from the high-frequency velocity and pressure bursts collected hourly 

by the ADVs or pressure sensors. Significant wave height, Hs, representative bottom orbital velocity, 

ubr, peak wave period, Tp, and wave direction were calculated from the 0.17-1 Hz frequency band 

according to the spectral methods of Madsen (1994) also described by Wiberg and Sherwood (2008). 

Because pressure fluctuations due to short-period small waves decay rapidly with depth, the algorithm 

for calculating wave statistics included a correction for the depth of the pressure sensor, but correction is 

impossible for strongly attenuated signals, and so results are noisy during periods of small waves. 

 
7 

Table 3. Bed-sediment grab-sample stations and times 

Station Sample ID Date Time (PST) Comments

S1 CMS1A 1/28/2010 13:20 top 2 cm 

S2 CMS2A 1/28/2010 13:35 top 2 cm 

S3 CMS3A 1/28/2010 15:18 top 2 cm 

DP CMDPTA 1/28/2010 14:15 top 2 cm 

 

S3 CM1S3B 3/18/10 13:10 top 2 cm 

S2 CM1S2B 3/18/10 13:51 top 2 cm 

S1 CM1S1B 3/18/10 14:00 top 2 cm 

DP CM1DPTB 3/18/10 12:47 top 2 cm 

Bed-sediment grain size 

The ability of waves and currents to mobilize or erode bed sediment strongly depends on grain size and 

other bed properties (Stevens and others, 2006). On January 28 and March 18, 2010 we collected bedsediment samples to determine grain-size distribution adjacent to each of the four stations in Corte 

Madera Bay (Table 3) from a small boat using a petite Ponar grab sampler. The top 2 cm of each sample 

was retained for analysis. Grain size distribution (1⁄4 phi (φ) size classes) was determined using standard 

techniques. Both the sand fraction (2 mm – 63 μm) and fine fraction (< 63 μm) were analyzed with a 

Beckman Coulter model LS230 laser-diffraction particle analyzer. 

Time and direction conventions 

Unless otherwise noted, all times in this report are in Universal Time, Coordinated (UTC) and 

altitudes are referenced to a vertical datum of MLLW. For wind and waves, compass directions follow 

the meteorologic convention; for example, easterly winds or waves are from the east and have an 

azimuth of 90o. For currents, however, compass directions indicate the direction of flow, and so an 

eastward flowing current has an azimuthof 90o. 

Results 

Conditions during deployment 

The data collection period spanned 61 days, encompassing more than two full spring-neap cycles (fig. 

4A). Instruments were deployed immediately after the largest storm of the winter, which occurred 

January 19-20, 2010. As a result, freshwater inflow from the Sacramento-San Joaquin Delta into 

northern San Francisco Bay (referred to as Delta outflow) was rising sharply when the instruments were 

deployed on January 22, and peaked during the first week of data collection (fig. 4B). Winds during the 

study period were typical, with wind speeds mostly less than 5 m/s and direction generally from the 

north-northwest or south-southeast. Several periods of stronger (5-8 m/s) winds occurred, with southsoutheasterly direction. During the large storm immediately before instrument deployment, there were 

sustained southerly winds of about 8 m/s, which had largely abated by January 22 (fig. 5). 
8 

Bed-sediment grain size 

Disaggregated bed sediment from all four stations was predominantly (>92 percent) silt, with a 

small fraction of very fine sand. All samples had a bimodal distribution, with the largest peak at 40 μm 

and a smaller peak at 4-6 μm (fig. 6). The grain size distribution was quite consistent between stations 

and across the two sampling dates, except for the January 28 sample from DP, in which the 40-μm peak 

is greater than in the March 18 sample. Because DP is the closest station to the channel and January 28 

immediately followed the peak in Delta outflow, the greater fraction of 40-μm particles may represent 

the contribution of fresh sediment supplied by rivers; however, additional sampling would be required 

to verify this hypothesis. Percentages sand, silt, and clay, as well as statistics for the grain size 

distributions, are presented in the appendix. 

Tidal elevations 

Tidal elevations were determined at all stations from pressure measurements. For each station, 

pressure data were corrected for atmospheric pressure, as measured at the Richmond Bridge 

meteorologic station (http://www.ndbc.noaa.gov/, station rcmc1) and the height of the pressure sensor 

above the bed. At the shallow stations (S1-S3), the height of the instrument above the bed was 

determined from the mean (during the deployment) distance to bed, as measured by the ADV, and the 

vertical distance between the ADV transducer and the pressure sensor, which was measured before 

deployment of the platforms. For the marsh stations, where we made no measurement of distance to 

bed, we used the height of the pressure sensor above the weight (6 cm), assuming that the weight sank 

Figure 4. Tides and Delta outflow for January-March 2010. A, Water surface elevation (WSE) relative to MLLW at 

Richmond tide station 9414683 (http://tidesandcurrents.noaa.gov). B, Net Delta outflow index (NDOI) in cubic 

meters per second (http://www.water.ca.gov/dayflow/). Red boxes delineate study period. 
9 

Figure 5. Meteorologic conditions at Richmond meteorological station RCMC1 (http://www.ndbc.noaa.gov/) 

January-March 2010. A, Wind speed. B, Wind direction. C, Atmospheric pressure. and D, Air temperature. 

Red dots in figure 6B, direction for wind speeds greater than 7 m/s. Red box delineates study period. 

in to the top of its 5-cm thickness. Although measured depths were not corrected for settling of 

platforms during the deployment, we consider this a minor source of error because the variation during 

the deployment in distance to bed (measured by the ADVs), which reflects the combination of settling, 

erosion, and deposition beneath the tripod, was less than 6 cm at all shallow stations. 

Tidal elevations at the shallow and marsh stations over 15 days are plotted in figure 7A. The tidal 

signal is truncated at the marsh stations, which were dry at low tide. Water depths below the sensor are 

plotted as 6 cm (the height of the pressure sensor above the bed). In general, the tidal elevations 

measured at all stations correspond well. Because the sensor at M1 was stationary, we relied on the 

difference in water depth between stations M2 and M1 (fig. 7B) to determine when the pressure sensor 

at M2 was moved and (or) tipped over. During each tidal cycle the difference ranges from close to zero, 
10 

when both sensors are exposed to air at low tide, to a relatively constant value corresponding to the 

difference in elevation between the two stations. The data indicate that the M2 sensor elevation was 

constant until February 6, when it decreased by approximately 5 cm, and that a second decrease 

occurred on February 10. The total change in elevation was approximately 7 cm, which can be 

accounted for by the tipping over of the pressure-sensor mount. The bathymetry is nearly flat between 

the deployed and retrieved locations. The largest differences in depth between M1 and M2 were caused 

by the tsunami originating in Chile at 0630 UTC February 27, 2010, which reached the northern 

California coast approximately 15 hours later. The tsunami waves were not fully resolved, owing to the 

15-minute sampling interval, but elevated water-surface elevations as well as anomalous fluctuations as 

great as 20 cm, were measured for about 48 hours after the arrival of the tsunami (fig. 8A). 

Figure 6. Grain-size distribution in top 2 cm of grab samples collected at S1-S3 and DP on January 28 and March 

18, 2010. A, Station S1. B, Station S2. C, Station S3. D, Station DP. 
11 

Figure 7. A, Tidal elevations measured at the three ADV stations, M1, and M2, from January 25 to February 8, 

2010. B, Difference in water depth between stations M2 and M1; difference is near zero when tidal elevation is 

below both sensors. Depths are calculated from pressure data and have been corrected for atmospheric 

pressure measured at station RCMC1 (fig. 1). 

Temperature and salinity 

Water temperatures increased over the deployment period as spring progressed (fig.8B). Diurnal 

variation in water temperature was greater within Corte Madera Bay (station S2) than in the channel 

(station DP), because the shallow waters of the Bay are more strongly influenced by air temperatures. 

Early in the deployment at station DP, water temperatures were higher near the bed, which is more 

influenced by ocean water, than at the surface, which is more influenced by Delta outflows. 

Subsequently surface and deep temperatures tracked one another closely until the last week of the study, 

when surface temperatures exceeded near-bed temperatures. 

Both the tidal cycle variation and the vertical stratification in salinity at DP were greater early in 

the study period, when Delta outflow was high, than later (fig. 8C). In addition, vertical stratification 

was less during spring tides than during neap tides, attributable to greater tidally driven vertical mixing 

during spring tides. In general, salinities within Corte Madera Bay (fig. 8, station S2) were more similar 

to the near-surface than to the near-bed salinities at DP. Early in the deployment, the salinity at S2 
12 

varied by as much as 10 psu over the course of spring diurnal tidal cycles (Jan. 29-Feb. 4), despite the 

weak tidal currents within Corte Madera Bay. This indicates that horizontal gradients in salinity were 

strong and likely influenced circulation. The occasional dips in salinity at S2 (for example, on February 

24) are likely due to local input of fresh water from Corte Madera creek. 

Figure 8. Time series from January 22 to March 24, 2010 of A, depth at S2 showing tidal fluctuations, and 

B, temperature and C, salinity, 1 m below the water surface and 0.5 m above the bed (mab) at DP, and 0.5 

mab at S2. 
13 

Currents 

Tidal currents at DP were aligned with the main channel (fig. 9D). Variation along the principal 

axis (azimuth 19 ̊-199 ̊) accounted for more than 85 percent of the total variation in tidal currents. The 

amplitude of spring-tide depth-averaged currents was approximately 80 cm/s. Current speeds were 

greater during ebb than flood tides. During strong ebb tides, along-channel currents were significantly 

greater at the surface than near the bed, whereas during flood tides there was less variation with depth 

(fig. 10A). 

Tidally averaged currents were determined for all stations by filtering the velocity data with a 

low-pass (30-h stopband, 40-h passband) Butterworth filter. At DP, tidally averaged currents were 

southwestward near the surface, and southward near the bed (figs 11, 12B). They were stronger near the 

surface than near the bed, and stronger during spring than neap tides. We attribute the down-estuary 

(southerly) component of the tidally averaged flow to the elevated Delta outflows during the study 

period. The westerly component near the surface results from density-driven pulses of cross-channel 

flow into Corte Madera Bay in the upper water column during the transition from ebb to flood tides (fig. 

10B), caused by the lower salinities at DP than in Corte Madera Bay (fig. 8C). 

At the stations within Corte Madera Bay (S1-S3), flood-tide currents were northwestward and 

ebb tide currents were southeastward (figs. 9, 12). The westerly component was greatest at station S2. 

The amplitude of spring-tide currents decreased with distance into the bay, from 30 cm/s at station S3 to 

10 cm/s at S1. Tidally averaged currents were also northwestward (into Corte Madera Bay) and were 

strongest during spring tides (fig. 11). During weak neap tides the currents briefly reversed to 

southeastward (for example, on Feb. 22 and Mar. 9). Tidally-averaged currents in Corte Madera Bay 

were 2 to 4 times weaker than at DP, and were weakest at the shallowest station (fig. 12B). Commonly, 

flow into an embayment like Corte Madera Bay is more focused into a jet than are ebb flows, which are 

more dispersed along the cross-section (Fisher and others., 1979). The net inward flow at stations S1 – 

S3, which were located along the axis of the embayment, is consistent with this pattern. 

Waves 

Wave conditions during the study are summarized in time series of wave statistics from station 

DP (fig. 13). During the largest wave events, significant wave height (Hs ) at station DP exceeded 0.5 

m, wave period was approximately 3 s, and wave azimuth was approximately 150 ̊. During these events, 

energy at low frequencies (periods > 5 s) was negligible, indicating that waves were locally generated 

by wind, rather than ocean swell (fig. 13E). During wave events with Hs > 0.3 m (red dots in fig. 13), 

wave period and azimuth were quite consistent (2-4 s and 120o-150o, respectively), although these 

parameters vary widely over the full time series. To examine wave attenuation within Corte Madera Bay 

and Marsh, we focus on the three largest wave events during the study, which occurred on February 5, 

24, and 26-27, 2010. 

Water depths at stations S1-S3 and M2 from the burst at 0400 UTC during the February 5 wave 

event (fig. 14) illustrate the short-term temporal variability in wave heights, which is not captured in the 

burst statistics. We note that the range of wave heights is reduced at M2, presumably due to breaking of 

the largest waves. Spectra of velocity and pressure from this burst (figs. 15A, 15B) show that energy is 

transferred from lower to higher frequencies, indicative of wave breaking, as the waves travel into 

shallower water at station M2. The peak frequency decreases slightly as water depth decreases, but the 

spread of frequencies increases considerably. In a burst collected at a higher tidal stage this effect is less 

pronounced (figs. 15C, 15D) 
14 

Figure 9. Tidal currents at 30-minute intervals from February 1 to February 6, 2010, showing variation from spring 

to neap tides. A, Station S1, 0.2 mab. B, Station S2, 0.3 mab. C, Station S3, 0.3 mab. D, Station DP, depth 

averaged. 

As waves penetrated into Corte Madera Bay (stations S1-S3), wave direction veered eastward 

owing to refraction, and wave height decreased, but wave period did not change significantly (figs. 16, 

17). Wave heights at M2, the station immediately bayward of the marsh, followed this pattern, except 

that Hs dropped to zero when tidal elevations were below the sensor (for example, on Feb. 4 at 20:00, 

Feb. 24 at 00:00, and Feb. 27 at 00:00). At station M1, 150 m inshore of the marsh edge, wave heights 
15 

were negligible. The greatest Hs measured at M1 was 2.3 cm on February 28 at 20:00 , when Hs at M2 

was 22.3 cm, and the tidal elevation was 2.1 m MLLW. At this time, water levels in the bay were 

influenced by the Chile tsunami, which may have contributed indirectly to the fluctuations in water 

surface elevation at M1 (although the calculation of Hs was based on frequencies between 0.125 and 0.5 

Hz, much higher than the tsunami frequency). The maximum Hs measured at M1 outside of the period 

influenced by the tsunami was 1.5 cm. 

Although wave height decreased substantially toward shore, bottom orbital velocity at stations 

S1-S3 was remarkably constant (for example, figs. 16A, 16B, Feb. 5, and figs. 17A, 17B, Feb. 26), 

except for brief peaks at the shallowest station at low tide. The near-constant bottom orbital velocities 

result from two opposing tendencies: a decrease in orbital velocity associated with lower wave height, 

and an increase in bottom orbital velocity due to the decrease in depth, because the orbital velocities of 

these short period waves decay with distance below the surface. Bed shear stress varies with the square 

of bottom orbital velocity, so our results indicate that the potential for wave-driven sediment 

resuspension is similar at the three stations, which represent much of Corte Madera Bay. 

Figure 10. Current profiles from ADCP at station DP for March 1-7, 2010. A, Along-channel component. B, Crosschannel component. Azimuths are 19 ̊(upstream) for positive along-channel velocities and 289 ̊ (toward Corte 

Madera) for positive cross-channel velocities. 
16 

Figure 11. Tidally averaged (30-hour lowpass filtered) currents at stations in Corte Madera Bay. A, East/west 

component. B, North/south component. 
17 

Figure 12. A, Speed and direction of spring-tide tidal currents at stations DP-T (depth averaged), S1, S2, and S3 

(compare to fig. 9). B, Speed and direction of mean tidally averaged currents at DP-T near surface (dashed) 

and near bottom (solid), and at S1, S2, and S3 (compare to fig. 11). 

.
18 

Figure 13. Time series of wave statistics and tidal elevations from ADCP at station DP-T. A, Significant wave height. B, Peak wave p

D, Water depth, and E, Nondirectional spectra of wave energy. Red dots indicate Hs> 0.3 m.
19 

Figure 14. High-frequency water depths from a burst at 0400 February 5, 2010 UTC at stations S3 (A), S2 (B), 

S1 (C), and M2 (D). 
20 

Figure 15. Spectra of wave height (A,C) and velocity in principal direction (B,D) from two 8-minute bursts, at 

stations S1-S3 and M2. A, B, burst at 04:00 February 5, 2010 with mean depth at M2 of 0.6 m. C, D, burst at 

09:00 February 24, 2010 with mean depth at M2 of 0.85 m. 
21 

Figure 16. Wave statistics at all stations for 5-day period including the February 5, 2010 wave event. A, Significant 

wave height Hs. B, Representative bottom orbital velocity. C, Peak wave period. D, Wave direction. 
22 

Figure 17. Wave statistics at all stations for 5-day period including the February 24 and 26-27, 2010 wave events. 

A, Significant wave height Hs. B, Representative bottom orbital velocity. C, Peak wave period. D, Wave 

direction. 

Typically, as waves enter shallower water approaching the shore, they increase in height and 

decrease in wavelength, steepen, and then break (Komar, 1998). The water depth at which this shoaling 

process begins depends on the wave period. For the short-period waves typical of San Francisco Bay, 
23 

shoaling is restricted to very shallow water: for example, less than 0.7 m for 3-s wave periods (based on 

the definition of shallow-water waves, ݄ ൏ ܮ∞ ⁄20, where L∞ is the deep-water wavelength from linear 

wave theory, calculated as ܮ ∞ൌ ݃ܶ ଶ⁄2 ߨ, T is the wave period, and g is gravitational acceleration). In 

the study area (fig. 1) the shoaling depth was always inshore of stations S3 and S2, and inshore of S1 for 

tidal elevations greater than 0.2 m MLLW. 

Waves only reach station M1 when the marsh plain bayward of the station is inundated, which 

occurs at tidal elevations greater than about 1.6 m MLLW (15 percent of the time during the study 

period). Waves break when their height H exceeds approximately 0.78 h, where h is the water depth 

(Komar, 1998). Thus, at a tidal elevation of 2 m MLLW (close to the maximum; see fig. 4A), incident 

waves with H>0.3 m would break simply owing to the shallow water depth over the marsh, and the 

maximum possible wave height decreases to zero for a tidal elevation of 1.6 m. Pickleweed and other 

vegetation extend at least 20 cm above the marsh plain, further impeding wave propagation and 

potentially causing waves to break. Note that in this study, fewer than 10 of 1456 bursts (0.7 percent) 

had Hs > 0.3 m at DP and a tidal elevation greater than 1.6 m MLLW. This low rate of incidence limits 

our ability to assess wave attenuation over the marsh but also provides an indication of the frequency of 

such conditions in a typical winter. 

To characterize the attenuation or damping of waves within the study area we use a normalized 

wave height, calculated as the ratio of Hs at each station to Hs at station DP: 

ܣ ൌ 1 െ ܪ௦/ܪ௦஽௉

where A is the fractional attenuation at each station. As illustrated in figures 16A and 17A, attenuation 

increased with distance from DP. Attenuation was also influenced by tidal elevation and wave direction 

but does not appear to depend on wave height (fig. 18). Wave period did not affect attenuation (not 

shown). The low normalized wave heights at M2 between tidal elevations of 0.67 m (inundation level) 

and approximately 1 m MLLW are influenced by wave breaking due to shallow water depths, which is 

not typically considered attenuation (fig. 18A). Depth limitation was insignificant at the other stations 

(H/h was always substantially less than 0.7). Normalized wave height approaches 1 between tidal 

elevations of 1.1 and 1.6 m MLLW (fig. 18A). At these depths, the mudflats are inundated but the marsh 

plain is not, so the decrease in attenuation may result from wave reflection off the marsh scarp, as 

numerical models predict for marshes with steep banks (Tonelli and others, 2010). 

Normalized wave height was maximum, and attenuation minimum, when the direction of waves 

at DP was most closely aligned with the axis of Corte Madera Bay, azimuth 110 ̊ - 140 ̊ (fig. 18B). 

Within this range, wave height at S3 is close to, and sometimes exceeds, that at DP, but wave height at 

the shallowest stations (S1 and M2) is typically reduced by about 40 percent. Outside of this range of 

wave directions, waves within Corte Madera Bay are more strongly damped because some of the wave 

energy reaching station DP is not refracted into the bay. 

Ferry wakes 

Although our data collection was designed to characterize wind waves, the data include many examples 

of ferry wakes. Figure 19 shows several examples of wakes and their propagation across the study area. 

The characteristics of the wakes were influenced by tidal stage. At low tide (figs. 19A, 19B), wave 

steepening occurred as the wakes reach shallower stations, and the wakes do not reach the marsh edge. 

At high tides, when the marsh plain is inundated (figs. 19E, 19F), wakes propagate to the marsh edge 

(station M2), and in some cases the wake is amplified as it reaches the shallower stations (fig. 19F). 

Only small-amplitude (< 5 cm), low-frequency oscillations were observed at M1. The largest and 
24 

Figure 18. Factors influencing wave damping. A, Normalized wave height (ratio of local significant wave height Hs

to Hs at station DP) versus water depth relative to MLLW. B, Normalized wave height versus wave direction at 

DP. C, Normalized wave height versus Hs at DP. 
25 

Figure 19. Examples of ferry wakes at low tide (A, B), mid tide (C, D) and high tide (E, F). Water depths at S3 have 

been offset by -0.5 m to facilitate comparison between stations. 
26 

steepest wakes reaching the marsh edge occurred at intermediate tidal elevations (figs. 19C, 19D). Some 

of these complex waveforms may result from the interaction of two wakes approaching from different 

angles. For example, the short travel times between stations for the second wake in figure 19C indicates 

that the propagation direction is closer to shore-parallel than shore-perpendicular, and the wave at M2 

may represent the interaction of the two wakes. At the intermediate tidal elevations of figures 19C and 

19D, the marsh plain is not inundated but the sensor at M1 is submerged by the tidal creek, in which 

low-frequency water-surface oscillations occurred. 

Summary and Conclusions 

Currents and wave properties were measured in a cross-shore transect from outside Corte 

Madera Bay to 150 m landward of the marsh edge from January 23 to March 22, 2010 to characterize 

currents, waves, and wave attenuation. The deployment captured three storm events with significant 

wave heights greater than 0.4 m at the deepest station (-7 m MLLW). At the station 150 m landward of 

the marsh edge, the maximum significant wave height was 2.3 cm, indicating that damping of the waves 

was essentially complete. In addition, wave height decreased by as much as 80 percent as waves 

propagated across the shallows of Corte Madera Bay. Mean attenuation for waves with Hs>0.3 m at 

station DP was 30 percent at station S3, 47 percent at S2, 55 percent at S1, 66 percent at M2, and 99.3 

percent at M1 (where percentage of attenuation is calculated as %ܣ ൌ 100 ቀ1 െ ுೞ

ுೞವು

ቁ). In calculating 

mean attenuation for the marsh stations, bursts with water level below the sensor (at M2) or below the 

marsh plain elevation (at M1) were excluded. Wave attenuation was lowest when the wave direction (at 

station DP) was aligned with the axis of Corte Madera Bay, and at intermediate tidal elevations. The 

dependence on direction indicates that some of the reduction in wave height reflected in the mean 

attenuation values is caused by sheltering. For waves directed along the bay’s axis, attenuation over the 

mudflats was nonetheless substantial, ranging from 20 to 60 percent at M2. 

The lower part of the marsh is inundated when tidal elevations exceed approximately 1.6 m 

MLLW, which occurred 15 percent of the time during the study. Similarly, the marsh was inundated for 

15 percent of the time that offshore wave heights exceeded 0.3 m. At lower tidal elevations, waves 

break against the edge of the marsh before reaching the marsh. Thus marsh vegetation plays a role in 

attenuating waves only during storms that occur at high tide. In addition, the low water depths over the 

marsh at high tide cause all but the smallest waves to break. Thus the wave damping that occurred over 

the marsh was a combination of bathymetric effects that are independent of vegetation, and the 

vegetative drag effect typically considered marsh attenuation. 

Ferry wakes arrive at the marsh edge regularly and appear to present the maximum potential for 

erosion at intermediate tidal elevations, when wakes break against the marsh scarp, and shallow water at 

the marsh edge causes the leading edges of wakes to steepen. Some wakes were amplified as they 

approached shore. However, the largest observed wakes were no larger than significant wave heights 

that persisted at the marsh edge for several hours during the February 2010 storm events. 

Although the damping of waves within Corte Madera Marsh during winter 2010 can be 

attributed largely to bathymetry, the marsh nonetheless serves as a barrier protecting the shoreline from 

waves. In the absence of the marsh, the wave forces currently eroding the marsh edge would be 

impacting a developed shoreline. The wave events from January 22 to March 23, 2010 were moderate, 

likely to occur each winter. The essentially complete damping within 150 m of the marsh edge observed 

during these events is not necessarily a good predictor for extreme events. During extreme events with 

greater wave heights and higher water surface elevations due to storm surge, attenuation by marsh 

vegetation is likely to be a more important component of total wave damping. 
27 

Acknowledgments 

Thanks to Joanne Ferreira, Pete DalFerro, Tim Elfers, Jamie Grover, Rob Wyland, Peter 

Harkins, and Shandy Buckley of the US Geological Survey (USGS) for excellent field support. Adam 

Parris (PWA) and Wendy Goodfriend of BCDC coordinated with the Environmental Protection Agency 

(EPA), the Corte Madera Ecological Reserve, and other scientists working in Corte Madera Marsh. The 

concept for this study was initiated by Dave Cacchione (CME), Bruce Jaffe (USGS), and Adam Parris. 

This report benefited from thoughtful reviews by Andrew Stevens and Renee Takesue of the USGS. 

Theresa Fregosa (USGS) prepared figures 1 and 13. This study is part of the Innovative Wetland 

Adaptation in the Lower Corte Madera Creek Watershed Project initiated by BCDC and funded by 

EPA; additional support was provided by the USGS Coastal and Marine Geology Program. 

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Appendix 

Bed-sediment grain size. Percentages of silt, clay, and sand, with distribution statistics. Statistics are in Φ units, 

calculated using the formulas of Folk and Ward (1957). 

Site Sample 

ID 

 Sand 

(%) 

 Silt 

(%) 

Clay

(%) 

Median Mean Sorting Skewnes

s 

Kurtosis

S1 CMS1A 6.1 66.7 27.2 6.434 6.603 2.048 0.148 0.771 

S2 CMS2A 3.2 65.0 31.8 6.979 6.978 1.975 0.041 0.788 

S3 CMS3A 2.9 65.9 31.1 6.827 6.865 2.015 0.075 0.736 

DP CMDPTA 3.5 69.8 26.7 6.217 6.530 2.003 0.254 0.736 

S3 CM1S3B 6.8 64.1 29.1 6.646 6.703 2.096 0.072 0.763 

S2 CM1S2B 7.0 65.4 27.6 6.435 6.609 2.087 0.136 0.778 

S1 CM1S1B 4.7 66.9 28.4 6.592 6.713 2.024 0.122 0.767 

DP CM1DPB 9.2 62.3 28.5 6.535 6.621 2.142 0.085 0.766