SEPTEMBER

2002

Restoration Ecology Vol. 10 No. 3, pp. 577–590

577

©

2002 Society for Ecological Restoration

Hydraulic Geometry: A Geomorphic Design Tool for Tidal Marsh Channel Evolution in Wetland Restoration Projects

Philip B. Williams

1,2

Michelle K. Orr

1

Nicholas J. Garrity

1

Abstract

Empirical hydraulic geometry relationships for tidalmarsh channels are a practical geomorphically baseddesign tool that can assist in the planning of tidal wet-land restoration projects. This study provides hydrau-lic geometry relationships for predicting the depth,width, and cross-sectional area of mature tidal chan-nels as functions of contributing marsh area or tidalprism. The relationships are based on data from SanFrancisco Bay coastal salt marshes ranging in sizefrom 2 to 5,700 ha. These hydraulic geometry relation-ships refine and expand on earlier relationships. Rela-tionships for mature marshes can be used to predictthe direction and rate of evolution of a channel in animmature or perturbed marsh system. Channel evolu-tion data for three youthful tidal channels, ages 4 to 13years, suggest that the channels are converging ontheir predicted equilibrium morphology. Two chan-nels are eroding in response to significant increases inupstream tidal prism. They have enlarged first by deep-ening, in one case after 13 years to beyond the pre-dicted equilibrium depth, and then widening throughslumping of the channel banks. The third channel, anew one forming in a depositional mudflat, is converg-

ing on its equilibrium morphology after 13 years butwill likely take several decades to equilibrate.

Key words:

hydraulic geometry, restoration, salt marsh,San Francisco Bay, tidal channel.

Introduction

S

ince at least the 17th century observers have notedhow the depth and width of tidal marsh channels

are affected by anthropogenic alterations in the upstreamtidal prism or volume of water exchanged upstream of apoint during a tidal cycle. This understanding was statedperceptively in 1637 by ship owners in the town of Cleyin Norfolk, England, who were petitioning to have newlyinstalled dikes on tidal marshes upstream of the shippingchannel in their harbor removed.

The banke of earth . . . taketh away . . . the indraught of wa-ter 80 rodds and upwards in breadth and one myle at leastin length [an area larger than 65 ha] . . . so that what sylt ormudd the flood tide bringeth in doth settle and remaine inthe navigable channel . . . through want of the ebb tidewhich formely overflowed the aforesaid 80 rodds ofground in breadth and one myle in length (Cozens-Hardy1927).

Intrinsic in this description is a concept that there is anequilibrium form of a tidal channel for a given-sized marshwith a particular tidal range within an estuary that is rela-tively stable over long periods of time. This form is the ex-pression of a dynamic equilibrium between erosional anddepositional processes.

It was not until the 1960s that scientists (Myrick & Le-opold 1963) attempted to systematize an understandingof the relationship between tidal flows and channel ge-ometry of tidal marsh channels using equations of hy-draulic geometry, as had been done for alluvial riversand canals 30 years before. These equations relate chan-nel cross-sectional geometry to discharge according tothe power functions:

W

�

a

Q

b

,

D

�

c

Q

f

, and

v

�

k

Q

m

,where

W

is the width,

Q

is the characteristic discharge,

D

is the average depth, and

v

is the characteristic veloc-ity. By continuity of flow the sum of the constants a, c,and k and the sum of the exponents b, f, and m are bothequal to 1. Various researchers have measured flow andchannel cross-sectional parameters and then calculatedthe exponential parameters for downstream changes inhydraulic geometry. (See Allen 2000 for a succinct de-scription of change in channel morphology).

With the growing interest in tidal marsh restorationin the 1970s there was a need for simple and practicaldesign tools that could predict equilibrium dimensionsof tidal channels in response to changes in flow. Usingthe above hydraulic geometry relationships has practi-cal drawbacks. Developing the relationships requires field

1

Philip Williams & Associates, Ltd., 720 California Street, Suite 600, San Francisco, CA 94108, U.S.A.

2

Address correspondence to P. B. Williams, sfo@pwa-ltd.com.

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578

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measurements of flow over a tide cycle at numerouscross-sections, and published relationships often reportexponent values only (Myrick & Leopold 1963; Pes-trong 1965; Allen 2000), limiting direct calculation ofchannel parameters.

In the early 1980s Philip Williams and Associates(PWA) developed a modified approach to determine em-pirical hydraulic geometry relationships to aid in the de-sign of marsh restoration projects being initiated in SanFrancisco Bay and other mesotidal estuaries on thePacific Coast. Building on earlier coastal inlet research(O’Brien 1931), this empirical method used tidal prismas a surrogate for discharge (Williams & Harvey 1983;Williams 1986; Haltiner & Williams 1987) and used mea-sures of channel dimensions based on geomorphic crite-ria rather than flow stage. Empirical correlations betweenchannel cross-section morphology and tidal prism for aSan Francisco Bay data set were used to predict equilib-rium cross-section morphology for a given tidal prism.

These empirical hydraulic geometry relationships canbe used for a variety of purposes, including sizing tidalchannel excavations in restored marshes, predicting chan-nel sedimentation or erosion responses to changes inupstream tidal prism, and estimating the minimum tidalprism and corresponding marsh size necessary to providesustainable subtidal channel habitat for resident fish. Thefirst known application of this approach to salt marshrestoration was the design of a self-sustaining tidal inletchannel leading to the 12-ha Shorebird Marsh in CorteMadera, California (Williams & Gale 1988).

The utility of this approach led the U.S. Army Corpsof Engineers to fund a report entitled “Design Guide-lines for Tidal Channels in Coastal Wetlands” (PWA et al.1995) that developed hydraulic geometry relationshipsbased on data available in the early 1990s. Two limita-tions to this earlier database have been addressed here:

(1) Data for both mature and evolving immature chan-nels were included. Monitoring data described laterin this article demonstrate how channel geometrycan lag changes in tidal prism in evolving systems.

(2) The database was limited to marshes smaller than60 ha. The current study expands the data set to in-clude historic data for marshes up to 5,700 ha. De-sign information for larger marshes is now requiredfor restorations planned in San Francisco Bay (Steere& Schaefer 2001; Williams & Orr 2002, this issue).

In addition, PWA et al. included data from other PacificCoast estuaries. Although the same design tool can beused for different estuaries, it is preferable to develophydraulic geometry relationships specific to the estuarywhere it is being applied. The current study uses onlySan Francisco Bay data.

Inherent in using empirical correlations for predic-tion is the assumption of homogeneity of the key mor-

phological parameters, previously identified as sedi-ment characteristics, tidal range, marshplain elevations,and bed and bank friction. (See Allen 2000 for a succinctdescription of change in channel morphology.) The chan-nels used in the hydraulic geometry correlations and thechannels to which predictions are applied must be simi-lar in terms of these key features.

As restoration practitioners have gained experiencein tidal wetland restoration in San Francisco Bay, theyhave recognized the need to better predict the evolu-tionary trajectory of important wetland habitats such astidal channels (Williams & Orr 2002, this issue). Theequilibrium hydraulic geometry relationships for ma-ture or several thousand-year-old “ancient” marshesdescribed here represent the dynamic equilibrium end-point, or asymptote, of channel morphologic character-istics of a fully mature tidal marsh system. They can beused to assess the degree of disequilibrium of per-turbed marsh channels and their evolutionary trajectory.Perturbations may include, for example, tidal prism re-duction by diking, tidal prism increase due to upstreamdike breaching for tidal wetland restoration, or artificialtidal channel deepening by dredging. Our review of theliterature reveals no systematic long-term geomorphicanalyses of how tidal channels in cohesive sedimentssilt in or erode in response to changes in tidal prism.Monitoring data from evolving tidal marsh channels inSan Francisco Bay are presented to provide insight intorates and patterns of evolution.

Study Area

San Francisco Bay formerly sustained 80,000 ha of ex-tensive coastal salt marshes before American coloniza-tion 150 years ago. These marshes began to form in thelatter part of the Holocene (in the last 6,000 years), whensea level rise slowed to 1 to 2 mm/yr, allowing vegetatedmarshes to keep pace and expand inland as sea level rose.As the marshes expanded the tidal channel system thatdrained the marshes expanded inland as well. Almost allthese tidal channels or “sloughs” are purely tidal features.In the Mediterranean climate of California run-off ishighly seasonal and riverine influences on channel mor-phology are observed only close to the mouths of the larg-est creeks tributary to the Bay. These “ancient” maturemarshplains were dominated by

Salicornia virginica

andtended to reach equilibrium at approximately the eleva-tion of the average diurnal high tide. Surveys by Atwa-ter et al. (1979) of San Francisco Bay salt marshes indi-cated that the average mature marshplain elevation iswithin decimeters of mean higher high water (MHHW).

In common with many other Pacific Coast estuariesSan Francisco Bay has lost a large percentage, approxi-mately 92%, of its ancient or mature tidal marshes (GoalsProject 1999). In addition, the remnant intact marshes

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are highly fragmented, and only in the Petaluma Marshare there large undisturbed ancient tidal channels.

San Francisco Bay has mixed semidiurnal tides. Theaverage diurnal tide ranges between 1.5 and 3.0 mthrough the system. Large flood events in the Sacra-mento River watershed provide the major input of sedi-ment to the Bay (Nichols et al. 1986). These sedimentsconsist mainly of flocculated clays that are readily re-suspended from the shallows within the Bay by strongwind wave action and redistributed by tidal and estua-rine circulation (Schoellhamer 1996; Buchanan & Ruhl2000). Consequently, average suspended sediment con-centrations in the flood tide water column can be high.

Methods and Data Set

In the first part of this study we develop relationshipsto predict downstream changes in equilibrium hydrau-

lic geometry for mature marsh channels. In the secondpart we use these relationships to predict and interpretchannel evolution in response to changes in tidal prismfor young nonequilibrium channels.

Equilibrium Hydraulic Geometry Relationships

We compiled a database of channel cross-sections,marsh area, and tidal prism for six existing and six his-toric ancient San Francisco Bay marshes with undis-turbed contributing tidal “watersheds” (Tables 1 & 2).We then used these data to derive regression relation-ships between specific channel parameters—depth, topwidth, and cross-sectional area—and both marsh areaand tidal prism.

We used U.S. Coast and Geodetic Survey maps fromthe mid to late 1800s to verify that the existing ancientmarshes were essentially undisturbed from pristine con-

Table 1.

Tidal channel hydraulic geometry of present-day mature marshes in theSan Francisco Bay estuary

Location

ThalwegDepth Below

MHHW

(

m

)

Top Width atMHHW

(

m

)

(Channel Cross-Sectional AreaBelow MHHW

(

m

2

)

ContributingMarsh Area

(

ha

)

DiurnalTidalRange

(

m

)

PotentialDiurnal Tidal

Prism

(

m

3

)

China Camp Marsh 1.5 7 5 5 1.8 4,100Heerdt Marsh 1.5 5 6 5 1.8 12,000

1.6 15 13 12 1.8 32,000Laumeister 2.1 18 15 5 2.6 17,000Newark Slough 2.0 N.A. 9 2 2.6 2,000

1.7 N.A. 7 3 2.6 2,6001.7 N.A. 11 3 2.6 4,4001.8 N.A. 12 6 2.6 5,9003.5 28 43 34 2.6 68,0003.3 23 36 28 2.6 56,0003.3 26 33 27 2.6 52,0003.1 23 35 26 2.6 46,0002.6 23 25 21 2.6 37,0002.6 22 25 20 2.6 33,0002.7 23 23 18 2.6 28,0002.3 20 18 11 2.6 20,0002.5 12 11 9 2.6 16,0002.2 10 11 8 2.6 15,0002.0 12 9 5 2.6 10,0001.7 8 10 4 2.6 8,800

Petaluma Marsh 4.0 29 33 115 1.9 270,0003.5 15 31 107 1.9 260,0003.8 15 37 135 1.9 310,0003.7 22 41 146 1.9 360,0003.8 N.A. N.A. 105 1.9 120,0003.6 N.A. N.A. 97 1.9 130,0002.6 N.A. N.A. 89 1.9 120,0002.7 N.A. N.A. 65 1.9 90,0002.5 N.A. N.A. 49 1.9 81,0002.2 N.A. N.A. 38 1.9 72,0001.6 N.A. N.A. 12 1.9 6,200

Wildcat Marsh 1.7 16 14 13 1.8 6,2001.3 7 5 5 1.8 1,900

*Deepest part of the channel.N.A.

�

not applicable.

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580

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ditions. The database combines new data from fieldsurveys and historic mapping with data derived fromprevious studies (Gilbert 1917; Leopold et al. 1984, 1993;PWA et al. 1995). We used data only from channelswith marsh watershed areas greater than 2 ha, corre-sponding to approximately third-order channels andlarger (PWA et al. 1995). Morphology of smaller chan-nels appears to be different (Pestrong 1965) and is com-plicated by proportionately higher bank friction, hy-draulic resistance of vegetation (Collins et al. 1987), andeffects of bank slumping. Channel cross-sections wereselected in locations where all tidal flows below marsh-plain elevations would flow through the channel (i.e.,no looped flow channel networks). All the channels se-lected are formed in cohesive sediments in saline, or insome cases slightly brackish, parts of the estuary wherefluvial flows are minimal. Channel cross-sections weremeasured in locations sheltered from offshore wave ac-tivity with tidal ranges between 1.8 and 2.6 m.

Existing Ancient Marsh Channels.

Channel cross-section datafor the existing marshes (Table 1) were obtained byground survey, using rod and level. Contributing marsharea was estimated by delineating approximate upstreamdrainage boundaries between tidal channel systems onlarge-scale topographic maps or aerial photographs andmeasuring the watershed area. All the marshes hadmarshplains that were near the elevation of the averagediurnal high tide (MHHW), which has previously beenestablished as an appropriate reference plane for calcu-

lating hydraulic geometry characteristics (see discus-sion in PWA et al. 1995). For these marshes MHHW ap-proximates a bankfull tidal stage.

Conceptually there is an average “dominant” ebb tideanalogous to a river’s dominant discharge that does mostof the channel-forming work. Research by French andStoddart (1992) indicates that this channel-forming tideis somewhat higher than the bankfull stage, with over-bank flow onto the marshplain. Spring tidal prism (tidalprism between mean spring high and spring low tide)therefore could be a better surrogate for channel-formingflow, because spring tides overtop the marshplain for SanFrancisco Bay marshes. However, no significant improve-ment in hydraulic geometry correlation has been foundusing spring tidal prism rather than diurnal tidal prism(PWA et al. 1995), which is easier to measure in the fieldand define from topography and published tidal datums.

For each cross-section we characterized depth, topwidth, cross-sectional area, contributing watershed area,and diurnal tidal range information. Depth was mea-sured at the thalweg—the deepest part of the channel—relative to MHHW. Widths were measured at the eleva-tion of MHHW, except in a few cases where the top ofbank was below MHHW. In these cases the top of bankwas projected vertically upward to MHHW. Cross-sec-tional area was calculated as the area below MHHW forthe part of the channel within the designated channelwidth. Contributing tidal watershed area is the arealandward, or “upstream,” of the cross-section, extend-ing to the drainage divide between channel networks.

Table 2.

Tidal channel hydraulic geometry of historical marshes in the San Francisco Bay estuary

Location

Thalweg

a

Depth BelowMHHW

(m)

Top Width atMHHW

(m)

Channel Cross-Sectional AreaBelow MHHW

(m

2

)

ContributingMarsh Area

(ha)

DiurnalTidalRange

(m)

PotentialDiurnal

Tidal Prism

b

(m

3

)

Gallinas 1856 2.7 150 330 410 1.8 1,000,000Napa 1860 10.1 670 3,532 5,300 1.9 21,000,000

6.9 190 929 1,400 1.9 4,500,0004.0 76 240 410 1.9 1,000,000

Petaluma 1860 5.9 724 2,824 5,300 1.9 21,000,0005.3 305 1,131 1,700 1.9 5,600,0005.0 95 370 490 1.9 1,300,0002.8 57 130 120 1.9 260,0002.8 38 85 80 1.9 160,000

Ravenswood 1914

c

7.0 110 370 730 2.4 3,800,000San Joaquin River 1867

d

17 975 7,090 73,000 1.2 NA16 885 7,020 73,000 1.2 NA

Sonoma Creek 1856 8.3 238 1,367 5,700 1.9 23,000,000

a

Deepest part of the channel.

b

Estimated diurnal tidal prism

�

935

�

(marsh area)

1.17

from Figure 2, except Ravenswood.

c

Data for Ravenswood from Gilbert (1917).

d

Brackish/freshwater marsh included here for comparison because it is the largest historic marsh in the San Francisco estuary. Not in-cluded in the regression correlations.NA

�

not available.Channel morphology data from U.S. Coast & Geodetic Survey bathymetric maps and marshplain areas from U.S. Coast & Geodetic Sur-vey topographic maps and Nichols and Wright (1971), except as noted.

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Diurnal tidal range was obtained from the nearest Na-tional Oceanic and Atmospheric Administration (NOAA)tide station.

Tidal prism (the volume of water between high andlow tide) was estimated for each cross-section. With oneexception, we used potential diurnal tidal prism, a spe-cific measure of tidal prism defined as the volume ofwater upstream of a cross-section between the eleva-tions of mean lower low water (MLLW) and MHHW.The one exception was Petaluma Marsh, where we usedobserved tidal prism calculated for a time series of highto low tide discharges. Potential diurnal tidal prism wascalculated as the sum of marshplain and channel vol-ume. Marshplain volume for those areas below MHHWwas estimated from approximate marshplain elevationsand drainage area. Channel volume was calculated fromtotal channel length and conical interpolation of chan-nel cross-sectional area between surveyed cross-sections.

Channel depth and discharge data for PetalumaMarsh were collected by Leopold et al. (1984, 1993). Ob-served tidal prism was previously computed from thesedata by analyzing the time series of synoptic discharges(PWA 1985). Discharge was integrated for the durationof the ebb flow hydrograph. Additional geometry and

tidal prism data for Petaluma Marsh were provided byJ. Collins (personal communication, 1988).

Historic Ancient Marsh Channels.

Except for the data forRavenswood Slough, channel cross-section and marsharea for the larger historic marsh channels (Table 2)were obtained from 19th century U.S. Coast and Geo-detic Survey charts. Before diking destroyed the exten-sive marshplains the U.S. Coast and Geodetic Surveyaccurately mapped channel locations in detailed topo-graphic and hydrographic maps and also sounded manyof the larger tidal sloughs for bathymetric mapping, asis illustrated for the Napa River tidal channel in Figure1. For all these maps we assumed that marshplains wereat approximately MHHW, as they are now. Thalwegsoundings shown on these maps were measured to localMLLW and converted to MHHW by adding the currenttidal range from NOAA tide station records. Channeltop width was measured from the topographic maps. Incases where the historical survey shows only one chan-nel depth (mid-channel) we assumed that the thalweg waslocated mid-channel and we calculated cross-sectionalarea assuming an elliptical cross-sectional shape. Contrib-uting marsh area was obtained from the same charts.

Figure 1. Example of a historical U.S. Coast Survey map—Napa River marshes. Cross-sections used in the database are indicated.

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Historical mapping was not sufficiently detailed toestimate tidal prism based on bathymetry. Instead, tidalprism was calculated based on a correlation of marsharea and potential tidal prism (Fig. 2), including boththe existing ancient marsh channel data and historicaltidal flow data from Ravenswood Slough (Gilbert 1917).Tidal prism was calculated as 935

�

(marsh area)

1.17

,where marsh area is in hectares and tidal prism in cubicmeters.

Gilbert (1917) surveyed channel data for the historicRavenswood Slough in 1914 using rod and level. Healso measured tidal velocities over a spring-neap cycle.PWA et al. (1995) estimated tidal prism by integratingGilbert’s time series of measured tidal velocities.

Channel Evolution in Young Marshes

Channel evolution data were available for three sites:two that enlarged in response to an increase in tidal prism(the Warm Springs and Sonoma Baylands inlet channels)and one that is forming in newly deposited mudflats (theWarm Springs internal transect). For each site we col-lected a time series of thalweg depth, top width, cross-sectional area, diurnal tidal range, and tidal prism (Table3). These were compared with predicted equilibrium val-ues. Each site is described further below. Surveyed cross-sections for each site are shown in Figure 3.

Sonoma Baylands Restoration Project.

A 12-ha self-containedportion of the larger project, referred to as the “pilot unit,”was breached in January 1996 (Williams & Florsheim1994). In part because of regulatory agency concernsover the possible impact to endangered species, a con-necting channel to the Bay was not excavated across anoutboard salt marsh to provide full tidal exchange to thesite. Instead it was decided to let a small existing 430-mlong tidal channel erode over time, recognizing that this

decision would delay evolution of wetland functions.Because of the limited hydraulic conveyance in thechannel the diurnal tidal range in the restored wetlandsite was initially very limited. Since breaching the leveeto Sonoma Baylands the channel has eroded and thetidal range has progressively increased. Inlet channelcross-sections and tidal range were measured for across-section located approximately 320 m downstreamof the breach every 6 months since the site was breached(PWA et al. 1999). During this period the site did notdrain completely at low tide, and so tidal prism was esti-mated as the product of site area and tidal range at thetime of the survey.

Warm Springs Restoration Project and Coyote Slough.

The 81-haWarm Springs site was restored in October 1986. Beforerestoration the site was diked, drained, and excavatedto more than 5 m below MHHW. Restoration consistedof breaching the perimeter levee to reconnect the site totwo tidal channels: Coyote Slough and Mud Slough(Fig. 4). Almost full diurnal tidal range was achievedwithin 1 year, and rapid sedimentation occurred withinthe site. Coyote Slough has the greater conveyance ca-pacity of the two inlet channels, and until the connect-ing channel to Mud Slough eroded sufficiently in 1991almost all the tidal flows to the site were carried throughCoyote Slough, 6,400 m upstream of the Bay. Since 1991Mud Slough has captured about 10% of the tidal prism.

Two cross-sections (Fig. 4) were surveyed every 2 to 5years: (1) the Coyote Slough inlet channel approxi-mately 1,070 m downstream of the breach and (2) atransect inside the restoration site. Before breaching thelevee to Warm Springs, Coyote Slough was assumed tobe in equilibrium with its existing upstream tidal prism,because no major changes had occurred in the marshwatershed for approximately 50 years. After breachingthe levee to Warm Springs the tidal prism increased

Figure 2. Diurnal tidal prism versus marsh watershed area for mature ancient marshes in San Francisco Bay.

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significantly. The additional tidal prism from WarmSprings was calculated based on measured tidal rangeand site bathymetry. Coyote Slough tidal prism was ad-justed downward to compensate for the estimated tidalprism carried through Mud Slough after 1991. As therestoration site silted in the tidal prism progressivelydecreased. Tidal prism for the Warm Springs interiortransect was calculated similarly, adjusted to reflect itslocation “upstream” of the breach to Coyote Slough,with a contributing marsh area of 62 ha. Here a newtidal channel is forming as intertidal mudflats emerge.

Results

Equilibrium Hydraulic Geometry Relationships

Figure 5 shows log-log linear regression plots of chan-nel morphology parameters versus contributing “water-shed” area for the data from mature marshes presentedin Tables 1 and 2. Figure 6 shows the same data as Fig-ure 5 but using potential diurnal tidal prism from Tables 1and 2 rather than marsh area. As expected there is a strongpositive correlation between channel dimensions (depth,width, cross-sectional area) and both tidal prism andmarsh area. The regressions of hydraulic geometry withmarsh area (Fig. 5) have similar standard deviations asthe diurnal tidal prism regressions (Fig. 6).

There is no discernible difference in the data we sur-veyed from existing mature marshes and data derivedfrom historic surveys of marshes that were later diked.However, data for channels within a particular marsh,although following the general regression line, may beslightly offset. The most significant data outliers arefor the top width and cross-sectional area of PetalumaMarsh channels. Data points for the historic San JoaquinRiver slough channel are shown (Fig. 5) for comparisonbut are not included in the regression. This historicchannel, the largest one that existed in the estuary, fedan approximately 73,000-ha freshwater tidal marsh. Thecross-sectional areas are similar to those predicted bythe regression developed for salt marshes (Fig. 5),though slightly deeper and narrower.

Channel Evolution in Young Marshes

Table 3 presents hydraulic geometry data for the threeevolving marsh channels. A plot of cross-sectional areaversus tidal prism (Fig. 7) for each cross-section in thetime series shows how the three channels are respond-ing over time to changes in tidal prism. Also shown inFigure 7 is the predicted cross-sectional area versustidal prism regression line from Figure 6. At each sitethe cross-sectional areas are increasing or decreasing toconverge on the mature marsh predicted equilibrium ge-

Table 3.

Evolution of tidal channels in response to changing tidal prism

Location

Date (yr since

restorativeaction)

Thalweg*DepthBelow

MHHW(m)

TopWidth

(m)

Cross-Sectional

Area BelowMHHW (m

2

)

DiurnalTidalRange

(m)

ActualDiurnal

Tidal Prism(m

3

) Description

SonomaBaylands,pilot unit

2/12/96 (0.5) 1.5 6.7 3.1 0.2 17,000 Undersized channeleroding, allowingincreased tidal exchange and tidal prism.

3/19/98 (2.2) 2.0 6.6 7.2 0.2 27,0003/23/00 (4.2) 1.9 7.7 9.0 0.3 30,000Predicted

equilibrium2.1 13 15 1.9 16,000

Warm Springs,CoyoteSlough

8/29/86 (

�

0.1;pre-breach)

3.1 38 72.5 2.5 2,300,000 Eroding channeladjusting to large, butdecreasing, tidal prism; estimated pre-breach tidal prism in Coyote Slough is 250,000 m

3

.

6/22/88 (1.7) 4.5 40 91.2 2.5 2,300,0005/25/90 (3.6) 4.6 36 93.8 2.5 2,300,0008/10/95 (8.8) 5.3 40 115 2.5 1,900,0008/10/99 (12.8) 5.6 41 144 2.5 910,000Predicted

equilibrium3.8 56 124 2.5 410,000

Warm Springs,interiortransect

9/19/86 (-0.1;pre-breach)

6.0 427 957 2.5 1,700,000 Oversized “channel”with decreasing tidal prism; new channelforming in a depositing mudflat.

6/21/88 (1.7) 4.6 416 957 2.5 1,700,0006/05/92 (5.6) 3.8 424 836 2.5 1,600,0008/10/99 (12.8) 3.0 402 325 2.5 570,000Predicted

equilibrium3.0 32 55 2.5 120,000

*Deepest part of the channel.Sources: Data for Sonoma Baylands from PWA et al

.

(1999); data for Warm Springs from PWA and Phyllis Faber & Associates (2000).

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ometry. The evolutionary path is not necessarily a straightline (some of the paths are “curved”) because the tidalprism is changing over time. Figure 8 shows a time seriesplot of actual and predicted equilibrium channel morphol-ogy for Coyote Slough and the Warm Springs interiortransect. Channel evolution is detailed by marsh below.

Discussion

Equilibrium Hydraulic Geometry Relationships

The correlation of mature marsh area and tidal prismpredicts a progressively proportional increase in diur-nal tidal prism with marsh area. For example, for a 2-mtidal range a 10-ha mature marsh will have about 7% ofits total volume between the planes of MHHW andMLLW occupied by tidal water, whereas for a 1,000-hamarsh this volume will be 15%. This prediction of tidalprism as a percentage of intertidal volume is lower than

the approximately 30% calculated from Boon (1975), butthe values are not directly comparable. Boon measuredcontributing marsh area as the actual area flooded for ahigh tide. This method yields a smaller marsh area thanthe one used in this study, where marsh area extends tothe tidal drainage divide.

The regression equations in Figures 5 and 6 are simi-lar to those in the earlier PWA et al. (1995) study, al-though they predict slightly deeper channels. For a sim-ilar range in drainage areas the scatter of data from themarsh area and tidal prism regression line is less thanthat of earlier PWA et al. (1995) regressions that in-cluded data from both mature and immature marshesand from southern California marshes.

The regression relationship for cross-sectional area asa function of tidal prism is similar to the one derived bySteel and Pye (1997) (

y

�

0.02

x

0.7

) in the only otherknown comparable study (Allen 2000). Steel and Pyesurveyed tidal channel dimensions in 13 British salt

Figure 3. Cross-section plots for three rap-idly evolving tidal channels: (a) Sonoma Baylands Pilot Unit inlet, (b) Coyote Slough, and (c) Warm Springs interior transect.

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marshes, including clay/silt and silt/sand marshes of var-ious ages, from approximately 30 to over 2,000 years old.

It is preferable to develop and apply these empiricalrelationships for relatively homogeneous conditions,because channel geometry will vary with system scale,tidal range, salinity, vegetation, and sediment charac-teristics. The empirical relationships presented here forthe San Francisco Bay estuary show less data scatter (

r

2

�

0.92) than those developed by Steel and Pye for moreheterogeneous conditions (

r

2

�

0.8).

Channel Evolution Response to Increased Tidal Prism

Sonoma Baylands Inlet Channel.

The channel has eroded sig-nificantly, tripling in cross-sectional area between breach-

ing in 1996 and 2000. Channel enlargement occurredthrough initial deepening, followed by widening. Deep-ening occurred relatively quickly, destabilizing the vege-tated cohesive banks. Widening occurred more slowlythrough progressive mass failure of the banks. As visiblein the cross-sections, the channel widens as slump blocksslide into the channel and are gradually eroded by tidalcurrents. Slump block failure has been well documentedin San Francisco Bay and other coastal marsh systems(Yapp et al. 1916; Chapman 1942; Pestrong 1965; Gabet1998). The evolutionary trajectory of the cross-sectionalarea appears to be converging on the predicted equilib-rium morphology. As the channel has eroded, tidal ex-change and therefore tidal prism has increased. Overtime the evolutionary trajectory is expected to “curve”

Figure 4. Warm Springs restoration site. Coyote Slough and Warms Springs internal transects shown as white bars. 1998 aerial photograph.

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as tidal prism decreases in response to intertidal sedi-mentation within the site.

Coyote Slough.

Before breaching there was sufficienttidal prism upstream of this location to scour a 72-m

2

channel cross-section. Within 2 years of breaching thechannel had deepened by about 1.5 m. Thirteen yearsafter breaching the channel has nearly doubled in size.As at Sonoma Baylands channel enlargement has oc-curred through initial deepening, followed by widen-ing. Erosion of the bed has resulted in channel depthsthat rapidly approached and then exceeded those pre-dicted using equilibrium relationships. Change in cross-sectional area has occurred more slowly but is ap-proaching equilibrium with the current tidal prism after13 years. Bank slumping was observed at Coyote Sloughas at Sonoma Baylands, but after 13 years channelwidths are still less than the predicted equilibrium. The

evolutionary trajectory of the site is curved because af-ter about 5 years appreciable intertidal sedimentation inthe Warm Springs Marsh started to reduce the diurnaltidal prism.

Channel Evolution Response to Decrease in Tidal Prism

Warm Springs Internal Transect.

For about the first 6 yearsof evolution the deeply excavated site filled rapidlywith sediment. By the sixth year intertidal mudflats hadformed and a subtidal channel was becoming defined.By the 13th year this channel had become better definedby adjacent mudflat channel banks. As sedimentationoccurred the tidal prism was reduced. The channel isshallower than the predicted equilibrium depth andmuch wider. Vegetation has not yet established itself onthe mudflats. The evolutionary trajectory is convergingon the expected equilibrium cross-section (Fig. 7).

Figure 5. Channel dimensions (depth, width, and cross-sectional area) versus marsh water-shed area for ancient marshes in San Fran-cisco Bay. Data points for the historic San Joaquin River channel are shown for compar-ison but are not included in the regression.

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Implications For Wetland Restoration Design

(1) The empirical correlation of hydraulic geometrywith mature marsh area provides a practical tool forpredicting the evolutionary end point for tidal chan-nels in restored marshes in San Francisco Bay. Thistool can be used to• Predict the end point of “self-designing” chan-

nels evolving in response to a change in upstreamtidal conditions, such as from a breached dikemarsh restoration;

• Specify excavation depths and widths for leveebreaches and tidal channels, helping to allowadequate tidal exchange while avoiding thefinancial and habitat costs of over-excavation;

• Identify the need for excavation of any erosion

resistant soil or infrastructure where tidal chan-nels are expected to form in a restoration site;

• Predict the approximate extent of subtidal andintertidal channel habitat expected to evolvewithin a restored marsh.

Predictions of extent and type of channel habitat can beobtained by using hydraulic geometry in combinationwith channel morphometric analysis as described byZeff (1999). Of particular importance for San FranciscoBay marshes is the prediction that in mature marsheswhere the diurnal range is about 2 m, an area of at least130 ha is required to sustain subtidal channels for resi-dent fish and other nekton, assuming a channel depthof 1.5 m at MLLW.

Figure 6. Channel dimensions (depth, width, and cross-sectional area) versus diurnal tidal prism for ancient marshes in San Fran-cisco Bay.

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(2) Careful contouring of created channels is often notnecessary, because natural erosional and deposi-tional processes guide channel evolution toward along-term equilibrium state. Channel grading maybe used to speed the evolutionary process.

(3) The methodology presented here for developing hy-draulic geometry relationships can be used as a designtool for wetland restoration projects in other estuariesby developing site-specific relationships based onanalysis of simple survey field data and detailed topo-graphic maps or aerial photos. In addition, this meth-odology can incorporate historical survey data for ma-ture marshes where few such marshes remain intact.

(4) Easily developed marsh area–hydraulic geometryrelationships can be quickly transformed to approx-imate tidal prism–hydraulic geometry relationshipsfor a particular estuary by assuming tidal prism is afixed percentage of the product of marsh area anddiurnal tidal range. For San Francisco Bay, for thesize of typical marsh restoration projects being con-sidered, this percentage ranges from 7 to 15%.

(5) Data from evolving tidal channels can be comparedwith predictions of equilibrium geometry to develop abetter understanding of the time scale of the evolution-ary trajectory of the channel that will be useful in anadaptive management strategy for restoration projects.

(6) It is important to note that hydraulic geometry rela-tionships are not deterministic and for a particularlocation may have a significant degree of uncertainty.Where greater certainty is required in restoration plan-

ning, other design tools such as numerical hydrody-namic modeling should also be used (Goodwin 1994).One must be cautious in extrapolating the hydraulicgeometry relationships beyond the range of data.

Conclusions

This study provides empirical hydraulic geometry rela-tionships for predicting the depth, width, and cross-sec-tional area of mature tidal channels as functions of con-tributing marsh area or tidal prism. The relationshipsare based on data from San Francisco Bay coastal saltmarshes ranging in size from 2 to 5,700 ha. Hydraulicgeometry relationships are a practical geomorphicallybased design tool that can assist in the planning of tidalwetland restoration projects. They allow estimation ofequilibrium channel parameters and can be used to pre-dict the direction and approximate rate of evolution of achannel in an immature or perturbed marsh system. Timeseries of cross-sections from three evolving tidal chan-nels ages 5 to 13 years indicates that the channels areconverging on the predicted equilibrium morphology.

Acknowledgments

Monitoring work on which this study is based wasfunded by the Marin Community Foundation and SanFrancisco Foundation on behalf of The Bay Institute andSave San Francisco Bay Association; the U.S. Army Corpsof Engineers, San Francisco District; the U.S. Army Corps

Figure 7. Evolutionary trajectory of channel cross-sectional area and tidal prism at rap-idly evolving sites. Number labels indicate the number of years of channel evolution fol-lowing increase or decrease in tidal prism. Arrows show direction of increasing time. Dashed lines show that channel dimensions should eventually reach the predicted equili-birum, though the exact trajectory toward this endpoint is not known. The regression line is from Figure 6.

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of Engineers Waterways Experiment Station; the Califor-nia State Coastal Conservancy; the Marin Audubon Soci-ety; and the California Department of Fish and Game.We thank our collaborators on monitoring and researchwork on various projects on the Pacific Coast who haveprovided valuable insights: Phyllis Faber, Denise Reed,Charles Simenstad, and Joy Zedler. Michael Lighthiserof PWA provided assistance with data collection, graph-ics, and preparation of an early draft of this paper. JamesKulpa of PWA staff also provided assistance.

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