Distribution of tidal bottom stress in a New Hampshire estuary

[From the U.S. Government Printing Office, www.gpo.gov]

University of New Hampshire
University of Maine
Sea Grant College Program

DISTRIBUTION OF

TIDAL BOTTOM STRESS

IN A NEW. HAMPSHIRE. ESTUARY

M. Robinson Swift
Wendell S. Brown
COAST AL L~~
INFORaMIATION CE-NTER

T TH-MP-/-SG-83-2

~57. 2
N4 516 ration of theLUNH/UMe` Sea'Grant College Program
no.83-2

Distribution of Tidal Bottom Stress in a

New Hampshire Estuary

M. Robinson Swift
Department of Mechanical Engineering . . .

Wendell S. Brown
Department of Earth Sciences

U. S- DEPARTMENT OF COMMERCE NOAA
COASTAL SERVICES CENTER
2234 SOUTH HOBSON AVENUE
Report No.: UNH-MP-T/(#g�E63@1, SC 29405-2413

This work is the result of research sponsored, in part, by the Office
of Sea Grant, NOAA, Department of Commerce, under Grant #04-8-M01-79
to the University of New Hampshire. The U.S. Government is authorized
to produce and distribute reprints for governmental purposes, any
copyright notation that may appear hereon notwithstanding.

The National Science Foundation (Grant #OCE78-26229) and the National
Ocean Survey also cooperated in this research.

University of New Hampshire
Durham, N.H. 03824, U.S.A.

February, 1983

Abstract

Estimates of area-averaged, tidal bottom stress are made

for four channel segments of the Great Bay Estuary, New Hamp-

shire. Sea level and current measurements are used to estimate

pressure gradient and acceleration terms in the equation of

motion, while the equation of motion itself is used to infer

the remaining stress term. Dynamic terms, bottom stress

values, friction coefficients and energy dissipation rates are

estimated for each site. To aid in interpreting the results,

sea level and current data are subject to a harmonic analysis

to determine the tidal constituents at 'a number of measurement

stationsilocated along the estuary's main channel. The varia-

tion of current amplitude along the channel axis, which must be

evaluated to compute the acceleration terms, is analyzed by

considering the distribution of tidal prism and cross-section

area.

The results show that at all locations the principal force

balance is between the frictional stress and the pressure

gradient forcing. RMS values of total bottom stress range from

2.7 to 10.4 N/in2, while friction coefficients vary from .015 to

.054. Energy dissipation was most intense in-the seaward

portion of the estuary with an order of magnitude decrease at

the most inland site.

Introduction

Bottom stress in estuaries and coastal waters can be

estimated from current and sea level data using the equation of

motion. The data are used to estimate acceleration and pressure

gradient terms, and the equation of motion-itself is used to

infer the remaining bottom stress term. This technique,

referred to here as the dynamic inference method, is based on a

simplified version of the momentum equation but requires no

assumptions regarding a direct relationship between stress and

current. Because dynamic terms in the equation of motion are

individually estimated, the instantaneous dynamic balances 'can

also be determined.

Bowden and Fairbairn (1952), Bowden et a]. (1959) and more

recently Wolf (1980) have applied the method to coastal waters

to estimate stress, friction coefficients and eddy viscosities.

Brown and Trask (1980) have used the method to study a site

within a tidal channel. In their formulation the equation of

motion is integrated over a channel segment and yields a spatially

averaged total stress. Problems of spatial variability, such

as those described by Smith and McLean (1977) and Gardner et

al. (1979) which plague single point estimates of stress, are

avoided. The total stress estimates include both skin friction

and the cumulative form drag due to individual roughness

elements. The dynamic inference method thus provides a representa-

tive estimate of the stress associated with the tidal hydro-

dynamics.

In this paper the dynamic inference method is applied to

four different locations in the main channel of the Great Bay

Estuary, New Hampshire. Measurements used include current, sea

level, and estimates of volume distribution. Sea level and

cross-section averaged current are subjected to harmonic

analysis to characterize the estuary's tidal kinematics. The

estuary's dynamics are then analyzed to determine how dynamic

balances, stress values, friction coefficients and energy

dissipation vary with position.

Theoretical Considerations

To obtain spatially averaged bottom stress estimates using

the dynamic inference method,,the equation of motion must be

volume-integrated. In this section the volume-integrated

equation of motion is developed for an estuarine channel segment,

and the important limitations are outlined. Detailed justifi-

cation of these equations for application to well-mixed tidal

channels has been provided by Brown and Trask (1980). Because

the specialized equation of motion contains spatially averaged

current terms, a procedure for estimating spatially averaged

current from point measurements of current is also discussed.

For the case of a narrow channel having constant density

flow with negligible vertical acceleration and effective

stresses due to depth variation in current, the vertically

averaged equation of motion is

4b
~U+ O~v= -g - (1)

Here (+) denotes a vector quantity; i is the vertically averaged

current; n, the surface elevation above mean sea level; Tb,

the bottom stress; t, the time; p, the density; g, the gravita-

tional acceleration; and H, the depth. Taking the scalar

product of this equation with a unit vector parallel to the

channel axis results in a longitudinal equation of motion. If

and %b are directed axially, the longitudinal equation becomes

Du + = (U2/2) = -g an b (2)
at ax ax pH

where x is an axial coordinate increasing along the channel

seaward.

Equation (2) is next integrated over the area of a channel

segment. In doing so we assume that longitudinal gradients of

current and surface elevation have small variation over the

width of the channel and that spatial changes in current,

surface elevation and channel width are small with respect to

their segment-averaged values. Thus the integrated longitudinal

equation of motion becomes

at ~2 -<Tb>()
3 a (U2/2) =a9 n (3
3-%- + x = gax pH(3

where 6( ) refers to changes over the length of the segment, ()

to cross-section averaged quantities, and <( )> to segment-

averaged quantities. The following rearranged form of Eq. (3)

provides an expression for segment-averaged bottom stress, <Tb>,

as a sum of local acceleration (LA), advective acceleration

(AA) and pressure gradient (PG) terms:

<T > = PH ( 22 + + g -(4)

LA AA PG

The pressure gradient term PG on the right hand side of

Equation (4) may be estimated straightforwardly using sea level

measurements at each end of the segment. Estimating spatially

averaged current values (occurring in the acceleration terms)

using point measurements of current, on the other hand, requires

additional information on the spatial distribution of current.

Consider the problem of estimating 0 using measurements from a

single current station consisting of a vertical array of

current meters located within the segment. One approach,

appropriate for cases of negligible mean flow, is to supplement

the current measurement with tidal prism estimates (obtained

independently from volume considerations) in the following

manner. Cross-section averaged current at the station, 0s, is

assumed proportional to the vertical average of measured

current time series, Uv, but with different proportionality

constants for the flood and ebb phases to account for tidal

asymmetry at the measurement location. Thus

Os = CEbb Uv H(Uv) + CFlood Uv H(-Uv) (5)

in which H is the Heaviside step function and the C's are

constants. The C's are evaluated by requiring the time integral

of transport over a flood or ebb phase to be equal to the tidal

prism so that

C~bb = Prism and C Prism (6)
CEbb AFlUvd
Aj U ,dtAl Uvdt
Ebb Flood

in which A is the cross-section area.

To estimate current distribution between measurement

stations, an average current, Ua, may be computed as a function

of longitudinal position x from

Ua A~l/2 Prism
Ua :A(1/2 semi-diurnal tidal period) (7)

The result is a cross-section averaged current which is time-

averaged over a flood or ebb phase. Cross-section averaged

current 0 at locations other than the current station may then

be estimated from U0 by assuming that at each cross-section 0
5
is proportional to Ua' Thus, for example, the segment-averaged

current time series is given by

<Ua>
 US (8)

Observations

A cooperative field program was carried out by National

Ocean Survey (NOS) and the University of New Hampshire (UNH)

during the summer and fall of 1975 in the Great Bay Estuary,

New Hampshire, which is shown in Fig. 1. The upper part of the

estuary, consisting of Great Bay and Little Bay, has extensive

Bellamy ' i'
Upper Piscataqua

Oyster

Ltt e AL Piscotaquo

Lamprey 2P 0m

Gulf of
Squamscott Maine
km

70050' 70040'

Figure 1. A map of the Great Bay Estuary system situated in

southeastern New Hampshire. The axial scale coincides with the

estuary's main channel and is divided into kilometers.

mud flat areas and includes several river tributaries. Depths

in the main channel are on the order of 10 m and maximum currents

are approximately 0.5 m/s. The Upper Piscataqua and its

tributaries are less significant to this study because of a

much smaller tidal prism. The upper estuary is connected to

the Gulf of Maine by the Lower Piscataqua River whose tidal

channel has a typical depth of 15 m, and maximum currents in

the range from 0.5 to 2 m/s. The estuary is characterized by

a low river discharge to tidal prism ratio which during the

measurement period was less than 1%. Consequently, density

gradients are small, and tidal currents are much larger than

the steady-state circulation. Data taken in the NOS/UNH

measurement program have been summarized by Swenson et al.

(1977) and Silver and Brown (1979).

Measurements of sea level and current used in this study

were made at the sites shown in Fig. 2. Most sea level mea-

surements were made by NOS using automatic digital recording

tide gauges, which employed a float in a tidal well. The UNH

station (T-UNH) used a resistance gauge. Currents were mea-

sured by NOS using Savonious rotor current meters deployed at

depths of 4.57 m and 9.15 m below MLW where possible. Results

from an additional UNH current meter (C-UNH) mounted 0.75 m

above the bottom are used in this study. Representative sea

level and current data are summarized in Figs. 3 and 4, respec-

tively. The direction of the longitudinal component was determined

430i-

T-16

�-uN~ , C;i24 ' :
, . . C 104

T-, . 1
seav
!. am

. 'j 0 km 5
70050' 70040'

Figure 2. Location map of the tidal elevation stations (A and A)

and current meter moorings (e and o) in the Great Bay Estuary, NH.

Solid symbols indicate current and sea level stations used in the

dynamic study of the four hatched areas.

0-3 T-16

-3 T-14

w | T-12

o03-I T-I I

-2
o | SEAVEY

0 T -5

-2
1I0....'' '1' .......'1 ''''' .........'''''' .........'l' '''''' .. ... . . . .
10 20 30 9 19 29 8 18 28
JULY AUGUST SEPTEMBER
1975

Figure 3. Representative sea level data from the Great Bay Estuary.

033~~~~~~ ~C 131 -A
.5

15 3C 131-B
.5;

0-I I C 124-A

IJ ok C 19-A

= o-1 C 119-B

--I

-1

C 104lll-lllIltilsitibltllilltlmlsill ll-11

I 0 20 301 9 19 29 18
JULY AUGUST SEPTEMBER
1975

Figure 4. Representative longitudinal current data for the

Great Bay Estuary. Suffixes A and B refer to measurements

made at depths of 4.75 and 9.15 m below MLW, respectively.

from local topography with the downstream direction considered

positive.

Cross-Section Averaged Current

Vertically averaged measurements of current were used to

estimate time series of cross-section averaged current using

Eqs. (5) and (6) which require tidal prism estimates. Tidal

prism was computed from an analysis of low and high water

volume distribution and is discussed in Appendix A. This

procedure for estimating the cross-section averaged current

removes the time-averaged current, but the error is small in

the Great Bay estuary since fresh water flow is low.

To determine the current distribution between measurement

stations, an average current, Ua , was estimated at half-kilometer

intervals using Eq. (7). In Appendix A it is shown how the

average tidal currents could be related to maximum tidal

currents for both the spring and neap tides. The results are

summarized in Fig. 5.

Cross-section averaged currents at arbitrary locations, as

required in the AA term of Equation (4), were then computed

from the time series of the nearest current station under the

assumption that current amplitude is proportional to the local

value of Ua. Similarly, the segment-averaged currents, neces-

sary for computing the LA term of Equation (4), were evaluated

under the assumption that the segment-averaged amplitude is

proportional to <Ua> as provided in Equation (8). An analysis

2.5 -

Maximum Spring Current
.......... Maximum Neap Current
2.0 ---- Average Current

a-
0c

Ir5 10 15 20 25
1II: 2
i'

5 10 15 20 25

DISTANCE (kin)

Figure 5. Great Bay Estuary tidal current distribution.

Distance corresponds to the axial scale shown in Fig. 1.

of the errors associated with estimating tidal prism and cross-

section area distribution in the Great Bay system indicates

that the uncertainty in using this procedure is less than +16%.

Tidal Analysis

A harmonic analysis was performed on sea levels and cross-

section averaged currents. The results were obtained using a

modified version of the NOS analysis described by Dennis and

Long (1971) and are tabulated in Appendix B. Sea level cotidal

charts for the principal semi-diurnal, M2 and diurnal, K1

constituents are shown in Figs. 6 and 7, respectively. The

corresponding cotidal charts for currents appear in Figs. 8 and

9. The amplitudes of the M2currents were found to be 1.5 + .2

times the average current Ua at each of the current stations.

This result was combined with the average current distribution

shown in Fig. 5 to estimate M2 amplitudes between current

stations.

Dynamic Analysis

Estimates of the dynamic terms in Eq. (4) are computed for

the four segments shown in Fig. 2. Each segment includes a

current station and is identified by the current station

designation. Tidal elevation stations bracket the segments at

their upstream and downstream ends. Time series for terms on

the right-hand side of Eq. (4) are computed for each segment

using appropriate sea level and current data (see Figs. 3 and

**.0k 4' .. 43q'~

"'~~~~~~~~~~~~~~~~~~~~~s0
s ~ ~ ~ ~ ~ ".s $ "i" ) . . : Io:. ..LL )~

:~~..... z -h ~

| T'50 71~4o. 70�50' rd'4o'
� II I~ ' I I

Figure 60 Corange and cophase charts for the M2 constituent of sea level are shown in (a) and (b),

respectively. Amplitudes are in meters, and Greenwich phases are in degrees.

.14
:. Ij I" : I o '

'~ ~ ~ ~ ~~0~ 7d4O 7d' :
I~~~~ I/~~~
":.'~~~~~~~~~~~~~~~~~~~~~~~~ 3'b-~

100501 ' 1(~' 1007 0'

Figure 7. Corange and cophase charts for the K1 constituent of sea level are shown in (a) and (b),

respectively. Amplitudes are in meters, and Greenwich phases are in degrees.

I,; d 4,II TO 4,C

It 15�' i� 70040' . . 7 10'd1 .4 7d'40,

Figure 8. Corange and cophase charts for the M2 constituent of cross-section averaged, longitudinal

current are shown in (a) and (b), respectively. Current amplitudes are in m/s, and.Greenwich phases

are in degrees. Current amplitudes between current stations, indicated by the dots (.), were

determined using the current distribution results shown in Fig. 5.

I' ,- 4 < 7 X 4 0

Figure 9. Corange and cophase charts for the K1 constituent of cross-section averaged, longitudinal

current are shown in (a) and (b),.respectively. Current amplitudes are in m/s, and Greenwich phases

are in degrees.

4), For example, Table I outlines how dynamic terms were

estimated for segment C119. Current differences and segment

averages were estimated using the velocity distribution shown

in Fig. 5 and current time series. The pressure gradient term,

PG, was estimated from sea level data using relations similar

to those in Table 1. For cases where sea level and current

data did not coincide, a prediction of PG based on harmonic

analysis was computed for the time period of the current

observations. Finally, segment-averaged stress is computed

according to Eq. (4). Time series of these results for each

segment are summarized in Fig. 10.

Friction coefficients CF were computed as segment-averaged

stress divided by the product of density times current velocity

squared. Table.2 lists friction coefficients for maximum

current calculated using segment-averaged velocities. Also pro-

vided is-a second'friction coefficient C' which is based on

current at the current measurement sites. Rate of energy

dissipation per unit area was estimated as the product of

segment-averaged current times segment-averaged stress. Mean

dissipation rates and RMS values of stress for each segment are

provided in Table 3.

Discussion

These results clearly show that the primary force balance

is between the pressure gradient and bottom stress. This is

in agreement with the conclusions of Brown and Trask (1980) who

Table 1. Details of dynamic term estimates for segment

Cl19 which extends from sea level station T-12 to T-ll and

includes current station C119. (See Fig. 2 for station loca-

tions).

Term Estimate

<Ua>
-pH a C119
a C119
TU a) - 2 Tua) 2
-pH 6( S (AA) T- 11 T-12 g2(xT 1lXT 12)

-pgH Fax (PG) -H -l
a LCa cll~J

-pgH dn (PG) -pgH (nT-11 x- T-12) (XT11 XT-12)

LA
AA
C 131 PG ..........
I 1 '-"' - wn1
O~~~~~~ - ~~~STRESS ",...W'.- .......

LA
AA
C 124
PG

nn-nnmnn 101 11n
-10
z
=~".. ................................ L................
g -A AA

tl llQhll l PG C 119

>. rell m an
l3 1gi U STRESS

;-____ _. ______T _ _.____ __ _ .._..'. ___.......,.. L A
AA

j111l-Ml-4llhlahfi,.hu PG c1o4

-|C 104

10 20 301 9 19 29 8 18
JULY AUGUST SEPTEMBER
1975

Figure 10. A summary of dynamic analysis time series at four

locations in the estuary. The terms are local acceleration (LA),

advective acceleration (AA), pressure gradient (PG), and stress

(<Tb>) as defined in Eq. (4). All terms are in units of N/m2.

Table 2. Summary of friction coefficients. CF is the segment-

averaged friction coefficient defined as <Tb>(P2)-I where

is the segment-averaged current. C' is a friction coefficient

defined by <Tb>(pUs)-1 where Us is the cross-section averaged

current at the current meter station.

Segment CF CF

C131 .038 .023

C124 .035 .007

C119 .015 .025

C104 .054 .063

Table 3. RMS values of segment-averaged stress and mean values

of dissipation rate per unit area.

Stress Dissipation
RMS Value Mean Value
Segment (N/m2) (N/m-s)

C131 2.7 �+ .6 .5

C124 10.4 + 1.1 5.1

C119 8.8 + 1.8 5.9

C104 9.3 � 1.9 3.4

applied the same dynamic inference method to a 2 km segment

centered at station C-UNH. Thus the pressure gradient/bottom

stress balance is maintained throughout the length of the main

channel. Experimental results for the Great Bay Estuary are

also consistent with a scaling analysis of the equation of

motion discussed by LeBlond (1978) which showed that shallow

rivers such as the Fraser and St. Lawrence have frictional

forces exceeding accelerations over most of the tidal cycle.

Stress values given in Table 3 for segments C124, C119 and

C104 are approximately twice as large as the stress estimated

by Brown and Trask (1980). Since a major factor in the choice

of the C-UNH site was the channel segment's uniformity, lowered

stress values are expected. Our stress of 2.67 N/in2 for

segment C131 compares with stress estimates of 2.32 N/rn2 and

3.15 N/m2 made by Swift et al. (1979) in Little Bay using
turbulence measurements and a current profiling technique,

respectively. This comparison suggests that segment-averaged

stress estimates are representative of local bottom stress

values under conditions of slowly varying topography.

All stress values discussed here are total bottom stress

values and include both skin friction and form drag due to

topographic features and individual roughness elements.

Because the skin friction component responsible for initiating

sediment movement may be much smaller than the total stress,

caution should be taken in using these values directly for

drawing conclusions in connection with sediment transport.

The dynamic analysis presented here has first order

accuracy and the results should be interpreted accordingly.

The conditions for application of Equation (4) were not satis-

fied exactly and errors were introduced in estimating terms as

summarized in Table 1. For example, the measurements used to

estimate terms did not allow computation of steady state contribu-

tions. The absolute datum for sea level measurements was not

known with sufficient accuracy, so mean pressure gradients were

neglected. The method for estimating cross-section averaged

velocity also eliminated the time-invariant component. There-

fore, second order effects leading to nonlinear residual

currents could not be inferred. However, the overall error in

these tidal stress estimates due to the neglect of steady state

contributions is small and is estimated to be less than 5% at

all locations. Similarly, because the LA and AA terms in

Equation (4) are both small, errors in estimating cross-section

and segment-averaged currents do not contribute significantly

to uncertainties in estimating stress. Instead, accuracy is

limited primarily by the ability of the tide gauges to resolve

small changes in height. Uncertainty estimates for stress from

all sources are provided in Table 3.

The dynamic analysis results indicate that, when modeling

estuarine processes, it is important to parameterize stress

terms accurately. In this connection Table 2 provides average

friction coefficients CF for each segment. A friction coeffi-

cient C', based on segment-averaged stress and a single point

current measurement, is listed only to show the differences

which may arise by using an inappropriate definition. Segment-

averaged friction coefficients, with the exception of C119,

differ by less than 55%. The lower value of CF for segment

C119 can be explained in part by the distribution of current

over the cross-section. Cross-channel transect current measure-

ments reported by Swenson et al. (1977) and dye study results

described by Schmidt (1980) indicate that, for much of the

Lower Piscataqua between sea level stations T-14A and T-11,

currents are concentrated in a narrow core. Velocity gradients
near the bottom and sides are lower, resulting in reduced

friction coefficients in comparison with other parts of the

estuary where more lateral mixing of momentum occurs.
Energy dissipation rates given in Table 3 show that most

dissipation takes place in the Lower Piscataqua with an order

of magnitude decrease in dissipation upstream from segment

C124. In the upper part of the estuary, cumulative prism has
decreased so that both current and stress are also much less.

The effects of dissipation are seen in the cotidal charts for

the M2 constituent of sea level (see Fig. 6). Amplitude
attenuation and phase delay changes are rapid in the Lower

Piscataqua, while amplitude and phase above C124 are compara-

tively uniform. The phase of the M2 constituent of current has

similar behavior, as seen in Fig. 8. The direct effects of

dissipation on current amplitude, on the other hand, are not

readily apparent on the cotidal chart because of the strong

dependence of current amplitude on local cross-section area.

Acknowledgements

This work was made possible with the field assistance of

Mr. Eric Swenson and Drs. Ronnal Reichard and Barbaros Celikkol.

Mr. Richard Trask and Dr. J.D. Irish provided valuable help in

the data analysis phase of this effort. Our appreciation is

also extended to NOS who acquired much of the sea level and

current data used in this study and made it available to us.

This material is based on research supported in part by

the Sea Grant Office of the National Oceanic and Atmospheric

Administration, U.S. Department of Commerce under Grant No. 04-

8-MO0-79, while the authors' time spent in manuscript prepara-

tion was supported by the National Science Foundation under

Grant 0CE78-26229.

References

Bowden, K.F. and L.A. Fairbairn, 1952, "A determination of

frictional forces in a tidal current," Proc. Roy. Soc., 214,

371-392.

Bowden, K.F., L.A. Fairbairn, and P. Hughes, 1959, "The dis-

tribution of shearing stresses in a tidal current,"

Geophys. J. R. Astr. Soc., 2, 288-305.

Brown, W.S. and E. Arellano, 1979, "The application of a seg-

mented tidal mixing model to the Great Bay Estuary,

N.H.," UNH Sea Grant Technical Report UNH-SG-162, 47 pp.

Brown, W.S. and R.P. Trask, 1980, "A study of tidal energy

dissipation and bottom stress in an estuary," J. Phys.

Ocean., 10, 1742-1754.

Dennis, R.E. and E.E. Long, 1971, "A user's guide to a computer

program for harmonic analysis of data at tidal frequencies,"

NOAA Technical Report NOS41.

Gardner, G.B., A.R.M. Nowell and J.D. Smith, 1979, "Turbulent

processes in estuaries," Wetland and Estuarine Processes and

Water Quality Modeling Workshop, U.S. Army Corp of Engineers,

New Orleans.

LeBlond, P.H., 1978, "On tidal propagation in shallow rivers,"

J. Geophys. Res., 83, 4717-4721.

Munk, W.H. and D.E. Cartwright, 1966, "Tidal spectroscopy and

prediction," Phil. Trans., A, 259, 533-581.

Schmidt, E., 1980, "Dispersion studies in the Piscataqua River,"

UNH Sea Grant Technical Report UNH-SG-167, 42 pp.

Silver, A.L. and W.S. Brown, 1979, "Great Bay estuarine field

program 1975 data report part 2: temperature, salinity

and density," UNH Sea Grant Technical Report UNH-SG-163,

59 pp.

Smith, J.D. and S.R. McLean, 1977, "Spatially averaged flow

over a wavy surface," J. Geophys. Res., 82, 1735-1746.

Swenson, E., W.S. Brown and RoP. Trask, 1977, "Great Bay

estuarine field program 1975 data report Part 1: currents

and sea levels," UNH Sea Grant Technical Report UNH-SG-

157, 109 pp.

Swift, M.R., R. Reichard and B. Celikkol, 1979, "Stress and

tidal current in a well-mixed estuary," ASCE J. Hydraul.,

105, 785-799.

Wolf, J., 1980, "Estimation of shearing stresses in a tidal

current with application to the Irish Sea," In: Marine

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344.

Appendix A

Volume, Area and Current Distribution

Table Al lists volume, area and current distribution for

the Great Bay Estuary. Cumulative low water volume (LWV),

cumulative high water volume (HWV), cumulative prism and cross-

section area were estimated for average conditions in the

spring/neap cycle using NOS sea level data, NOS charts and UNH

bathymetry data reported by Swenson et al. (1977). The volume

and area distributions presented here are primarily based on

estimates made for the main channel by Brown and Arellano

(1979). Their results were modified for this study to include

volume distribution for the whole system. Added to Brown and

Arellano's (1979) estimates were volume contributions due to

river tributaries (listed separately in Table A2), and a prism

contribution of 4.96 x 106 m3 which enters the channel south of

the main estuary axis at 21.2 km on the estuarine scale shown

in Fig. 1 of the main text. Fig. Al shows low and high water

volume distribution, plotted from Table Al, while Fig. A2

depicts cumulative prism and cross-section area.

Table Al. Cumulative volume, area and velocity distribution for the
Great Bay Estuary, NH. Distance corresponds to the channel axis

scale shown on the location map, Fig. 1. LWV and HWV are the cumu-
lative low water volume and high water volume, respectively, for
average conditions. Prism is HWV minus LWV. Area is estuary cross-
section area. Average current is prism divided by the product of area

times one half of the semi-diurnal tidal period. At distances of 5.8,
11.6, 18.0 and 22.8 km, maximum neap and spring currents were obtained
directly from current measurements. Values at other points were ob-

tained using average current and the average ratios of (maximum neap
current) (average current)-1 = 1.77, and (maximum spring current)
(average current)-l = 2.41.

LW -x_6 -6 -6 Maximum Maximum
Distance LWVxlO HWVxO'6 PrismxlO-6 Area Average Current Neap Current Spring Current
(km) (m3) (m31 (m3) (m2) (m/s) (m/s) (m/s)
0.0 2.20 7.33 5.13 1440 .159 .281 .383
0.5 2.52 8.45 5.93 1420 .187 .331 .451
1.0 2.93 9.65 6.72 1920 .157 .278 .378
1.5 3.37 11.13 7.76 2580 .135 .239 .325
2.0 3.90 13.19 9.29 3580 .116 .205 .280
2.5 4.48 16.20 11.72 7780 .067 .119 .161
3.0 6.45 22�02 15.57 13740 .051 .090 .123
3.5 11.32 30.89 19.57 7980 .110 .195 .265
4.0 13.96 36.23 22.27 8560 .116 .205 .280
4.5 16.61 40.15 23.54 6100 .173 .306 .417
5.0 18.43 44.43 26.00 6880 .169 .299 .407
5.5 21.05 47.69 26.64 6980 .171 .303 .412
5.8 22.81 50.12 27.31 5120 .239 .438 .563
6.0 23.98 51.74 27.76 5080 .244 .432 .588
6.5 26.19 54.61 28.42 7640 .166 .294 .400
7.0 29.49 58.96 29.47 8580 .154 .273 .371
7.5 33.33 63.70 30.37 6820 .199 .352 .480
8.0 36.24 67.62 31.38 6980 .201 .356 .484
8.6 41.13 77.38 36.25 11760 .138 .244 .333
9.4 46.33 83.94 37.61 9960 .169 .299 .407
9.9 51.35 93.57 42.22 7780 .243 .430 .586
10.4 54.73 97.97 43.24 6020 .321 .568 .774
10 9 57.38 101.35 43.97 4460 .441 .781 1.063
11.4 58.44 102.95 44.51 4680 .425 .752 1.024
11.6 59.29 103.98 44.69 1860 1.075 1.375 1.625
11.9 60.55 105.52 44.97 5380 .374 .662 .901
12.6 74.42 128.46 54.04 4680 .517 .915 1.246
13.1 76.42 131.15 54.73 4300 .569 1.007 1.371
13.6 78.16 133.20 55.04 3840 .629 1.113 1.516
14.1 79.89 135.83 55.94 5020 .498 .881 1.200
14.6 82.16 138.57 56.41 5300 .476 .843 1.147
14.8 83.08 139.73 56.65 4660 .544 .963 1.311
15.1 84.48 141.48 57.00 3700 .689 1.220 1.660
15.6 87.10 144.57 57.47 4380 .587 1.039 1.415
16.1 89.11 146.95 57.84 3340 .774 1.370 1.865
16.5 90.37 148.37 58.00 4530 .573 1.014 1.382
16.6 90.68 148.72 58.04 2880 .901 1.595 2.171
17.1 92.08 150.21 58.13 3780 .689 1.220 1.660

Table Al. Continued

LW-x1~6 H ~6 P -6 Ae Araeuen Maximum Maximum
Distance LWVxlO6 HWVxlO6 PrismxlO Area Average Current Neap Current Spring Current
(km) (m3) (m3) (m3) (m2) (m/s) (m/s) (m/s)
17.6 93.96 152.11 58.15 4420 .588 1.041 1.417
18.0 95.62 153.98 58.36 5420 .482 .813 1.188
18.1 96.04 154.45 58.41 5140 .508 .899 1.224
18.6 98.38 157.25 58.87 4780 .551 .975 1.328
18.8 99.20 158.34 59.14 4770 .552 .977 1.330
19.1 100.43 159.97 59.54 7960 .335 .593 .807
19.6 102.95 164.55 61.60 6760 .408 .722 .983
20.1 105.90 168.36 62.46 7340 .378 .669 .911
20.6 109.26 172.34 63.08 8060 .350 .620 .844
21.1 112.17 176.29 64.12 6240 .459 .812 1.106
21.6 115.53 185.36 69.83 9040 .346 .612 .834
22.1 119.68 190.24 70.56 12140 .260 .460 .627
22.6 125.26 196.80 71.54 13500 .237 .419 .571
22.8 127.79 199.68 71.89 10300 .313 .563 .750
23.1 131.58 203.99 72.41 14260 .227 .402 .547
23.6 138.00 211.84 73.84 13740 .240 .425 .578
24.1 144.29 219.30 75.01 13380 .251 .444 .605
24.6 150.27 226.69 76.42 15920 .215 .381 .518
25.1 156.91 235.98 79.07 19440 .182 .322 .439

Table A2. Tributary contributions to the Great Bay Estuary

cumulative volume distribution.

LWVxlO-6 HWVxlO-6 Prism x 10-6
Location (m3) (m3) (m3)

Squamscott 1.88 6.47 4.58

Lamprey .32 .86 .54

Oyster 2.00 4.82 2.82

Bellamy 1.24 3.70 2.46

Upper Piscataqua 11.47 19.64 8.17

250 -

*-----....... High Water Volume
rt o
E- Low Water Volume .
_ 200-
D :
0

> 100 -
t-
~~~~~~~XX
-J

o 50-
_>..

2~~~~~~~ ...�
o :..o-/

Wn .---'-a I

5 10 15 20 25

DISTANCE (kin)

Figure Al. Great Bay Estuary cumulative volume distribution.

Distance corresponds to the axial scale shown in Fig. 1 of

the main text.

100 - - 20
---- Cumulative Prism
" 90- cN
E ........ Cross Section Area E
co ,80-
' -15
70- :
x
; 60-

a 50- -I0 z
W 40- j
--20 < '"N S ad '' U5 U)
130- U)
_j20- 3 '� 1 :0 r
O

10 ~ ~ , I I

5 10 15 20 25
DISTANCE (km)

Figure A2. Great Bay Estuary cumulative prism and cross-section

area distribution. Distance corresponds to the axial scale shown

in Fig. 1 of the main text.

The distribution of average current listed in Table Al was

obtained by dividing cumulative prism by cross-section area

times one half the semi-diurnal tidal period. The average

current, therefore, represents a current spatially averaged

over the channel cross-section and time-averaged over half a

semi-diurnal tidal cycle during average conditions in the

spring/neap cycle. The average current at each tidal station

was then compared to maximum current during both neap and

spring tide conditions. Ratios of maximum current to average

current are given in Table A3. Ratios at different stations,

with the exception of 0124, are seen to be consistent (within

10%). The inconsistency of C124 is explained in part by its

very small cross-section area (see Fig. A2 at 11.6 kin). C124

was, therefore, omitted in computing "average" maximum current

to average current ratios. The "average" maximum current to

average current ratios were then used to infer maximum current

distributions for both neap and spring tidal conditions.

Maximum and average current distributions given in Table Al are

plotted in Fig. 5 of the main text.

Table A3. Ratios of maximum current during neap and spring conditions

to average current. Station C124 was neglected in calculating average

ratios.

Maximum Neap Current Maximum Spring Current
Station average current average current

C131 1.83 2.36

C124 1.28 1.51

Cll9 1.69 2.46

C104 1.80 2.40

average ratios 1.77 2.41

Appendix B

Tidal Analysis

Harmonic constituents were obtained for sea level and

cross-section averaged current using a modified version of the

harmonic analysis method described by Dennis and Long (1971).

The 95% confidence limits were estimated for the dominant M

constituent using a method adapted from procedures outlined by

Munk and Cartwright (1966). They relate error estimates to a

noise parameter defined as the ratio of background noise energy

density in the frequency domain at the semi-diurnal tidal

frequency to the corresponding value for tidal energy. The

noise parameter is then used to find amplitude and phase

uncertainties from figures found in Munk and Cartwright (1966).

The results of the tidal analysis are listed in Tables Bl

and B2 for constituents found to be significant. Constituents

considered significant had sea level amplitude greater than I

cm or current amplitude greater than I cm/sec.

Table B1. Summary of principal sea level harmonic constituents for

locations in the Great Bay Estuary, N.H. The parameters K and G are

local and Greenwich epoch, respectively. The amplitude and phase

uncertainties (see text) are shown for the M2 constituent only. The

variances for the observed and residual signal are included.

T-UNH r-16 T-14
43� 05.4'N 430 07.8'N 430 07.3'N
70� 51.9'W 700 50.81W 700 49.7'W
Amplitude : G Amplitude : G Amplitude < G
Constituents (m) (deg) (deg) (m) (deg) (deg) (m) (deg) (deg)

M2 .87+.04 29+2 171+2 .83+.04 24+2 166+2 .94+.03 3+2 145+2
S2 .13 80 221 .07 51 193 .12 38 179
N2 .19 342 124 .18 344 126 .21 335 116
K1 .11 160 301 .11 172 313 .14 162 303
01 .10 145 287 .09 147 288 .10 134 275
M4 .03 158 300 .01 252 34 .03 153 294
M6 .02 50 191 .03 79 220 .02 48 189
Recorded
variance 4.59 x 10-1 4.82 x 10'- 5.23 x 10-1
(m2)
Residual
variance 2.08 x 102 2.20 x 9.60 x 10-
(m2)

T-12 T-l1 Seavey
43� 05.8'N 430 05.1'N 430 04.8'N
70� 47.0'W 700 45.8'W 700 44.5'W
Amplitude < G Amplitude c G Amplitude < G
Constituents (m) (deg) (deg) (m) (deg) (deg) (m) (deg) (deg)

M2 1.00+.03 346+2 128+2 1.12+.03 336+1 117+1 1.20+.02 333+1 114+1
S2 .15 29 170 .15 10 152 .17 8 149
N2 .23 318 99 .25 308 90 .28 306 87
K1 .13 140 282 .13 140 282 .13 138 279
01 .10 131 273 .11 123 264 .11 121 262
M4 .03 101 243 .03 69 210 .02 99 241
M6 .01 100 242 .01 61 202 .01 117 259
Recorded
variance 6.05 x 10l1 7.06 x 10' 8.16 x 10-'
(m )
Residual
variance 1.97 x 10-2 7.44 x 10'3 7.43 x 10'3
(m2)

Table Bi. Continued.

T-5
43� 04.4'N
70� 43.1 'W

Amplitude K G
Constituents (m) (deg) (deg)

M2 1.29+.02 325+1 106+1
S2 .19 359 140
N2 .30 297 78
K1 .14 132 274
01 .12 115 256
M4 .02 52 193
M6 .01 84 226
Recorded
variance 9.36 x 10-1
(m2)
Residual
variance 7.39 x 10
(m2)

Table B2. Summary of significant current harmonic constituents.

The parameters K and G are local and Greenwich epoch, respectively.

The amplitude and phase uncertainties (see text) are shown for the

M2 constituent only. The variances for the observed and residual

signal are included.

C1 31 C124 C1 19
43� 06.0'N 43� 07.0-N 43� 05.5'N
700 51.7'W 70� 49.7'W 700 45.8'W
Amplitude K G Amplitude K G Ampli tude K G
Constituents (m) (deg) (deg) (m) (deg) (deg) (m) (deg) (deg)

M2 .31+.01 120+2 261+2 1.48+;08 120+3 262+3 .70+.03 109+3 248+3
S 2 .03 186 328 .19 168 309 .10 160 286
N2 .06 124 266 .26 99 241 .12 96 225
K1 .03 294 76 .09 262 44 .04 265 44
01 .02 212 354 .08 254 35 .04 254 32
M44 .03 267 49 .04 18 159 .02 89 248
M 6 .05 182 324 .14 189 330 .07 180 318
Recorded
variance 6.82 x 1-2 1.26 x 100 1.28 x 101
(m/s)2
Residual
variance 3.17 x 10-3 5.11 x 10-2 4.575 x 10'3
(m/s)2

C104
430 04.6'N
70� 43.0'W
Amplitude K G
Constituents (m/s) (deg) (deg)

M2 .47+.02 107+3 248+3
S2 .05 144 286
N2 .10 84 225
K1 .03 263 44
01 .02 251 32
M4 .04 107 248
M6 .03 176 318
Recorded
variance 1.28 x 101
(m/s)2
Residual
variance 4.58 x 10'3
(m/s)2

)` 40