Diurnal Cross-Shore Exchange on the Inner-Shelf in Southern Monterey Bay, CA 

Operational Oceanography & Meteorology  

LCDR John Hendrickson 

9/19/2008  

 

 

 

Abstract

Diurnal Cross-Shore Exchange on the Inner-Shelf in Southern Monterey Bay, CA

John Hendrickson, Jamie MacMahan, Ed Thornton, Mike Cook, Tim Stanton, Ad Reniers

The effects of a strong diurnal sea-breeze on the cross-shore exchange on the inner shelf is investigated by comparing wind stress estimates and ocean currents over the vertical at three locations in southern Monterey Bay, CA . Cross-shore exchange on the inner shelf significantly impacts the ecosystem by transporting heat, nutrients, pollutants and phytoplankton between the inner-shelf and surf zone. Spectral analysis of surface winds at three coastal locations within the bay indicates a significant diurnal wind component. The observed subaqueous velocity profiles and pressure time series are measured by bottom mounted 1200-kHz Broad-band Acoustic Doppler Current Profilers (ADCPs) deployed at three separate alongshore locations in ~13 m water depth. The velocity and pressure signals were collected continuously at 1 Hz for all three locations for over 2 years. The cross-shore wind stress is significantly correlated to the cross-shore subaqueous velocity with onshore flow near the surface and offshore flow near the bottom. Cross-rotary spectral analysis is used to describe the rotational coherence and phase over the vertical with respect to the wind stress. It is further hypothesized that normally-incident sea-swell waves (0.04-0.2 Hz) will modify net cross-shore transport. Cross-shore transport is evaluated for conditions that are dominated by either waves or cross-shore wind stress. Results indicate that when waves are small, the cross-shore wind stress associated with the diurnal sea-breeze is the primary forcing mechanism for cross-shore exchange on the inner-shelf.

1. Introduction and Literature Review

On continental shelves all over the world, cross-shelf circulations influence the water column

density structure and the distributions of heat, salt, phytoplankton, nutrients, and pollutants.

Cross-shelf exchange is an important mechanism for supplying nutrients to continental shelf

ecosystems, which are some of the most productive on Earth (Falkowski et al., 1998). On the

inner continental shelf in particular, cross-shelf exchange is thought to influence the ecosystem

by transporting heat, nutrients, and larvae between the surf zone and mid-shelf (Roughgarden et

al., 1988).

The inner shelf is a complex region offshore of the surf zone, where the surface and bottom

boundary layers interact (Austin et al., 2002, Lentz, 1994, 1995). The location of the boundary

between the inner shelf and the mid-shelf changes with time, depending on the thicknesses of the

surface and bottom boundary layers, which determine the water depth where the boundary layers

overlap. As a result of the overlapping boundary layers, the inner shelf exhibits a divergence in

the cross-shelf transport driven by along-shelf winds, which leads to coastal upwelling and

downwelling (Ekman, 1905; Austin et al., 2002).

The mechanisms that drive cross-shelf flow over the inner shelf are not well understood.

In the middle and outer regions of the shelf, along-shelf winds drive coastal upwelling and

downwelling circulations that transport material and heat in the cross-shelf direction (Ekman,

1905; Smith, 1981). Observations on the North Carolina (Lentz, 2001), Oregon (Kirincich et al.,

2005), and California (Cudaback et al., 2005) continental shelves and numerical model studies

(Austin et al, 2002; Tilburg, 2003) show, however, that along-shelf wind driven upwelling or

downwelling is not sufficient to provide transport to or from a coastal boundary on its own.

Other proposed mechanisms for cross-shelf exchange include vertical migration of larvae and

along-shelf variations in topography (Austin et al, 2002). Cross-shelf wind stresses have usually

been assumed ineffective at driving shelf circulations (Csanady, 1978). However, in this

investigation, we will look at the effects of a strong diurnal sea-breeze on the cross-shore

exchange on the inner shelf.

Over middle and outer continental shelves, the cross-shelf momentum balance is typically

geostrophic on subtidal time scales, meaning the cross-shelf pressure gradient force balances out

the Coriolis force as a result of the along-shelf flow (Noble and Butman, 1983; Liu and

Weisberg, 2005). Therefore, the cross-shelf wind stress is relatively unimportant in the steady

depth-average momentum balance at mid-shelf. The cross-shelf wind stress, in addition to being

important in the momentum balance, may also drive a substantial cross-shelf circulation.

Analytical theories (Ekman, 1905; Garvine, 1971) and a recent simplified 2-D numerical

modeling study (Tilburg, 2003) have suggested that cross-shelf winds could drive significant

cross-shelf circulations where the water is so shallow that the circulation through the entire water

column takes place within the overlapping top and bottom boundary layers of the inner shelf.

Numerical modeling studies (Li and Weisberg, 1999) off the West Florida Shelf reveal that the

cross-shelf wind stress plays an important role in driving along-shelf and cross-shelf currents

over that inner shelf. In the Santa Barbara channel in California, strong offshore wind

significantly correlated with a two-layer cross-shelf circulation over the inner shelf, with surface-

intensified offshore flow in the upper water column and onshore flow in the lower water column

(Cudaback et al., 2005).

It is difficult to separate the influences of waves, cross-shelf wind, and along-shelf wind in

observational studies because all three types of forcing are normally correlated. With over 2-

year-long time series of wind, wave, and velocity data, however, we are able to look at the

structure of the cross-shelf flow during times when only one of the three types of forcing was

strong. Cross-shore transport is evaluated for conditions that are dominated by either waves or

cross-shore wind stress. We present observations that demonstrate that cross-shelf winds are

more effective than along-shelf winds at driving cross-shelf exchange flow at an inner shelf site

dominated by a diurnal sea breeze.

2. Methodology

2.1 Monterey Bay

Strong land-sea breeze circulation often dominates the surface wind field over Monterey Bay,

especially during the summer. Typically sunlight warms the land surface in the Salinas Valley

(east of Monterey Bay) beginning at sunrise. The warm ground heats the cooler surface layer of

the atmosphere and convection proceeds with rising air over the Salinas Valley. This action in

turn causes cool air over Monterey Bay to flow from the sea toward the land. By noon a

circulation is established with air flowing from sea to land near the surface and from land to sea

at about a kilometer altitude. This process often produces westerly surface: winds of 8 to 12 m/s

by about 4 pm local time. After sunset the air over the ocean cools rapidly and the process

reverses due to the relatively warm sea surface at night, but is significantly weaker.

2.2 Raw Data

We use time series of water velocity profiles, wave, and meteorological data that extend over 2

years from 3 separate locations in southern Monterey Bay (Figure 1). Each time series are from

a bottom-mounted acoustic Doppler current profiler (ADCP) located at 12-m water depth (just

outside the surf zone) and connected to a shore laboratory by underwater power and fiber-optic

data transmission cables. Meteorological data are from two masts, one located at Marina Airport

and the other at Del Monte Beach.

 

Figure 1 Map of Monterey Bay and locations of the 3 ADCP's

The first step in analyzing the raw data sets is to remove bad data. Each time series was first run

thru a 3- standard deviation filter three times to remove any spikes. Then, a visual inspection of

each column of data was done ensuring all bad data points have been resolved.

2.3 Normalizing the Data

The ADCP data was then put into a depth-relative framework. Instead of using velocities for a

corresponding depth or ADCP bin, velocities were interpolated to a ratio scale giving the height

in the water column (z) versus the depth of water (H) at the location. The scale was ordered 0 to

1.5, with 0 at the bottom and 1.5 at the top of a high wave crest. The scale was set with a 0.05

increment. To account for tidal action and low-frequency infra-gravity waves on the water depth

of the location, H was calculated by taking the low-frequency oscillation ( < .04 Hz) of the

instantaneous depth of water. This technique allowed for direct comparison of results between

instruments and between different times using the same instrument, as the data at the locations

would be in the same relative position in the water column.

2.4 Coordinate System

Principal Component Analysis is used to determine the coordinate frame orientation due to the

tides moving parallel shore (Rosenfeld, etal., 2008). The along shore component is defined as

the major principal direction of the depth averaged flow between the normalized depths of 0.25

to 0.75. These depths were chosen taking into account bottom friction and surface gravity waves

respectively. The resulting minor principal axis is roughly perpendicular to the local isobaths.

A west coast coordinate system is used where x is positive onshore eastward, y is positive along

shore northward, and z is positive upward. The surface wind stress is denoted as τs = (τsx , τs

y)

and the horizontal component of the subaqueous velocity is u = (u, v).

2.5 Wind Stress

Surface wind stress is calculated from STRESSTC (Smith 1988) using wind speed and air

temperature at height 10 m above sea level. τsx and τs

y were then calculated and rotated to the

proper coordinate system.

2.6 Subaqueous Velocity

The ADCP’s are a 1200 kHz RDI Workhorse Monitor, with 0.5-m bins, deployed

in a bottom-mounted, upward-looking configuration. We used data from the bottom most

bin, at depth zbot = -10.5 m, to the top good bin, ztop = -0.5 m. We determined the top good bin

based on the bin-bin shear and the signal correlation returned by the ADCP. To calculate depth-

average velocities (z/h between 0 and 1), we assumed the velocity is constant from the lowest

ADCP bin to the bottom (z = -12 m), and from the top good ADCP bin to the water surface.

2.7 Waves

The significant wave height Hsig , dominant wave period Tw and wave speed c are calculated

from the ADCP velocity measurements. The predicted onshore volume transport due to

dominant waves, Qw, is (Longuet-Higgins, 1953): 2

cos16sig

w

gHw cQ θ=

where g is the acceleration due to gravity and �w is the direction the waves are going, measured

counterclockwise from the positive x axis. Therefore �w = 0° indicates waves propagating

directly onshore. It’s important to note, volume transport Qw takes place above the wave troughs

in an Eulerian reference frame. 2 cossig wH θ is the measure of the strength of the wave forcing at a

given time.

2.7 Removing Tides

The tidal velocities at Monterey Bay are dominated by both the M2 tide (the principal lunar

semidiurnal tide, with period 12.42 hr) and the K1 tide (the principal luni-solar diurnal tide, with

a period of 23.93 hr)(Rosenfeld et al, 2008). Both are relatively large (Figure 2). Because we

are interested here in the non-tidal component of the velocity, we subtract from the observed

velocity time series (at each ADCP bin depth) a least squares fit tidal prediction generated by T

TIDE (Pawlowicz et al., 2002). The principal meteorological constituent S1 (period of 24 hr)

must not be removed from the data since we are looking specifically at diurnal wind events. It is

also important to note that the tidal prediction must be run for 366 days or more in order for the

prediction to differentiate between S1 and K1. Finally, to avoid removing seasonal variability,

we limit the prediction to tidal frequencies greater than 1 cycle/month.

 

Figure 2.  Monterey Bay's top 8 tidal constuents

2.8 Creation of a Master Data set

Finally, after doing all the above functions to the raw data, a master data set must be created for

each location. That is, one .mat file that contains cross-shore and along shore wind stresses as

well as subaqueous u and v components. Significant wave height and period are also included,

all in hourly means. This now becomes my starting point from which all analysis is done. For

each location there are two master data sets, one with tides and one without.

2.9 Bin Averaging

We take advantage of the large number of synoptic wind and wave forcing events in each time

series to separate those events into cases where only the cross-shelf wind or the along-shelf wind

forcing is strong, and the other two forcings are weak. By examining those three cases

separately, we are able to isolate the effect of each forcing mechanism on the cross-shelf flow.

This also allows us to separate out when the significant sea breeze events occur and compare

them to the subsequent relaxation events (This is potentially the road I will be going down but I

am not there yet).

3. Results

To this point in my research, I only have preliminary results as discussed in my brief.

We will look at the Marina site first since the majority of the surface wind stress is shore normal.

Spectral Analysis was run on non-detided data in order to see if there was a correlation between

the subaqueous velocity(u and v components) and both the along shore and cross shore wind

stresses (Figure 3).

The spectral analysis indicates there is significant energy at 0.043 Hz, indicating a 24 hour

period. In comparing wind stresses, the diurnal effect is more than tenfold stronger in the cross

shore component. The u component of the subaqueous velocity at the surface contains a

majority of the energy as well. This would indicate that the diurnal sea breeze induced cross

shore wind stress acting on the ocean surface is forcing the u component significantly.

 

Figure 3. Spectral Analysis of subaqueous u and v components(near the surface) and the along shore and cross shore wind stresses.

 

To get an indication of how far down the water column the cross-shore wind stress forces, I ran

spectral analysis at z/h values of 0.75, 0.5 and 0.25 (Figs 4-6). At z/h = 0.75, the cross shore

velocity energy is significantly less than the along shore velocity energy at 0.043 Hz. This trend

continues down the column, indicating that the K1 constituent becomes significant deeper into

the water column as the S1 forcing reduces dramatically. There may also be a rotation in the

column. Cross rotary spectral analysis has not been done yet. Its also important to note that M2

begins to strengthen deeper down the column as well.

 

Figure 4. Spectral analysis for u and v at z/h = 0.75

 

Figure 5. Spectral analysis for u and v at z/h =0.5

 

Figure 6. Spectral analysis for u and v at z/h = 0.25

Coherence gives a measure of the dependence of two random variables. In our case, we

compared τsx and u as well as τs

y and v at different levels in the water column (Figs. 7-10).

Focusing on the cross-shore components, at the surface there is strong coherence between τsx and

u with no phase shift at 0.043 Hz. Deeper down the water column, the coherence reduces

slightly and there is a 180 deg rotation, indicating offshore flow. This does not definitively mean

that there is rotation due to the surface wind wind stress since K1 has a period so close to S1,

there may be spill over between energies. More analysis will be needed.

Figure 7. Coherence at the surface 

Figure 8. Coherence at z/h = 0.75

 

Figure 9. Coherence at z/h = 0.5 

 

Figure 10. Coherence at z/h = 0.25 

3. Discussion

The preliminary results are promising but the next step will be a cross rotary spectral analysis to

see if there indeed is rotation in the column. Once we have those results, the bin averaging will

be done for time periods when only one forcing element is present. This will give us an idea as

to how the cross-shore vertical profiles look for each forcing element. From what we have so

far, we are expecting to see a significant onshore flow near the top of the column and offshore

flow thru the rest of the column (undertow).

The biggest challenge with this research is that any number of factors may be impacting the

water column at any given time. I presented Marina in this paper and in my research we have

moved this to the top of the list due to it being the northern most location thus having the most

significant cross shore wind stress. At Del Monte for example, the sea breeze is not shore

normal and actually has a stronger along shore component. The key in this research to this point,

is to minimize the amount of unknowns.

4. Conclusion

The interesting thing about scientific research is that at each point in your analysis you have to

carefully review what you have because it may take you in a different direction or provide you

with insight you didn’t expect. I’m still traveling down that path, but will be presenting at the

AGU conference in December. We are not sure if we will continue on what is discussed in this

document or analyze diurnal events and their subsequent relaxation periods case by case. Its

attacking the same problem, just looking at it differently. It depends on which direction allows

us to isolate the forcing element of interest most directly.

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