Using HF Radar to Observe Coastal Ocean Tidal FeaturesUsing HF Radar to Observe Coastal Ocean Tidal Features

Alexander R. Davies1 John Moisan2

Ajoy Kumar11Department of Earth Science, Millersville University, Millersville, PA 17551 2NASA/GSFC Wallops Flight Facility. Wallops Island, VA 23337

ABSTRACTA long term coastal ocean observational network is being developed in order to improve our understanding of the dynamics of coastal environments. One aspect of this observing system is the deployment of High Frequency Radar (primarily CODAR) systems that can measure surface coastal ocean currents on hourly time scales up to 200 km offshore and at spatial resolutions of about 10 km. Tidal harmonics were computed using a year of observations from 3 CODAR systems deployed along the Delaware, Maryland, and Virginia coast under support from the NOAA Integrated Ocean Observing System (IOOS). The resulting tidal current estimates were then removed from the raw HF Radar current estimates to render a composite of the mean surface circulation pattern for this coastal ocean region. Tidal currents in this region account for up to 60% of the total current variability, particularly at the mouth of the Chesapeake Bay. Using the tidal harmonics, a year’s worth of daily progressive vector diagrams were analyzed in order to ascertain the level of ‘jitter’ that one could expect from obtaining hourly images from a geostationary hyperspectral ocean color satellite such as NASA’s GEO-CAPE mission.

BACKGROUNDLittle is known about the global dynamics of terrestrial waters and their interaction with open ocean sources. Newly emerging long term coastal ocean observation systems are being developed to improve our understand of these phenomena, in near real time. A key to this new network of observation systems is coastal high frequency radar observation system, in this case, CODAR. Wallops Coastal Ocean Observation Laboratory (WaCOOL) is a collaborative effort by the National Aeronautics and Space Administration (NASA)/Wallops Flight Facility (WFF), the National Oceanic and Atmospheric Administration (NOAA), the Center for Innovative Technology (CIT), and other academic and commercial institutes to study the coastal waters surrounding the Delmarva Peninsula (Delaware, Maryland Virginia). Among other state of the art ocean observing systems, the Hydrospheric and Biospheric Sciences Laboratory (HBSL) at WFF has deployed two CODAR Ocean Sensors (COS). The sensors are strategically located on Assateague Island, a barrier island along the Delmarva Peninsula, at 38º 12’ 20.81”N and 75º 09’ 10.50”W and on Cedar Island, VA at 37º 40’ 22.31”N and 75º 35’ 38.06”W.

COS high frequency radars work by propagating an electro-magnetic wave from an onshore transmitter antenna toward the sea surface. The sea surface is naturally rough and thus the electro-magnetic signal is scattered in all directions depending on the wavelength of the sea surface waves, a process known as Bragg Scattering. The only signal that is recovered by the receiver antenna is that which is backscattered radially off propagating sea surface waves at exactly one-half the transmitted wavelength. Using the principles of Doppler shift, the radial wave speed can be calculated. Once this process has been done for both COS sites (Assateague and Cedar Island), averaged “totals” currents can be computed for further analysis where it is archived by the WFF Coastal Data Acquisition and Archive Center (CODAAC).

The purpose of the study is to examine dynamic and physical features along the shore of Maryland, Delaware, and Virginia. However, in this region tidal forcing is typically dominate so it is critical to account for this forcing when evaluating residual features or variability. The long time series of CODAAC archived COS data extends from December 12th, 2006, to September 24th, 2008, which is sufficient for tidal harmonic studies. This makes high frequency coastal radars ideal for this study.

DISCUSSIONPCA is a strong tool for statistically recognizing patterns within a data set and highlighting a data set’s similarities and differences. A variance ellipse about the newly-oriented data adds additional analytical information. Variance ellipses give a sense of co-variability about the data with square-root ellipses providing more information because it gives a sense of the first order standard deviation of the observation with preserved units. Figure 2 shows standard deviation ellipses for each point and is overlaid with a 5 km2 grid which gives a sense of the degree of variability associated with the tidal forcing. Figure 3 demonstrates the mean residual current in this region for 2007. If overlaid with a bathymetric map, it would be fair to speculate the importance of Ertel’s Potential Vorticity along the coast. Figure 4 illustrates where the effects of the tidal forcing are the greatest. The signature from the tidal surge in and out of the Chesapeake Bay can be clearly observed.

Single Value Decommission Single (SVD) will decompose matrix A into an (n x m) orthogonal array, an (n x n) diagonal array, and the transpose of an (n x n) orthogonal array. Matrix x, for each coefficient and component, is then solved by “back substituted” the orthogonal array, diagonal array, and transposed orthogonal array—along with the observational data, matrix B. With the set of tidal coefficients solved for each velocity component, the tidal forcing can be represented using equation 1. The residual velocities are then just tidal harmonics subtracted from the raw, observational data contained in matrix B at each time step. This analysis yields not only a harmonic time series for surface current velocities for each point, but also a residual or non-tidal harmonic surface current velocity time series as well.

Now that tidal harmonic coefficients, Ak and Bk, have been identified, finite differencing can be used to represent tidal forcing on a parcel of water for any time interval. Finite differencing was done at each point for daily and yearly time periods over a one minute time interval. The simple finite differencing assumes that the parcel of water starting at a given location, (0,0) in an x-y plane, will retain the harmonic forcing from the initial starting location throughout. This assumption is likely strong for short time periods (hours to days), but will likely fold over longer time periods due to larger displacement from the initial point due to tidal forcing.

For each point, finite differencing was used to represent the location of a tidally-forced parcel of water, at one minute time intervals, for each day of the year, all else being equal. If each daily representation starting at the initial point (0,0) in an x-y plane, they can be plotted on top of each other. Directional variability and co-variability can be assessed and principle component analysis (PCA) can be preformed. Using the eigenvalues and eigenvectors from PCA, scaled variance position ellipses can be constructed for a given data point (Figure 1). PCA and variance ellipses can also be calculated for to analyze the variability and covariance about the tidal-forced u and v component velocities.

METHODSAs mentioned above, the data set contains a times series of observations from December 12, 2006, to September 24, 2008. Within the observational area there are 1257 individual points representing a 6 km grid about each. Mean surface u and v component velocities are recorded hourly at each of the points. After poor data was removed from the time series at each of the individual 1257 points, it became a “gappy” non-continuous function. Data points that failed to contain sufficient observations needed to identify tidal components (with phases up to one year in length) were not considered. Additionally, only data from January 1st, 2007, through December 31st, 2007, will be analyzed in this study. Given the gaps and often inconsistent time-steps within the CODAR COS data, harmonic analysis is the best method to identify the tidal constituents. Any time series of n observations can be represented harmonically in n/2 harmonic functions in the form of:

Yt = ybar + Σ {Ak cos[2πkt/n] + Bk sin[2πkt/n]} (1)

where ybar is the mean of the time series and the coefficients Ak and Bk are associated with each individual harmonic or component, k. The summation notation is evaluated from k = 1 (or the fundamental harmonic) to k = n/2 harmonics.

In the case of harmonic analysis to identify tides, there are only thirty-seven tidal harmonics that need to be considered. All harmonics and observations beyond these known tidal harmonics represent residual data or error. The thirty-seven tidal harmonics are well known and studied. Each of the tidal harmonics has a constant speed, or rates of change in the phase of the individual constituent, which are readily available through NOAA via tidesandcurrents.noaa.gov.

Harmonic analysis begins by calculating the thirty-seven sets of tidal coefficients, Ak and Bk, for each of the data points for both the u and v components. Although multiple linear regressions are a valid option for solving the tidal coefficients, the problem is much clearer by representing it using linear matrix notation.

Ax = B (2)

where the matrix B is the u or v component velocity time series for a given point, the matrix A either the sine (Bk) or cosine (Ak) function of known the expression [2πkt/n] in equation 1 that corresponds with each of the 37 tidal harmonics, and the matrix x is the tidal coefficients to be solved. For any given observational point, equation 2 is used to solve matrix x four times representing each u and v component velocity, a set of coefficients is required, Ak and Bk.

Figure 1. Tidally-forced daily finite differencing representations plotted over one another. Principle Component Analysis (PCA) eigenvalues and eigenvectors are used to construct scaled variance ellipse to statistically characterize the extent of tidal forcing for the observational point 75.0593 W and 37.7251 N (brown).

Figure 2. Tidally-forced standard deviation ellipses overlaying a 5 km2 grid.

Figure 3. Mean Residual Currents in 2007. Figure 4. Mean Percent Surface Current forced by tidal Harmonics in 2007.

Standard Deviation Ellipse

REFERENCES“Reverse Observing Oceanic Submesoscale Processes From Space,” EOS, Vol. 89, No. 4, 25 November 2008, pp. 488.

Fu, L-L., Alsdorf, A., Rodriguez, E., Morrow, R., Mognard, N., Lambin, J., Vaze, P., and Lafon, T., “The SWOT (Surface Water and Ocean Topography) Mission: Spaceborne Radar Interferometry for Oceanographic and Hydrological Applications,” White paper submitted to OCEANOBS’09 Conference, 2009 March.

Defant, A., Ebb and Flow, The Tides and Earth, Air, and Water, University of Michigan Press, Ann Arbor, 1958, Chaps. 1, 2, 5.

Wilks, D. S., Statistical Methods in the Atmospheric Sciences, 2nd Edition, International Geophysics Series, Vol. 91, Elsevier Inc., Boston, 2006, Chaps. 8, 9.

Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P., Numerical Recipes in C++, The Art of Scientific Computing, 2nd Edition, Cambridge University Press, New York, 2002, Chap. 2.

Preisendorfer, R. W., Principle Component Analysis in Meteorology and Oceanography, Elsevier Science Publishing Company, Inc, New York, 1988, Chap. 2

ACKNOWLEDGMENTSThis research was supported by an appointment to the National Aeronautics and Space Administration (NASA) Undergraduate Student Research Program (USRP)

Travel to the Ocean Science Meeting was funded by the Millersville University Noonan Grant and an AGU Student Travel Grant.

I would like to thank Dr. John Moisan, Dr. Tiffany Moisan, Dr. Ajoy Kumar, everyone at NASA GSFC Wallops Flight Facility, and Everyone at Millersville University for their support.