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- Author or Editor: Robert H. Weisberg x
- Journal of Atmospheric and Oceanic Technology x
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Abstract
This paper addresses a bias problem in the estimate of wavelet power spectra for atmospheric and oceanic datasets. For a time series comprised of sine waves with the same amplitude at different frequencies the conventionally adopted wavelet method does not produce a spectrum with identical peaks, in contrast to a Fourier analysis. The wavelet power spectrum in this definition, that is, the transform coefficient squared (to within a constant factor), is equivalent to the integration of energy (in physical space) over the influence period (time scale) the series spans. Thus, a physically consistent definition of energy for the wavelet power spectrum should be the transform coefficient squared divided by the scale it associates. Such adjusted wavelet power spectrum results in a substantial improvement in the spectral estimate, allowing for a comparison of the spectral peaks across scales. The improvement is validated with an artificial time series and a real coastal sea level record. Also examined is the previous example of the wavelet analysis of the Niño-3 SST data.
Abstract
This paper addresses a bias problem in the estimate of wavelet power spectra for atmospheric and oceanic datasets. For a time series comprised of sine waves with the same amplitude at different frequencies the conventionally adopted wavelet method does not produce a spectrum with identical peaks, in contrast to a Fourier analysis. The wavelet power spectrum in this definition, that is, the transform coefficient squared (to within a constant factor), is equivalent to the integration of energy (in physical space) over the influence period (time scale) the series spans. Thus, a physically consistent definition of energy for the wavelet power spectrum should be the transform coefficient squared divided by the scale it associates. Such adjusted wavelet power spectrum results in a substantial improvement in the spectral estimate, allowing for a comparison of the spectral peaks across scales. The improvement is validated with an artificial time series and a real coastal sea level record. Also examined is the previous example of the wavelet analysis of the Niño-3 SST data.
Abstract
Neural network analyses based on the self-organizing map (SOM) and the growing hierarchical self-organizing map (GHSOM) are used to examine patterns of the sea surface temperature (SST) variability on the West Florida Shelf from time series of daily SST maps from 1998 to 2002. Four characteristic SST patterns are extracted in the first-layer GHSOM array: winter and summer season patterns, and two transitional patterns. Three of them are further expanded in the second layer, yielding more detailed structures in these seasons. The winter pattern is one of low SST, with isotherms aligned approximately along isobaths. The summer pattern is one of high SST distributed in a horizontally uniform manner. The spring transition includes a midshelf cold tongue. Similar analyses performed on SST anomaly data provide further details of these seasonally varying patterns. It is demonstrated that the GHSOM analysis is more effective in extracting the inherent SST patterns than the widely used EOF method. The underlying patterns in a dataset can be visualized in the SOM array in the same form as the original data, while they can only be expressed in anomaly form in the EOF analysis. Some important features, such as asymmetric SST anomaly patterns of winter/summer and cold/warm tongues, can be revealed by the SOM array but cannot be identified in the lowest mode EOF patterns. Also, unlike the EOF or SOM techniques, the hierarchical structure in the input data can be extracted by the GHSOM analysis.
Abstract
Neural network analyses based on the self-organizing map (SOM) and the growing hierarchical self-organizing map (GHSOM) are used to examine patterns of the sea surface temperature (SST) variability on the West Florida Shelf from time series of daily SST maps from 1998 to 2002. Four characteristic SST patterns are extracted in the first-layer GHSOM array: winter and summer season patterns, and two transitional patterns. Three of them are further expanded in the second layer, yielding more detailed structures in these seasons. The winter pattern is one of low SST, with isotherms aligned approximately along isobaths. The summer pattern is one of high SST distributed in a horizontally uniform manner. The spring transition includes a midshelf cold tongue. Similar analyses performed on SST anomaly data provide further details of these seasonally varying patterns. It is demonstrated that the GHSOM analysis is more effective in extracting the inherent SST patterns than the widely used EOF method. The underlying patterns in a dataset can be visualized in the SOM array in the same form as the original data, while they can only be expressed in anomaly form in the EOF analysis. Some important features, such as asymmetric SST anomaly patterns of winter/summer and cold/warm tongues, can be revealed by the SOM array but cannot be identified in the lowest mode EOF patterns. Also, unlike the EOF or SOM techniques, the hierarchical structure in the input data can be extracted by the GHSOM analysis.
Abstract
Current observations are compared from upward- and downward-looking acoustic Doppler current profilers (ADCPs) deployed on the West Florida Shelf (WFS). Despite regional differences, statistical analyses show good agreement between all sets of observations throughout the water column except in the upper few meters where all downward-looking ADCPs exhibit small, but significant, reduction in rms speed values. Evidence suggests that this reduction is mooring related. It is possible that the presence of near-surface bubbles caused by wave activity could bias the near-surface observations. Otherwise, either the upward- or downward-looking mooring systems produce equivalent observations with differences due to spatial variations.
Abstract
Current observations are compared from upward- and downward-looking acoustic Doppler current profilers (ADCPs) deployed on the West Florida Shelf (WFS). Despite regional differences, statistical analyses show good agreement between all sets of observations throughout the water column except in the upper few meters where all downward-looking ADCPs exhibit small, but significant, reduction in rms speed values. Evidence suggests that this reduction is mooring related. It is possible that the presence of near-surface bubbles caused by wave activity could bias the near-surface observations. Otherwise, either the upward- or downward-looking mooring systems produce equivalent observations with differences due to spatial variations.
Abstract
To assess the spatial structures and temporal evolutions of distinct physical processes on the West Florida Shelf, patterns of ocean current variability are extracted from a joint HF radar and ADCP dataset acquired from August to September 2003 using Self-Organizing Map (SOM) analyses. Three separate ocean–atmosphere frequency bands are considered: semidiurnal, diurnal, and subtidal. The currents in the semidiurnal band are relatively homogeneous in space, barotropic, clockwise polarized, and have a neap-spring modulation consistent with semidiurnal tides. The currents in the diurnal band are less homogeneous, more baroclinic, and clockwise polarized, consistent with a combination of diurnal tides and near-inertial oscillations. The currents in the subtidal frequency band are stronger and with more complex patterns consistent with wind and buoyancy forcing. The SOM is shown to be a useful technique for extracting ocean current patterns with dynamically distinctive spatial and temporal structures sampled by HF radar and supporting in situ measurements.
Abstract
To assess the spatial structures and temporal evolutions of distinct physical processes on the West Florida Shelf, patterns of ocean current variability are extracted from a joint HF radar and ADCP dataset acquired from August to September 2003 using Self-Organizing Map (SOM) analyses. Three separate ocean–atmosphere frequency bands are considered: semidiurnal, diurnal, and subtidal. The currents in the semidiurnal band are relatively homogeneous in space, barotropic, clockwise polarized, and have a neap-spring modulation consistent with semidiurnal tides. The currents in the diurnal band are less homogeneous, more baroclinic, and clockwise polarized, consistent with a combination of diurnal tides and near-inertial oscillations. The currents in the subtidal frequency band are stronger and with more complex patterns consistent with wind and buoyancy forcing. The SOM is shown to be a useful technique for extracting ocean current patterns with dynamically distinctive spatial and temporal structures sampled by HF radar and supporting in situ measurements.
Abstract
Concurrently operated on the West Florida shelf for the purpose of observing surface currents are three long-range (4.9 MHz) Coastal Ocean Dynamics Applications Radar (CODAR) SeaSonde and two median-range (12.7 MHz) Wellen Radar (WERA) high-frequency (HF) radar systems. These HF radars overlook an array of moored acoustic Doppler current profilers (ADCPs), three of which are presently within the radar footprint. Analyzed herein are 3 months of simultaneous observations. Both the SeaSonde and WERA systems generally agree with the ADCPs to within root-mean-square differences (rmsd) for hourly radial velocity components of 5.1–9.2 and 3.8–6.5 cm s−1 for SeaSonde and WERA, respectively, and within rmsd for 36-h low-pass filtered radial velocity components of 2.8–6.0 and 2.2–4.3 cm s−1 for SeaSonde and WERA, respectively. The bearing offset and tidal and subtidal currents of total velocities are also assessed using the ADCP data. Despite differences in a variety of aspects between the direction-finding CODAR SeaSonde (long range, effective depth of 2.4 m, integration time of 4 h, and idealized antenna patterns) and the beam-forming WERA (median range, effective depth of 0.9 m, and integration time of 1 h), both HF radar systems demonstrated good surface current mapping capability. The differences between the velocities measured with the HF radar and the ADCP are sufficiently small in this low-energy shelf that much of these rmsd values may be accounted for by the expected measurement differences due to the horizontal, vertical, and temporal sampling differences of the ocean current observing systems used.
Abstract
Concurrently operated on the West Florida shelf for the purpose of observing surface currents are three long-range (4.9 MHz) Coastal Ocean Dynamics Applications Radar (CODAR) SeaSonde and two median-range (12.7 MHz) Wellen Radar (WERA) high-frequency (HF) radar systems. These HF radars overlook an array of moored acoustic Doppler current profilers (ADCPs), three of which are presently within the radar footprint. Analyzed herein are 3 months of simultaneous observations. Both the SeaSonde and WERA systems generally agree with the ADCPs to within root-mean-square differences (rmsd) for hourly radial velocity components of 5.1–9.2 and 3.8–6.5 cm s−1 for SeaSonde and WERA, respectively, and within rmsd for 36-h low-pass filtered radial velocity components of 2.8–6.0 and 2.2–4.3 cm s−1 for SeaSonde and WERA, respectively. The bearing offset and tidal and subtidal currents of total velocities are also assessed using the ADCP data. Despite differences in a variety of aspects between the direction-finding CODAR SeaSonde (long range, effective depth of 2.4 m, integration time of 4 h, and idealized antenna patterns) and the beam-forming WERA (median range, effective depth of 0.9 m, and integration time of 1 h), both HF radar systems demonstrated good surface current mapping capability. The differences between the velocities measured with the HF radar and the ADCP are sufficiently small in this low-energy shelf that much of these rmsd values may be accounted for by the expected measurement differences due to the horizontal, vertical, and temporal sampling differences of the ocean current observing systems used.
Abstract
A dual-station high-frequency Wellen Radar (WERA), transmitting at 16.045 MHz, was deployed along the west Florida shelf in phased array mode during the summer of 2003. A 33-day, continuous time series of radial and vector surface current fields was acquired starting on 23 August ending 25 September 2003. Over a 30-min sample interval, WERA mapped coastal ocean currents over an ≈40 km × 80 km footprint with a 1.2-km horizontal resolution. A total of 1628 snapshots of the vector surface currents was acquired, with only 70 samples (4.3%) missing from the vector time series. Comparisons to subsurface measurements from two moored acoustic Doppler current profilers revealed RMS differences of 1 to 5 cm s−1 for both radial and Cartesian current components. Regression analyses indicated slopes close to unity with small biases between surface and subsurface measurements at 4-m depth in the east–west (u) and north–south (υ) components, respectively. Vector correlation coefficients were 0.9 with complex phases of −3° and 5° at EC4 (20-m isobath) and NA2 (25-m isobath) moorings, respectively.
Complex surface circulation patterns were observed that included tidal and wind-driven currents over the west Florida shelf. Tidal current amplitudes were 4 to 5 cm s−1 for the diurnal and semidiurnal constituents. Vertical structure of these tidal currents indicated that the semidiurnal components were predominantly barotropic whereas diurnal tidal currents had more of a baroclinic component. Tidal currents were removed from the observed current time series and were compared to the 10-m adjusted winds at a surface mooring. Based on these time series comparisons, regression slopes were 0.02 to 0.03 in the east–west and north–south directions, respectively. During Tropical Storm Henri’s passage on 5 September 2003, cyclonically rotating surface winds forced surface velocities of more than 35 cm s−1 as Henri made landfall north of Tampa Bay, Florida. These results suggest that the WERA measured the surface velocity well under weak to tropical storm wind conditions.
Abstract
A dual-station high-frequency Wellen Radar (WERA), transmitting at 16.045 MHz, was deployed along the west Florida shelf in phased array mode during the summer of 2003. A 33-day, continuous time series of radial and vector surface current fields was acquired starting on 23 August ending 25 September 2003. Over a 30-min sample interval, WERA mapped coastal ocean currents over an ≈40 km × 80 km footprint with a 1.2-km horizontal resolution. A total of 1628 snapshots of the vector surface currents was acquired, with only 70 samples (4.3%) missing from the vector time series. Comparisons to subsurface measurements from two moored acoustic Doppler current profilers revealed RMS differences of 1 to 5 cm s−1 for both radial and Cartesian current components. Regression analyses indicated slopes close to unity with small biases between surface and subsurface measurements at 4-m depth in the east–west (u) and north–south (υ) components, respectively. Vector correlation coefficients were 0.9 with complex phases of −3° and 5° at EC4 (20-m isobath) and NA2 (25-m isobath) moorings, respectively.
Complex surface circulation patterns were observed that included tidal and wind-driven currents over the west Florida shelf. Tidal current amplitudes were 4 to 5 cm s−1 for the diurnal and semidiurnal constituents. Vertical structure of these tidal currents indicated that the semidiurnal components were predominantly barotropic whereas diurnal tidal currents had more of a baroclinic component. Tidal currents were removed from the observed current time series and were compared to the 10-m adjusted winds at a surface mooring. Based on these time series comparisons, regression slopes were 0.02 to 0.03 in the east–west and north–south directions, respectively. During Tropical Storm Henri’s passage on 5 September 2003, cyclonically rotating surface winds forced surface velocities of more than 35 cm s−1 as Henri made landfall north of Tampa Bay, Florida. These results suggest that the WERA measured the surface velocity well under weak to tropical storm wind conditions.
Abstract
Three long-range (5 MHz) Coastal Ocean Dynamics Application Radar (CODAR) SeaSonde HF radars overlooking an array of as many as eight moored acoustic Doppler current profilers (ADCPs) have operated on the West Florida Shelf since September 2003 for the purpose of observing the coastal ocean currents. HF radar performance on this low-energy (currents and waves) continental shelf is evaluated with respect to data returns, the rms differences between the HF radar and the ADCP radial currents, bearing offsets, and radial velocity uncertainties. Possible environmental factors affecting the HF radar performance are discussed, with the findings that both the low-energy sea state and the unfavorable surface wave directions are the main limiting factors for these HF radar observations of currents on the WFS. Despite the challenge of achieving continuous backscatter from this low-energy environment, when acquired the data quality is good in comparison with the ADCP measurements. The rms differences range from 6 to 10 cm s−1 for hourly and from 3 to 6 cm s−1 for 36-h low-pass-filtered radial currents, respectively. Bearing offsets are in the range from −15° to +9°. Coherent variations of the HF radar and ADCP radial currents are seen across both tidal and subtidal frequency bands. By examining the HF radar radial velocities at low wave energy, it is found that the data returns decrease rapidly for significant wave heights smaller than 1 m, and that the rms differences between the HF radar and ADCP radials are degraded when the significant wave height is smaller than 0.3 m.
Abstract
Three long-range (5 MHz) Coastal Ocean Dynamics Application Radar (CODAR) SeaSonde HF radars overlooking an array of as many as eight moored acoustic Doppler current profilers (ADCPs) have operated on the West Florida Shelf since September 2003 for the purpose of observing the coastal ocean currents. HF radar performance on this low-energy (currents and waves) continental shelf is evaluated with respect to data returns, the rms differences between the HF radar and the ADCP radial currents, bearing offsets, and radial velocity uncertainties. Possible environmental factors affecting the HF radar performance are discussed, with the findings that both the low-energy sea state and the unfavorable surface wave directions are the main limiting factors for these HF radar observations of currents on the WFS. Despite the challenge of achieving continuous backscatter from this low-energy environment, when acquired the data quality is good in comparison with the ADCP measurements. The rms differences range from 6 to 10 cm s−1 for hourly and from 3 to 6 cm s−1 for 36-h low-pass-filtered radial currents, respectively. Bearing offsets are in the range from −15° to +9°. Coherent variations of the HF radar and ADCP radial currents are seen across both tidal and subtidal frequency bands. By examining the HF radar radial velocities at low wave energy, it is found that the data returns decrease rapidly for significant wave heights smaller than 1 m, and that the rms differences between the HF radar and ADCP radials are degraded when the significant wave height is smaller than 0.3 m.
