• Aparna, M., , S. R. Shetye, , D. Shankar, , S. S. C. Shenoi, , P. Mahra, , and R. G. P. Desai, 2005: Estimating the seaward extent of sea breeze from QuikSCAT scatterometry. Geophys. Res. Lett., 32 , L13601. doi:10.1029/2005GL023107.

    • Search Google Scholar
    • Export Citation
  • Belabbassi, L., 2006: Examination of the relationship of river water to occurrences of the bottom water with reduced oxygen concentrations in northern Gulf of Mexico. Ph.D. thesis, Texas A&M University, 119 pp.

  • Bunge, L., , C. Provost, , J. Lilly, , M. D’Orgeville, , A. Kartavtseff, , and J. Melice, 2006: Variability of the horizontal velocity structure in the upper 1600 m of the water column on the equator at 10°W. J. Phys. Oceanogr., 36 , 12871304.

    • Search Google Scholar
    • Export Citation
  • Chen, C., , and L. Xie, 1997: A numerical study of wind-induced, near-inertial oscillations over the Texas–Louisiana shelf. J. Geophys. Res., 102 , (C7). 1558315593.

    • Search Google Scholar
    • Export Citation
  • Chen, C., , R. O. Reid, , and W. D. Nowlin Jr., 1996: Near-inertial oscillations over the Texas–Louisiana shelf. J. Geophys. Res., 101 , (C2). 35093524.

    • Search Google Scholar
    • Export Citation
  • Cho, K., , R. O. Reid, , and W. D. Nowlin Jr., 1998: Objectively mapped streamfunction fields on the Texas–Louisiana shelf based on 32 months of moored current meter data. J. Geophys. Res., 103 , (C5). 1037710390.

    • Search Google Scholar
    • Export Citation
  • Cochrane, J. D., , and F. J. Kelly, 1986: Low-frequency circulation on the Texas–Louisiana continental shelf. J. Geophys. Res., 91 , (C9). 1064510659.

    • Search Google Scholar
    • Export Citation
  • Craig, P. D., 1989a: Constant eddy-viscosity models of vertical structure forced by periodic winds. Cont. Shelf Res., 9 , 343358.

  • Craig, P. D., 1989b: A model of diurnally forced vertical current structure near 30° latitude. Cont. Shelf Res., 9 , 965980.

  • Davis, W. M., , L. G. Schultz, , and R. De C Ward, 1890: An investigation of the sea breeze. Ann. Observ. Astron. Harvard. Coll., 21 , 215265.

    • Search Google Scholar
    • Export Citation
  • DiMarco, S. F., , and R. O. Reid, 1998: Characterization of the principal tidal current constituents on the Texas–Louisiana shelf. J. Geophys. Res., 103 , (C2). 30923109.

    • Search Google Scholar
    • Export Citation
  • DiMarco, S. F., , A. E. Jochens, , and M. K. Howard, 1997: LATEX shelf data report: Current meter moorings, April 1992 through December 1994. Dept. of Oceanography Tech. Rep. 97-01-T, Texas A&M University, College Station, TX, 61 pp. plus appendixes.

    • Search Google Scholar
    • Export Citation
  • DiMarco, S. F., , M. K. Howard, , and R. O. Reid, 2000: Seasonal variation of wind-driven diurnal current cycling on the Texas–Louisiana continental shelf. Geophys. Res. Lett., 27 , 10171020.

    • Search Google Scholar
    • Export Citation
  • DiMego, G. L., , L. F. Bosart, , and G. W. Endersen, 1976: An examination of the frequency and mean conditions surrounding frontal incursions into the Gulf of Mexico and Caribbean Sea. Mon. Wea. Rev., 104 , 708718.

    • Search Google Scholar
    • Export Citation
  • Foufoula-Georgiou, E., , and P. Kumar, Eds. 1995: Wavelets in Geophysics. Academic Press, 373 pp.

  • Furberg, M., , D. G. Steyn, , and M. Baldi, 2002: The climatology of sea breezes on Sardinia. Int. J. Climatol., 22 , 917932.

  • Gille, S. T., , S. G. Llewellyn Smith, , and S. M. Lee, 2003: Measuring the seabreeze from QuikSCAT scatterometry. Geophys. Res. Lett., 30 , 1114. doi:10.1029/2002GL016230.

    • Search Google Scholar
    • Export Citation
  • Gregg, M. C., 1989: Scaling turbulent dissipation in the thermocline. J. Geophys. Res., 94 , (C7). 96869698.

  • Grinsted, A., , J. C. Moore, , and S. Jevrejeva, 2004: Application of the cross wavelet transform and wavelet coherence to geophysical time series. Nonlinear Processes Geophys., 11 , 561566.

    • Search Google Scholar
    • Export Citation
  • Hetland, R. D., , and S. F. DiMarco, 2008: How does the character of oxygen demand control the structure of hypoxia on the Texas–Louisiana continental shelf? J. Mar. Syst., 70 , 4962.

    • Search Google Scholar
    • Export Citation
  • Howard, M. K., , and S. F. DiMarco, 1998: LATEX shelf DATA report: Drifters and Miscellaneous Instruments, April 1992 through December 1994. Dept. of Oceanography Tech. Rep. 98-2-T, Texas A&M University, College Station, TX, 34 pp. plus appendixes.

    • Search Google Scholar
    • Export Citation
  • Hsu, S. A., 1970: Coastal air-circulation system: Observations and empirical model. Mon. Wea. Rev., 98 , 487509.

  • Hunter, E., , R. Chant, , L. Bowers, , S. Glenn, , and J. Kohut, 2007: Spatial and temporal variability of diurnal wind forcing in the coastal ocean. Geophys. Res. Lett., 34 , L03607. doi:10.1029/2006GL028945.

    • Search Google Scholar
    • Export Citation
  • Hyder, P., , J. H. Simpson, , and S. Christopoulos, 2002: Sea-breeze forced diurnal surface currents in the Thermaikos Gulf, north-west Aegean. Cont. Shelf Res., 22 , 585601.

    • Search Google Scholar
    • Export Citation
  • Liu, Y., , X. S. Liang, , and R. H. Weisberg, 2007: Rectification of the bias in the wavelet power spectrum. J. Atmos. Oceanic Technol., 24 , 20932102.

    • Search Google Scholar
    • Export Citation
  • MacKinnon, J. A., , and K. B. Winters, 2005: Subtropical catastrophe: Significant loss of low-mode tidal energy at 28.9°N. Geophys. Res. Lett., 32 , L15605. doi:10.1029/2005GL023376.

    • Search Google Scholar
    • Export Citation
  • Masselink, G., , and C. B. Pattiaratchi, 2001: Characteristics of the sea breeze system in Perth, Western Australia, and its effect on the nearshore wave climate. J. Coastal Res., 17 , 173187.

    • Search Google Scholar
    • Export Citation
  • Nielsen-Gammon, J. W., 2001: Initial modeling of the August 2000 Houston–Galveston ozone episode. Rep. to the Texas Natural Resource Conservation Commission (TNRCC), 71 pp. [Available online at http://www.tceq.state.tx.us].

    • Search Google Scholar
    • Export Citation
  • Nielsen-Gammon, J. W., 2002a: Evaluation and comparison of preliminary meteorological modeling for the August 2000 Houston–Galveston ozone episode. Rep. to TNRCC, 83 pp. [Available online at http://www.tceq.state.tx.us].

    • Search Google Scholar
    • Export Citation
  • Nielsen-Gammon, J. W., 2002b: Meteorological modeling for the August 2000 Houston–Galveston ozone episode: PBL characteristics, nudging procedure, and performance evaluation. Rep. to TNRCC, 109 pp. [Available online at http://www.tceq.state.tx.us].

    • Search Google Scholar
    • Export Citation
  • Nowlin Jr., W. D., , A. E. Jochens, , R. O. Reid, , and S. F. DiMarco, 1998: Texas–Louisiana Shelf Circulation and Transport Processes Study: Synthesis report. Vol. I. Tech. Rep. OCS Study MMS 98-0035, Gulf of Mexico OCS Region, Minerals Management Service, U.S. Dept. of the Interior, New Orleans, LA, 502 pp.

    • Search Google Scholar
    • Export Citation
  • Nowlin Jr., W. D., , A. E. Jochens, , S. F. DiMarco, , R. O. Reid, , and M. K. Howard, 2005: Low-frequency circulation over the Texas-Louisiana continental shelf. Circulation in the Gulf of Mexico: Observations and Models, Geophys. Monogr., Vol. 161, Amer. Geophys. Union, 219–240.

    • Search Google Scholar
    • Export Citation
  • Oey, L-Y., 1995: Eddy- and wind-forced shelf circulation. J. Geophys. Res., 100 , (C5). 86218637.

  • Pawlowicz, R., , B. Beardsley, , and S. Lentz, 2002: Classical tidal harmonic including error estimates in MATLAB using T-TIDE. Comput. Geosci., 28 , 929937.

    • Search Google Scholar
    • Export Citation
  • Price, J. F., , R. A. Weller, , and R. Pinkel, 1986: Diurnal cycling: Observations and models of the upper ocean response to diurnal heating, cooling, and wind mixing. J. Geophys. Res., 91 , (C7). 84118427.

    • Search Google Scholar
    • Export Citation
  • Rabalais, N. N., , R. E. Turner, , B. K. Sen Gupta, , D. F. Boesch, , P. Chapman, , and M. C. Murrell, 2007: Hypoxia in the northern Gulf of Mexico: Does the science support the plan to reduce, mitigate, and control hypoxia? Estuaries Coasts, 30 , 753772.

    • Search Google Scholar
    • Export Citation
  • Rippeth, T. P., , J. H. Simpson, , R. J. Player, , and M. Garcia, 2002: Current oscillations in the diurnal–inertial band on the Cataloninan shelf in spring. Cont. Shelf Res., 22 , 247265.

    • Search Google Scholar
    • Export Citation
  • Rotunno, R., 1983: On the linear theory of the land and sea breeze. J. Atmos. Sci., 40 , 19992009.

  • Schott, F. A., , M. Dengler, , R. Zantopp, , L. Stramma, , J. Fischer, , and P. Brandt, 2005: The shallow and deep western boundary circulation of the South Atlantic at 5°–11°S. J. Phys. Oceanogr., 35 , 20312053.

    • Search Google Scholar
    • Export Citation
  • Simmons, H. L., , R. W. Hallberg, , and B. K. Arbic, 2004: Internal wave generation in a global baroclinic tide model. Deep-Sea Res. II, 51 , 30433068.

    • Search Google Scholar
    • Export Citation
  • Simpson, J. E., 1994: Sea Breeze and Local Wind. Cambridge University Press, 234 pp.

  • Simpson, J. H., , T. P. Rippeth, , P. Hyder, , and I. M. Lucas, 2002: Forced oscillations near the critical latitude for diurnal–inertial resonance. J. Phys. Oceanogr., 32 , 177187.

    • Search Google Scholar
    • Export Citation
  • Torrence, C., , and G. P. Compo, 1998: A practical guide to wavelet analysis. Bull. Amer. Meteor. Soc., 79 , 6178.

  • Torrence, C., , and P. J. Webster, 1999: Interdecadal changes in the ENSO–monsoon system. J. Climate, 12 , 26792690.

  • Turner, R. E., , and N. N. Rabalais, 1994: Coastal eutrophication near the Mississippi River delta. Nature, 368 , 619621.

  • van Haren, H., 2005: Tidal and near-inertial peak variations around the diurnal critical latitude. Geophys. Res. Lett., 32 , L23611. doi:10.1029/2005GL024160.

    • Search Google Scholar
    • Export Citation
  • van Haren, H., 2007: Longitudinal and topographic variations in North Atlantic tidal and inertial energy around latitudes 30 ± 10°N. J. Geophys. Res., 112 , C10020. doi:10.1029/2007JC004193.

    • Search Google Scholar
    • Export Citation
  • Walker, N. D., , G. S. Fargion, , L. J. Rouse, , and D. C. Biggs, 1994: The great flood of summer 1993: Mississippi River discharge studied. Eos, Trans. Amer. Geophys. Union, 75 (36) 409.

    • Search Google Scholar
    • Export Citation
  • Wang, W., , M. K. Howard, , W. D. Nowlin Jr., , and R. O. Reid, 1996: LATEX shelf data report: Meteorological, April 1992 through December 1994. Dept. of Oceanography Tech. Rep. 96-2-T, Texas A&M University, College Station, TX, 34 pp. plus appendixes.

    • Search Google Scholar
    • Export Citation
  • Wiseman, W. J., , N. N. Rabalais, , R. E. Turner, , S. P. Dinnel, , and A. MacNaughton, 1997: Seasonal and interannual variability within the Louisiana coastal current: Stratification and hypoxia. J. Mar. Syst., 12 , 237248.

    • Search Google Scholar
    • Export Citation
  • Yan, H., , and R. A. Anthes, 1987: The effect of latitude on sea breeze. Mon. Wea. Rev., 115 , 936956.

  • Zhang, X., , D. C. Smith IV, , S. F. DiMarco, , and R. D. Hetland, 2009: A numerical study of sea-breeze-driven ocean Poincare wave propagation and mixing near the critical latitude. J. Phys. Oceanogr., in press.

    • Search Google Scholar
    • Export Citation
  • View in gallery

    Map of the northwest Gulf of Mexico showing the TLS. Wind observations are available at all of these stations during the LATEX period. Current measurements at LATEX moorings 21 and 22 are analyzed and discussed in this paper. Isobaths shown are 10, 50, 100, 200, and 1000 m.

  • View in gallery

    (top) Wavelet power spectrum (unitless) of the normalized 10-m east–west wind component (mean value was subtracted from the time series and then normalized by the standard deviation) at NDBC buoy station PTAT2 (27.83°N, 97.05°W). Only significant values are plotted, which are >95% confidence for a red-noise process with a lag-1 coefficient of 0.72 (Torrence and Compo 1998). (bottom) The gray solid curve is the frequency- (period) averaged wavelet variance time series (m2 s−2) over the 0.83–1.17-cpd band during the observation period. The black solid curve is the 3-month low-passed values of the gray curve. The horizontal gray dashed line is the 95% confidence level. The black bars indicate summer periods.

  • View in gallery

    Diurnal wind ellipses for 4–11 Jul 1992, calculated from harmonic analysis of the wind measurement time series taken at the center of each ellipse during the LATEX project (see Fig. 1 for base map). The vectors shown are displayed in the oceanographic convention (vectors show direction toward which flow is going) and represent a synoptic snapshot of sea breeze at 1900 LT. The diurnal band used for this plot is from 0.95 to 1.05 cpd. Note: only stations that have data coverage during this period are plotted.

  • View in gallery

    (top) Wavelet power spectrum (unitless) for the hourly north–south current time series at the upper meter (14 m) of mooring 21. Only significant values are plotted, which are those >95% confidence for a red-noise process with a lag-1 coefficient of 0.72 (Torrence and Compo 1998). The two gray lines on either end indicate the “cone of influence,” where edge effects become important. (bottom) The gray solid curve is the frequency- (period) averaged wavelet variance time series (cm2 s−2) over the 0.83–1.17-cpd band during the observation period. The black curve is the 1-month low-passed values of the gray curve. The horizontal gray dashed line is the 95% confidence level. The black dashed–dotted curve is the 2-day running averaged salinity time series at the top meter of mooring 21.

  • View in gallery

    (top) Wavelet power spectrum (unitless) for the hourly north–south current time series from December 1993 to November 1994 at the top meter (3 m) of mooring 22. Only the wavelet spectrum from June to August 1994 is plotted. Only significant values are plotted, which are those >95% confidence for a red-noise process with a lag-1 coefficient of 0.72 (Torrence and Compo 1998). (middle) The black curve is the frequency- (period) averaged wavelet variance time series (cm2 s−2) over the 0.83–1.17-cpd band, and the gray curve is the frequency- (period) averaged wavelet variance over the 2–8-cpd band during summer 1994. The horizontal gray dashed line is the 95% confidence level. (bottom) North–south semidiurnal tidal current time series in summer 1994, calculated using the T_Tide Harmonic Analysis Toolbox of Pawlowicz et al. (2002).

  • View in gallery

    (a) Squared wavelet coherency and phase spectra between the north–south wind component and the north–south current component at mooring 22 during January 1994. The thick contour encloses regions of >95% confidence from a Monte Carlo simulation of wavelet coherency between 300 sets (two each) of red-noise time series. The vectors indicate the phase difference between the wind and current at different frequencies (with in phase pointing right, out of phase pointing left, and wind leading current by 90° pointing straight down). Only one vector is plotted for each day. Thirty vectors are plotted in the frequency–period domain. (b) Same as in (a), but for June 1994. (c) Same as in (a), but for August 1994.

  • View in gallery

    (a) Profiles of salinity and temperature at mooring 21. The measurements were made on 28 May 1994. (b) Same as in (a), but for 1 Aug 1994. (c) Profiles of temperature and salinity at mooring 22. The measurements were made on 29 May 1994. (d) Same as in (c), but on 1 Aug 1994. Triangles in each panel represent the current meter locations on moorings 21 and 22, respectively.

  • View in gallery

    Salinity time series at moorings 21 and 22 from June to August 1994. Black curve is the top meter (14 m) salinity time series at mooring 21 and gray curve is the top meter (3 m) salinity time series at mooring 22. Note: scale is changed for clarity.

  • View in gallery

    (a) Squared wavelet coherency and phase between the north–south current components of mooring 22 at 3 m (top meter) and at 23 m (middle meter) in June 1994. (b) Squared wavelet coherency and phase between the north–south current components of mooring 21 at 14 m (top meter) and at 22 m (bottom meter) during June 1994.

  • View in gallery

    (top) The black and gray curves are the Brunt–Väisälä frequency and squared shear time series calculated from the temperature, conductivity, and current measurements at mooring 22, respectively. (bottom) Bulk Richardson number time series calculated from the Brunt–Väisälä frequency and squared shear time series (Rib). For clarity, the bulk Richardson number is plotted only when it is less than 50.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 0 0 0
PDF Downloads 0 0 0

Near-Resonant Ocean Response to Sea Breeze on a Stratified Continental Shelf

View More View Less
  • 1 Department of Oceanography, Texas A&M University, College Station, Texas
© Get Permissions
Full access

Abstract

The spatial structure and temporal characteristics of sea breeze and the associated coastal ocean response in the northwest Gulf of Mexico are investigated using moored instruments, hydrographic stations, and wind measurements. Near the study area of 30°N, motions in the diurnal–inertial band (DIB) may be significantly enhanced by a near-resonant condition between local inertial and diurnal forcing frequencies. Wavelet analysis is used to quantify the results. Results indicate that diurnal sea-breeze variability peaks in summer and extends at least 300 km offshore with continuous seaward phase propagation. The maximum DIB oceanic response occurs in June when there is a shallow mixed layer, strong stratification, and an approximately 10-day period of continuous sea-breeze forcing. DIB current variance decreases in July and August as the consequence of the deepening of the mixed layer and a more variable phase relationship between the wind and current. River discharge varies interannually and can significantly alter the oceanic response during summer. The “great flood” of the Mississippi River in 1993 deepened the summer mixed layer and reduced the sea-breeze response during that year. Vertically, DIB currents are surface intensified, with a first baroclinic modal structure. The significance of these DIB motions on the shelf is that they can provide considerable vertical mixing in summer, as seen by the suppression of the bulk Richardson number (by a factor of 30) during strong DIB events. This provides a potential mechanism to ventilate seasonally occurring near-bottom hypoxic waters of the coastal ocean.

Corresponding author address: Xiaoqian Zhang, 3146 TAMU, College Station, TX 77843-3146. Email: zhangxq@tamu.edu

Abstract

The spatial structure and temporal characteristics of sea breeze and the associated coastal ocean response in the northwest Gulf of Mexico are investigated using moored instruments, hydrographic stations, and wind measurements. Near the study area of 30°N, motions in the diurnal–inertial band (DIB) may be significantly enhanced by a near-resonant condition between local inertial and diurnal forcing frequencies. Wavelet analysis is used to quantify the results. Results indicate that diurnal sea-breeze variability peaks in summer and extends at least 300 km offshore with continuous seaward phase propagation. The maximum DIB oceanic response occurs in June when there is a shallow mixed layer, strong stratification, and an approximately 10-day period of continuous sea-breeze forcing. DIB current variance decreases in July and August as the consequence of the deepening of the mixed layer and a more variable phase relationship between the wind and current. River discharge varies interannually and can significantly alter the oceanic response during summer. The “great flood” of the Mississippi River in 1993 deepened the summer mixed layer and reduced the sea-breeze response during that year. Vertically, DIB currents are surface intensified, with a first baroclinic modal structure. The significance of these DIB motions on the shelf is that they can provide considerable vertical mixing in summer, as seen by the suppression of the bulk Richardson number (by a factor of 30) during strong DIB events. This provides a potential mechanism to ventilate seasonally occurring near-bottom hypoxic waters of the coastal ocean.

Corresponding author address: Xiaoqian Zhang, 3146 TAMU, College Station, TX 77843-3146. Email: zhangxq@tamu.edu

1. Introduction

The existence of sea-breeze circulation patterns in the atmosphere at coastal boundaries was recognized over a century ago (Davis et al. 1890). The diurnal heating of the land surface during summer months produces a land–sea thermal gradient that propagates as an atmospheric gravity current and forces cyclic onshore–offshore wind flows with 24-h periodicity. The traditional view of sea breeze is onshore flow during the day to replace rising motions heated at the coast. Numerous factors can contribute to the strength of the sea breeze, including synoptic and seasonal weather patterns, coastal topography, and latitude. Simpson (1994) provides an overview of many aspects of sea-breeze systems. Scatterometer satellite data indicate that sea-breeze winds are a ubiquitous feature of all ocean coastlines and can extend 100s of kilometers from the coast (Gille et al. 2003; Aparna et al. 2005).

Sea breeze has been investigated analytically and numerically. The previous theoretical investigation that has most relevance to our study is that of Rotunno (1983). His study considers the atmospheric response to heating at a land–sea boundary. Considering the linear and inviscid response, he determined the horizontal and vertical structure of sea-breeze circulation, which has the characteristics of a propagating wave equatorward of the critical latitude (30°N–S), but a trapped solution poleward of this. Another and perhaps more significant aspect of Rotunno’s results is the finding of a phase shift in sea breeze, with sea breeze being onshore during the night equatorward of 30° latitude. This is the result of the Coriolis and buoyancy terms in his circulation solution being in phase equatorward of 30° latitude. Poleward of 30° latitude, these terms are out of phase, making sea breeze onshore during the day. The reader is referred to Rotunno (1983) for the mathematical details [his Eqs. (4), (27), and (32)]. Thus, Rotunno’s results are only consistent with the conventional view of an onshore sea breeze during the day poleward of 30° latitude. This phase shift with latitude about 30° has not been previously observed, but is also seen in nonlinear numerical models (Yan and Anthes 1987).

The theory of the oceanic response to sea-breeze forcing is explored in two illuminating papers by Craig (1989a,b). At latitudes of 30°N–S, the diurnal period of sea-breeze forcing coincides with the Coriolis frequency of planetary rotation, resulting in a resonant effect that leads to a maximum ocean diurnal–inertial band (DIB) response. This resonance has been identified by Simpson et al. (2002) in current meter moorings off the coast of Namibia, which is close to 30°S. The oceanic response to sea-breeze forcing has also been studied at locations that are farther away from the critical latitude (Hunter et al. 2007; Rippeth et al. 2002). Sea-breeze winds decrease markedly at latitudes higher than 50°N/S (Gille et al. 2003).

The goal of this paper is to examine the spatial structure of sea-breeze winds in summer and the DIB ocean response to these winds on the Texas–Louisiana shelf (TLS) in the Gulf of Mexico, which is located at ∼30°N. DIB motions on this shelf have been studied by Chen et al. (1996) using the data collected during the first 6 months of the Texas–Louisiana Shelf Circulation and Transport Processes Study (LATEX) and by Chen and Xie (1997) using numerical simulations. DiMarco et al. (2000) found a near-resonant diurnal ocean response to sea-breeze forcing in the Gulf of Mexico with sea-breeze-driven motions representing the largest non-storm-driven motions on the TLS. This paper provides a more in-depth and quantitative analysis of diurnal wind fields over several years and illustrates the oceanic response from a more extensive dataset than has been considered previously. In particular, we focus on the following four new objectives: 1) to characterize the spatial structure of sea-breeze forcing in summer on the TLS, 2) to explain the occurrence of maximum DIB responses to sea-breeze forcing in June, 3) to examine the influence of buoyancy forcing (Mississippi River discharge) on the DIB response to sea-breeze forcing on the TLS, and 4) to explore the effects of sea-breeze-driven DIB motions on the promotion of vertical mixing on the TLS. We will begin with a description of the observational data and methodology in section 2. Section 3 discusses the temporal evolution and spatial structure of wind in the northwest Gulf of Mexico. The oceanic response to wind forcing (focusing on DIB) is addressed in section 4. We present the vertical structure of the DIB current and its effects on vertical mixing in section 5. A discussion and our conclusions are given in sections 6 and 7, respectively. Appendix A contains a description of the wavelet power spectrum, wavelet coherency, and phase spectrum used in this paper. The possibility of another critical latitude mechanism that can contribute to the DIB oceanic energy in the Gulf of Mexico is considered in appendix B.

2. Data and methodology

The oceanographic and meteorological observations used in this study were mainly collected during the LATEX project. The field component of the LATEX study spanned from April 1992 through December 1994 (Nowlin et al. 1998). Data considered include meteorological fields (Wang et al. 1996), moored current meter (DiMarco et al. 1997), and CTD temperature–salinity profiles (Howard and DiMarco 1998).

a. Data

1) Wind observations

A network of wind observation sites was maintained at eight meteorological buoys over the northwestern Gulf of Mexico throughout the LATEX study (Wang et al. 1996). The LATEX wind observations, in combination with the meteorological measurements collected from six National Data Buoy Center (NDBC) buoys, and nine Coastal-Marine Automated Network (C-MAN) sites (Fig. 1), were used in this paper to study the temporal evolution and spatial structures of sea breeze on the TLS. All wind products have a 1-h temporal sampling interval.

2) Moored time series

Horizontal current velocity, temperature, and conductivity (salinity) data were observed with 81 current meters from April 1992 through November 1994 at 31 mooring locations on the TLS (DiMarco et al. 1997). These current meters recorded at 5-min to 2-h intervals; however, most recorded at 30 min. Raw data were first 3-h, low-pass filtered using Lanczos filters to reduce high-frequency sampling noise. Filtered data were subsequently resampled to 1-h intervals. Data gaps of less than 6 h (mainly due to instrument replacement) were filled using linear interpolation, while longer gaps were filled using a maximum entropy (spectral preserving) method (DiMarco et al. 1997; DiMarco and Reid 1998).

This study focuses principally on two current mooring locations: moorings 21 (28.84°N, 94.08°W) and 22 (28.36°N, 93.96°W) (Fig. 1). Mooring 21 was in a total water depth of 24 m and had two current instruments positioned at 14 and 22 m below the surface. Mooring 22 was in a total water depth of 55 m and had three current instruments positioned at 3, 23, and 48 m, respectively. Prior to the analyses in this paper, eight principal tidal constituents (O1, K1, P1, Q1, S2, M2, K2, and N2) were removed from the current measurements using the T_Tide Harmonic Analysis Toolbox of Pawlowicz et al. (2002) to eliminate the influence of principal tidal energy. Estimated amplitudes of the diurnal tidal current components at moorings 21 and 22 average around 5 cm s−1 (DiMarco and Reid 1998).

3) Hydrographic data

Eighteen mooring maintenance cruises were undertaken during the LATEX study with a general interval of 60 days for the shallow-water moorings. CTD casts were taken during these cruises using a Sea-Bird SBE 19 self-contained CTD profiling instrument (Howard and DiMarco 1998). These casts were usually taken prior to the recovery and after the deployment of the mooring instruments. The CTD profiles taken at moorings 21 and 22 were used to show the temporal variability of stratification during spring and summer.

b. Wavelet methodology

To study the temporal evolution of different frequency components (especially the DIB component), wind and current measurements are analyzed with the wavelet transform. The Morlet wavelet is used in this paper and a description regarding the details of the wavelet methodology can be found in appendix A. The window width of the Morlet wavelet is approximately 22 × period and, so, is a function of the period of oscillation being analyzed. Therefore, for the DIB motions, the window width of the Morlet wavelet is ∼2.8 day (Torrence and Compo 1998). The main objective of this paper is to study the temporal variability that is associated with sea-breeze forcing. Therefore, after the wavelet spectrum is estimated, the variance associated with periods near 24 h, that is, the DIB, are calculated and analyzed. The definition of the DIB used here is from 20 (0.83 cpd) to 28 h (1.17 cpd), which covers both the diurnal (24 h) and inertial periods at moorings 21 (24.87 h) and 22 (25.26 h).

3. Temporal evolution and spatial structure of winds

In this section, we present an analysis of the meteorological forcing of the northwest Gulf of Mexico to characterize the spatial structure and temporal evolution of sea breeze based on the wind measurements described in section 2.

a. Sea breeze as the primary driver of summer diurnal wind variability

First, we consider the establishment of sea breeze as the primary driver of summer diurnal wind variability in the northern Gulf of Mexico. The presence of diurnal period wind energy is an assumption for the occurrence of the land–sea breeze and has been used to identify land–sea breeze regimes (Rotunno 1983; Masselink and Pattiaratchi 2001; Hyder et al. 2002; Simpson et al. 2002). Diurnal winds may be forced by mechanisms other than sea breeze on the TLS, such as synoptic wind events (Chen et al. 1996).

However, for the summer months (∼ the focus period of this paper) on the TLS, we determined that sea-breeze forcing is the main driver for the diurnal wind variability for the following reasons. First, from the diurnal wind ellipses in summer 1992 at stations SRST2 (Sabine Pass, Texas), 51, 22, GBCL1 (Garden Banks off the coast of Louisiana), and 42002 (east of Brownsville, Texas; see Fig. 1 for locations), we can see the phase propagation of the diurnal wind signal from the coast to 300 km offshore (see section 3c below). Second, we calculated the Fourier spectrum for the summer and nonsummer wind measurements at NDBC buoy 42002 (more than 300 km offshore) separately. The summer diurnal band wind energy is about 4 times as large as that of the nonsummer seasons (not shown). The significant summer enhancement of the diurnal peak at NDBC buoy 42002 and the clear phase propagation of sea-breeze signal offshore corroborate the fact that it is sea breeze driven. Third, large-scale synoptic wind events (i.e., atmospheric fronts) are rare on the TLS in the summer period, with an average of approximately one event per month in June and July (Nowlin et al. 1998).

For these reasons, the dominant temporal and spatial structures we find for the diurnal winds on the TLS in summer will be considered to represent that of sea breeze. During the nonsummer seasons, sea breeze becomes weaker and other mechanisms could contribute more to the diurnal wind energy. This hypothesis is consistent with the climatology of a land–sea-breeze system, which indicates the majority of land–sea-breeze days occur during the hot summer season due to the day–night variation of the temperature gradient between the land and the sea, with few such days in winter and the transitional periods of spring and fall (Hsu 1970; Hunter et al. 2007; Masselink and Pattiaratchi 2001; Furberg et al. 2002).

b. Temporal evolution

The wavelet power spectrum for the east–west wind component at NDBC buoy station PTAT2 (Port Aransas, Texas; Fig. 2) illustrates the temporal evolution of the wind variance from December 1997 to April 2004, which is the longest continuous wind time series available at these stations without any large gaps (small gaps are filled with linear interpolation). The magnitude of diurnal wind variance peaks in summer (June–August) and is weaker during the nonsummer (September–May) months. The summer diurnal peaks in the wind spectrum are mainly associated with sea breeze. The integrated variance in the diurnal band at this station is shown in the bottom panel of Fig. 2. Here, the diurnal wind variance is more than 6 m2 s−2 in summer and usually on the order of 0.1 m2 s−2 in the nonsummer months. The magnitude of the 3-month smoothed diurnal wind energy is remarkably similar during all six summers of the observation period. However, the greatest diurnal wind variance of up to 12 m2 s−2 occurs in July 2003 as a consequence of Hurricane Claudette during that month. This severe hurricane impulsively inputs a significant amount of energy in all frequency bands. This feature reveals an advantage of wavelet analysis compared to the often-used Fourier spectrum, by illustrating the temporal evolution of the spectrum associated with an extremely strong weather event, whereas with a Fourier representation, this event would be averaged into a spectral band estimated over the entire record length.

Wind energy in the weather band (periods of 2–8 days) is seen to be low during summer as compared to the nonsummer seasons (Fig. 2). As will be discussed, the absence of weather-band wind variance is important for the development of strong ocean DIB current oscillations in summer.

c. Spatial structure of sea breeze

Previously, sea breeze was considered to be confined to coastal areas in the Gulf of Mexico extending less than 50 km offshore from the coast (e.g., Chen et al. 1996). To investigate the spatial distribution of sea breeze in the northwestern Gulf of Mexico, wind measurements during the LATEX period were analyzed at locations shown in Fig. 1. Figure 3 shows the spatial distribution of the diurnal wind ellipses during the period 4–11 July 1992. This period of measurement is selected based on the following criteria: 1) the diurnal wind was strong, 2) the phase and amplitude of the diurnal wind were nearly constant, 3) there were no atmosphere frontal passages in this month (Nowlin et al. 1998), and 4) the data coverage was good on the shelf during this period. A Butterworth digital bandpass filter is first applied to the wind data at each station to isolate the diurnal wind component from other spectral components. A least squares harmonic analysis is then used to fit the 1-week diurnal wind time series to estimate the phase and amplitude of the east–west and north–south wind components, respectively. The diurnal ellipses in Fig. 3 are constructed from the phase and amplitude of the east–west and north–south diurnal wind components. A quantitative summary of these wind ellipses is listed in Table 1.

The magnitude of the diurnal wind ellipse (Fig. 3) exhibits somewhat complex spatial structure, presumably depending on a number of issues such as coastal geometry, Louisiana inland waters, and differential coastal heating. The magnitude of sea breeze increases offshore first and then decreases with distance offshore. The reason why sea breeze is relatively small near the coast might be related to frictional effects near the coast. The phase information of the diurnal winds is displayed as a solid red triangle on each ellipse; this represents a synoptic snapshot of the diurnal wind vectors at 1900 local time (Fig. 3). In some early analyses using the rotary spectrum, we determined that the energy in the anticyclonic (clockwise rotating) component of sea breeze and the near-inertial current exceeded the cyclonic (anticlockwise rotating) component by at least an order (and sometimes two orders) of magnitude on the TLS (not shown). The dominance of the anticyclonic motions is signified by the green arrow on land at the top of Fig. 3. This phase distribution indicates that the diurnal phase is leading at the near-coast stations and propagates offshore; this is consistent with the coastal origination of sea breeze. The phase distribution along the transect stations SRST2, 51, 22, GBCL1, and 42002 (Fig. 3 and Table 1) indicates sea breeze is not restricted to the coastal area, but can extend to more than 300 km offshore in summer, beyond the TLS to the deep ocean. Since all the diurnal wind vectors rotate clockwise, this phase distribution shows that it takes about 3 h for the sea-breeze signal to propagate from 30° to 26°N, indicating a phase speed of the diurnal winds of around 120 km h−1 during this time period. Figure 3 is shown here to be an example. We have examined these phase relationships for several other summer periods and find these results to be robust. More wind data are used in the full analysis later in this paper (see the next section).

4. Ocean current variability

Ocean currents on the continental shelf of the northwestern Gulf of Mexico are analyzed in a manner similar to that used for winds presented previously in section 3. First, wavelet power spectra are constructed for selected mooring locations. The top panel in Fig. 4 shows the wavelet power spectrum of the north–south current time series at the top meter (14 m) of mooring 21. From Fig. 4, the DIB current energy is clearly seen to peak in summer compared to the nonsummer seasons. The maximum DIB current variance occurs around 10 June during 1992 and 1994, and on 3 July during 1993. The increase in DIB current energy is episodic and can last from 2 to 10 days. The gray curve in the bottom panel in Fig. 4 shows the DIB current variance time series at the upper meter of mooring 21 during the LATEX study period, which can be as large as 200 cm2 s−2 and is an order of magnitude greater than that in the nonsummer seasons. The peaks of the DIB current are largest in summer 1994 and smallest in 1993. The reasons for the interannual variability are related to changes in stratification and will be discussed later.

The magnitude of the DIB currents is variable among different summer months. A wavelet analysis is performed on the 1-yr time series from December 1993 to November 1994 for the top meter (3 m) at mooring 22, when the observations have no gaps. The top panel in Fig. 5 shows the wavelet power spectrum of the north–south current time series from June to August 1994. The DIB current variance is much larger at mooring 22 in the summer of 1994 (Fig. 5) compared to that at mooring 21 (Fig. 4). This appears to be caused by the fact that the top meter at mooring 22 (3 m) is in the summer mixed layer while the top meter at mooring 21 (14 m) is below it. The maximum DIB current variance at mooring 22 is as large as 1400 cm2 s−2 in June while it only reaches about 700 cm2 s−2 in July or August (black curve in the middle panel in Fig. 5). In comparison, the weather band (2–8 days) current variance is also plotted in the middle panel in Fig. 5 (gray curve), which is much lower and less than 50 cm2 s−2 during most of the summertime. This demonstrates that the DIB current energy dominates on the shelf during the summertime, and when the DIB current variance is strongest in June, it contributes more than 90% of the total current energy at this location. The bandpassed diurnal wind time series at this station shows that sea breeze actually peaks during August 1994. The larger DIB response in June at moorings 21 and 22, despite peak sea-breeze forcing in August, appears to be related to two factors: the duration of the diurnal wind with uninterrupted phase and the strength of the stratification. We now examine these effects on the development of the DIB current response to sea-breeze forcing.

a. Effects of DIB phase on DIB response

The wavelet coherency and phase spectra between the north–south wind and current components at mooring 22 (3-m instrument) in January, June, and August 1994 are estimated (Figs. 6a–c, respectively). The red color in Fig. 6 means the coherency is high, while the blue means it is low. The arrows in Fig. 6 indicate the phase difference between the wind and current at each time with in phase pointing right, out of phase pointing left, and wind leading current by 90° pointing straight down. For clarity, only one vector is plotted per day at each period. We can see from Fig. 6b that the wind and current show significant coherency (γ2 > 0.9) in the DIB for most of June 1994. Low coherency occurs around 16 June 1994, when a cold front passes through the northwestern part of the Gulf of Mexico. In the DIB, the wind and current are almost in phase during June except for the interruption period of the front. During the frontal passage, the DIB wind and current become approximately 90° out of phase with the wind leading the currents and the coherency low and insignificant. The DIB wind and current are almost in phase with very high coherency for about 10 days during the period 5–14 June 1994. This corresponds to the period when the DIB current variance reaches 1400 cm2 s−2 (Fig. 5) and is also the highest of the measurement period. This suggests that the duration of the in-phase relationship between the wind and currents is important for the generation and accumulation of the DIB current energy. In the weather band, we can see that both the variance and coherency are very low during this period (Figs. 5 and 6b), indicating few events in the weather band. From this result, we conclude that the infrequency of summer frontal passages, particularly in June, contributes to the in-phase relationship between the wind and current in the DIB, and allows it to persist for up to 10 days without phase interruption. Because infrequent summer frontal passages are typical for this region (DiMego et al. 1976; Nowlin et al. 1998), we can expect these conditions to occur each summer. Because of the near-resonant condition at this latitude, the diurnal wind is very efficient in generating large DIB current energy. It can generate DIB ocean energy in several cycles, and the longer this in-phase relationship persists, the larger the magnitude of the DIB current becomes until a steady state is reached. The coherency is also very high, with an almost in-phase relationship in the DIB, during the periods of 21–24 June and 28–30 June, with a 3-day interruption from 25 to 27 June. The increased wind variance at this station around 25 June (not shown), as well as the high coherency in the weather band (Fig. 6b), indicates the occurrence of weather band processes. With this interference, the DIB current variance is only about 250 cm2 s−2 (Fig. 5).

Figure 6c shows the wavelet coherency and phase spectra for August 1994. The coherency between the wind and current is low compared to that found in June (Fig. 6b), with 95% of the significant coherency between 0.7 and 0.9 during 14–20, 22, and 28–29 August and very low coherency, less than 0.4, during the rest of the month. In August, the phase between the wind and current in the DIB changes more frequently than in June. However, during the high-coherency period of 14–20 August, the DIB wind and current are almost in phase, when the DIB current variance increases to 700 cm2 s−2 (Fig. 5). After that, the phase between the DIB wind and current gradually changes from in phase to 90° out of phase with leading wind on 22 August; the corresponding DIB current energy drops to 400 cm2 s−2. On 23 August, a relatively strong atmospheric front approaches the mooring location, which can also be seen from the high current variance between the 2- and 4-day periods in Fig. 5, and the DIB current energy drops down precipitously to less than 50 cm2 s−2 on 26 August, which is below the 95% significant level. The DIB current variance increases again to about 150 cm2 s−2 after the front (Fig. 5), which corresponds to the high-coherency patch between 28 and 29 August in Fig. 6c.

In comparison with the summer situation, the wavelet coherency and phase spectra for January 1994 at mooring 22 are an example that shows the phase relationship between the wind and currents during the nonsummer months (September–May; Fig. 6a). The diurnal wind variance in this month is typically less than 1.0 m2 s−2, indicating that strong sea breeze does not usually occur in nonsummer months. The wind and current coherencies in the DIB are low, below 0.4, and are not significant during most of January. In comparison with summer, the distribution of the DIB phase between the wind and current is highly variable and is, mainly, due to the passage of seven cold fronts (Nowlin et al. 1998). There is high coherency in the weather band in January. From Fig. 2, the weather band wind energy is strong in January on the TLS. This high coherency between the wind and current suggests that weather band processes dominate in this month of the year and is consistent with previous observational and numerical studies of the circulation of this shelf, which support the dominance of wind driving of the inner-shelf flow (DiMarco et al. 2000; Nowlin et al. 2005; Cho et al. 1998; Chen et al. 1996; Oey 1995).

b. Effects of stratification on DIB response

The DIB current energy at mooring 22 during June 1994 is approximately double that of August. This is likely because sea-breeze winds are continuous in June with fewer interruptions compared to August. This is also manifested in the coherency, which is also higher in June.

Additionally, stratification plays an important role in controlling the oceanic response to the sea breeze. Figure 7 shows a comparison of temperature and salinity profiles at moorings 21 and 22 for 28–29 May and 1 August 1994. (Because no CTD profiles are available for early June, we assume that the temperature and salinity profiles for 28–29 May are representative of the stratification in early June. This assumption is not unreasonable based on our examination of the moored time series records.) Figure 7 shows that the mixed layer depth in late May 1994 is about 3 m at both mooring stations. In contrast, on 1 August, the mixed layer extends to ∼15 m at mooring 21 and to ∼25 m at mooring 22. Considering a first baroclinic mode ocean response, diurnal wind forcing of a thicker upper layer can result in a weaker depth-averaged DIB response in August.

To further illustrate the importance of stratification, we calculate the correlation of the salinity and the DIB current variance time series at the top meter of mooring 21. The DIB current variance peaks are quite coincident with the salinity minimum period in summer (Fig. 4). The correlation coefficient between the salinity time series and the DIB current variance time series is 0.25 and is significant at the 99% significance level. This also indicates the important influence of stratification, which is partially determined by the river runoff (Belabbassi 2006), in determining the DIB ocean response to the sea-breeze forcing. The gray curve in Fig. 8 shows the top-meter salinity time series at mooring 22 in the summer months of 1994. We can see that the salinity changes from around 30 in June to around 33 in July and August 1994. This suggests the change in mixed layer depth from June to August, consistent with the CTD profiles.

From the wavelet power spectrum of 30-month current measurements for the top meter at mooring 21 (Fig. 4), the interannual variability of the DIB current energy is apparent. Peak DIB current variances during 1992 and 1994 are of similar magnitude and both occur in mid-June of each year. However, in 1993, the maximum value of the DIB current variance is about one-half to one-third of that in 1992 and 1994. Further, it occurs in early July 1993, or about 1 month from the peak time in 1992 and 1994. These differences are mainly caused by two factors: the difference in the stratification and the occurrence of synoptic wind variations in June 1993.

During 1993 an anomalously large discharge of the Mississippi River occurred when the Mississippi River basin in the midwestern United States recorded unusually high rainfall totals (Nowlin et al. 1998; Walker et al. 1994). The river discharge in April and May 1993 was on average 31 000 to approximately 32 000 m3 s−1, compared to typical spring values of 20 000 m3 s−1. It is estimated that there is about a 1-month lag between the discharge observations at Tarbert Landing, Mississippi, and arrival of river waters at midshelf locations (Wiseman et al. 1997). Therefore, the freshwater discharge reached moorings 21 and 22 around June. CTD profiles collected on 23 May 1993 indicate that the mixed layer depth is about 15 m (not shown), much deeper than the 3-m mixed layer observed at about the same time in 1994 (Fig. 7). Further, the vertical salinity gradient is significantly reduced as compared with 1992 and 1994. This deeper mixed layer at the mooring locations in June 1993 is probably caused by the combined effects of the large volume of freshwater discharge and the associated vertical mixing along the ∼500 km path from the mouth of the Mississippi River to the middle of the TLS. However, the details of the mixing between the freshwater and the fluid below along this long pathway are beyond the scope of this paper. The second factor is the occurrence of weather-band wind processes around 1 and 13 June 1994. As a consequence, the coherency is relatively low between the wind and current in June 1993 compared to that in 1992 and 1994, and the DIB phase between the wind and current is variable (not shown). Together, these two reasons explain the relative low DIB current energy in June 1993 and the forward shift in time of the peak variance compared with 1992 and 1994.

5. Vertical structure of the sea-breeze-driven DIB current and its effects on the vertical mixing on the TLS

In this section, the vertical structure of the DIB current and its effects on the vertical mixing will be discussed. First, the wavelet power spectrum is estimated for the current velocity time series collected in 1994 at the bottom meter (22 m) of mooring 21 and the middle meter (23 m) of mooring 22 (not shown; the current data for the bottom meter of mooring 22 are not suitable for analysis). The bottom meter at mooring 21 has about 6 months’ worth of continuous current records (May–November) and the middle meter at mooring 22 has about 10 month’s worth of continuous current records (February–November) during 1994. The DIB current variances at the bottom meter of mooring 21 and the middle meter of mooring 22 also peak in summer. However, the magnitude in the lower layer is weaker than that found at the top meters. The maximum DIB current variance at the bottom meter of mooring 21 is about 150 cm2 s−2, but the average value is <50 cm2 s−2 most of the time. The maximum DIB current variance at the middle meter of mooring 22 is only 200 cm2 s−2 and one-seventh of that at the top meter depth.

The wavelet coherency and phase spectra between the top and middle meter currents in June 1994 at mooring 22 (Fig. 9a) show a strong DIB current period during 1–16 June. The DIB currents at 3 and 23 m are very well correlated, with coherency greater than 0.9 and 180° phase. Based on the temperature and salinity profiles (Fig. 7), the pycnocline at mooring 22 in early June 1994 is between 5 and 15 m. Therefore, the top and middle current meters at mooring 22 are above and below the pycnocline, respectively. This reversal of the DIB current’s direction at depth indicates the first baroclinic mode response, which is consistent with the previous study on the TLS (Chen et al. 1996) and the Namibian shelf (Simpson et al. 2002).

Figure 9b shows the wavelet coherency and phase spectra between the top (14 m) and bottom (22 m) meter currents at mooring 21 during June 1994. The coherency is high during three time periods: 1–5, 9–12, and 23–26 June. DIB current variance is also large during these three periods (Fig. 4). The DIB currents for the top and bottom meters are out of phase (180° phase) during the first high-coherency period and in phase (zero phase) during the other two periods. A shoaling of the mixed layer may have occurred on 6 June 1994, which is indicated by the sudden decrease in the salinity from 35 to 33 at 14-m depth on 6 June (black curve in Fig. 8). This changes the location of the top current meter (14 m) from within the mixed layer to below the mixed layer. The top and bottom meters at mooring 21 change from being on different sides of the pycnocline during 1–5 June to being on the same side of the pycnocline during 9–12 June. As a consequence, the phase difference between the DIB currents for the top and bottom meters changes from being out of phase to in phase. This result also indicates that the first baroclinic mode structure existed for the DIB current at mooring 21 during these strong DIB current events during June 1994.

Previous research on this topic has indicated the first baroclinic mode structure associated with sea-breeze-driven DIB currents (Chen et al. 1996; Simpson et al. 2002; Rippeth et al. 2002). However, observations of vertically sheared currents are not in themselves evidence of mixing. To study the effects of sea-breeze-driven DIB currents on the vertical mixing, we need to know the relative importance of stratification versus shear, which can be characterized by the Richardson number. In this paper, the temperature, conductivity (salinity), and current measurements at the top (3 m) and middle (23 m) meters of mooring 22 are used to estimate the bulk Richardson number time series during June 1994, when sea-breeze-driven DIB currents are strongest at this location (Fig. 5). Previously, the bulk Richardson number has been used to study the stability of the upper ocean due to diurnal heating, cooling, and wind forcing (Price et al. 1986), as well as the vertical mixing rates in the thermocline (Gregg 1989). The bulk Richardson number calculated here from these two meters suggests the stability of the water column between 3 and 23 m. Mathematically, the bulk Richardson number can be calculated by
i1520-0485-39-9-2137-e51
where N is the Brunt–Väisälä frequency and S is the vertical current shear. The Brunt–Väisälä frequency N is defined as
i1520-0485-39-9-2137-e52
where ρ is the potential density calculated from the temperature and conductivity measurements at the top and middle meters, respectively; g is the gravity constant; ρ0 is the averaged potential density; and Δz is the distance between the two meters (20 m in this case). The vertical squared shear is defined as
i1520-0485-39-9-2137-e53
where Δu and Δυ are the east–west and north–south current differences between the top and middle meters, respectively.

Figure 10 shows the Brunt–Väisälä frequency, squared shear, and bulk Richardson number time series in June 1994 at mooring 22. Comparing Figs. 5 and 10, we find that when sea-breeze-driven DIB currents are strongest (∼12 June 1994), the velocity shear in the water column increases significantly and the stratification decreases, while the bulk Richardson number is smallest, with values on the order of 1. After the front passes by mooring 22 on 16 June 1994, the DIB motions are suppressed during the following week (Fig. 5). The corresponding bulk Richardson number becomes much larger (∼30 most of the time and occasionally even larger) because of the increase of the stratification and the significant decrease of the velocity shear. During another strong DIB current event (21–24 June 1994; Fig. 5), the bulk Richardson number is also suppressed. The bulk Richardson number time series shown in Fig. 10 supports the idea that strong DIB response events to sea-breeze forcing in summer could significantly enhance the vertical mixing in the water column on the TLS.

The eastern TLS experiences seasonal near-bottom hypoxia [dissolved oxygen concentration of less than 1.4 mL L−1; Rabalais et al. (2007)], which is believed to be caused by the combined effects of high nutrient loading that leads to eutrophication of the coastal waters (Turner and Rabalais 1994) and increased water column stability in summer (Wiseman et al. 1997; Hetland and DiMarco 2008). A mechanism such as sea breeze for increasing the vertical mixing and therefore increasing the ventilation of oxygen-poor bottom waters would contribute to the control of the extent, duration, and severity of the TLS hypoxic region; the details of which are beyond the scope of this paper.

6. Discussion

a. Cross-shelf phasing of sea breeze

The analyses of the observations presented here have provided some new details of the character of the sea-breeze wind field over the Gulf. Since the wind vectors in Fig. 3 represent a synoptic snapshot of the diurnal winds at 1900 local time (LT) and all rotate clockwise, we can see that sea breeze blows onshore approximately from 2100 to 0800 LT and is offshore from 0900 to 2000 LT in the middle of the shelf. This is counterintuitive from the traditional idea of an onshore sea breeze during the day and an offshore sea breeze at night, but is consistent with previous theoretical and numerical simulations (Rotunno 1983; Yan and Anthes 1987), which attributed this pattern to Coriolis and buoyancy forces in the solution being in phase equatorward of 30°N–S. The same theory and numerical simulations also predicted that, poleward of 30°N–S, the sea breeze winds are in phase with the heating cycle. The fact that sea breeze blows onshore north of 30° at 1900 LT at stations DPIA1 (Dauphin Island, Alabama) and 42007 (22 n mi south-southeast of Biloxi, Mississippi; see Fig. 1), and in the opposite direction as sea breeze in the middle shelf, is in agreement with their theory and numerical simulations. However, we realize that this phase shift at those two stations might also be related to the complexity of the coastline, and more measurements over a larger spatial scale are needed to fully evaluate this phenomenon in the future.

We note, however, that the phasing of the onshore wind along the Texas coastline can be quite complicated. For example, by comparing the phases of the onshore wind in Fig. 3, we note that the diurnal wind will blow shoreward near Port Aransas, Texas, roughly 5 h prior to a shoreward breeze at Sabine Pass, Texas. We have also documented cases in which the onshore–seaward oscillation is in phase along the curved coastline. Whether this is due to differential heating and cooling along the coastline or to larger mesoscale wind variability is not clear and warrants further investigation.

b. Connections to ocean inertial wave propagation

Although the present analysis is confined mostly to the continental shelf, the wind observations strongly indicate that the diurnal signal extends to the deep Gulf of Mexico and to the southern shelves. This will likely have implications for the mixing of upper-oceanic layers through the deepening of the mixed layer depth and the exchange between the continental shelf and the open ocean. Modeling analysis (Zhang et al. 2009 hereafter ZSDH) indicates that the oceanic response to sea-breeze forcing can be manifested as propagating Poincare waves, south of 30° latitude, thus establishing a basin-wide response. Therefore, the shelf response reported here is but a small part of a much larger response. Poincare waves have the characteristic that the group speed decreases with latitude, making them more efficient at transferring energy offshore in the southern portion of a basin with geometry like the Gulf of Mexico. Therefore, it is important to understand the dynamics of these propagating Poincare waves (e.g., wavelength, phase and group speed, energetics, and lateral energy flux), and their influence on the redistribution of sea-breeze-driven oceanic energy and mixing in the upper ocean. However, the present observations are unable to resolve these issues. A future publication emphasizing these aspects based on our numerical simulations is planned to clarify these issues (ZSDH).

7. Conclusions

This paper illustrates the spatial and temporal evolution of sea breeze and the near-resonant diurnal–inertial band (DIB) oceanic responses to sea breeze on the TLS in the Gulf of Mexico from an analysis of wind and current fields measured during the LATEX study. This research builds on several publications that covered similar topics (DiMarco et al. 2000; Simpson et al. 2002; Chen et al. 1996); however, this paper provides a more in-depth and quantitative analysis from a more extensive dataset than has been considered previously. In addition, wavelet analysis is used to quantify the results. Specific new results are listed as follow:

  1. The temporal and spatial structures of sea breeze on the TLS are examined. The diurnal wind energy in summer is significantly enhanced both at the nearshore stations and at stations as far as 300 km offshore (the offshore extent of the available wind observations). Sea-breeze winds are not trapped along the coast in summer, as was previously thought, but extend to at least 300 km from the coast and also propagate with time from the coast outward with offshore observations lagging those at the coast by as much as 3 h. These results are in agreement with linear theory, which posits that, equatorward of 30°, the atmospheric response takes the form of inertia–gravity waves that can propagate long distances up- and outward from the coast (Rotunno 1983; Nielsen-Gammon 2001, 2002a,b). The sea breeze blows offshore during the day and onshore at night south of 30°N over the middle of the TLS. This is counterintuitive from the traditional idea of an onshore sea breeze during the day and an offshore land breeze at night, but is consistent with previous theoretical and numerical simulations (Rotunno 1983; Yan and Anthes 1987).
  2. Considering the long east–west coastline involved, the near-resonant condition between local inertial and diurnal forcing frequencies makes the Gulf of Mexico particularly responsive to sea-breeze forcing during summer. Wavelet analysis results indicate a strong correlation between the onset sea-breeze forcing and the subsequent DIB ocean response in the upper mixed layer during this period. The maximum DIB currents occur in June over the middle TLS despite the sea-breeze peaks in August. In this paper, we use the wavelet analysis and hydrographic data to give an explanation of this apparent mismatch in the phase of the peak sea breeze (August) and peak DIB currents (June). This pattern is mainly caused by two reasons. First, the in-phase relationship of the sea-breeze forcing and DIB currents can persist longer without interruptions in June compared to August, which allows for the DIB currents to have longer periods to accumulate energy. Second, the ocean has a much shallower mixed layer in June (∼3 m) in comparison with August (∼25 m). The deepening of the mixed layer in August is mainly caused by the advection of the warmer and saltier water from the southwest portion of the TLS upcoast to the middle TLS due to the change of the prevailing wind direction in July (Nowlin et al. 2005; Nowlin et al. 1998; Cochrane and Kelly 1986; Cho et al. 1998).
  3. The Mississippi River discharge plays an important role in controlling the DIB ocean response to sea-breeze forcing over the TLS and this can vary interannually during summer months. This is evidenced by the “great flood” of the Mississippi River in 1993. In summer 1993, the DIB current peak over the middle TLS is about one-half to one-third of that in 1992 and 1994 and the peak variance time is shifted forward for about 1 month. The Mississippi River discharge increases by about 50% in spring 1993 compared to a normal year. This large influx of freshwater reaches the mooring locations in June and contributes to the deepening of the mixed layer. The deepening of mixed layer depth weakens the DIB current variance in June 1993 and causes the shift in the peak variance time.
  4. The sea-breeze-driven DIB currents could significantly enhance the vertical mixing over the TLS in summer as indicated by a reduction in the Richardson number. The bulk Richardson number calculated near the surface can be suppressed at least by a factor of 30 during strong DIB current events as compared to those periods when the DIB responses are small. High vertical mixing associated with sea breeze is of particular interest in regions on the TLS where hypoxia is found (Wiseman et al. 1997; Hetland and DiMarco 2008).
  5. Despite the fact that the emphasis here is on the TLS, these results have significant applications for other coastal oceans near 30°N–S. Likely examples are the East China Sea, where there is a broad shelf and large river inflow (Yangtze River); the mid-Atlantic Bight region of the eastern U.S. coastline; and the Persian–Arabian Gulf.

Acknowledgments

This work is dedicated to the memory of our friend and mentor Professor R. O. Reid who passed away in January 2009 and who provided many useful comments on this research. This study is funded by the U.S. Minerals Management Service under Contracts 1435-01-05-CT-39051 and 1435-0001-30509 and NOAA CSCOR Grant NA06NOS4780198. The program for the wavelet power spectrum used in this paper is based on the wavelet software provided by C. Torrence and G. Compo, which is available online (http://paos.colorado.edu/research/wavelets/). The program used for the wavelet coherency and phase spectra used in this paper is based on the software provided by A. Grinsted, J. C. Moore, and S. Jevrejeva and is available online (http://www.pol.ac.uk/home/research/waveletcoherence/). The authors thank Dr. D. A. Brooks and Dr. C. Epifanio (TAMU) for useful discussions on this research. We also thank three anonymous reviewers for their valuable comments and suggestions.

REFERENCES

  • Aparna, M., , S. R. Shetye, , D. Shankar, , S. S. C. Shenoi, , P. Mahra, , and R. G. P. Desai, 2005: Estimating the seaward extent of sea breeze from QuikSCAT scatterometry. Geophys. Res. Lett., 32 , L13601. doi:10.1029/2005GL023107.

    • Search Google Scholar
    • Export Citation
  • Belabbassi, L., 2006: Examination of the relationship of river water to occurrences of the bottom water with reduced oxygen concentrations in northern Gulf of Mexico. Ph.D. thesis, Texas A&M University, 119 pp.

  • Bunge, L., , C. Provost, , J. Lilly, , M. D’Orgeville, , A. Kartavtseff, , and J. Melice, 2006: Variability of the horizontal velocity structure in the upper 1600 m of the water column on the equator at 10°W. J. Phys. Oceanogr., 36 , 12871304.

    • Search Google Scholar
    • Export Citation
  • Chen, C., , and L. Xie, 1997: A numerical study of wind-induced, near-inertial oscillations over the Texas–Louisiana shelf. J. Geophys. Res., 102 , (C7). 1558315593.

    • Search Google Scholar
    • Export Citation
  • Chen, C., , R. O. Reid, , and W. D. Nowlin Jr., 1996: Near-inertial oscillations over the Texas–Louisiana shelf. J. Geophys. Res., 101 , (C2). 35093524.

    • Search Google Scholar
    • Export Citation
  • Cho, K., , R. O. Reid, , and W. D. Nowlin Jr., 1998: Objectively mapped streamfunction fields on the Texas–Louisiana shelf based on 32 months of moored current meter data. J. Geophys. Res., 103 , (C5). 1037710390.

    • Search Google Scholar
    • Export Citation
  • Cochrane, J. D., , and F. J. Kelly, 1986: Low-frequency circulation on the Texas–Louisiana continental shelf. J. Geophys. Res., 91 , (C9). 1064510659.

    • Search Google Scholar
    • Export Citation
  • Craig, P. D., 1989a: Constant eddy-viscosity models of vertical structure forced by periodic winds. Cont. Shelf Res., 9 , 343358.

  • Craig, P. D., 1989b: A model of diurnally forced vertical current structure near 30° latitude. Cont. Shelf Res., 9 , 965980.

  • Davis, W. M., , L. G. Schultz, , and R. De C Ward, 1890: An investigation of the sea breeze. Ann. Observ. Astron. Harvard. Coll., 21 , 215265.

    • Search Google Scholar
    • Export Citation
  • DiMarco, S. F., , and R. O. Reid, 1998: Characterization of the principal tidal current constituents on the Texas–Louisiana shelf. J. Geophys. Res., 103 , (C2). 30923109.

    • Search Google Scholar
    • Export Citation
  • DiMarco, S. F., , A. E. Jochens, , and M. K. Howard, 1997: LATEX shelf data report: Current meter moorings, April 1992 through December 1994. Dept. of Oceanography Tech. Rep. 97-01-T, Texas A&M University, College Station, TX, 61 pp. plus appendixes.

    • Search Google Scholar
    • Export Citation
  • DiMarco, S. F., , M. K. Howard, , and R. O. Reid, 2000: Seasonal variation of wind-driven diurnal current cycling on the Texas–Louisiana continental shelf. Geophys. Res. Lett., 27 , 10171020.

    • Search Google Scholar
    • Export Citation
  • DiMego, G. L., , L. F. Bosart, , and G. W. Endersen, 1976: An examination of the frequency and mean conditions surrounding frontal incursions into the Gulf of Mexico and Caribbean Sea. Mon. Wea. Rev., 104 , 708718.

    • Search Google Scholar
    • Export Citation
  • Foufoula-Georgiou, E., , and P. Kumar, Eds. 1995: Wavelets in Geophysics. Academic Press, 373 pp.

  • Furberg, M., , D. G. Steyn, , and M. Baldi, 2002: The climatology of sea breezes on Sardinia. Int. J. Climatol., 22 , 917932.

  • Gille, S. T., , S. G. Llewellyn Smith, , and S. M. Lee, 2003: Measuring the seabreeze from QuikSCAT scatterometry. Geophys. Res. Lett., 30 , 1114. doi:10.1029/2002GL016230.

    • Search Google Scholar
    • Export Citation
  • Gregg, M. C., 1989: Scaling turbulent dissipation in the thermocline. J. Geophys. Res., 94 , (C7). 96869698.

  • Grinsted, A., , J. C. Moore, , and S. Jevrejeva, 2004: Application of the cross wavelet transform and wavelet coherence to geophysical time series. Nonlinear Processes Geophys., 11 , 561566.

    • Search Google Scholar
    • Export Citation
  • Hetland, R. D., , and S. F. DiMarco, 2008: How does the character of oxygen demand control the structure of hypoxia on the Texas–Louisiana continental shelf? J. Mar. Syst., 70 , 4962.

    • Search Google Scholar
    • Export Citation
  • Howard, M. K., , and S. F. DiMarco, 1998: LATEX shelf DATA report: Drifters and Miscellaneous Instruments, April 1992 through December 1994. Dept. of Oceanography Tech. Rep. 98-2-T, Texas A&M University, College Station, TX, 34 pp. plus appendixes.

    • Search Google Scholar
    • Export Citation
  • Hsu, S. A., 1970: Coastal air-circulation system: Observations and empirical model. Mon. Wea. Rev., 98 , 487509.

  • Hunter, E., , R. Chant, , L. Bowers, , S. Glenn, , and J. Kohut, 2007: Spatial and temporal variability of diurnal wind forcing in the coastal ocean. Geophys. Res. Lett., 34 , L03607. doi:10.1029/2006GL028945.

    • Search Google Scholar
    • Export Citation
  • Hyder, P., , J. H. Simpson, , and S. Christopoulos, 2002: Sea-breeze forced diurnal surface currents in the Thermaikos Gulf, north-west Aegean. Cont. Shelf Res., 22 , 585601.

    • Search Google Scholar
    • Export Citation
  • Liu, Y., , X. S. Liang, , and R. H. Weisberg, 2007: Rectification of the bias in the wavelet power spectrum. J. Atmos. Oceanic Technol., 24 , 20932102.

    • Search Google Scholar
    • Export Citation
  • MacKinnon, J. A., , and K. B. Winters, 2005: Subtropical catastrophe: Significant loss of low-mode tidal energy at 28.9°N. Geophys. Res. Lett., 32 , L15605. doi:10.1029/2005GL023376.

    • Search Google Scholar
    • Export Citation
  • Masselink, G., , and C. B. Pattiaratchi, 2001: Characteristics of the sea breeze system in Perth, Western Australia, and its effect on the nearshore wave climate. J. Coastal Res., 17 , 173187.

    • Search Google Scholar
    • Export Citation
  • Nielsen-Gammon, J. W., 2001: Initial modeling of the August 2000 Houston–Galveston ozone episode. Rep. to the Texas Natural Resource Conservation Commission (TNRCC), 71 pp. [Available online at http://www.tceq.state.tx.us].

    • Search Google Scholar
    • Export Citation
  • Nielsen-Gammon, J. W., 2002a: Evaluation and comparison of preliminary meteorological modeling for the August 2000 Houston–Galveston ozone episode. Rep. to TNRCC, 83 pp. [Available online at http://www.tceq.state.tx.us].

    • Search Google Scholar
    • Export Citation
  • Nielsen-Gammon, J. W., 2002b: Meteorological modeling for the August 2000 Houston–Galveston ozone episode: PBL characteristics, nudging procedure, and performance evaluation. Rep. to TNRCC, 109 pp. [Available online at http://www.tceq.state.tx.us].

    • Search Google Scholar
    • Export Citation
  • Nowlin Jr., W. D., , A. E. Jochens, , R. O. Reid, , and S. F. DiMarco, 1998: Texas–Louisiana Shelf Circulation and Transport Processes Study: Synthesis report. Vol. I. Tech. Rep. OCS Study MMS 98-0035, Gulf of Mexico OCS Region, Minerals Management Service, U.S. Dept. of the Interior, New Orleans, LA, 502 pp.

    • Search Google Scholar
    • Export Citation
  • Nowlin Jr., W. D., , A. E. Jochens, , S. F. DiMarco, , R. O. Reid, , and M. K. Howard, 2005: Low-frequency circulation over the Texas-Louisiana continental shelf. Circulation in the Gulf of Mexico: Observations and Models, Geophys. Monogr., Vol. 161, Amer. Geophys. Union, 219–240.

    • Search Google Scholar
    • Export Citation
  • Oey, L-Y., 1995: Eddy- and wind-forced shelf circulation. J. Geophys. Res., 100 , (C5). 86218637.

  • Pawlowicz, R., , B. Beardsley, , and S. Lentz, 2002: Classical tidal harmonic including error estimates in MATLAB using T-TIDE. Comput. Geosci., 28 , 929937.

    • Search Google Scholar
    • Export Citation
  • Price, J. F., , R. A. Weller, , and R. Pinkel, 1986: Diurnal cycling: Observations and models of the upper ocean response to diurnal heating, cooling, and wind mixing. J. Geophys. Res., 91 , (C7). 84118427.

    • Search Google Scholar
    • Export Citation
  • Rabalais, N. N., , R. E. Turner, , B. K. Sen Gupta, , D. F. Boesch, , P. Chapman, , and M. C. Murrell, 2007: Hypoxia in the northern Gulf of Mexico: Does the science support the plan to reduce, mitigate, and control hypoxia? Estuaries Coasts, 30 , 753772.

    • Search Google Scholar
    • Export Citation
  • Rippeth, T. P., , J. H. Simpson, , R. J. Player, , and M. Garcia, 2002: Current oscillations in the diurnal–inertial band on the Cataloninan shelf in spring. Cont. Shelf Res., 22 , 247265.

    • Search Google Scholar
    • Export Citation
  • Rotunno, R., 1983: On the linear theory of the land and sea breeze. J. Atmos. Sci., 40 , 19992009.

  • Schott, F. A., , M. Dengler, , R. Zantopp, , L. Stramma, , J. Fischer, , and P. Brandt, 2005: The shallow and deep western boundary circulation of the South Atlantic at 5°–11°S. J. Phys. Oceanogr., 35 , 20312053.

    • Search Google Scholar
    • Export Citation
  • Simmons, H. L., , R. W. Hallberg, , and B. K. Arbic, 2004: Internal wave generation in a global baroclinic tide model. Deep-Sea Res. II, 51 , 30433068.

    • Search Google Scholar
    • Export Citation
  • Simpson, J. E., 1994: Sea Breeze and Local Wind. Cambridge University Press, 234 pp.

  • Simpson, J. H., , T. P. Rippeth, , P. Hyder, , and I. M. Lucas, 2002: Forced oscillations near the critical latitude for diurnal–inertial resonance. J. Phys. Oceanogr., 32 , 177187.

    • Search Google Scholar
    • Export Citation
  • Torrence, C., , and G. P. Compo, 1998: A practical guide to wavelet analysis. Bull. Amer. Meteor. Soc., 79 , 6178.

  • Torrence, C., , and P. J. Webster, 1999: Interdecadal changes in the ENSO–monsoon system. J. Climate, 12 , 26792690.

  • Turner, R. E., , and N. N. Rabalais, 1994: Coastal eutrophication near the Mississippi River delta. Nature, 368 , 619621.

  • van Haren, H., 2005: Tidal and near-inertial peak variations around the diurnal critical latitude. Geophys. Res. Lett., 32 , L23611. doi:10.1029/2005GL024160.

    • Search Google Scholar
    • Export Citation
  • van Haren, H., 2007: Longitudinal and topographic variations in North Atlantic tidal and inertial energy around latitudes 30 ± 10°N. J. Geophys. Res., 112 , C10020. doi:10.1029/2007JC004193.

    • Search Google Scholar
    • Export Citation
  • Walker, N. D., , G. S. Fargion, , L. J. Rouse, , and D. C. Biggs, 1994: The great flood of summer 1993: Mississippi River discharge studied. Eos, Trans. Amer. Geophys. Union, 75 (36) 409.

    • Search Google Scholar
    • Export Citation
  • Wang, W., , M. K. Howard, , W. D. Nowlin Jr., , and R. O. Reid, 1996: LATEX shelf data report: Meteorological, April 1992 through December 1994. Dept. of Oceanography Tech. Rep. 96-2-T, Texas A&M University, College Station, TX, 34 pp. plus appendixes.

    • Search Google Scholar
    • Export Citation
  • Wiseman, W. J., , N. N. Rabalais, , R. E. Turner, , S. P. Dinnel, , and A. MacNaughton, 1997: Seasonal and interannual variability within the Louisiana coastal current: Stratification and hypoxia. J. Mar. Syst., 12 , 237248.

    • Search Google Scholar
    • Export Citation
  • Yan, H., , and R. A. Anthes, 1987: The effect of latitude on sea breeze. Mon. Wea. Rev., 115 , 936956.

  • Zhang, X., , D. C. Smith IV, , S. F. DiMarco, , and R. D. Hetland, 2009: A numerical study of sea-breeze-driven ocean Poincare wave propagation and mixing near the critical latitude. J. Phys. Oceanogr., in press.

    • Search Google Scholar
    • Export Citation

APPENDIX A

Wavelet Analysis Methodology

Wavelet analysis has been used in previous studies to examine the temporal variability of ocean currents at certain frequency bands (e.g., Schott et al. 2005; Bunge et al. 2006). The wavelet package developed by Torrence and Compo (1998, hereafter TC98) is used for this study. The wavelet base function is chosen to be Morlet, which is often used in geographical data analyses. The functional form of the Morlet wavelet is composed of a complex exponential modulated by a Gaussian envelope: , where t is the time, s is the wavelet scale, and ω0 is a nondimensional frequency. For ω0 = 6 used here, there are approximately three oscillations within the Gaussian envelope. For the Morlet wavelet, the wavelet scale s is almost identical to the corresponding Fourier period of the complex exponential; hence, the two terms scale and period are used interchangeably in this paper. A recent reported bias problem in TC98 is also removed based on Liu et al. (2007). Further details on wavelet analysis can be found in Foufoula-Georgiou and Kumar (1995).

Wavelet power spectrum

The wavelet power spectrum, defined as the squared absolute value of the wavelet transform, estimates the variance at each period as a function of time. To test our confidence in the peaks in the wavelet power spectrum, an appropriate background spectrum is needed. Based on the data analyzed in this paper, a theoretical red-noise wavelet power spectrum (TC98) is used to establish a null hypothesis for the confidence of a peak in the wavelet power spectrum. The wavelet power spectrum is then distributed as a chi square about the background spectrum.

Wavelet coherency spectrum

In this paper, the wavelet-squared coherency is used to study the temporal change of coherency for a given frequency band. The cross-wavelet spectrum is defined as
i1520-0485-39-9-2137-ea1
where Wnx(s) and Wny(s) are the wavelet transforms of two time series x and y, respectively; n is the time index; s is the scale; and the asterisk (*) indicates a complex conjugate. The wavelet squared coherency is then defined as the squared absolute value of the smoothed cross-wavelet spectrum, normalized by the smoothed wavelet power spectra:
i1520-0485-39-9-2137-ea2
where 〈·〉 indicates ensemble averaging in both time and scale (Torrence and Webster 1999).

The statistical confidence level of the wavelet coherence is estimated using Monte Carlo methods. A large number (300 in this paper) of red-noise time series pairs with similar distributions of the data are generated. For each pair, the wavelet coherence is calculated, and the confidence level for each scale is then estimated based on this large set of wavelet coherence spectra. A detailed description of how the confidence level is estimated for the wavelet coherency spectrum can be found in Grinsted et al. (2004) and TC98.

APPENDIX B

Parametric Subharmonic Instability

This paper examines the near-resonant DIB coastal ocean response to sea-breeze forcing near a critical latitude. Previously, modeling results and observations have demonstrated locally enhanced DIB energy and diminished semidiurnal tidal energy near 30°N/S; these results are partially due to another critical latitude mechanism: parametric subharmonic instability (PSI; van Haren 2005, 2007). This mechanism, which involves the nonlinear transfer of energy among energetic tidal frequency ocean wave modes, was not considered in previous sea-breeze papers. MacKinnon and Winters (2005) found significant energy transfer from semidiurnal tides to higher-frequency near-inertial motions near 28.9°N using numerical simulations. Since our mooring locations are so close to this latitude, we find it necessary to address this mechanism and our rationale for excluding it as a resonant mechanism over the TLS in more detail.

We believe the enhancement of DIB energy over the TLS in summer is not mainly caused by PSI for the following reasons. First, the dominant semidiurnal tide, M2, is weak over the TLS, with an averaged amplitude of roughly 5 cm s−1 at moorings 21 and 22 (midshelf), and less than 1 cm s−1 at the shelf edge, which is an order of magnitude smaller and less than the DIB motions in summer (DiMarco and Reid 1998). The north–south semidiurnal tidal current time series at mooring 22 in summer 1994 displays little variability from June to August (Fig. 5, bottom). The tidal current ranges from 3.5 (neap tide) to 5.3 cm s−1 (spring tide) at this location. This is not consistent with the variation of the DIB band variance during the same period (Fig. 5, middle). Second, we do not see any evidence that indicates that the semidiurnal tides are larger in summer than the nonsummer seasons. Therefore, if the PSI mechanism is important on the shelf, we should see a transfer of semidiurnal tidal energy to the DIB in all seasons. However, these motions are much weaker during the nonsummer seasons. Third, modeling results and observations suggest PSI might be important near the hot spots of baroclinic semidiurnal tidal energy conversion (e.g., midocean ridges) (van Haren 2005; Simmons et al. 2004). However, the TLS has a very shallow and wide bathymetry and the baroclinic semidiurnal tidal conversion rate is low in the Gulf of Mexico (Simmons et al. 2004), which makes PSI less likely to be important in the Gulf.

Fig. 1.
Fig. 1.

Map of the northwest Gulf of Mexico showing the TLS. Wind observations are available at all of these stations during the LATEX period. Current measurements at LATEX moorings 21 and 22 are analyzed and discussed in this paper. Isobaths shown are 10, 50, 100, 200, and 1000 m.

Citation: Journal of Physical Oceanography 39, 9; 10.1175/2009JPO4054.1

Fig. 2.
Fig. 2.

(top) Wavelet power spectrum (unitless) of the normalized 10-m east–west wind component (mean value was subtracted from the time series and then normalized by the standard deviation) at NDBC buoy station PTAT2 (27.83°N, 97.05°W). Only significant values are plotted, which are >95% confidence for a red-noise process with a lag-1 coefficient of 0.72 (Torrence and Compo 1998). (bottom) The gray solid curve is the frequency- (period) averaged wavelet variance time series (m2 s−2) over the 0.83–1.17-cpd band during the observation period. The black solid curve is the 3-month low-passed values of the gray curve. The horizontal gray dashed line is the 95% confidence level. The black bars indicate summer periods.

Citation: Journal of Physical Oceanography 39, 9; 10.1175/2009JPO4054.1

Fig. 3.
Fig. 3.

Diurnal wind ellipses for 4–11 Jul 1992, calculated from harmonic analysis of the wind measurement time series taken at the center of each ellipse during the LATEX project (see Fig. 1 for base map). The vectors shown are displayed in the oceanographic convention (vectors show direction toward which flow is going) and represent a synoptic snapshot of sea breeze at 1900 LT. The diurnal band used for this plot is from 0.95 to 1.05 cpd. Note: only stations that have data coverage during this period are plotted.

Citation: Journal of Physical Oceanography 39, 9; 10.1175/2009JPO4054.1

Fig. 4.
Fig. 4.

(top) Wavelet power spectrum (unitless) for the hourly north–south current time series at the upper meter (14 m) of mooring 21. Only significant values are plotted, which are those >95% confidence for a red-noise process with a lag-1 coefficient of 0.72 (Torrence and Compo 1998). The two gray lines on either end indicate the “cone of influence,” where edge effects become important. (bottom) The gray solid curve is the frequency- (period) averaged wavelet variance time series (cm2 s−2) over the 0.83–1.17-cpd band during the observation period. The black curve is the 1-month low-passed values of the gray curve. The horizontal gray dashed line is the 95% confidence level. The black dashed–dotted curve is the 2-day running averaged salinity time series at the top meter of mooring 21.

Citation: Journal of Physical Oceanography 39, 9; 10.1175/2009JPO4054.1

Fig. 5.
Fig. 5.

(top) Wavelet power spectrum (unitless) for the hourly north–south current time series from December 1993 to November 1994 at the top meter (3 m) of mooring 22. Only the wavelet spectrum from June to August 1994 is plotted. Only significant values are plotted, which are those >95% confidence for a red-noise process with a lag-1 coefficient of 0.72 (Torrence and Compo 1998). (middle) The black curve is the frequency- (period) averaged wavelet variance time series (cm2 s−2) over the 0.83–1.17-cpd band, and the gray curve is the frequency- (period) averaged wavelet variance over the 2–8-cpd band during summer 1994. The horizontal gray dashed line is the 95% confidence level. (bottom) North–south semidiurnal tidal current time series in summer 1994, calculated using the T_Tide Harmonic Analysis Toolbox of Pawlowicz et al. (2002).

Citation: Journal of Physical Oceanography 39, 9; 10.1175/2009JPO4054.1

Fig. 6.
Fig. 6.

(a) Squared wavelet coherency and phase spectra between the north–south wind component and the north–south current component at mooring 22 during January 1994. The thick contour encloses regions of >95% confidence from a Monte Carlo simulation of wavelet coherency between 300 sets (two each) of red-noise time series. The vectors indicate the phase difference between the wind and current at different frequencies (with in phase pointing right, out of phase pointing left, and wind leading current by 90° pointing straight down). Only one vector is plotted for each day. Thirty vectors are plotted in the frequency–period domain. (b) Same as in (a), but for June 1994. (c) Same as in (a), but for August 1994.

Citation: Journal of Physical Oceanography 39, 9; 10.1175/2009JPO4054.1

Fig. 7.
Fig. 7.

(a) Profiles of salinity and temperature at mooring 21. The measurements were made on 28 May 1994. (b) Same as in (a), but for 1 Aug 1994. (c) Profiles of temperature and salinity at mooring 22. The measurements were made on 29 May 1994. (d) Same as in (c), but on 1 Aug 1994. Triangles in each panel represent the current meter locations on moorings 21 and 22, respectively.

Citation: Journal of Physical Oceanography 39, 9; 10.1175/2009JPO4054.1

Fig. 8.
Fig. 8.

Salinity time series at moorings 21 and 22 from June to August 1994. Black curve is the top meter (14 m) salinity time series at mooring 21 and gray curve is the top meter (3 m) salinity time series at mooring 22. Note: scale is changed for clarity.

Citation: Journal of Physical Oceanography 39, 9; 10.1175/2009JPO4054.1

Fig. 9.
Fig. 9.

(a) Squared wavelet coherency and phase between the north–south current components of mooring 22 at 3 m (top meter) and at 23 m (middle meter) in June 1994. (b) Squared wavelet coherency and phase between the north–south current components of mooring 21 at 14 m (top meter) and at 22 m (bottom meter) during June 1994.

Citation: Journal of Physical Oceanography 39, 9; 10.1175/2009JPO4054.1

Fig. 10.
Fig. 10.

(top) The black and gray curves are the Brunt–Väisälä frequency and squared shear time series calculated from the temperature, conductivity, and current measurements at mooring 22, respectively. (bottom) Bulk Richardson number time series calculated from the Brunt–Väisälä frequency and squared shear time series (Rib). For clarity, the bulk Richardson number is plotted only when it is less than 50.

Citation: Journal of Physical Oceanography 39, 9; 10.1175/2009JPO4054.1

Table 1.

Statistics for the diurnal wind ellipses during the period 4–11 Jul 1992. All the angles are compass angles relative to north.

Table 1.
Save