Abstract

We flew an airborne lidar perpendicular to the coastline along straight-line transects that varied in length between 230 and 280km. The sample spacing was 3m, so we sampled almost five decades of spatial scales. Except for the return from right at the surface, the power spectra of backscattered power had a power-law dependence on spatial frequency, with a slope of 1.49. This corresponds to a fractal dimension of 1.76. This implies that the distribution is not as patchy as that of a purely turbulent process.

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References

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  1. J. Feder, Fractals (Plenum, l988).
  2. V. V. Zosimov and K. A. Naugolnykh, "Fractal structure of large-scale variability of wind-driven waves according to laser-scanning data," Chaos 4, 21-24 (1994).
    [CrossRef] [PubMed]
  3. J. A. Shaw and J. H. Churnside, "Fractal laser glints from the ocean surface," J. Opt. Soc. Am. A 14, 1144-1150 (1997).
    [CrossRef]
  4. S. Lovejoy, D. Schertzer, Y. Tessier, and H. Gaonac'h, "Multifractals and resolution-independent remote sensing algorithms: the example of ocean colour," Int. J. Remote Sens. 22, 1191-1234 (2001).
    [CrossRef]
  5. J. H. Churnside, J. J. Wilson, and V. V. Tatarskii, "Airborne LIDAR for fisheries applications," Opt. Eng. 40, 406-414 (2001).
    [CrossRef]
  6. E. D. Brown, J. H. Churnside, R. L. Collins, T. Veenstra, J. J. Wilson, and K. Abnett, "Remote sensing of capelin and other biological features in the North Pacific using LIDAR and video technology," ICES J. Mar. Sci. 59, 1120-1130 (2002).
    [CrossRef]
  7. J. H. Churnside, D. A. Demer, and B. Mahmoudi, "A comparison of LIDAR and echosounder measurements of fish schools in the Gulf of Mexico," ICES J. Mar. Sci. 60, 147-154 (2003).
    [CrossRef]
  8. J. H. Churnside and L. A. Ostrovsky, "LIDAR observation of a strongly nonlinear internal wave train in the Gulf of Alaska," Int. J. Remote Sens. 26, 167-177 (2005).
    [CrossRef]
  9. See National Data Buoy Center at http://www.ndbc.noaa.gov/index.shtml.
  10. L. Seuront, F. Schmitt, Y. Lagadeuc, D. Schertzer, and S. Lovejoy, "Multifractal analysis of phytoplankton biomass and temperature in the ocean," Geophys. Res. Lett. 23, 3591-3594 (1996).
    [CrossRef]
  11. N. C. Makris, P. Ratilal, D. T. Symonds, S. Jagannathan, S. Lee, and R. W. Nero, "Fish population and behavior revealed by instantaneous continental shelf-scale imaging," Science 311, 660-663 (2006).
    [CrossRef] [PubMed]

2006

N. C. Makris, P. Ratilal, D. T. Symonds, S. Jagannathan, S. Lee, and R. W. Nero, "Fish population and behavior revealed by instantaneous continental shelf-scale imaging," Science 311, 660-663 (2006).
[CrossRef] [PubMed]

2005

J. H. Churnside and L. A. Ostrovsky, "LIDAR observation of a strongly nonlinear internal wave train in the Gulf of Alaska," Int. J. Remote Sens. 26, 167-177 (2005).
[CrossRef]

2003

J. H. Churnside, D. A. Demer, and B. Mahmoudi, "A comparison of LIDAR and echosounder measurements of fish schools in the Gulf of Mexico," ICES J. Mar. Sci. 60, 147-154 (2003).
[CrossRef]

2002

E. D. Brown, J. H. Churnside, R. L. Collins, T. Veenstra, J. J. Wilson, and K. Abnett, "Remote sensing of capelin and other biological features in the North Pacific using LIDAR and video technology," ICES J. Mar. Sci. 59, 1120-1130 (2002).
[CrossRef]

2001

S. Lovejoy, D. Schertzer, Y. Tessier, and H. Gaonac'h, "Multifractals and resolution-independent remote sensing algorithms: the example of ocean colour," Int. J. Remote Sens. 22, 1191-1234 (2001).
[CrossRef]

J. H. Churnside, J. J. Wilson, and V. V. Tatarskii, "Airborne LIDAR for fisheries applications," Opt. Eng. 40, 406-414 (2001).
[CrossRef]

1997

1996

L. Seuront, F. Schmitt, Y. Lagadeuc, D. Schertzer, and S. Lovejoy, "Multifractal analysis of phytoplankton biomass and temperature in the ocean," Geophys. Res. Lett. 23, 3591-3594 (1996).
[CrossRef]

1994

V. V. Zosimov and K. A. Naugolnykh, "Fractal structure of large-scale variability of wind-driven waves according to laser-scanning data," Chaos 4, 21-24 (1994).
[CrossRef] [PubMed]

Abnett, K.

E. D. Brown, J. H. Churnside, R. L. Collins, T. Veenstra, J. J. Wilson, and K. Abnett, "Remote sensing of capelin and other biological features in the North Pacific using LIDAR and video technology," ICES J. Mar. Sci. 59, 1120-1130 (2002).
[CrossRef]

Brown, E. D.

E. D. Brown, J. H. Churnside, R. L. Collins, T. Veenstra, J. J. Wilson, and K. Abnett, "Remote sensing of capelin and other biological features in the North Pacific using LIDAR and video technology," ICES J. Mar. Sci. 59, 1120-1130 (2002).
[CrossRef]

Churnside, J. H.

J. H. Churnside and L. A. Ostrovsky, "LIDAR observation of a strongly nonlinear internal wave train in the Gulf of Alaska," Int. J. Remote Sens. 26, 167-177 (2005).
[CrossRef]

J. H. Churnside, D. A. Demer, and B. Mahmoudi, "A comparison of LIDAR and echosounder measurements of fish schools in the Gulf of Mexico," ICES J. Mar. Sci. 60, 147-154 (2003).
[CrossRef]

E. D. Brown, J. H. Churnside, R. L. Collins, T. Veenstra, J. J. Wilson, and K. Abnett, "Remote sensing of capelin and other biological features in the North Pacific using LIDAR and video technology," ICES J. Mar. Sci. 59, 1120-1130 (2002).
[CrossRef]

J. H. Churnside, J. J. Wilson, and V. V. Tatarskii, "Airborne LIDAR for fisheries applications," Opt. Eng. 40, 406-414 (2001).
[CrossRef]

J. A. Shaw and J. H. Churnside, "Fractal laser glints from the ocean surface," J. Opt. Soc. Am. A 14, 1144-1150 (1997).
[CrossRef]

Collins, R. L.

E. D. Brown, J. H. Churnside, R. L. Collins, T. Veenstra, J. J. Wilson, and K. Abnett, "Remote sensing of capelin and other biological features in the North Pacific using LIDAR and video technology," ICES J. Mar. Sci. 59, 1120-1130 (2002).
[CrossRef]

Demer, D. A.

J. H. Churnside, D. A. Demer, and B. Mahmoudi, "A comparison of LIDAR and echosounder measurements of fish schools in the Gulf of Mexico," ICES J. Mar. Sci. 60, 147-154 (2003).
[CrossRef]

Feder, J.

J. Feder, Fractals (Plenum, l988).

Gaonac'h, H.

S. Lovejoy, D. Schertzer, Y. Tessier, and H. Gaonac'h, "Multifractals and resolution-independent remote sensing algorithms: the example of ocean colour," Int. J. Remote Sens. 22, 1191-1234 (2001).
[CrossRef]

Jagannathan, S.

N. C. Makris, P. Ratilal, D. T. Symonds, S. Jagannathan, S. Lee, and R. W. Nero, "Fish population and behavior revealed by instantaneous continental shelf-scale imaging," Science 311, 660-663 (2006).
[CrossRef] [PubMed]

Lagadeuc, Y.

L. Seuront, F. Schmitt, Y. Lagadeuc, D. Schertzer, and S. Lovejoy, "Multifractal analysis of phytoplankton biomass and temperature in the ocean," Geophys. Res. Lett. 23, 3591-3594 (1996).
[CrossRef]

Lee, S.

N. C. Makris, P. Ratilal, D. T. Symonds, S. Jagannathan, S. Lee, and R. W. Nero, "Fish population and behavior revealed by instantaneous continental shelf-scale imaging," Science 311, 660-663 (2006).
[CrossRef] [PubMed]

Lovejoy, S.

S. Lovejoy, D. Schertzer, Y. Tessier, and H. Gaonac'h, "Multifractals and resolution-independent remote sensing algorithms: the example of ocean colour," Int. J. Remote Sens. 22, 1191-1234 (2001).
[CrossRef]

L. Seuront, F. Schmitt, Y. Lagadeuc, D. Schertzer, and S. Lovejoy, "Multifractal analysis of phytoplankton biomass and temperature in the ocean," Geophys. Res. Lett. 23, 3591-3594 (1996).
[CrossRef]

Mahmoudi, B.

J. H. Churnside, D. A. Demer, and B. Mahmoudi, "A comparison of LIDAR and echosounder measurements of fish schools in the Gulf of Mexico," ICES J. Mar. Sci. 60, 147-154 (2003).
[CrossRef]

Makris, N. C.

N. C. Makris, P. Ratilal, D. T. Symonds, S. Jagannathan, S. Lee, and R. W. Nero, "Fish population and behavior revealed by instantaneous continental shelf-scale imaging," Science 311, 660-663 (2006).
[CrossRef] [PubMed]

Naugolnykh, K. A.

V. V. Zosimov and K. A. Naugolnykh, "Fractal structure of large-scale variability of wind-driven waves according to laser-scanning data," Chaos 4, 21-24 (1994).
[CrossRef] [PubMed]

Nero, R. W.

N. C. Makris, P. Ratilal, D. T. Symonds, S. Jagannathan, S. Lee, and R. W. Nero, "Fish population and behavior revealed by instantaneous continental shelf-scale imaging," Science 311, 660-663 (2006).
[CrossRef] [PubMed]

Ostrovsky, L. A.

J. H. Churnside and L. A. Ostrovsky, "LIDAR observation of a strongly nonlinear internal wave train in the Gulf of Alaska," Int. J. Remote Sens. 26, 167-177 (2005).
[CrossRef]

Ratilal, P.

N. C. Makris, P. Ratilal, D. T. Symonds, S. Jagannathan, S. Lee, and R. W. Nero, "Fish population and behavior revealed by instantaneous continental shelf-scale imaging," Science 311, 660-663 (2006).
[CrossRef] [PubMed]

Schertzer, D.

S. Lovejoy, D. Schertzer, Y. Tessier, and H. Gaonac'h, "Multifractals and resolution-independent remote sensing algorithms: the example of ocean colour," Int. J. Remote Sens. 22, 1191-1234 (2001).
[CrossRef]

L. Seuront, F. Schmitt, Y. Lagadeuc, D. Schertzer, and S. Lovejoy, "Multifractal analysis of phytoplankton biomass and temperature in the ocean," Geophys. Res. Lett. 23, 3591-3594 (1996).
[CrossRef]

Schmitt, F.

L. Seuront, F. Schmitt, Y. Lagadeuc, D. Schertzer, and S. Lovejoy, "Multifractal analysis of phytoplankton biomass and temperature in the ocean," Geophys. Res. Lett. 23, 3591-3594 (1996).
[CrossRef]

Seuront, L.

L. Seuront, F. Schmitt, Y. Lagadeuc, D. Schertzer, and S. Lovejoy, "Multifractal analysis of phytoplankton biomass and temperature in the ocean," Geophys. Res. Lett. 23, 3591-3594 (1996).
[CrossRef]

Shaw, J. A.

Symonds, D. T.

N. C. Makris, P. Ratilal, D. T. Symonds, S. Jagannathan, S. Lee, and R. W. Nero, "Fish population and behavior revealed by instantaneous continental shelf-scale imaging," Science 311, 660-663 (2006).
[CrossRef] [PubMed]

Tatarskii, V. V.

J. H. Churnside, J. J. Wilson, and V. V. Tatarskii, "Airborne LIDAR for fisheries applications," Opt. Eng. 40, 406-414 (2001).
[CrossRef]

Tessier, Y.

S. Lovejoy, D. Schertzer, Y. Tessier, and H. Gaonac'h, "Multifractals and resolution-independent remote sensing algorithms: the example of ocean colour," Int. J. Remote Sens. 22, 1191-1234 (2001).
[CrossRef]

Veenstra, T.

E. D. Brown, J. H. Churnside, R. L. Collins, T. Veenstra, J. J. Wilson, and K. Abnett, "Remote sensing of capelin and other biological features in the North Pacific using LIDAR and video technology," ICES J. Mar. Sci. 59, 1120-1130 (2002).
[CrossRef]

Wilson, J. J.

E. D. Brown, J. H. Churnside, R. L. Collins, T. Veenstra, J. J. Wilson, and K. Abnett, "Remote sensing of capelin and other biological features in the North Pacific using LIDAR and video technology," ICES J. Mar. Sci. 59, 1120-1130 (2002).
[CrossRef]

J. H. Churnside, J. J. Wilson, and V. V. Tatarskii, "Airborne LIDAR for fisheries applications," Opt. Eng. 40, 406-414 (2001).
[CrossRef]

Zosimov, V. V.

V. V. Zosimov and K. A. Naugolnykh, "Fractal structure of large-scale variability of wind-driven waves according to laser-scanning data," Chaos 4, 21-24 (1994).
[CrossRef] [PubMed]

Chaos

V. V. Zosimov and K. A. Naugolnykh, "Fractal structure of large-scale variability of wind-driven waves according to laser-scanning data," Chaos 4, 21-24 (1994).
[CrossRef] [PubMed]

Geophys. Res. Lett.

L. Seuront, F. Schmitt, Y. Lagadeuc, D. Schertzer, and S. Lovejoy, "Multifractal analysis of phytoplankton biomass and temperature in the ocean," Geophys. Res. Lett. 23, 3591-3594 (1996).
[CrossRef]

ICES J. Mar. Sci.

E. D. Brown, J. H. Churnside, R. L. Collins, T. Veenstra, J. J. Wilson, and K. Abnett, "Remote sensing of capelin and other biological features in the North Pacific using LIDAR and video technology," ICES J. Mar. Sci. 59, 1120-1130 (2002).
[CrossRef]

J. H. Churnside, D. A. Demer, and B. Mahmoudi, "A comparison of LIDAR and echosounder measurements of fish schools in the Gulf of Mexico," ICES J. Mar. Sci. 60, 147-154 (2003).
[CrossRef]

Int. J. Remote Sens.

J. H. Churnside and L. A. Ostrovsky, "LIDAR observation of a strongly nonlinear internal wave train in the Gulf of Alaska," Int. J. Remote Sens. 26, 167-177 (2005).
[CrossRef]

S. Lovejoy, D. Schertzer, Y. Tessier, and H. Gaonac'h, "Multifractals and resolution-independent remote sensing algorithms: the example of ocean colour," Int. J. Remote Sens. 22, 1191-1234 (2001).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Eng.

J. H. Churnside, J. J. Wilson, and V. V. Tatarskii, "Airborne LIDAR for fisheries applications," Opt. Eng. 40, 406-414 (2001).
[CrossRef]

Science

N. C. Makris, P. Ratilal, D. T. Symonds, S. Jagannathan, S. Lee, and R. W. Nero, "Fish population and behavior revealed by instantaneous continental shelf-scale imaging," Science 311, 660-663 (2006).
[CrossRef] [PubMed]

Other

J. Feder, Fractals (Plenum, l988).

See National Data Buoy Center at http://www.ndbc.noaa.gov/index.shtml.

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Figures (6)

Fig. 1
Fig. 1

Flight tracks off the coast of Oregon and Washington along integer latitude lines from 44 ° N to 48 ° N . Location of the shelf break ( 200 m isobath) is shown off the coastline.

Fig. 2
Fig. 2

Logarithm of power spectrum of lidar return S as a function of spatial frequency f along 45 ° N latitude for a depth of 20 m during the day (lower curve) and a depth of 10 m the same night (upper curve). Also shown are the linear fits with slopes of 1.47 and 1.52 , respectively.

Fig. 3
Fig. 3

Logarithm of power spectrum of lidar return S as a function of spatial frequency f along 44 ° N latitude for a depth of 0 m at night. The shallower line is the fit from 4 to 1 with a slope of 0.51 , and the steeper line is the fit from 4 to 2 with a slope of 1.36 .

Fig. 4
Fig. 4

Depth dependence of power spectral slopes (from Table 2).

Fig. 5
Fig. 5

Day and night values of power spectral slopes of below-surface data (from Table 2).

Fig. 6
Fig. 6

Latitude dependence of power spectral slopes of below-surface data (from Table 2).

Tables (2)

Tables Icon

Table 1 Spectral Slopes by Latitude, Time of Day, Flight Direction, and Depth

Tables Icon

Table 2 Mean Slope and Uncertainty in Mean for Day and Night (Neglecting Surface) by Depth and by Latitude (Neglecting Surface)

Equations (2)

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S = f β ,
D = 2.5 0.5 β .

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