The degree of anisotropy for mid - ocean currents from 1 satellite observations and an eddy - permitting model

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Lau (1985) On the role of barotropic energy conversions in the519general circulation, Adv. Geophys., 28A, 33–74520 D R A F TApril 30, 2007, 11:42amD R A F T HUANG ET AL.: ANISOTROPY OF MID-OCEAN CURRENTSX 27 Figure 1. (a) A randomly selected weekly map of the zonal component of the surfacegeostrophic velocity derived from AVISO altimetry SSH anomaly. (b) Same as (a) butfor the meridional component. Color scales are ± 2, 4, 8, 16 cms with red and blueindicating positive and negative values, respectively.D R A F TApril 30, 2007, 11:42amD R A F T X 28HUANG ET AL.: ANISOTROPY OF MID-OCEAN CURRENTS Figure 2. Same as Fig. 1 but for a randomly selected 50-week averaged surfacegeostrophic velocity field. (a) Zonal component. (b) Meridional component. The colorscales are ± 1, 2, 4, 8cms. D R A F TApril 30, 2007, 11:42amD R A F T HUANG ET AL.: ANISOTROPY OF MID-OCEAN CURRENTSX 29 Figure 3. The degree of anisotropy, α, calculated from the surface geostrophic velocityfield for (a) The North Pacific, (b) Box 1, (c) Box2, and (d) Box 3. The geostrophicvelocity is derived from altimetry SSH. The numbers on the abscissa indicate that thestatistics of α are constructed from 1-week, 5-week, ..., 100-week averaged data. Thecircles and vertical sticks are mean and standard deviation.D R A F TApril 30, 2007, 11:42amD R A F T X 30HUANG ET AL.: ANISOTROPY OF MID-OCEAN CURRENTS Figure 4. The velocity fields from the ocean model simulation. (a) The long-term(12-yr) mean of the surface zonal velocity. (b) A selected 1-yr (last year of a 20-yr run)mean of the surface zonal velocity. (c) The 1-yr average of the anomalous surface zonalvelocity, defined as (b) minus (a). (d) Same as (c) but for the surface meridional velocity.Color scales are ± 2, 4, 8, 16 cms for (a) and (b) and ± 1, 2, 4, 8 cms for (c) and(d). Red and blue colors indicate positive and negative values, respectively. D R A F TApril 30, 2007, 11:42amD R A F T HUANG ET AL.: ANISOTROPY OF MID-OCEAN CURRENTSX 31 Figure 5. The filled circles and error bars are same as Fig. 3 but are for the statisticsof α derived from the surface velocity in the model simulation. The open circles arecounterparts of the filled circles with the long-term mean included in the velocity field inthe calculations of α (see Section 3.5). D R A F TApril 30, 2007, 11:42amD R A F T X 32HUANG ET AL.: ANISOTROPY OF MID-OCEAN CURRENTS Figure 6. Same as Fig. 4 but for the model simulated velocity fields at 1000 m. (a)Long-term mean of u. (b) One-year average of u. (c) One-year average of the anomalyof u, defined as (b) minus (a). The period chosen for (b) and (c) is the same as that forFig. 4c. (d) Same as (c) but for the v component. Color scales are ± 0.5, 1, 2, 4 cmsfor all panels. Red and blue indicate positive and negative values, respectively. D R A F TApril 30, 2007, 11:42amD R A F T HUANG ET AL.: ANISOTROPY OF MID-OCEAN CURRENTSX 33 Figure 7. Same as Fig. 5 but for the statistics of α derived from the model simulatedvelocity at 1000 m. D R A F TApril 30, 2007, 11:42amD R A F T X 34HUANG ET AL.: ANISOTROPY OF MID-OCEAN CURRENTS Figure 8. Same as Figs. 3 and 5 but for the statistics of α for the simulated velocityin the Tropics (between 18N and 18S). (a) Surface. (b) 1000 m. D R A F TApril 30, 2007, 11:42amD R A F T HUANG ET AL.: ANISOTROPY OF MID-OCEAN CURRENTSX 35 Figure 9. The zonal component of the surface geostrophic velocity derived from the10-year mean absolute dynamic topography of Maximenko and Niiler (2005). Color scalesare ± 1, 4, 8, 16cms. Red and blue indicate positive and negative values, respectively. D R A F TApril 30, 2007, 11:42amD R A F T X 36HUANG ET AL.: ANISOTROPY OF MID-OCEAN CURRENTS Figure 10. (a) Selected curves of α as a function of T plotted in linear scale for(top to bottom) γ = 8, 16, 32, and 64 weeks based on Eq. (3). The symbols are theobserved and simulated values of α for the Box 1 region from Figs. 3b (open circle), 5b(filled circle), and 7b (triangle). (The filled circle almost coincide with open circle at T= 100.) (b) The values of γ as a function of T using Eq. (4) and the observed andsimulated values of α from Figs. 3b, 5b, and 7b. The symbols used here correspond totheir counterparts in (a). D R A F TApril 30, 2007, 11:42amD R A F T HUANG ET AL.: ANISOTROPY OF MID-OCEAN CURRENTSX 37 Figure 11. The model domain and bathymetry used for the ocean model simulation.The gray scales for depth are 0.5, 1, 2, 3, 4, 5, 6, 7 km. Areas that are shallower than 500m are white. D R A F TApril 30, 2007, 11:42amD R A F T X 38HUANG ET AL.: ANISOTROPY OF MID-OCEAN CURRENTS Figure 12. An illustration of the geometry of the terrain-following vertical levels ofthe model. Shown is the cross section for the North Pacific along 40N. The scales on theordinate are in km. D R A F TApril 30, 2007, 11:42amD R A F T HUANG ET AL.: ANISOTROPY OF MID-OCEAN CURRENTSX 39 Figure 13. Same as Fig. 5 but with α calculated from the surface geostrophic velocityderived from the simulated SSH anomalies. D R A F TApril 30, 2007, 11:42amD R A F T X 40HUANG ET AL.: ANISOTROPY OF MID-OCEAN CURRENTS Figure 14. (a) The setup of an idealized scenario for the increase of α with timeaveraging discussed in Appendix D. The solid curves are contours of constant frequency forthe barotropic Rossby mode, with a darker shading corresponding to a higher frequency.The dashed curves are contours of constant energy, and kx and ky are zonal and meridionalwavenumbers. See Appendix D for detail. (b) The change in α with the length of timeaveraging (in number of weeks, N) for the idealized model for p = 3 (black solid), p =3.5 (black dashed), and p = 4 (black dot-dashed), all with the value of β for 40N and aspectral truncation at total wavenumber 300. The two gray curves are the cases with asimilar setting as the black solid curve but one with a truncation at K = 250 (solid) andanother with the value of β given as that at 50N (dashed). The horizontal dashed lineindicates the observed value of α at N = 100 for the North Pacific taken from Fig. 3a.D R A F TApril 30, 2007, 11:42amD R A F T