Cross-spectral analysis of the SST/10-m wind speed coupling resolved by satellite products and climate model simulations

Abstract

This study aims to determine the spatial–temporal scales where the SST forcing of the near-surface winds takes places, and its relationship with the action of coherent ocean eddies. Here, cross-spectral statistics are used to examine the relationship between satellite-based SST and 10-m wind speed (w) fields at scales between 10\(^2\)–10\(^4\) km and 10\(^1\)–10\(^3\) days. It is shown that the transition from negative SST/w correlations at large-scales to positive at oceanic mesoscales occurs at wavelengths coinciding with the atmospheric first baroclinic Rossby radius of deformation; and that the dispersion of positively-correlated signals resembles tropical instability waves near the equator, and Rossby waves in the extratropics. Transfer functions are used to estimate the SST-driven w response in physical space (\(w_c\)), a signal that explains 5–40% of the mesoscale w variance in the equatorial cold tongues, and 2–15% at extratropical SST fronts. The signature of ocean eddies is clearly visible in \(w_c\), accounting for 20–60% of its variability in eddy-rich regions. To provide further insight on the role of ocean eddies in the SST-driven coupling, the analysis is repeated for two climate model (CCSM) simulations using ocean grid resolutions of \(1^\circ\) (eddy-parameterized, LR) and \(0.1^\circ\) (eddy-resolving, HR). The lack of resolved eddies in LR leads to a significantly underestimated mesoscale w variance relative to HR. Conversely, the \(w_c\) variability in HR can exceed the satellite estimates by a factor of two at extratropical SST fronts and underestimate it by a factor of almost six near the equator, reflecting shortcomings of the CCSM to be addressed in its future developments.

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Acknowledgements

The authors thank Drs. William Johns and Igor Kamenkovich for very helpful discussions throughout the development of this work. Constructive comments by Dr. Frank Bryan and one anonymous reviewer are also gratefully acknowledged. This research was supported by grants from The Gulf of Mexico Research Initiative, and from the National Science Foundation (OCE1419569). Model experiments were performed using computing resources provided by the University of Miami Center for Computational Science, and by the Climate Simulation Laboratory at NCAR’s Computational and Information Systems Laboratory. Post-processed versions of the model outputs analyzed in this study, that can be used to replicate the presented results, are publicly available through the Gulf of Mexico Research Initiative Information and Data Cooperative (GRIIDC) at https://data.gulfresearchinitiative.org (http://dx.doi.org/10.7266/N70R9N1Q). The source code for the CCSM4 model is available at http://www.cesm.ucar.edu/models/ccsm4.0/, where the full outputs of the model experiments described here, and the input data necessary to reproduce them, are available from the authors upon request (bkirtman@miami.edu). Finally, the software used in the spectral calculations based on the multitaper method are from the jLab data analysis package for Matlab (version 1.6.5) developed by Dr. Jonathan M. Lilly, available at http://www.jmlilly.net/jmlsoft.html.

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Appendices

Appendix

Calculating w from CCSM4 wind stress data

As the CCSM4 model currently does not save the equivalent-neutral 10-m wind speed in its output files, this parameter is estimated from the model’s wind stress data by solving a cubic equation defined from the CCSM4 air–sea flux parametrization expressions. Specifically, the model calculates wind stress using a traditional bulk formulation, where an expression for the wind stress magnitude (\(\tau\)) can be written as:

$$\begin{aligned} \tau = \rho _a c_d w^2 {,} \end{aligned}$$
(9)

where w is the equivalent-neutral 10-m wind speed, \(\rho _a\) is the surface atmospheric density, and \(c_d\) is the equivalent-neutral drag coefficient at 10-m. The latter is parameterized as:

$$\begin{aligned} c_d = aw + b + \frac{c}{w} {,} \end{aligned}$$
(10)

where \(a = 7.64 \times 10^{-5}\) m\(^{-1}\), \(b = 1.42 \times 10^{-4}\), and \(c = 2.7 \times 10^{-3}\) m.s\(^{-1}\) are empirical coefficients (Large and Yeager 2004). Considering that \(\tau\) is known, and assuming a constant \(\rho _a = 1.225\) kg/m\(^3\), a cubic equation for w can be obtained by substituting (10) in (9):

$$\begin{aligned} a w^3 + b w^2 + c w - \frac{\tau }{\rho _a} = 0 {.} \end{aligned}$$
(11)

For any ratio \(\tau /\rho _a\), Eq. (11) has two complex conjugate roots (without physical meaning), and one real root. By preliminarily defining the parameters \(\varDelta _0\), \(\varDelta _1\), and C as:

$$\begin{aligned}&\varDelta _0 = b^2 - 3 a c {,} \end{aligned}$$
(12a)
$$\begin{aligned}&\varDelta _1 = 2 b^3 - 9 a b c - 27 a^2 \frac{\tau }{\rho _a} {,} \end{aligned}$$
(12b)
$$\begin{aligned}&C = \root 3 \of {\frac{1}{2} \left( \varDelta _1 + \sqrt{\varDelta _1^2 - 4 \varDelta _0^3} \right) } {,} \end{aligned}$$
(12c)

a general solution for the real root can then be expressed as:

$$\begin{aligned} w = - \frac{1}{3a} \left( b + C + \frac{\varDelta _0}{C} \right) {.} \end{aligned}$$
(13)

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Laurindo, L.C., Siqueira, L., Mariano, A.J. et al. Cross-spectral analysis of the SST/10-m wind speed coupling resolved by satellite products and climate model simulations. Clim Dyn 52, 5071–5098 (2019). https://doi.org/10.1007/s00382-018-4434-6

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Keywords

  • Air–sea interaction
  • Cross-spectral analysis
  • Satellite observations
  • Climate modeling
  • Mesoscale ocean eddies
  • Oceanic Rossby waves