diff --git a/writeup/rocha_etal_draft-like.tex b/writeup/rocha_etal_draft-like.tex new file mode 100755 index 0000000..59d224a --- /dev/null +++ b/writeup/rocha_etal_draft-like.tex @@ -0,0 +1,1084 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% AGUtmpl.tex: this template file is for articles formatted with LaTeX2e, +% Modified July 2014 +% +% This template includes commands and instructions +% given in the order necessary to produce a final output that will +% satisfy AGU requirements. +% +% PLEASE DO NOT USE YOUR OWN MACROS +% DO NOT USE \newcommand, \renewcommand, or \def. +% +% FOR FIGURES, DO NOT USE \psfrag or \subfigure. +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% +% All questions should be e-mailed to latex@agu.org. +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% +% Step 1: Set the \documentclass +% +% There are two options for article format: two column (default) +% and draft. +% +% PLEASE USE THE DRAFT OPTION TO SUBMIT YOUR PAPERS. +% The draft option produces double spaced output. +% +% Choose the journal abbreviation for the journal you are +% submitting to: + +% jgrga JOURNAL OF GEOPHYSICAL RESEARCH +% gbc GLOBAL BIOCHEMICAL CYCLES +% grl GEOPHYSICAL RESEARCH LETTERS +% pal PALEOCEANOGRAPHY +% ras RADIO SCIENCE +% rog REVIEWS OF GEOPHYSICS +% tec TECTONICS +% wrr WATER RESOURCES RESEARCH +% gc GEOCHEMISTRY, GEOPHYSICS, GEOSYSTEMS +% sw SPACE WEATHER +% ms JAMES +% ef EARTH'S FUTURE +% ea EARTH AND SPACE SCIENCE +% +% +% +% (If you are submitting to a journal other than jgrga, +% substitute the initials of the journal for "jgrga" below.) + +\documentclass[draft,grl]{agutex2015} +%\documentclass[grl]{agutex2015} + +% To create numbered lines: + +% If you don't already have lineno.sty, you can download it from +% http://www.ctan.org/tex-archive/macros/latex/contrib/ednotes/ +% (or search the internet for lineno.sty ctan), available at TeX Archive Network (CTAN). +% Take care that you always use the latest version. + +% To activate the commands, uncomment \usepackage{lineno} +% and \linenumbers*[1]command, below: + +% \usepackage{lineno} +% \linenumbers*[1] +% To add line numbers to lines with equations: +% \begin{linenomath*} +% \begin{equation} +% \end{equation} +% \end{linenomath*} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Figures and Tables +% +% +% DO NOT USE \psfrag or \subfigure commands. +% +% +% Uncomment the following command to include .eps files +% (comment out this line for draft format): +%\usepackage[dvipdf]{graphicx} +\usepackage{graphicx} + +% CR added this +\usepackage{color} +\usepackage{amsmath} + +% +% Uncomment the following command to allow illustrations to print +% when using Draft: +%\setkeys{Gin}{draft=false} +% +% Substitute one of the following for [dvips] above +% if you are using a different driver program and want to +% proof your illustrations on your machine: +% +% [xdvi], [dvipdf], [dvipsone], [dviwindo], [emtex], [dviwin], +% [pctexps], [pctexwin], [pctexhp], [pctex32], [truetex], [tcidvi], +% [oztex], [textures] +% +% See how to enter figures and tables at the end of the article, after +% references. +% +%% ------------------------------------------------------------------------ %% +% +% ENTER PREAMBLE +% +%% ------------------------------------------------------------------------ %% + +% Author names in capital letters: +\authorrunninghead{ROCHA ET AL.} + +% Shorter version of title entered in capital letters: +\titlerunninghead{Seasonality at submesoscales} + +%Corresponding author mailing address and e-mail address: +\authoraddr{Corresponding author: Cesar B. Rocha, +Scripps Institution of Oceanography, University of California San Diego, La Jolla, CA, USA. +(crocha@ucsd.edu)} + +\begin{document} + +%% ------------------------------------------------------------------------ %% +% +% TITLE +% +%% ------------------------------------------------------------------------ %% + + +\title{Seasonality of submesoscale dynamics in the Kuroshio Extension} +% +% e.g., \title{Terrestrial ring current: +% Origin, formation, and decay $\alpha\beta\Gamma\Delta$} +% + +%% ------------------------------------------------------------------------ %% +% +% AUTHORS AND AFFILIATIONS +% +%% ------------------------------------------------------------------------ %% + + +%Use \author{\altaffilmark{}} and \altaffiltext{} + +% \altaffilmark will produce footnote; +% matching \altaffiltext will appear at bottom of page. + +\authors{Cesar B. Rocha\altaffilmark{1}, Sarah T. Gille\altaffilmark{1}, + Teresa K. Chereskin\altaffilmark{1}, and Dimitris Menemenlis\altaffilmark{2}} +% Eric Brown,\altaffilmark{1,2} Rick Williams,\altaffilmark{3} +% John B. McDougall\altaffilmark{4}, and S. Visconti\altaffilmark{5}} + +\altaffiltext{1}{Scripps Institution of Oceanography, University of California San Diego, La Jolla, CA, USA.} +\altaffiltext{2}{Earth Sciences Division, Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA.} + + +%\altaffiltext{2}{Department of Geography, Ohio State University, +%Columbus, Ohio, USA.} + +%\altaffiltext{3}{Department of Space Sciences, University of +%Michigan, Ann Arbor, Michigan, USA.} + +%\altaffiltext{4}{Division of Hydrologic Sciences, Desert Research +%Institute, Reno, Nevada, USA.} + +%\altaffiltext{5}{Dipartimento di Idraulica, Trasporti ed +%Infrastrutture Civili, Politecnico di Torino, Turin, Italy.} + +%% ------------------------------------------------------------------------ %% +% +% KEYPOINTS +% +%% ------------------------------------------------------------------------ %% + +% Key points are 1 to 3 points that the author provides, +% that are 100 characters or less, that are ultimately published +% with the article. +%% for example: +% \keypoints{\item Here is the first keypoint. what happens if it is a +% long keypoint, like this one. We want to see this wrap please. +% \item This is the second. +% \item And here is the third keypoint +% } + +\keypoints{\item Upper-ocean submesoscale (10-100 km) turbulence and inertia-gravity waves + undergo strong seasonal cycles that are out of phase. + \item Submesoscale turbulence dominates the horizontal velocity and + sea-surface height variability in late winter/early spring. + \item Submesoscale inertia-gravity waves dominate the horizontal velocity and + sea-surface height variability in late summer/early fall. + } + +%% Keypoints will print underneath the abstract. + + +%% ------------------------------------------------------------------------ %% +% +% ABSTRACT +% +%% ------------------------------------------------------------------------ %% + +% >> Do NOT include any \begin...\end commands within +% >> the body of the abstract. + +\begin{abstract} + Two new high-resolution numerical simulations with embedded tides show a + strong modulation of near-surface dynamics at submesoscales + (roughly 10-100 km) in the Kuroshio Extension. Consistent with recent studies, deep late-winter mixed layers + are prone to baroclinic instabilities, and submesoscale turbulence + prevails in late winter/early spring. While summertime + re-stratification weakens submesoscale turbulence, it also enhances submesoscale inertia-gravity + waves near the surface. In the Kuroshio Extension, + inertia-gravity waves strongly dominate the submesoscale surface kinetic energy and + sea-surface height variance in late summer/early fall. +\end{abstract} + +%% ------------------------------------------------------------------------ %% +% +% BEGIN ARTICLE +% +%% ------------------------------------------------------------------------ %% + +% The body of the article must start with a \begin{article} command +% +% \end{article} must follow the references section, before the figures +% and tables. + +\begin{article} + +%% ------------------------------------------------------------------------ %% +% +% TEXT +% +%% ------------------------------------------------------------------------ %% + +\section{Introduction} + +Recent interest in upper-ocean dynamics has focused on the strong seasonal +cycle of shallow baroclinic instabilities and their role in submesoscale (roughly 1-100 km) +turbulence and mesoscale (roughly 100-300 km) modulation \citep{sasaki_etal2014,qiu_etal2014, +callies_etal2015, thompson_etal2016,buckingham_etal2016}. Contemporary studies +have also shown that inertia-gravity waves contribute significantly +to the near-surface variability at submesoscales \citep{richman_etal2012, +buhler_etal2014,rocha_etal2016}, but their seasonality has not been investigated. + +Using the output of $1/24^\circ$ and $1/48^\circ$ global +numerical simulations with embedded tides, we show that inertia-gravity waves undergo +a strong seasonality near the surface in the Kuroshio Extension region. +Interestingly, the seasonal cycle of inertia-gravity waves is out of phase +with the seasonal cycle of submesoscale turbulence. On one hand, consistent with previous studies, +deep late-winter mixed layers are prone to +shallow baroclinic instabilities that are roughly in geostrophic balance +and flux energy upscale \citep{sasaki_etal2014,callies_etal2016}, +driving a mild seasonal modulation of the mesoscales \citep{sasaki_etal2014,qiu_etal2014}. + +Inertia-gravity waves, on the other hand, peak in late summer/early fall, +when the upper ocean is strongly stratified. Thus there exists a +strong seasonal modulation of upper-ocean submesoscale dynamics: +submesoscale turbulence dominates the upper-ocean dynamics in late winter/early, +whereas submesoscale inertia-gravity waves prevail in late summer/early fall. +Because submesoscale turbulence is weakest in late summer/early fall, +the present results indicate that inertia-gravity waves account for most of the +summertime submesoscale sea-surface height variability. + +\section{The LLC numerical simulations} +We use results of two latitude-longitude polar cap (LLC) +realistic numerical simulations. The outputs +analyzed here, LLC2160 (1/24$^\circ$) and LLC4320 (1/48$^\circ$), are +forward Massachusetts Institute of Technology general circulation model \citep[MITgcm; ][]{marshall_etal1997} +numerical solutions on a LLC grid \citep{forget_etal2015} with +90-vertical-levels. The coarser-resolution LLC simulation was +spun up from an Estimating the Circulation and Climate of the Ocean, Phase II \citep[ECCO2; ][]{menemenlis_etal2008} +adjoint-method state estimate, constrained to millions +of observations from 2009 through 2011. Both simulations were forced by +tides hourly and by 6-hourly surface atmospheric fields. The LLC2160 +output spans two years from March 2011 to April 2013; the LLC4320 was spun up from +the LLC2160 simulation, spanning one year from September 2011 to October 2012. +The LLC4320 simulation is an extension of the 3-month long output used by +\citet{rocha_etal2016}. Details of the LLC simulations are provided in the supplemental material. + +A key aspect of the LLC2160 and LLC4320 simulations is that they were forced by +the 16 most-significant tidal components. +Because barotropic tides interact with topography and generate internal +tides that project onto mesoscales to submesoscales +\citep[e.g., ][]{rocha_etal2016}, tidal forcing fundamentally distinguishes our analysis +from other modeling studies of seasonality \citep{sasaki_etal2014,qiu_etal2014}. + +To study seasonal variations in the upper-ocean dynamics, we focus on the northwest +Pacific, in the vicinity of the Kuroshio +Extension, where previous studies have shown strong mesoscale and submesoscale seasonality +\citep{sasaki_etal2014,qiu_etal2014}. +We analyze a sub-domain of the LLC4320 and LLC2160 simulations of about 2000 km$^2$ +spanning 155-175$^\circ$E; 25-40$^\circ$N (Figure \ref{fig1}a). The stratification +in this mesoscale-rich subtropical region undergoes a vigorous seasonal cycle: wintertime-enhanced +small-scale turbulence de-stratifies the upper ocean, yielding mixed layers +as deep as 300 m (Figure \ref{fig1}d). In late spring/early summer enhanced solar radiation and mixed-layer +instabilities re-stratify the upper ocean, yielding mixed layers as shallow as 40 m (Figure \ref{fig1}e). +Fundamentally, the upper-ocean density structure is well-captured by both LLC simulations: +a comparison with Argo climatology shows that both simulations skillfully represent the Kuroshio +Extension stratification and its seasonal variability (supporting information). + +\section{Statistics of the surface lateral velocity gradient tensor} +To study the seasonality in the surface velocity, we calculate the lateral velocity gradient tensor +\begin{equation} +\left[\begin{matrix} u_x & u_y\\ v_x&v_y \end{matrix}\right] +\end{equation} +using a centered +second-order finite difference scheme. We then diagnose +the vertical vorticity + +\begin{equation} +\zeta \equiv v_x - u_y\, , +\end{equation} +lateral rate of strain +\begin{equation} + \alpha \equiv [(u_x-v_y)^2 + (u_y + v_x)^2]^{1/2}\,,\\ +\end{equation} +and horizontal divergence +\begin{equation} +\delta \equiv u_x + v_y\, . +\end{equation} +These diagnostics highlight the submesoscale structures in the flow +\citep[e.g.,][]{capet_etal2008a,shcherbina_etal2013}. + +Figures \ref{fig1}b-c show snapshots of vertical vorticity $\zeta$ in early spring +(April 15) and fall (October 15) in the LLC4320 (1/48$^\circ$) simulation. +The model solutions depict seasonality in vorticity: large values of +fine-grained vertical vorticity are observed in early spring with maximum +values as large as $4f$, where $f$ is +the local planetary vorticity, and root-mean-square (RMS) of about $0.4f$. In early +fall, the situation is the opposite: the vertical vorticity is relatively coarse-grained; +its local maximum and RMS are both smaller than $0.5f$. +Indeed, the vorticity and rate of strain are strongest in wintertime (Figure \ref{fig2}): +in both simulations, the RMS vorticity and strain rate are about twice as large in +late winter/early spring +than in late summer/early fall. Because the wintertime vorticity and strain rate +are dominated by the smallest scales in the flow (the KE spectra is shallower than +a $-3$ power law in winter), increasing the resolution from +1/24$^\circ$ to 1/48$^\circ$ increases the wintertime RMS vorticity +and strain by about 40$\%$. + + +The bulk of vertical vorticity and strain rate are associated with subinertial flows +($T_f = 2\pi/f_0\approx 23.5$h, where $f_0$ is the inertial frequency at +the mean latitude): daily-averaging the velocity fields suppresses super-inertial +motions and reduces the RMS +vorticity by 40$\%$ and the RMS strain by 10$\%$; the seasonal +cycle remains strong (see +dashed lines in figures \ref{fig2}a-b). Indeed, most of this seasonal cycle is associated +with submesoscale flows: smoothing the velocity fields +with a Hanning filter with cut off scale of 100 km dramatically reduces the RMS +vorticity and strain rate. The reduction in variance is about 80$\%$ in winter, +yielding RMS vorticity and strain rate roughly consistent with the diagnostics from +AVISO gridded geostrophic velocities (compare red lines to black lines in figures \ref{fig2}a-b). +The picture that emerges is consistent with recent studies: shallow baroclinic +instabilities energize the submesoscales in late winter, drawing from the available +potential energy stored in large lateral buoyancy gradients in deep mixed layers \citep{sasaki_etal2014,callies_etal2015,callies_etal2016}. + +The seasonal cycle of the horizontal divergence, however, showcases the complexity +of the upper-ocean annual variability. If submesoscale eddies and fronts dominated +the near-surface variability all year, then the seasonal cycle of horizontal divergence, +vertical vorticity, and lateral strain rate would be in phase \citep[e.g.,][]{sasaki_etal2014}. +While there is a clear wintertime peak in divergence of daily-averaged velocity +(see dashed lines in figure \ref{fig2}c; RMS divergence $\sim0.1 f$ in the 1/48$^\circ$ +simulation), the hourly fields show +a stronger enhancement of +lateral divergence in late summer/early fall (RMS divergence $\sim0.22 f$ the 1/48$^\circ$ +simulation). Because the 1/48$^\circ$ simulation better resolves +smaller-scale submesoscale flows, a secondary RMS divergence peak in winter is +nearly as strong as in summer. Submesoscale fronts and eddies evolve +relatively fast, and there is no clear +temporal and spatial scale separation between those motions and inertia-gravity waves +\citep{mcwilliams2016}: +daily-averaging the velocity fields efficiently suppresses the summertime horizontally +divergent flows, but also reduces the wintertime lateral divergence by about 50$\%$. +Figure \ref{fig2}c also shows that most of the lateral divergence is associated +with submesoscale flows: smoothing the velocity fields with a 100-km-cutoff +suppresses more than 80$\%$ of the RMS divergence. + +\section{Seasonality of submesoscale dynamics} +The results of figure \ref{fig2}a-c show that submesoscale surface + variability stems from different dynamics in summer than in winter. + To characterize these differences, we calculate +joint probability distributions (jPDF) of +vorticity-strain and vorticity-Laplacian of sea-surface height (Figure \ref{fig3}). + +The April vorticity-strain jPDF has a shape characteristic of submesoscale turbulence + (Figures \ref{fig3}a-b). The alignment of vorticity and strain $\alpha \sim \pm\zeta$ + with strong positive skewness are fingerprints of submesoscale fronts + \citep{shcherbina_etal2013,mcwilliams2016}. The shape of the vorticity-strain + jPDF is similar for hourly and daily-averaged fields, although + the vorticity skewness reduces from 1.4 to 1.13 from hourly to daily-averaged. + The April results are characteristic of winter, indicating that wintertime submesoscale + surface velocity is strongly dominated by submesoscale turbulence. + The hourly velocity and sea-surface heigh fields have an important +ageostrophic component as depicted by the jPDF of vorticity-Laplacian of SSH +winter (Figure \ref{fig3}e). In other words, even in April, when submesoscale turbulence +prevails, only the daily-averaged fields +are largely +in geostrophic balance (the jPDF of daily-averaged vorticity vs.\\ Laplacian of sea-surface height +is an ellipse with large eccentricity and main axis tilted by 45$^\circ$; Figure \ref{fig3}f). + +The October vorticity-strain jPDF shows much weaker skewness (the vorticity skewness +is 0.68 and 0.67 for hourly and daily-averaged velocities). The shape of the +vorticity-strain jPDF appears to be a combination of two half-ellipses centered +about $\zeta=0$, one with a 45$^\circ$ slope (characteristic of submesocale fronts +that persist in summer) and one with a very steep slope. +That the submesoscale dynamics in October are mainly ageostrophic is clearly depicted +in the shape of jPDF of vorticity-Laplacian of sea-surface height for hourly fields + (Figure \ref{fig3}g), which is an ellipse aligned in the vertical axis. +Daily-averaging the model suppresses the ageostrophic, super-inertial flows, and, therefore, +the daily-averaged flow is essentially geostrophic as depicted by the 45$^\circ$-tilted +ellipse in the vorticity-Laplacian of sea-surface height jPDF. + + Time series of PDFs of vorticity and divergence (supporting information) show + a strong oscillation between these two regimes. In late winter/early spring + the vorticity is strongly positively skewed, whereas the divergence is moderately + negatively skewed as predicted by frontogenesis \citep[e.g., ][]{capet_etal2008a,mcwilliams2016} +. In late summer/early fall, the divergence is stronger, but PDFs are much less skewed, +consistent with linear inertia-gravity waves. + +\section{Projection onto horizontal scales} + +To better quantify the projection of these flows onto different horizontal +scales, we calculate wavenumber spectra of kinetic energy and sea-surface height + variance. Before calculating the spectra, time-mean and spatial linear +trends were removed, and the resulting fields were multiplied by a two-dimensional Hanning ``spectral window''. +The two-dimensional spectra were averaged azimuthaly \citep[e.g., ][]{rocha_etal2016} . +We discuss only spectra for the 1/48$^\circ$ simulation, which extends the 1/24$^\circ$ simulation +towards smaller scales (supporting information). + +Figure \ref{fig4}a depicts the horizontal wavenumber spectra of surface KE in +April and October. At scales larger than 20 km, the April and October spectra based on hourly +velocity snapshots (solid lines) are nearly indistinguishable from each other within 95$\%$ confidence level. +Consistent with the results of +\citet{rocha_etal2016}, who analyzed a 3-month output of the LLC4320 simulation in Drake Passage, +there is significant high-frequency variabilty at submesoscales. Daily-averaging +the velocity field suppresses spatial variability at scales smaller than about 250 +km, both in April and October (compare solid lines against dashed lines in Figure +\ref{fig4}a). But this suppression is dramatic in October, when the inertia-gravity waves peak. At scales +smaller than 100 km, 39$\%$ of the surface KE in April is accounted for by super-inertial +flows as opposed to 79$\%$ in October. The seasonality of subinertial submesoscale flows +is strong, consistent +with the results of \citet{sasaki_etal2014}, which are +based on daily-averaged velocity fields of a different model without tidal forcing +(P. Klein, personal communication). + +The inertia-gravity waves project on the sea-surface. +There is a dramatic difference between the spectra +based on hourly and daily-averaged sea-surface height in October (Figure \ref{fig4}b): at scales smaller than 100 km, the spectra +of hourly sea-surface height roughly follows a $-2$ power-law, whereas the spectra of daily-averaged +sea-surface height roughly follows a $-5$ power-law. At these scales, 33$\%$ of the sea-surface height variance in April is accounted for by super-inertial +flows as opposed to 83$\%$ in October! Curiously, the out-of-phase seasonal cycle of submesoscale +turbulence and near-surface submesoscale inertia-gravity waves conspire to yield weak seasonality +in the spectra of KE and sea-surface height variance based on hourly fields. + + +\section{Summary and Conclusion} +Our work adds to recent modeling \citep{sasaki_etal2014} +and observational \citep{callies_etal2015,buckingham_etal2016} evidence of vigorous seasonality in +submesoscale turbulence. In particular, our main finding is that in global simulations with embedded tides the +near-surface submesoscale inertia-gravity waves in the Kuroshio Extension undergo +a strong seasonal cycle that is out of phase with the seasonal cycle of +submesoscale turbulence. We conjecture that the summertime dominance of inertia-gravity waves + \citep{callies_etal2015} is a consequence both of suppression of submesoscale turbulence and +enhancement of inertia-gravity waves due to re-stratification of +the upper ocean. + +\cite{dasaro1978} showed that the velocity of linear internal waves +in the mixed layer strongly depends on the density jump at the mixed layer +base, with largest mixed layer velocities when the jump is strongest. +In summer, the shallow mixed layer overlays a strong seasonal pycnocline, +and thus the internal waves projection onto the mixed layer may be stronger +according to \cite{dasaro1978}'s arguments. An +alternative explanation is that the shape of the baroclinic modes +changes seasonally. In particular the baroclinic modes are +significantly more surface intensified in late summer/early fall + (supporting information). +If the internal wave source has weak seasonal dependence, then a strong +seasonal cycle in the near-surface expression of internal waves is expected. +Internal tide generation does not show a seasonal modulation \citep[e.g.,][]{alford2003}, +and therefore one expects a strong seasonality in the near-surface +expression of internal tides and +other submesoscale inertia-gravity waves generated through internal tide interactions. +Near-inertial wave generation peaks in winter \citep[e.g.,][]{alford2003}, but +those waves project onto large horizontal scales \citep[e.g, ][]{qi_etal1995}. + +An important caveat is that this study focuses on a single patch of ocean in the +vicinity of the Kuroshio Extension. This may be typical of a mesoscale-rich +subtropical region, but it is unlikely to be +representative of other regions such as low-eddy-kinetic-energy eastern boundary currents +and the middle of the subtropical gyre. We plan to report on the geographic variability of submesoscale + seasonality in a future study. + +%The effects of smaller-scale/higher-frequency +%``sub-submesoscale'' flows on the submesoscale surface velocity and SSH variability +%are presently unknown. + +% That the surface velocity and SSH submesoscale variability may be +% dominated by ageostrophic flows in +% summer/fall has consequences for the interpretation of data from +% the future SWOT and COMPIRA altimeter missions, +% which will deliver SSH measurements at submesoscales. To the extent that +% high-frequency flows are dominated by spatially incoherent internal tides and other +% internal waves, it may be very difficult (if not impossible) to +% separate SSH submesoscale variability associated with geostrophic motions +% from high-frequency, ageostrophic flows. Thus, previous claims that +% one will be able to easily obtain submesoscale surface +% geostrophic velocities and monitor such seasonal cycle on global scales +% \citep{sasaki_etal2014,qiu_etal2014} are overstated. + + + + +% Here we argue that those divergent motions are likely inertia-gravity waves. +% We can show a couple of spectra and argue that they roughly satisfy polarization +% relations. +% +% We can also try and show some observations here. Any cruises with ADCP data. +% While it may be hard to have enough data for the errorbars to be small, a +% rough consistency may be better than nothing. +% +% Perhaps a mooring data should show strong seasonal modulation at high-frequencies? +% +% We must be able to present some observational evidence that the model is not +% misleading at high-frequencies. + + +% Here we argue that high-frequency (supra-daily) flows significantly project +% on the sea-surface, and thus estimation of submesoscale (10-100 km) geostrophic +% velocity from sea-surface height (SSH) is not warranted. Calculating spectral +% KE fluxes from both velocity and geostrophic velocity (from SSH) would +% contrast with the results in Sasaki et al. + +% \section{Projection on time scales} +% To better understand the high-frequency/high-wavenumber flows we calculate frequency +% spectra of surface KE winter \ref{fig4}). To obtain statistically meaningful results, +% we average spectral estimates along a section at 165$^\circ$E. There is about 50 +% independent spectral realizations. +% +% The surface KE spectra of subinertial flows very roughly follow a $-2$ power-law. +% The high-frequency flows are split near-inertial flows, tidal signals and their +% higher harmonics. Hence these high-frequency flows are dominated by inertia-gravity +% waves. (Note that the inertial peak nearly merges with the +% diurnal tide peak.) There is statistically significant seasonality. The seasonal +% cycle of the sub-inertial motions (at least for periods between 5-20 days) +% is out-of-phase with the seasonal cycle of supra-inertial flows: the former flows +% are more energetic in April and the latter in October. +% +% Most of these high-frequency inertia-gravity waves project onto scales smaller +% than 100 km. The surface KE spectra of 100-km-smoothed velocity field is significantly +% suppressed in supra-inertial frequencies --- there are no statistically significant +% changes at sub-inertial frequencies (see dashed lines in figure \ref{fig4}). + +% say something about relative energy in smoother vs.\\ unsmoothed fields. +% also say something about comparison with observations. + +%\begin{figure}[ht] +% \begin{center} +% \includegraphics[width=.45\textwidth]{figs/fig4.pdf} +% \caption{Surface (horizontal) KE frequency spectra. Solid lines +% are spectra based on the 1/24$^\circ$ fields, dashed line are spectra +% based on 100-km-smoothed fields.} +% \label{fig4} +% \end{center} +%\end{figure} + + +% +% ACKNOWLEDGMENTS + +\begin{acknowledgments} + William R. Young provided helpful feedback on the first draft. Greg Wagner first + suggested that the near-surface shape of the baroclinic modes may change seasonally. + We thank the MITgcm community and our colleagues at the NASA Advanced +Supercomputing (NAS) Division for their awesome support. +This research was funded by NSF (OCE1357047) and NASA (NNX13AE44G,NNX13AE85G,NNX16AH67G). +The LLC output can be obtained from the ECCO project (\texttt{http://ecco2.org/llc$\_$hires}). The altimeter products were produced by Ssalto/Duacs +and distributed by AVISO, with support from CNES (\texttt{http://www.aviso.altimetry.fr/duacs/}). +Codes and output files are available online at the project repository + (\texttt{https://github.com/crocha700/UpperOceanSeasonality}). +\end{acknowledgments} + +\bibliographystyle{agufull08} +%\bibliography{rocha_etal} + +\begin{figure*}[ht] +\begin{center} +\hspace{-1.25cm}\includegraphics[width=.75\textwidth]{figs/fig1_1.pdf}\\ +\vspace{-.125cm} +\includegraphics[width=.75\textwidth]{figs/fig1_2.pdf} + \caption{(a) The study region with the subregion where the LLC outputs are + analyzed. Colors represent the topography and white lines are contours of absolute + dynamic topography every 0.1 m from AVISO. LLC 4320 (1/48$^\circ$) snapshots of surface vorticity (b and c) and transects + of potential density at 165$^\circ$E (d and e). The snapshots were + taken at 00:00 UTC.} +\vspace{-1.5cm} + \label{fig1} + \end{center} + \end{figure*} + + \begin{figure*}[ht] + \begin{center} + \includegraphics[width=.75\textwidth]{figs/fig2.pdf} + \caption{Time series of the root-mean-square (RMS) of (a) vorticity, + (b) rate of strain, and (c) horizontal divergence in the LLC outputs and gridded AVISO data.} + \label{fig2} + \end{center} +\end{figure*} + +\begin{figure*}[ht] + \begin{center} + \includegraphics[width=.95\textwidth]{figs/fig3.pdf} + \caption{Seasonal variation of joint probability distributions: vorticity vs.\ strain rate (a through d), + and vorticity vs.\ Laplacian of sea-surface height (e through h) in April (a, b, + e, f) and October (c, d, g, h). + Dashed lines in (a) through (d) represent one dimensional shear flow $\alpha = \pm\zeta$, + characteristic of fronts. Dashed lines in (e) through + (h) represent geostrophic flow $\zeta = \frac{g}{f}\nabla_h^2 \eta$.} + \label{fig3} + \end{center} +\end{figure*} + +\begin{figure*}[ht] + \begin{center} + \includegraphics[width=1.\textwidth]{figs/fig4.pdf} + \caption{Surface (horizontal) kinetic energy (a) and sea-surface height variance wavenumber spectra (b) + in the 1/48$^\circ$ simulation. Solid lines + are spectra based on hourly snapshots, and dashed lines are spectra based on daily-averaged + fields.} + \label{fig4} + \end{center} +\end{figure*} + +% this should go in a supplementary material +%\clearpage + +%\section{Supplemental material 1: Spectral errors} + + + +%%% End of body of article: +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Optional Appendix goes here +% +% \appendix resets counters and redefines section heads +% but doesn't print anything. +% After typing \appendix +% +%\section{Here Is Appendix Title} +% will show +% Appendix A: Here Is Appendix Title +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% +% Optional Glossary or Notation section, goes here +% +%%%%%%%%%%%%%% +% Glossary is only allowed in Reviews of Geophysics +% \section*{Glossary} +% \paragraph{Term} +% Term Definition here +% +%%%%%%%%%%%%%% +% Notation -- End each entry with a period. +% \begin{notation} +% Term & definition.\\ +% Second term & second definition.\\ +% \end{notation} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + +%% ------------------------------------------------------------------------ %% +%% REFERENCE LIST AND TEXT CITATIONS +% +% Either type in your references using +% \begin{thebibliography}{} +% \bibitem{} +% Text +\begin{thebibliography}{18} +\providecommand{\natexlab}[1]{#1} +\expandafter\ifx\csname urlstyle\endcsname\relax + \providecommand{\doi}[1]{doi:\discretionary{}{}{}#1}\else + \providecommand{\doi}{doi:\discretionary{}{}{}\begingroup + \urlstyle{rm}\Url}\fi + +\bibitem[{\textit{Alford}(2003)}]{alford2003} +Alford, M.~H. (2003), {Redistribution of energy available for ocean mixing by + long-range propagation of internal wave}, \textit{Nature}, + \textit{423}(6936), 159--162. + +\bibitem[{\textit{Buckingham et~al.}(2016)\textit{Buckingham, Naveira~Garabato, + Thompson, Brannigan, Lazar, Marshall, George~Nurser, Damerell, Heywood, and + Belcher}}]{buckingham_etal2016} +Buckingham, C.~E., A.~C. Naveira~Garabato, A.~F. Thompson, L.~Brannigan, + A.~Lazar, D.~P. Marshall, A.~George~Nurser, G.~Damerell, K.~J. Heywood, and + S.~E. Belcher (2016), {Seasonality of submesoscale flows in the ocean surface + boundary layer}, \textit{Geophysical Research Letters}, \textit{43}(5), + 2118--2126. + +\bibitem[{\textit{B{\"u}hler et~al.}(2014)\textit{B{\"u}hler, Callies, and + Ferrari}}]{buhler_etal2014} +B{\"u}hler, O., J.~Callies, and R.~Ferrari (2014), {Wave--vortex decomposition + of one-dimensional ship-track data}, \textit{Journal of Fluid Mechanics}, + \textit{756}, 1007--1026. + +\bibitem[{\textit{Callies et~al.}(2015)\textit{Callies, Ferrari, Klymak, and + Gula}}]{callies_etal2015} +Callies, J., R.~Ferrari, J.~M. Klymak, and J.~Gula (2015), {Seasonality in + submesoscale turbulence}, \textit{Nature communications}, \textit{6}. + +\bibitem[{\textit{Callies et~al.}(2016)\textit{Callies, Flierl, Ferrari, and + Fox-Kemper}}]{callies_etal2016} +Callies, J., G.~Flierl, R.~Ferrari, and B.~Fox-Kemper (2016), {The role of + mixed-layer instabilities in submesoscale turbulence}, \textit{Journal of + Fluid Mechanics}, \textit{788}, 5--41. + +\bibitem[{\textit{Capet et~al.}(2008)\textit{Capet, McWilliams, Molemaker, and + Shchepetkin}}]{capet_etal2008a} +Capet, X., J.~C. McWilliams, M.~J. Molemaker, and A.~Shchepetkin (2008), + {Mesoscale to submesoscale transition in the California Current System. Part + I: Flow structure, eddy flux, and observational tests}, \textit{Journal of + Physical Oceanography}, \textit{38}(1), 29--43. + +\bibitem[{\textit{D'Asaro}(1978)}]{dasaro1978} +D'Asaro, E.~A. (1978), {Mixed layer velocities induced by internal wave}, + \textit{Journal of Geophysical Research: Oceans}, \textit{83}(C5), + 2437--2438. + +\bibitem[{\textit{Forget et~al.}(2015)\textit{Forget, Campin, Heimbach, Hill, + Ponte, and Wunsch}}]{forget_etal2015} +Forget, G., J.-M. Campin, P.~Heimbach, C.~Hill, R.~Ponte, and C.~Wunsch (2015), + {ECCO version 4: an integrated framework for non-linear inverse modeling and + global ocean state estimation}, \textit{Geosci. Model Dev.}, \textit{8}, + 3071--3104. + + \bibitem[{\textit{Marshall et~al.}(1997)\textit{Marshall, Hill, Perelman, and + Adcroft}}]{marshall_etal1997} + Marshall, J., C.~Hill, L.~Perelman, and A.~Adcroft (1997), Hydrostatic, + quasi-hydrostatic, and nonhydrostatic ocean modeling, \textit{Journal of + Geophysical Research: Oceans}, \textit{102}(C3), 5733--5752. + + \bibitem[{\textit{McWilliams}(2016)}]{mcwilliams2016} + McWilliams, J.~C. (2016), {Submesoscale currents in the ocean}, in + \textit{Proc. R. Soc. A}, vol. 472, p. 20160117, The Royal Society. + + \bibitem[{\textit{Menemenlis et~al.}(2008)\textit{Menemenlis, Campin, Heimbach, + Hill, Lee, Nguyen, Schodlok, and Zhang}}]{menemenlis_etal2008} + Menemenlis, D., J.-M. Campin, P.~Heimbach, C.~Hill, T.~Lee, A.~Nguyen, + M.~Schodlok, and H.~Zhang (2008), ECCO2: High resolution global ocean and sea + ice data synthesis, \textit{Mercator Ocean Quarterly Newsletter}, + \textit{31}, 13--21. + +\bibitem[{\textit{Qi et~al.}(1995)\textit{Qi, De~Szoeke, Paulson, and + Eriksen}}]{qi_etal1995} +Qi, H., R.~A. De~Szoeke, C.~A. Paulson, and C.~C. Eriksen (1995), {The + structure of near-inertial waves during ocean storms}, \textit{Journal of + Physical Oceanography}, \textit{25}, 2853--2871. + +\bibitem[{\textit{Qiu et~al.}(2014)\textit{Qiu, Chen, Klein, Sasaki, and + Sasai}}]{qiu_etal2014} +Qiu, B., S.~Chen, P.~Klein, H.~Sasaki, and Y.~Sasai (2014), {Seasonal mesoscale + and submesoscale eddy variability along the North Pacific Subtropical + Countercurrent}, \textit{Journal of Physical Oceanography}, \textit{44}(12), + 3079--3098. + +\bibitem[{\textit{Richman et~al.}(2012)\textit{Richman, Arbic, Shriver, + Metzger, and Wallcraft}}]{richman_etal2012} +Richman, J.~G., B.~K. Arbic, J.~F. Shriver, E.~J. Metzger, and A.~J. Wallcraft + (2012), {Inferring dynamics from the wavenumber spectra of an eddying global + ocean model with embedded tides}, \textit{Journal of Geophysical Research: + Oceans}, \textit{117}(C12). + +\bibitem[{\textit{Rocha et~al.}(2016)\textit{Rocha, Chereskin, Gille, and + Menemenlis}}]{rocha_etal2016} +Rocha, C.~B., T.~K. Chereskin, S.~T. Gille, and D.~Menemenlis (2016), + {Mesoscale to submesoscale wavenumber spectra in Drake Passage}, + \textit{Journal of Physical Oceanography}, \textit{46}, 601--620. + +\bibitem[{\textit{Sasaki et~al.}(2014)\textit{Sasaki, Klein, Qiu, and + Sasai}}]{sasaki_etal2014} +Sasaki, H., P.~Klein, B.~Qiu, and Y.~Sasai (2014), {Impact of oceanic-scale + interactions on the seasonal modulation of ocean dynamics by the atmosphere}, + \textit{Nature communications}, \textit{5}. + +\bibitem[{\textit{Shcherbina et~al.}(2013)\textit{Shcherbina, D'Asaro, Lee, + Klymak, Molemaker, and McWilliams}}]{shcherbina_etal2013} +Shcherbina, A.~Y., E.~A. D'Asaro, C.~M. Lee, J.~M. Klymak, M.~J. Molemaker, and + J.~C. McWilliams (2013), {Statistics of vertical vorticity, divergence, and + strain in a developed submesoscale turbulence field}, \textit{Geophysical + Research Letters}, \textit{40}(17), 4706--4711. + +\bibitem[{\textit{Thompson et~al.}(2016)\textit{Thompson, Lazar, Buckingham, + Naveira~Garabato, Damerell, and Heywood}}]{thompson_etal2016} +Thompson, A.~F., A.~Lazar, C.~Buckingham, A.~C. Naveira~Garabato, G.~M. + Damerell, and K.~J. Heywood (2016), {Open-ocean submesoscale motions: A full + seasonal cycle of mixed layer instabilities from gliders}, \textit{Journal of + Physical Oceanography}, \textit{46}(4), 1285--1307. + +\end{thebibliography} + + +% Or, +% +% If you use BiBTeX for your references, please use the agufull08.bst file (available at % ftp://ftp.agu.org/journals/latex/journals/Manuscript-Preparation/) to produce your .bbl +% file and copy the contents into your paper here. +% +% Follow these steps: +% 1. Run LaTeX on your LaTeX file. +% +% 2. Make sure the bibliography style appears as \bibliographystyle{agufull08}. Run BiBTeX on your LaTeX +% file. +% +% 3. Open the new .bbl file containing the reference list and +% copy all the contents into your LaTeX file here. +% +% 4. Comment out the old \bibliographystyle and \bibliography commands. +% +% 5. Run LaTeX on your new file before submitting. +% +% AGU does not want a .bib or a .bbl file. Please copy in the contents of your .bbl file here. + +%\begin{thebibliography}{} + +%\providecommand{\natexlab}[1]{#1} +%\expandafter\ifx\csname urlstyle\endcsname\relax +% \providecommand{\doi}[1]{doi:\discretionary{}{}{}#1}\else +% \providecommand{\doi}{doi:\discretionary{}{}{}\begingroup +% \urlstyle{rm}\Url}\fi +% +%\bibitem[{\textit{Atkinson and Sloan}(1991)}]{AtkinsonSloan} +%Atkinson, K., and I.~Sloan (1991), The numerical solution of first-kind +% logarithmic-kernel integral equations on smooth open arcs, \textit{Math. +% Comp.}, \textit{56}(193), 119--139. +% +%\bibitem[{\textit{Colton and Kress}(1983)}]{ColtonKress1} +%Colton, D., and R.~Kress (1983), \textit{Integral Equation Methods in +% Scattering Theory}, John Wiley, New York. +% +%\bibitem[{\textit{Hsiao et~al.}(1991)\textit{Hsiao, Stephan, and +% Wendland}}]{StephanHsiao} +%Hsiao, G.~C., E.~P. Stephan, and W.~L. Wendland (1991), On the {D}irichlet +% problem in elasticity for a domain exterior to an arc, \textit{J. Comput. +% Appl. Math.}, \textit{34}(1), 1--19. +% +%\bibitem[{\textit{Lu and Ando}(2012)}]{LuAndo} +%Lu, P., and M.~Ando (2012), Difference of scattering geometrical optics +% components and line integrals of currents in modified edge representation, +% \textit{Radio Sci.}, \textit{47}, RS3007, \doi{10.1029/2011RS004899}. + +%\end{thebibliography} + +%Reference citation examples: + +%...as shown by \textit{Kilby} [2008]. +%...as shown by {\textit {Lewin}} [1976], {\textit {Carson}} [1986], {\textit {Bartholdy and Billi}} [2002], and {\textit {Rinaldi}} [2003]. +%...has been shown [\textit{Kilby et al.}, 2008]. +%...has been shown [{\textit {Lewin}}, 1976; {\textit {Carson}}, 1986; {\textit {Bartholdy and Billi}}, 2002; {\textit {Rinaldi}}, 2003]. +%...has been shown [e.g., {\textit {Lewin}}, 1976; {\textit {Carson}}, 1986; {\textit {Bartholdy and Billi}}, 2002; {\textit {Rinaldi}}, 2003]. + +%...as shown by \citet{jskilby}. +%...as shown by \citet{lewin76}, \citet{carson86}, \citet{bartoldy02}, and \citet{rinaldi03}. +%...has been shown \citep{jskilbye}. +%...has been shown \citep{lewin76,carson86,bartoldy02,rinaldi03}. +%...has been shown \citep [e.g.,][]{lewin76,carson86,bartoldy02,rinaldi03}. +% +% Please use ONLY \citet and \citep for reference citations. +% DO NOT use other cite commands (e.g., \cite, \citeyear, \nocite, \citealp, etc.). + +%% ------------------------------------------------------------------------ %% +% +% END ARTICLE +% +%% ------------------------------------------------------------------------ %% +\end{article} +% +% +%% Enter Figures and Tables here: +% +% DO NOT USE \psfrag or \subfigure commands. +% +% Figure captions go below the figure. +% Table titles go above tables; all other caption information +% should be placed in footnotes below the table. +% +%---------------- +% EXAMPLE FIGURE +% + %\begin{figure} + %\noindent\includegraphics[width=20pc]{samplefigure.eps} + %\caption{Caption text here} + %\label{figure_label} + %\end{figure} + + + +% +% --------------- +% EXAMPLE TABLE +% +%\begin{table} +%\caption{Time of the Transition Between Phase 1 and Phase 2\tablenotemark{a}} +%\centering +%\begin{tabular}{l c} +%\hline +% Run & Time (min) \\ +%\hline +% $l1$ & 260 \\ +% $l2$ & 300 \\ +% $l3$ & 340 \\ +% $h1$ & 270 \\ +% $h2$ & 250 \\ +% $h3$ & 380 \\ +% $r1$ & 370 \\ +% $r2$ & 390 \\ +%\hline +%\end{tabular} +%\tablenotetext{a}{Footnote text here.} +%\end{table} + +% See below for how to make sideways figures or tables. + +\end{document} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +More Information and Advice: + +%% ------------------------------------------------------------------------ %% +% +% SECTION HEADS +% +%% ------------------------------------------------------------------------ %% + +% Capitalize the first letter of each word (except for +% prepositions, conjunctions, and articles that are +% three or fewer letters). + +% AGU follows standard outline style; therefore, there cannot be a section 1 without +% a section 2, or a section 2.3.1 without a section 2.3.2. +% Please make sure your section numbers are balanced. +% --------------- +% Level 1 head +% +% Use the \section{} command to identify level 1 heads; +% type the appropriate head wording between the curly +% brackets, as shown below. +% +%An example: +%\section{Level 1 Head: Introduction} +% +% --------------- +% Level 2 head +% +% Use the \subsection{} command to identify level 2 heads. +%An example: +%\subsection{Level 2 Head} +% +% --------------- +% Level 3 head +% +% Use the \subsubsection{} command to identify level 3 heads +%An example: +%\subsubsection{Level 3 Head} +% +%--------------- +% Level 4 head +% +% Use the \subsubsubsection{} command to identify level 3 heads +% An example: +%\subsubsubsection{Level 4 Head} An example. +% +%% ------------------------------------------------------------------------ %% +% +% IN-TEXT LISTS +% +%% ------------------------------------------------------------------------ %% +% +% Do not use bulleted lists; enumerated lists are okay. +% \begin{enumerate} +% \item +% \item +% \item +% \end{enumerate} +% +%% ------------------------------------------------------------------------ %% +% +% EQUATIONS +% +%% ------------------------------------------------------------------------ %% + +% Single-line equations are centered. +% Equation arrays will appear left-aligned. + +Math coded inside display math mode \[ ...\] + will not be numbered, e.g.,: + \[ x^2=y^2 + z^2\] + + Math coded inside \begin{equation} and \end{equation} will + be automatically numbered, e.g.,: + \begin{equation} + x^2=y^2 + z^2 + \end{equation} + +% IF YOU HAVE MULTI-LINE EQUATIONS, PLEASE +% BREAK THE EQUATIONS INTO TWO OR MORE LINES +% OF SINGLE COLUMN WIDTH (20 pc, 8.3 cm) +% using double backslashes (\\). + +% To create multiline equations, use the +% \begin{eqnarray} and \end{eqnarray} environment +% as demonstrated below. +\begin{eqnarray} + x_{1} & = & (x - x_{0}) \cos \Theta \nonumber \\ + && + (y - y_{0}) \sin \Theta \nonumber \\ + y_{1} & = & -(x - x_{0}) \sin \Theta \nonumber \\ + && + (y - y_{0}) \cos \Theta. +\end{eqnarray} + +%If you don't want an equation number, use the star form: +%\begin{eqnarray*}...\end{eqnarray*} + +% Break each line at a sign of operation +% (+, -, etc.) if possible, with the sign of operation +% on the new line. + +% Indent second and subsequent lines to align with +% the first character following the equal sign on the +% first line. + +% Use an \hspace{} command to insert horizontal space +% into your equation if necessary. Place an appropriate +% unit of measure between the curly braces, e.g. +% \hspace{1in}; you may have to experiment to achieve +% the correct amount of space. + + +%% ------------------------------------------------------------------------ %% +% +% EQUATION NUMBERING: COUNTER +% +%% ------------------------------------------------------------------------ %% + +% You may change equation numbering by resetting +% the equation counter or by explicitly numbering +% an equation. + +% To explicitly number an equation, type \eqnum{} +% (with the desired number between the brackets) +% after the \begin{equation} or \begin{eqnarray} +% command. The \eqnum{} command will affect only +% the equation it appears with; LaTeX will number +% any equations appearing later in the manuscript +% according to the equation counter. +% + +% If you have a multiline equation that needs only +% one equation number, use a \nonumber command in +% front of the double backslashes (\\) as shown in +% the multiline equation above. + +%% ------------------------------------------------------------------------ %% +% +% SIDEWAYS FIGURE AND TABLE EXAMPLES +% +%% ------------------------------------------------------------------------ %% +% +% For tables and figures, add \usepackage{rotating} to the paper and add the rotating.sty file to the folder. +% AGU prefers the use of {sidewaystable} over {landscapetable} as it causes fewer problems. +% +% \begin{sidewaysfigure} +% \includegraphics[width=20pc]{samplefigure.eps} +% \caption{caption here} +% \label{label_here} +% \end{sidewaysfigure} +% +% +% +% \begin{sidewaystable} +% \caption{} +% \begin{tabular} +% Table layout here. +% \end{tabular} +% \end{sidewaystable} +% +%