arXiv subjects

Stephen M. Griffies

Publications and source records attributed to Stephen M. Griffies.

9 recordsLinked to original sources

arXiv2023

Global Cascade of Kinetic Energy in the Ocean and the Atmospheric Imprint

We present the first estimate for the ocean's global scale-transfer of kinetic energy (KE), across scales from 10~km to 40000~km. We show the existence of oceanic KE transfer between gyre-scales and mesoscales induced by the atmosphere's Hadley, Ferrel, and polar cells, and intense downscale KE transfer associated with the Inter-Tropical Convergence Zone. We report peak upscale transfer of 300 GigaWatts across mesoscales of 120~km in size, roughly 1/3rd the energy input by winds into the oceanic general circulation. This "cascade" penetrates almost the entire water column, with nearly three quarters of it occurring south of 15$^\circ$S. The mesoscale cascade has a self-similar seasonal cycle with characteristic lag-time of $\mathbf{\approx27~}$days per octave of length-scales such that transfer across 50~km peaks in spring while transfer across 500~km peaks in summer. KE content of those mesoscales follows the same self-similar cycle but peaks $\mathbf{\approx40~}$days after the peak cascade, suggesting that energy transferred across a scale is primarily deposited at a scale 4$\times$ larger.

physics.ao-ph↗

arXiv2023

Exploring the non-stationarity of coastal sea level probability distributions

Studies agree on a significant global mean sea level rise in the 20th century and its recent 21st century acceleration in the satellite record. At regional scale, the evolution of sea level probability distributions is often assumed to be dominated by changes in the mean. However, a quantification of changes in distributional shapes in a changing climate is currently missing. To this end, we propose a novel framework quantifying significant changes in probability distributions from time series data. The framework first quantifies linear trends in quantiles through quantile regression. Quantile slopes are then projected onto a set of four $orthogonal$ polynomials quantifying how such changes can be explained by $independent$ shifts in the first four statistical moments. The framework proposed is theoretically founded, general and can be applied to any climate observable with close-to-linear changes in distributions. We focus on observations and a coupled climate model (GFDL-CM4). In the historical period, trends in coastal daily sea level have been driven mainly by changes in the mean and can therefore be explained by a shift of the distribution with no change in shape. In the modeled world, robust changes in higher order moments emerge with increasing CO2 concentration. Such changes are driven in part by ocean circulation alone and get amplified by sea level pressure fluctuations, with possible consequences for sea level extremes attribution studies.

physics.ao-ph↗

arXiv2023

Spatio-temporal coarse-graining decomposition of the global ocean geostrophic kinetic energy

We expand on a recent determination of the first global energy spectrum of the ocean's surface geostrophic circulation (Storer et al., 2022) using a coarse-graining (CG) method. We compare spectra from CG to those from spherical harmonics by treating land in a manner consistent with the boundary conditions. While the two methods yield qualitatively consistent domain-averaged results, spherical harmonics spectra are too noisy at gyre-scales ($>1000~$km). More importantly, spherical harmonics are inherently global and cannot provide local information connecting scales with currents geographically. CG shows that the extra-tropics mesoscales (100-500~km) have a root-mean-square (rms) velocity of $\sim15~$cm/s, which increases to $\sim30$-40~cm/s locally in the Gulf Stream and Kuroshio and to $\sim16$-28~cm/s in the ACC. There is notable hemispheric asymmetry in mesoscale energy-per-area, which is higher in the north due to continental boundaries. We estimate that $\approx25$-50\% of total geostrophic energy is at scales smaller than 100~km, and is un(der)-resolved by pre-SWOT satellite products. Spectra of the time-mean component show that most of its energy (up to $70\%$) resides in stationary mesoscales ($<500~$km), highlighting the preponderance of `standing' small-scale structures in the global ocean. By coarse-graining in space and time, we compute the first spatio-temporal global spectrum of geostrophic circulation from AVISO and NEMO. These spectra show that every length-scale evolves over a wide range of time-scales with a consistent peak at $\approx200$ km and $\approx2$-3~weeks.

physics.ao-ph↗

arXiv2022

Global Energy Spectrum of the General Oceanic Circulation

Since the advent of satellite altimetry, our perception of the oceanic circulation has brought into focus the pervasiveness of mesoscale eddies that have typical scales of tens to hundreds of kilometers [5], are the ocean's analogue of weather systems, and are often thought of as the peak of the ocean's kinetic energy (KE) wavenumber spectrum [7, 19, 23]. Yet, our understanding of the ocean's spatial scales has been derived mostly from Fourier analysis in small representative regions (e.g. [16, 14, 4]), typically a few hundred kilometers in size, that cannot capture the vast dynamic range at planetary scales. Here, we present the first truly global wavenumber spectrum of the oceanic circulation from satellite data and high-resolution re-analysis data, using a coarse-graining method to analyze scales much larger than what had been possible before. Spectra spanning over three orders of magnitude in length-scale reveal the Antarctic Circumpolar Current (ACC) as the spectral peak of the global extra-tropical ocean, at $\approx 10 \times 10^3~$km. We also find a previously unobserved power-law scaling over scales larger than $10^3~$km. A smaller spectral peak exists at $\approx 300~$km associated with the mesoscales, which, due to their wider spread in wavenumber space, account for more than $50\%$ of the resolved surface KE globally. Length-scales that are twice as large (up to $10^3$~km) exhibit a characteristic lag time of $\approx40~$days in their seasonal cycle, such that in both hemispheres KE at $100~$km peaks in late spring while KE at $10^3~$km peaks in late summer. The spectrum presented here affords us a new window for understanding the multiscale general oceanic circulation within Earth's climate system, including the largest planetary scales.

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arXiv2022

Surface Quasigeostrophic Turbulence in Variable Stratification

Numerical and observational evidence indicates that, in regions where mixed-layer instability is active, the surface geostrophic velocity is largely induced by surface buoyancy anomalies. Yet, in these regions, the observed surface kinetic energy spectrum is steeper than predicted by uniformly stratified surface quasigeostrophic theory. By generalizing surface quasigeostrophic theory to account for variable stratification, we show that surface buoyancy anomalies can generate a variety of dynamical regimes depending on the stratification's vertical structure. Buoyancy anomalies generate longer range velocity fields over decreasing stratification and shorter range velocity fields over increasing stratification. As a result, the surface kinetic energy spectrum is steeper over decreasing stratification than over increasing stratification. An exception occurs if the near surface stratification is much larger than the deep ocean stratification. In this case, we find an extremely local turbulent regime with surface buoyancy homogenization and a steep surface kinetic energy spectrum, similar to equivalent barotropic turbulence. By applying the variable stratification theory to the wintertime North Atlantic, and assuming that mixed-layer instability acts as a narrowband small-scale surface buoyancy forcing, we obtain a predicted surface kinetic energy spectrum between $k^{-4/3}$ and $k^{-7/3}$, which is consistent with the observed wintertime $k^{-2}$ spectrum. We conclude by suggesting a method of measuring the buoyancy frequency's vertical structure using satellite observations.

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arXiv2021

On the Discrete Normal Modes of Quasigeostrophic Theory

The discrete baroclinic modes of quasigeostrophic theory are incomplete and the incompleteness manifests as a loss of information in the projection process. The incompleteness of the baroclinic modes is related to the presence of two previously unnoticed stationary step-wave solutions of the Rossby wave problem with flat boundaries. These step-waves are the limit of surface quasigeostrophic waves as boundary buoyancy gradients vanish. A complete normal mode basis for quasigeostrophic theory is obtained by considering the traditional Rossby wave problem with prescribed buoyancy gradients at the lower and upper boundaries. The presence of these boundary buoyancy gradients activates the previously inert boundary degrees of freedom. These Rossby waves have several novel properties such as the presence of multiple modes with no internal zeros, a finite number of modes with negative norms, and their vertical structures form a basis capable of representing any quasigeostrophic state with a differentiable series expansion. Using this complete basis, we are able to obtain a differentiable series expansion to the potential vorticity of Bretherton (with Dirac delta contributions). We also examine the quasigeostrophic vertical velocity modes and derive a complete basis for such modes as well. A natural application of these modes is the development of a weakly non-linear wave-interaction theory of geostrophic turbulence that takes topography into account.

physics.ao-ph↗

arXiv2018

The KPP boundary layer scheme: revisiting its formulation and benchmarking one-dimensional ocean simulations relative to LES

We evaluate the Community ocean Vertical Mixing (CVMix) project version of the K-profile parameterization (KPP). For this purpose, one-dimensional KPP simulations are compared across a suite of oceanographically relevant regimes against large eddy simulations (LES). The LES is forced with horizontally uniform boundary fluxes and has horizontally uniform initial conditions, allowing its horizontal average to be compared to one-dimensional KPP tests. We find the standard configuration of KPP consistent with LES across many forcing regimes, supporting the physical basis of KPP. Our evaluation motivates recommendations for "best practices" for using KPP within ocean circulation models, and identifies areas where further research is warranted. Further, our test suite can be used as a baseline for evaluation of a broad suite of boundary layer models. The original treatment of KPP recommends the matching of interior diffusivities and their gradients to the KPP predicted values computed in the ocean surface boundary layer (OSBL). However, we find that difficulties in representing derivatives of rapidly changing diffusivities near the base of the OSBL can lead to loss of simulation fidelity. We propose two alternative approaches. We find the KPP entrainment buoyancy flux to be sensitive to vertical grid resolution and details of how to diagnose the KPP boundary layer depth. We modify the KPP turbulent shear velocity parameterization to reduce resolution dependence. Additionally, our results show that the KPP parameterized non-local tracer flux is incomplete due to the assumption that it solely redistributes the surface tracer flux. However, examination of the LES vertical turbulent scalar flux budgets show that non-local fluxes can exist in the absence of surface tracer fluxes. This result motivates further studies of the non-local flux parameterization.

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arXiv1995

North Atlantic thermohaline circulation predictability in a coupled ocean-atmosphere model

Predictability of the North Atlantic thermohaline circulation (THC) variability as simulated in the GFDL coupled ocean-atmosphere general circulation model is established for a set of ensemble experiments. The ensembles consist of identical oceanic initial conditions underneath a model atmosphere chosen randomly from the model climatology. This experimental design is based on the separation in time scales present in the model which motivates the assumption that the predictability deduced from these ensembles provides an upper limit to the model's THC predictability. The climatology is taken from a multi-century model integration whose THC variability has power concentrated at the 40-60 year time scale. A linear stochastic perspective is shown to be generally consistent with the ensemble statistics. The linear theory suggests a natural measure of ensemble predictability as the time at which the ensemble variance becomes a subjectively defined fraction (0.5 used here) of the climatological variance. It is furthermore of interest to distinguish predictability of the rapidly de-correlating portion of the model's THC from the longer time correlated portion. The rapidly de-correlating portion shows predictability for $\approx 1.5$ years. The slower portion shows predictability for $\approx 5-7$ years. The linear stochastic framework provides for the straightforward construction of an optimal forecast of the model's THC variability and an understanding of why the optimal forecast is useless beyond a particular limit.

ao-sci↗

arXiv1995

A linear thermohaline oscillator driven by stochastic atmospheric forcing

The interdecadal variability of a stochastically forced four-box model of the oceanic meridional thermohaline circulation (THC) is described and compared to the THC variability in the coupled ocean-atmosphere GCM of Delworth, Manabe, and Stouffer (1993). The box model is placed in a linearly stable thermally dominant mean state under mixed boundary conditions. A linear stability analysis of this state reveals one damped oscillatory THC mode in addition to purely damped modes. The variability of the model under a moderate amount of stochastic forcing, meant to emulate the random variability of the atmosphere affecting the coupled model's interdecadal THC variability, is studied. A linear interpretation, in which the damped oscillatory mode is of primary importance, is sufficient for understanding the mechanism accounting for the stochastically forced variability. Direct comparison of the variability in the box model and coupled GCM reveals common qualitative aspects. Such a comparison supports, although does not verify, the hypothesis that the coupled model's THC variability can be interpreted as the result of atmospheric weather exciting a linear damped oscillatory THC mode.

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