Lyapunov, Floquet, and singular vectors for baroclinic waves

The dynamics of the growth of linear disturbances to a chaotic basic state is analyzed in an asymptotic model of weakly nonlinear, baroclinic wave-mean interaction. In this model, an ordinary differential equation for the wave amplitude is coupled to a partial differential equation for the zonal flow correction. The leading Lyapunov vector is nearly parallel to the leading Floquet vector ø1 of the lowest-order unstable periodic orbit over most of the attractor. Departures of the Lyapunov vector from this orientation are primarily rotations of the vector in an approximate tangent plane to the large-scale attractor structure. Exponential growth and decay rates of the Lyapunov vector during individual Poincaré section returns are an order of magnitude larger than the Lyapunov exponent λ ≈ 0.016. Relatively large deviations of the Lyapunov vector from parallel to ø1 are generally associated with relatively large transient decays. The transient growth and decay of the Lyapunov vector is well described by the transient growth and decay of the leading Floquet vectors of the set of unstable periodic orbits associated with the attractor. Each of these vectors is also nearly parallel to ø1. The dynamical splitting of the complete sets of Floquet vectors for the higher-order cycles follows the previous results on the lowest-order cycle, with the vectors divided into wavedynamical and decaying zonal flow modes. Singular vectors and singular values also generally follow this split. The primary difference between the leading Lyapunov and singular vectors is the contribution of decaying, inviscidly-damped wave-dynamical structures to the singular vectors

The effects of uncorrelated measurement noise on SWOT estimates of sea-surface height, velocity and vorticity

Author Posting. © American Meteorological Society, 2022. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of the Atmospheric and Oceanic Technology 39(7), (2022): 1053–1083, https://doi.org/10.1175/jtech-d-21-0167.1.The Ka-band Radar Interferometer (KaRIn) on the Surface Water and Ocean Topography (SWOT) satellite will revolutionize satellite altimetry by measuring sea surface height (SSH) with unprecedented accuracy and resolution across two 50-km swaths separated by a 20-km gap. The original plan to provide an SSH product with a footprint diameter of 1 km has changed to providing two SSH data products with footprint diameters of 0.5 and 2 km. The swath-averaged standard deviations and wavenumber spectra of the uncorrelated measurement errors for these footprints are derived from the SWOT science requirements that are expressed in terms of the wavenumber spectrum of SSH after smoothing with a filter cutoff wavelength of 15 km. The availability of two-dimensional fields of SSH within the measurement swaths will provide the first spaceborne estimates of instantaneous surface velocity and vorticity through the geostrophic equations. The swath-averaged standard deviations of the noise in estimates of velocity and vorticity derived by propagation of the uncorrelated SSH measurement noise through the finite difference approximations of the derivatives are shown to be too large for the SWOT data products to be used directly in most applications, even for the coarsest footprint diameter of 2 km. It is shown from wavenumber spectra and maps constructed from simulated SWOT data that additional smoothing will be required for most applications of SWOT estimates of velocity and vorticity. Equations are presented for the swath-averaged standard deviations and wavenumber spectra of residual noise in SSH and geostrophically computed velocity and vorticity after isotropic two-dimensional smoothing for any user-defined smoother and filter cutoff wavelength of the smoothing.This research was supported by NASA Grant NNX16AH76G

Towed thermister chain observations of fronts in the subtropical North Pacific

A thermistor chain was towed 1400 km through the eastern North Pacific subtropical frontal zone in January 1980. The observations resolve surface layer temperature features with horizontal wavelengths of 0.2-200 km and vertical scales of 10-70 m. The dominant features, which have horizontal wavelengths of 10-100 km, amplitudes of 0.2°-1.0°C, and random orientation, likely arise from baroclinic instability. Associated with them is a plateau below 0.1 cpkm in the horizontal temperature gradient spectrum. Strong temperature fronts O(1°-2°C/3-10 km) are observed near 33°N, 31°N, and 27°N. Temperature variability is partially density compensated by salinity, with the fraction of compensation increasing northward. There is evidence of vertical mixing during high winds. Temperature at 15-m depth is roughly normally distributed around the climatological surface mean, with a standard deviation of approximately 0.5°C. The standard deviation would correspond to an adiabatic meridional displacement of 80-100 km in the mean gradient. Horizontal temperature gradient at 15-m depth has maximum values in excess of 0.25°C/100 m and kurtosis near 80. In the band 0.10-1 cpkm, the 15-m gradient spectrum is inversely proportional to wave number, consistent with predictions from geostrophic turbulence theory, while the spectrum at 70-m depth has additional variance that is consistent with Garrett-Munk internal wave displacements.Keywords: upper ocean processes, eddies and mesoscale processes, Fronts and jets, Pacific OceanKeywords: upper ocean processes, eddies and mesoscale processes, Fronts and jets, Pacific Ocea

Satellite observations of mesoscale eddy-induced Ekman pumping

Author Posting. © American Meteorological Society, 2015. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 45 (2015): 104–132, doi:10.1175/JPO-D-14-0032.1.Three mechanisms for self-induced Ekman pumping in the interiors of mesoscale ocean eddies are investigated. The first arises from the surface stress that occurs because of differences between surface wind and ocean velocities, resulting in Ekman upwelling and downwelling in the cores of anticyclones and cyclones, respectively. The second mechanism arises from the interaction of the surface stress with the surface current vorticity gradient, resulting in dipoles of Ekman upwelling and downwelling. The third mechanism arises from eddy-induced spatial variability of sea surface temperature (SST), which generates a curl of the stress and therefore Ekman pumping in regions of crosswind SST gradients. The spatial structures and relative magnitudes of the three contributions to eddy-induced Ekman pumping are investigated by collocating satellite-based measurements of SST, geostrophic velocity, and surface winds to the interiors of eddies identified from their sea surface height signatures. On average, eddy-induced Ekman pumping velocities approach O(10) cm day−1. SST-induced Ekman pumping is usually secondary to the two current-induced mechanisms for Ekman pumping. Notable exceptions are the midlatitude extensions of western boundary currents and the Antarctic Circumpolar Current, where SST gradients are strong and all three mechanisms for eddy-induced Ekman pumping are comparable in magnitude. Because the polarity of current-induced curl of the surface stress opposes that of the eddy, the associated Ekman pumping attenuates the eddies. The decay time scale of this attenuation is proportional to the vertical scale of the eddy and inversely proportional to the wind speed. For typical values of these parameters, the decay time scale is about 1.3 yr.This work was funded by NASA Grants NNX08AI80G, NNX08AR37G, NNX13AD78G, NNX10AE91G, NNX13AE47G, and NNX10AO98G.2015-07-0

Coastal Atmospheric Circulation around an Idealized Cape during Wind-Driven Upwelling Studied from a Coupled Ocean–Atmosphere Model

The study analyzes atmospheric circulation around an idealized coastal cape during summertime upwelling-favorable wind conditions simulated by a mesoscale coupled ocean–atmosphere model. The domain resembles an eastern ocean boundary with a single cape protruding into the ocean in the center of a coastline. The model predicts the formation of an orographic wind intensification area on the lee side of the cape, extending a few hundred kilometers downstream and seaward. Imposed initial conditions do not contain a low-level temperature inversion, which nevertheless forms on the lee side of the cape during the simulation, and which is accompanied by high Froude numbers diagnosed in that area, suggesting the presence of the supercritical flow. Formation of such an inversion is likely caused by average easterly winds resulting on the lee side that bring warm air masses originating over land, as well as by air warming during adiabatic descent on the lee side of the topographic obstacle. Mountain leeside dynamics modulated by differential diurnal heating is thus suggested to dominate the wind regime in the studied case. The location of this wind feature and its strong diurnal variations correlate well with the development and evolution of the localized lee side trough over the coastal ocean. The vertical extent of the leeside trough is limited by the subsidence inversion aloft. Diurnal modulations of the ocean sea surface temperatures (SSTs) and surface depth-averaged ocean current on the lee side of the cape are found to strongly correlate with wind stress variations over the same area. Wind-driven coastal upwelling develops during the simulation and extends offshore about 50 km upwind of the cape. It widens twice as much on the lee side of the cape, where the coldest nearshore SSTs are found. The average wind stress–SST coupling in the 100-km coastal zone is strong for the region upwind of the cape, but is notably weaker for the downwind region, estimated from the 10-day-average fields. The study findings demonstrate that orographic and diurnal modulations of the near-surface atmospheric flow on the lee side of the cape notably affect the air–sea coupling on various temporal scales: weaker wind stress–SST coupling results for the long-term averages, while strong correlations are found on the diurnal scale.Keywords: Wind, Coupled models, Coastal flows, UpwellingKeywords: Wind, Coupled models, Coastal flows, Upwellin

Summertime Coupling between Sea Surface Temperature and Wind Stress in the California Current System

Satellite observations of wind stress and sea surface temperature (SST) are analyzed to investigate ocean–atmosphere interaction in the California Current System (CCS). As in regions of strong SST fronts elsewhere in the World Ocean, SST in the CCS region is positively correlated with surface wind stress when SST fronts are strong, which occurs during the summertime in the CCS region. This ocean influence on the atmosphere is apparently due to SST modification of stability and mixing in the atmospheric boundary layer and is most clearly manifest in the derivative wind stress fields: wind stress curl and divergence are linearly related to, respectively, the crosswind and downwind components of the local SST gradient. The dynamic range of the Ekman upwelling velocities associated with the summertime SST-induced perturbations of the wind stress curl is larger than that of the upwelling velocities associated with the mean summertime wind stress curl. This suggests significant feedback effects on the ocean, which likely modify the SST distribution that perturbed the wind stress curl field. The atmosphere and ocean off the west coast of North America must therefore be considered a fully coupled system. It is shown that the observed summertime ocean–atmosphere interaction is poorly represented in the NOAA North American Mesoscale Model (formerly called the Eta Model). This is due, at least in part, to the poor resolution and accuracy of the SST boundary condition used in the model. The sparse distribution of meteorological observations available over the CCS for data assimilation may also contribute to the poor model performance

The ventilated pool: a model of subtropical mode water

An analytical model of subtropical mode water is presented, based on ventilated thermocline theory and on numerical solutions of a planetary geostrophic basin model. In ventilated thermocline theory, the western pool is a region bounded on the east by subsurface streamlines that outcrop at the western edge of the interior, and in which additional dynamical assumptions are necessary to complete the solution. Solutions for the western pool were originally obtained under the assumption that the potential vorticity of the subsurface layer was homogenized. In the present theory, it is instead assumed that all of the water in the pool region is ventilated, and therefore that all the Sverdrup transport is carried in the uppermost, outcropping layer. The result is the formation of a deep, vertically homogeneous, fluid layer in the northwest corner of the subtropical gyre that extends from the surface to the base of the ventilated thermocline. This ventilated pool is an analog of the observed subtropical mode waters. The pool also has the interesting properties that it determines its own boundaries and affects the global potential vorticity-pressure relationship. When there are multiple outcropping layers, ventilated pool fluid is subducted to form a set of nested annuli in ventilated, subsurface layers, which are the deepest subducted layers in the ventilated thermocline.KEYWORDS: Ventilated thermocline, Mode water, Ocean circulation, Planetary geostroph

Evidence for atmospheric control of sea-ice motion through Nares Strait

Satellite observations of ice motion are combined with model estimates of low‐level winds and surface wind stress to provide evidence for atmospheric control of sea‐ice motion through Nares Strait, between Ellesmere Island and Greenland, during two periods in 2004. The results suggest that ice flux through the strait, and its shutdown through the formation of a landfast ice mass in the strait, can be controlled by wind stress and atmospheric cooling. Analysis of the model results during these two periods also suggest that the intense, low‐level, along‐strait winds are strongly ageostrophic, and may be usefully estimated from pressure differences along the Strait

The winds and currents mission concept

© The Author(s), 2019. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Rodriguez, E., Bourassa, M., Chelton, D., Farrar, J. T., Long, D., Perkovic-Martin, D., & Samelson, R. The winds and currents mission concept. Frontiers in Marine Science, 6, (2019): 438, doi:10.3389/fmars.2019.00438.The Winds and Currents Mission (WaCM) is a proposed approach to meet the need identified by the NRC Decadal Survey for the simultaneous measurements of ocean vector winds and currents. WaCM features a Ka-band pencil-beam Doppler scatterometer able to map ocean winds and currents globally. We review the principles behind the WaCM measurement and the requirements driving the mission. We then present an overview of the WaCM observatory and tie its capabilities to other OceanObs reviews and measurement approaches.ER was funded under NASA grant NNN13D462T. DC was funded under NASA grant NNX10AO98G. JF was funded under NASA grants NNX14AM71G and NNX16AH76G. DL was funded under NASA grant NNX14AM67G. DP-M was funded under NASA grant NNH13ZDA001N. RS was funded under NASA grant NNX14AM66G