The omega equation and potential vorticity

Hoskins, Brian J.; Pedder, M. A.; Jones, David W.

doi:10.1256/qj.02.135

Cited by 63 publications

(58 citation statements)

References 23 publications

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“…As flow along isentropic surfaces leaves the height of the isentropic surfaces unchanged, only deviations of w from w i u induce a tendency of the height. Therefore, we introduce the isentropic displacement vertical wind, defined as (Hoskins et al )

\begin{matrix} alignleft \\ align-1 w_{id} \equiv w - w_{i u} . & align-2 \end{matrix}

Note that the isentropic displacement vertical wind includes the response of the flow to adiabatic as well as diabatic processes.…”

Section: Diagnosing the Tendency Of The Slope Of Isentropic Surfacesmentioning

confidence: 99%

Analysis of the slope of isentropic surfaces and its tendencies over the North Atlantic

Papritz

Spengler

2015

Quart J Royal Meteoro Soc

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The maintenance of baroclinicity along mid‐ and high‐latitude storm tracks is a matter of ongoing debate. Using an isentropic framework, a novel diagnostic based on the tendency equation for the slope of isentropic surfaces – a measure of the potential for baroclinic development – is presented. The tendency comprises contributions from dynamic processes, latent heat release, radiation and subgrid‐scale turbulence, which incorporates the effect of sensible heat fluxes. A climatology of these tendencies over the North Atlantic is compiled for the winters of 2009 and 2010. It is found that adiabatic tilting flattens the isentropic surfaces, reflecting the action of growing baroclinic cyclones. This tendency is balanced climatologically by the generation of slope by diabatic processes. In the lower troposphere, the most intense diabatic increase of slope is found along the oceanic frontal zone associated with the Gulf Stream and at higher latitudes in the Labrador Sea, the Nordic Seas and the Barents Sea. Latent heat release and sensible heat fluxes both contribute substantially in these regions. A quantitative analysis of cold‐air outbreaks emphasizes their important role in restoring the slope in the lower troposphere over the Gulf Stream region and off the sea‐ice edge at high latitudes. In the upper troposphere, latent heat release due to cloud microphysical processes is the dominant mechanism maintaining the slope.

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\begin{matrix} alignleft \\ align-1 w_{id} \equiv w - w_{i u} . & align-2 \end{matrix}

Note that the isentropic displacement vertical wind includes the response of the flow to adiabatic as well as diabatic processes.…”

Section: Diagnosing the Tendency Of The Slope Of Isentropic Surfacesmentioning

confidence: 99%

Analysis of the slope of isentropic surfaces and its tendencies over the North Atlantic

Papritz

Spengler

2015

Quart J Royal Meteoro Soc

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“…Except for experiments based on neutrally buoyant RAFOS floats (e.g., Bower & Rossby, ; Levine et al, ; Rossby, ; Song et al, ), observations cannot provide direct measurements of the vertical velocities, which are thus commonly inferred from 2‐D or 3‐D reconstructions of the density field and horizontal velocities through the Omega equation (Giordani et al, ; Hoskins, ; Hoskins & Draghici, ; Hoskins et al, ), a well‐known diagnostic tool that has been applied to the data collected during several field campaigns (Allen et al, ; Barceló‐Llull et al, ; Buongiorno Nardelli et al, ; Gomis et al, ; Naveira Garabato et al, ; Pollard & Regier, ; Rodríguez et al, ; Rudnick, ; Ruiz et al, ; Tintoré et al, ). Oceanographic surveys, however, suffer from the difficulty to guarantee both high spatial resolution and synopticity.…”

Section: Introductionmentioning

confidence: 99%

“…This is due to the fact that observations only provide limited views of the three-dimensional (3-D) ocean state, primarily in terms of resolution and coverage, but also reflects our incomplete understanding of boundary layer dynamics and imperfect or missing parameterization of processes occurring at the unresolved scales, such as turbulent mixing and diffusion or submesoscale (Bachman et al, 2016(Bachman et al, , 2017Canuto, 2015;Fox-Kemper and Ferrari, 2008;Hamlington et al, 2014;Li et al, 2017). 1977;Hoskins et al, 1978Hoskins et al, , 2003, a well-known diagnostic tool that has been applied to the data collected during several field campaigns Barcel o-Llull et al, 2017;Buongiorno Nardelli et al, 2001;Gomis et al, 2001;Naveira Garabato et al, 2001;Pollard & Regier, 1992;Rodr ıguez et al, 2001;Rudnick, 1996;Ruiz et al, 2014;Tintor e et al, 1991). Oceanographic surveys, however, suffer from the difficulty to guarantee both high spatial resolution and synopticity.…”

Section: Introductionmentioning

confidence: 99%

Three‐Dimensional Ageostrophic Motion and Water Mass Subduction in the Southern Ocean

2018

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Vertical velocities at the ocean mesoscale are several orders of magnitude smaller than corresponding horizontal flows, making their direct monitoring a still unsolved challenge. Vertical motion is generally retrieved indirectly by applying diagnostic equations to observation‐based fields. The most common approach relies on the solution of an adiabatic version of the Omega equation, neglecting the ageostrophic secondary circulation driven by frictional effects and turbulent mixing in the boundary layers. Here we apply a diabatic semigeostrophic diagnostic model to two different 3‐D reconstructions covering the Southern Ocean during the period 2010–2012. We incorporate the effect of vertical mixing through a modified K‐profile parameterization and using ERA‐interim data, and perform an indirect validation of the ageostrophic circulation with independent drifter observations. Even if horizontal gradients and associated vertical flow are likely underestimated at 1/4° × 1/4° resolution, the exercise provides an unprecedented relative quantification of the contribution of vertical mixing and adiabatic internal dynamics on the vertical exchanges along the Antarctic Circumpolar Current. Kinematic estimates of subduction rates show the destruction of poleward flowing waters lighter than 26.6 kg/m3 (14 ÷ 15 Sv) and two main positive bands associated with the Antarctic Intermediate Water (7 ÷ 11 Sv) and Sub‐Antarctic Mode Waters (4 ÷ 7 Sv) formation, while Circumpolar Deep Water upwelling attains around 3 ÷ 6 Sv. Diabatic and adiabatic terms force distinct spatial responses and vertical velocity magnitudes along the water column and the restratifying effect of adiabatic internal dynamics due to mesoscale eddies is shown to at least partly compensate the contribution of wind‐driven vertical exchanges to net subduction.

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“…In a different context, Hoskins et al (2003) proposed to compute a system velocity c based on the density conservation equation. When this is written in a frame of reference moving with speed c, it becomes:…”

Section: It Then Resultsmentioning

confidence: 99%

“…In other cases, however, the definition of a homogeneous system velocity may be more problematic, in which case the correction method proposed by Rixen et al (2001) may be more convenient. A first method to compute such a system velocity has been proposed by Hoskins et al (2003), though not for the purpose of station relocation. A second method has been suggested by Pascual et al (2004), who also proposed to relocate the stations in order to mitigate the impact of the lack of synopticity.…”

Section: Introductionmentioning

confidence: 99%

Errors in dynamical fields inferred from oceanographic cruise data

Gomis

Pascual

Pedder

2005

Journal of Marine Systems

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Diagnostic studies of ocean dynamics based on the analysis of oceanographic cruise data are usually quite sensitive to observation errors, to the station distribution and to the synopticity of the sampling. The first two sources have been evaluated in Part I of this work. Here we evaluate synopticity errors for different sampling strategies applied to simulated unstable baroclinic waves. As suggested in previous studies, downstream and upstream cross-front samplings produce larger errors than along-front samplings. In our particular case study, the along-front sampling results in fractional errors (rms error divided by the standard deviation of the field) of about 15% for dynamic height and more than 50% for relative vorticity and vertical velocity. These values are significantly higher than those obtained in Part I for typical observation errors and sampling limitations (about 6% for dynamic height and between 15 and 30% for geostrophic vorticity and vertical velocity).We also propose and test two methods aimed at reducing the impact of the lack of synopticity. The first one corrects the observations using the quasi-geostrophic tendency equation. The second method combines the relocation of stations (based on a system velocity) and the correction of observations (through the estimation of a growth rate). For the fields simulated in this work, the second method gives better results than the first, being able to eliminate practically all synopticity errors in the case of the along-front sampling. In practice, the error reduction is likely to be less effective, since actual fields cannot be expected to have a system velocity as homogeneous as for the single-mode waves simulated in this work.

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The omega equation and potential vorticity

Cited by 63 publications

References 23 publications

Analysis of the slope of isentropic surfaces and its tendencies over the North Atlantic

Analysis of the slope of isentropic surfaces and its tendencies over the North Atlantic

Three‐Dimensional Ageostrophic Motion and Water Mass Subduction in the Southern Ocean

Errors in dynamical fields inferred from oceanographic cruise data

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