omega equation
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Abstract A four-dimensional survey by a fleet of 7 underwater gliders was used to identify pathways of subduction at the Almeria-Oran front in the western Mediterranean Sea. The combined glider fleet covered nearly 9000 km over ground while doing over 2500 dives to as deep as 700 m. The gliders had sensors to measure temperature, salinity, velocity, chlorophyll fluorescence and acoustic backscatter. Data from the gliders were analyzed through objective maps that were functions of across-front distance, along-front distance, and time on vertical levels separated by 10 m. Geostrophic velocity was inferred using a variational approach, and the quasigeostrophic omega equation was solved for vertical and ageostrophic horizontal velocities. Peak downward vertical velocities were near 25 m day-1 in an event that propagated in the direction of the frontal jet. An examination of an isopycnal surface that outcropped as the front formed showed consistency between the movement of the tracers and the inferred vertical velocity. The vertical velocity tended to be downward on the dense side of the front and upward on the light side so as to flatten the front in the manner of a baroclinic instability. The resulting heat flux approached 80 W m-2 near 100 m depth with a structure that would cause restratification of the front. One glider was used to track an isotherm over a day for a direct measure of vertical velocity as large as 50 m day-1, with a net downward displacement of 15 m over the day.


MAUSAM ◽  
2021 ◽  
Vol 22 (1) ◽  
pp. 35-46
Author(s):  
J. SHUKLA

The quasi-geostrophic omega equation has been numerically solved to get the vertical velocity distribution in a typical westerly disturbance. The effects of sensible heat and latent heat of condensation are also for a 4-layer model. The computations were performed on HITAC 5020. The numerically obtained vertical velocity field is in good agreement with the observed weather pattern associated with the middle latitude large-scale disturbance, i.e., ascending motion in front of the trough and downward motion in the rear of the trough.


Author(s):  
Alice Pietri ◽  
Xavier Capet ◽  
Francesco d’Ovidio ◽  
Marina Levy ◽  
Julien Le Sommer ◽  
...  

AbstractThe quasi-geostrophic and the generalized omega equations are the most widely used methods to reconstruct vertical velocity (w) from in-situ data. As observational networks with much higher spatial and temporal resolutions are being designed, the question rises of identifying the approximations and scales at which an accurate estimation of w through the omega equation can be achieved and what are the critical scales and observables needed. In this paper we test different adiabatic omega reconstructions of w over several regions representative of main oceanic regimes of the global ocean in a fully eddy-resolving numerical simulation with a 1=60o horizontal resolution. We find that the best reconstructions are observed in conditions characterized by energetic turbulence and/or weak stratification where near-surface frontal processes are felt deep into the ocean interior. The quasi-geostrophic omega equation gives satisfactory results for scales larger than ~ 10 km horizontally while the improvements using a generalized formulation are substantial only in conditions where frontal turbulent processes are important (providing improvements with satisfactory reconstruction skill down to ~ 5 km in scale). The main sources of uncertainties that could be identified are related to processes responsible for ocean thermal wind imbalance (TWI), which is particularly difficult to account for (especially in observation-based studies) and to the deep flow which is generally improperly accounted for in omega reconstructions through the bottom boundary condition. Nevertheless, the reconstruction of mesoscale vertical velocities may be sufficient to estimate vertical fluxes of oceanic properties in many cases of practical interest.


2021 ◽  
Vol 51 (1) ◽  
pp. 229-246
Author(s):  
Peiran Yang ◽  
Zhao Jing ◽  
Bingrong Sun ◽  
Lixin Wu ◽  
Bo Qiu ◽  
...  

AbstractOceanic eddies play a crucial role in transporting heat from the subsurface to surface ocean. However, dynamics responsible for the vertical eddy heat transport QT have not been systematically understood, especially in the mixed layer of western boundary current extensions characterized by the coincidence of strong eddy activities and air–sea interactions. In this paper, the winter (December–March) QT in the Kuroshio Extension is simulated using a 1-km regional ocean model. An omega equation based on the geostrophic momentum approximation and generalized to include the viscous and diabatic effects is derived and used to decompose the contribution of QT from different dynamics. The simulated QT exhibits a pronounced positive peak around the center of the mixed layer (~60 m). The value of QT there exhibits multi-time-scale variations with irregularly occurring extreme events superimposed on a slowly varying seasonal cycle. The proposed omega equation shows good skills in reproducing QT, capturing its spatial and temporal variations. Geostrophic deformation and vertical mixing of momentum are found to be the two major processes generating QT in the mixed layer with the former and the latter accounting for its seasonal variation and extreme events, respectively. The mixed layer instability and the net effect of frontogenesis/frontolysis contribute comparably to the geostrophic deformation induced QT. The contribution of QT from vertical mixing of momentum can be understood on the basis of turbulent thermal wind balance.


2020 ◽  
Vol 33 (16) ◽  
pp. 7125-7139 ◽  
Author(s):  
Ziwei Li ◽  
Paul A. O’Gorman

AbstractPrecipitation extremes intensify in most regions in climate model projections. Changes in vertical velocities contribute to the changes in intensity of precipitation extremes but remain poorly understood. Here, we find that midtropospheric vertical velocities in extratropical precipitation extremes strengthen overall in simulations of twenty-first-century climate change. For each extreme event, we solve the quasigeostrophic omega equation to decompose this strengthening into different physical contributions. We first consider a dry decomposition in which latent heating is treated as an external forcing of upward motion. Much of the positive contribution to upward motion from increased latent heating is offset by negative contributions from increases in dry static stability and changes in the horizontal length scale of vertical velocities. However, taking changes in latent heating as given is a limitation when the aim is to understand changes in precipitation, since latent heating and precipitation are closely linked. Therefore, we also perform a moist decomposition of the changes in vertical velocities in which latent heating is represented through a moist static stability. In the moist decomposition, changes in moist static stability play a key role and contributions from other factors such as changes in the depth of the upward motion increase in importance. While both dry and moist decompositions are self-consistent, the moist dynamical perspective has greater potential to give insights into the causes of the dynamical contributions to changes in precipitation extremes in different regions.


2020 ◽  
Vol 77 (6) ◽  
pp. 2067-2090
Author(s):  
Satoki Tsujino ◽  
Hung-Chi Kuo

Abstract The inner-core dynamics of Supertyphoon Haiyan (2013) undergoing rapid intensification (RI) are studied with a 2-km-resolution cloud-resolving model simulation. The potential vorticity (PV) field in the simulated storm reveals an elliptical and polygonal-shaped eyewall at the low and middle levels during RI onset. The PV budget analysis confirms the importance of PV mixing at this stage, that is, the asymmetric transport of diabatically generated PV to the storm center from the eyewall and the ejection of PV filaments outside the eyewall. We employ a piecewise PV inversion (PPVI) and an omega equation to interpret the model results in balanced dynamics. The omega equation diagnosis suggests eye dynamical warming is associated with the PV mixing. The PPVI indicates that PV mixing accounts for about 50% of the central pressure fall during RI onset. The decrease of central pressure enhances the boundary layer (BL) inflow. The BL inflow leads to contraction of the radius of the maximum tangential wind (RMW) and the formation of a symmetric convective PV tower inside the RMW. The eye in the later stage of the RI is warmed by the subsidence associated with the convective PV towers. The results suggest that the pressure change associated with PV mixing, the increase of the symmetric BL radial inflow, and the development of a symmetric convective PV tower are the essential collaborating dynamics for RI. An experiment with 500-m resolution shows that the convergence of BL inflow can lead to an updraft magnitude of 20 m s−1 and to a convective PV tower with a peak value of 200 PVU (1 PVU = 10−6 K kg−1 m2 s−1).


2020 ◽  
Vol 1 (1) ◽  
pp. 1-25 ◽  
Author(s):  
Victoria A. Sinclair ◽  
Mika Rantanen ◽  
Päivi Haapanala ◽  
Jouni Räisänen ◽  
Heikki Järvinen

Abstract. Little is known about how the structure of extra-tropical cyclones will change in the future. In this study aqua-planet simulations are performed with a full-complexity atmospheric model. These experiments can be considered an intermediate step towards increasing knowledge of how, and why, extra-tropical cyclones respond to warming. A control simulation and a warm simulation in which the sea surface temperatures are increased uniformly by 4 K are run for 11 years. Extra-tropical cyclones are tracked, cyclone composites created, and the omega equation applied to assess causes of changes in vertical motion. Warming leads to a 3.3 % decrease in the number of extra-tropical cyclones, with no change to the median intensity or lifetime of extra-tropical cyclones but to a broadening of the intensity distribution resulting in both more stronger and more weaker storms. Composites of the strongest extra-tropical cyclones show that total column water vapour increases everywhere relative to the cyclone centre and that precipitation increases by up to 50 % with the 4 K warming. The spatial structure of the composite cyclone changes with warming: the 900–700 hPa layer averaged potential vorticity, 700 hPa ascent, and precipitation maximums associated with the warm front all move polewards and downstream, and the area of ascent expands in the downstream direction. Increases in ascent forced by diabatic heating and thermal advection are responsible for the displacement, whereas increases in ascent due to vorticity advection lead to the downstream expansion. Finally, maximum values of ascent due to vorticity advection and thermal advection weaken slightly with warming, whereas those attributed to diabatic heating increase. Thus, cyclones in warmer climates are more diabatically driven.


2020 ◽  
Vol 72 (1) ◽  
pp. 1-26 ◽  
Author(s):  
Mika Rantanen ◽  
Jouni Räisänen ◽  
Victoria A. Sinclair ◽  
Juha Lento ◽  
Heikki Järvinen

2019 ◽  
Vol 77 (1) ◽  
pp. 113-129
Author(s):  
Mahnoosh Haghighatnasab ◽  
Mohammad Mirzaei ◽  
Ali R. Mohebalhojeh ◽  
Christoph Zülicke ◽  
Riwal Plougonven

Abstract The parameterization of inertia–gravity waves (IGWs) is of considerable importance in general circulation models. Among the challenging issues faced in studies concerned with parameterization of IGWs is the estimation of diabatic forcing in a way independent of the physics parameterization schemes, in particular, convection. The requirement is to estimate the diabatic heating associated with balanced motion. This can be done by comparing estimates of balanced vertical motion with and without diabatic effects. The omega equation provides the natural method of estimating balanced vertical motion without diabatic effects, and several methods for including diabatic effects are compared. To this end, the assumption of spatial-scale separation between IGWs and balanced flows is combined with a suitable form of the balanced omega equation. To test the methods constructed for estimating diabatic heating, an idealized numerical simulation of the moist baroclinic waves is performed using the Weather Research and Forecasting (WRF) Model in a channel on the f plane. In overall agreement with the diabatic heating of the WRF Model, in the omega-equation-based estimates, the maxima of heating appear in the warm sector of the baroclinic wave and in the exit region of the upper-level jet. The omega-equation-based method with spatial smoothing for estimating balanced vertical motion is thus presented as the proper way to evaluate diabatic forcing for parameterization of IGWs.


2019 ◽  
Author(s):  
Victoria A. Sinclair ◽  
Mika Rantanen ◽  
Päivi Haapanala ◽  
Jouni Räisänen ◽  
Heikki Järvinen

Abstract. Little is known about how the structure of extra-tropical cyclones will change in the future. In this study aquaplanet simulations are performed with a full complexity atmospheric model. These experiments can be considered as an intermediate step towards increasing knowledge of how, and why, extra-tropical cyclones respond to warming. A control simulation and a warm simulation in which the sea surface temperatures are increased uniformly by 4 K are run for 11 years. Extra-tropical cyclones are tracked, cyclone composites created, and the omega equation applied to assess causes of changes in vertical motion. Warming leads to a 3.3 % decrease in the number of extra-tropical cyclones, no change to the median intensity nor life time of extra-tropical cyclones, but to a broadening of the intensity distribution resulting in both more stronger and more weaker storms. Composites of the strongest extra-tropical cyclones show that total column water vapour increases everywhere relative to the cyclone centre and that precipitation increases by up to 50 % with the 4 K warming. The spatial structure of the composite cyclone changes with warming: the 900–700-hPa layer averaged potential vorticity, 700-hPa ascent and precipitation maximums associated with the warm front all move polewards and downstream and the area of ascent expands in the downstream direction. Increases in ascent forced by diabatic heating and thermal advection are responsible for the displacement whereas increases in ascent due to vorticity advection lead to the downstream expansion. Finally, maximum values of ascent due to vorticity advection and thermal advection weaken slightly with warming whereas those attributed to diabatic heating increase. Thus, cyclones in warmer climates are more diabatically driven.


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