Selection of Momentum Variables for a Three-Dimensional Variational Analysis

Three choices of control variables for meteorological variational analysis (3DVAR or 4DVAR) are associated with horizontal wind: (1) streamfunction and velocity potential, (2) eastward and northward velocity, and (3) vorticity and divergence. This study shows theoretical and numerical differences of these variables in practical 3DVAR data assimilation through statistical analysis and numerical experiments. This paper demonstrates that (a) streamfunction and velocity potential could potentially introduce analysis errors; (b) A 3DVAR using velocity or vorticity and divergence provides a natural scale dependent influence radius in addition to the covariance; (c) for a regional analysis, streamfunction and velocity potential are retrieved from the background velocity field with Neumann boundary condition. Improper boundary conditions could result in further analysis errors; (d) a variational data assimilation or an inverse problem using derivatives as control variables yields smoother analyses, for example, a 3DVAR using vorticity and divergence as controls yields smoother wind analyses than those analyses obtained by a 3DVAR using either velocity or streamfunction/velocity potential as control variables; and (e) statistical errors of higher order derivatives of variables are more independent, e.g., the statistical correlation between U and V is smaller than the one between streamfunction and velocity potential, and thus the variables in higher derivatives are more appropriate for a variational system when a cross-correlation between variables is neglected for efficiency or other reasons. In summary, eastward and northward velocity, or vorticity and divergence are preferable control variables for variational systems and the former is more attractive because of its numerical efficiency. Numerical experiments are presented using analytic functions and real atmospheric observations.     

Observations of submesoscale eddies using high-frequency radar-derived kinematic and dynamic quantities

The spatio-temporal variability of submesoscale eddies off southern San Diego is investigated with two-year observations of subinertial surface currents [O(1) m depth] derived from shore-based high-frequency radars. The kinematic and dynamic quantities — velocity potential, stream function, divergence, vorticity, and deformation rates — are directly estimated from radial velocity maps using optimal interpolation. For eddy detection, the winding-angle approach based on flow geometry is applied to the calculated stream function. A cluster of nearly enclosed streamlines with persistent vorticity in time is identified as an eddy. About 700 eddies were detected for each rotation (clockwise and counter-clockwise). The two rotations show similar statistics with diameters in the range of 5–25 km and Rossby number of 0.2–2. They persist for 1–7 days with weak seasonality and migrate with a translation speed of 4–15 cm s⁻¹ advected by background currents. The horizontal structure of eddies exhibits nearly symmetric tangential velocity with a maximum at the defined radius of the eddy, non-zero radial velocity due to background flows, and Gaussian vorticity with the highest value at the center. In contrast divergence has no consistent spatial shape. Two episodic events are presented with other in situ data (subsurface current and temperature profiles, and local winds) as an example of frontal-scale secondary circulation associated with drifting submesoscale eddies.     

Divergent-rotational Nonlinear Energy Conversions in Wavenumber-frequency Domain During Summer Monsoon

--This work deals with computational modelling designed to understand the dynamical mechanism of low frequency monsoonal transients that results from nonlinear divergent-rotational (&gif1;) kinetic energy (KE) conversions due to the effects of Coriolis force, vorticity and divergence during the summer monsoon 1988 over the latitudinal belt 20°S-30°N at 850 hPa and 200 hPa. The results show two distinct spectral peaks spanning 30-45 days and 18-25 days in the energy conversions from the transient divergent motions to rotational motions. Due to the latitudinal variation of the earth's rotational effects, the conversion from the transient divergent to rotational motions, associated mainly with wavenumbers 1 and 2, tend to be more pronounced to the north of 15°N on the 30-45-day and 18-25-day time scales in the upper and lower tropospheres, respectively. The contribution of the stationary waves to maintenance of the low frequency rotational flow due to the effect of divergence through barotropic instability is significant at the upper troposphere. Divergent to rotational KE conversion by wave-wave interaction due to divergence is identified as an important mechanism for maintenance of low frequency oscillations in the lower troposphere. The upper tropospheric planetary scale divergent motions associated with 30-45-day oscillation gain substantial energy through nonlinear &gif1; interaction due to vorticity.     

On the topographic coupling at the core-mantle interface

The mean tangential stresses at a corrugated interface between a solid, electrically insulating mantle and a liquid core of magnetic diffusivity λ are calculated for uniform rotation of both mantle and core at an angular velocity Ω in the presence of a corotating magnetic field B. The core and mantle are assumed to extend indefinitely in the horizontal plane. The interface has the form z = η(x, y), where z is the upward vertical distance and x, y are the zonal and latitudinal distances respectively. The function η(x, y) has a planetary horizontal length scale (i.e. of the order of the radius of the Earth) and small amplitude and vertical gradient. The liquid core flows with uniform mean zonal velocity U₀ relative to the mantle. Ω and B possess vertical and horizontal components.The vertical (poloidal) component B_p is uniform and has a value of 5 G while the horizontal (toroidal) field B_T = B_pαz, where α is a constant. When |α| ? 1, the mean horizontal stresses are found to have the same order of magnitude (10^?2 N m^?2) as those inferred from variations in the decade fluctuations in the length of the day, although the exact numerical values depend on the orientation of Ω as well as on the wavenumbers in the zonal and latitudinal directions.The influence of the steepness (as measured by α) of the toroidal field on the stresses is investigated to examine whether the constraint that the mean horizontal stresses at the core-mantle interface be of the order of 10^?2 N m^?2 might provide a selection mechanism for the behaviour of the toroidal field in the upper reaches of the outer core of the Earth. The results indicate that the restriction imposed on α is related to the value assigned to the toroidal field deep into the core. For example, if |α| ? 1 then the tangential stresses are of the right order of magnitude only if the toroidal field is comparable with the poloidal field deep in the core.     

Residual vorticity induced by the action of tidal currents in combination with bottom topography in the Southern Bight of the North Sea

Abstract

Results are presented of calculations on the generation of residual vorticity by tidal currents over the bottom topography of the Southern Bight of the North Sea. A typical order of magnitude is 10^?6 to 10^?7 s ^?1. This is compared with current measurements on calm days, when similar magnitudes are found. At windspeeds less than about 5 m/s tidal generation of residual vorticity is important; at higher windspeeds wind effects begin to dominate. Our results are relevant in understanding the spatial variability of residual currents, because a non-zero vorticity implies the existence of horizontal gradients in the residual current field.     

Finite element-fractional steps solution of the 3-D coastal circulation model

The mathematical model for the nearly horizontal circulation due to wind, tides and density gradients in 3-D coastal areas is solved by a combined use of the method of finite elements and the integration in fractional steps. The discretisation of the flow domain is achieved through a system of 1-D finite elements over the depth, z, and 2-D finite elements in x?y space. The differential operators of the momentum equations in x and y, are split and integrated separately in z and x?y dimensions. The method is an extension of a previously presented approach combining finite differences and expansion in series. The application refers to the wind induced circulation in the 3-D coastal basin of Thessaloniki Bay.     

加速度迁移项位势及其在高原低涡及台风系统分析中的应用

依据水平风矢量场的分解思路,应用调和-余弦的二维风场分解方法,对水平风场的加速度迁移项也进行调和-余弦的分解,引入加速度迁移项位势概念,用加速度迁移项对应的位势分量部分对东移高原低涡及登陆台风系统的演变过程进行分析.结果表明:加速度迁移项位势对东移高原低涡系统有较好的描述作用.利用加速度迁移项位势追踪东移的高原低涡系统比常用的500 hPa位势高度场对低涡进行追踪更为清晰.此外,加速度迁移项位势在登陆台风Bilis的分析中也有较好的应用,可用以指示台风系统,判断台风中心的位置以及表示台风强度的变化.由于加速度迁移项位势可反映出水平风场平流的辐合辐散特征,因此对低涡及台风等与平流场的辐合辐散关系密切的天气系统的动力结构有较好的识别能力,可以作为一个新的动力诊断变量来诊断示踪天气系统的演变.     

Objective criteria for discrimination of irrotational and rotational motions in the atmosphere

Summary Objective criteria are obtained for irrotational frictionless flow in the case of pure geostrophic, isallobaric and thermal wind flow. For rotational flow, a criterion is obtained in the case of non-permanent barotropic conditions, by introducing the concept ofabsolute potential vorticity. These criteria permit practical discrimination of conditions related to rotational or irrotational motion in the atmosphere, in an objective way.     

Comparison of geostrophic and nonlinear balanced winds from LIMS data and implications for derived dynamical quantities

Nimbus 7 LIMS geopotential height data are utilized to infer the rotational wind distribution in the Northern Hemisphere stratosphere and lower mesosphere during a period of substantial wave-mean flow interaction in January, 1979. Rotational winds are derived from the application of a successive relaxation numerical procedure which incorporates the spherical polar coordinate iterative algorithm ofPaegle andTomlinson (1975) for the nondivergent nonlinear balance equation. Optimum convergence of the numerical solutions is found to occur when under-relaxation is utilized. The LIMS height analyses were also latitudinally smoothed and constrained to obey the ellipticity criterion for spherical coordinates. The balanced winds are compared with geostrophically derived values and within situ radiosonde reports for 100 mb to 10 mb over Berlin.From a localized perspective, the Berlin-LIMS comparison indicates that radiosonde and balanced wind vectors exhibit somewhat closer agreement in direction than is associated with the geostrophic estimates. However, substantial quantitative differences between radiosonde, balanced, and geostrophic wind speeds are also evident, suggesting that caution should be exercised in the local application of derived winds, as for example in the quantitative interpretation of trajectories derived from satellite height analyses during periods of enhanced stratospheric wave activity.On a longitudinally averaged basis, balanced zonal-mean wind speeds are typically 20% weaker than geostrophic values in polar latitudes, and as much as 50% weaker in tropical and midlatitude regions. Meridional balanced wind velocities, at a given longitude, are generally within ±10% of geostrophic values. Although these alterations in horizontal wind components result in only modest differences between balanced and geostrophic meridional eddy heat fluxes, a more substantial change appears in the meridional eddy momentum flux analysis. The corresponding patterns of Eliassen-Palm flux divergence are found to be somewhat more (less) intense for the balanced wind case in the stratosphere (lower mesosphere) in polar latitudes.     

Non-linear wave loads on large circular cylinders: a perturbation technique

The forces and overturning moments exerted by second order waves on large vertical circular cylinders are analysed. The mathematical equations governing the physical system are the three-dimensional Laplace's equation satisfied by the velocity potential ?(x,y,z,t) and the boundary conditions, namely the dynamic boundary condition which is obtained from the Bernoulli's equation, kinematic boundary condition, radiation condition, bottom boundary condition and the zero radial velocity condition on the surface of the cylinder. The non-linearity of the mathematical problem is evidenced in the free surface boundary conditions viz. dynamic and kinematic boundary conditions. Analytical solutions are obtained using the perturbation technique. These solutions are compared with various experimental data. The comparison shows favourable agreement between the theory and the experimental results.     

An observational study of 300 mb winds in the tropical belt. Part II: Dynamical interpretation

An estimate of the magnitudes of the absolute vorticity advection terms and the terms in the balance equation suggest that the use of the barotropic vorticity equation within 5 degrees of latitude of the equator is not very good and that the linear balance equation is as good as the nonlinear balance equation in the equatorial region. Zonal Fourier analysis has revealed that the contribution from planetary scale waves is much larger than that from synoptic scale waves, being more in the winter hemisphere than in the summer hemisphere. In classical scale analysis there must be a distinction in wavelength between the zonal and the meridional directions for planetary scale waves. This distinction does not appear to be necessary for synoptic scale waves.     

Planetary Boundary Layer Flows in the Atmosphere and the Ocean at the Equator

—The boundary layer flows created by the frictional dissipation of the wind speed at the surface in the atmosphere and by surface wind stress in the ocean at the equator and in the equatorial region, are obtained by taking the influence of the surface friction on the zonal velocity as being balanced by vertical transport for the long-term mean flow and by a corresponding time variation for time-dependent flow fields. Solutions are expressed in terms of the velocities in zonal and vertical directions and the divergence of the horizontal current in the two media. It is found that under the ever present easterly flow in the lower atmosphere, the boundary layer flow in the atmosphere is convergence and ascending motion in the lower troposphere, and divergence at the surface and uplift in ocean, and in reverse directions for the westerly flow. Similar results are obtained for time-dependent wind fields and they give way to the steady asymptotic solutions when the period of the variation exceeds 10 months.     

Contemporary horizontal movements and seismicity of the south Baikal Basin (Baikal rift system)

The contemporary horizontal movements and deformations in the central and southern parts of the Baikal depression are analyzed, and their relationship with contemporary seismicity is studied. Based on the long-term measurements by the Baikal geodynamical GPS monitoring network, the refined estimate is obtained for the velocity of the divergence of the Siberian and Transbaikalian blocks, which is found to occur in the southeastward direction (130°) at 3.4 ± 0.7 mm per annum. This agrees with the parameters of the long-term extension component estimated from the geological data and with the direction of extension determined from the seismic data. The distribution of the displacement velocity across the strike of the rift, which gradually increases from one block to another, suggests a nonrigid behavior of the continental lithospheric plates at the divergent boundary. About 30% (1.0–1.5 mm per annum) of the total increase in the velocity is accommodated by the Baikal Basin. The strain rate within the trough reaches 3.1 × 10^?8 yr^?1 and decreases on either side across the structure. The character of distribution of the horizontal displacement velocities on the Baikal divergent boundary between the Eurasian and Amurian plates favors the model of passive rifting. The zones of highly contrasting topography and increased seismicity are localized within the area of contemporary deformations, and the seismic moment release rate directly depends on the strain rate. Here, the rate of the seismic moment release rate makes up a few percent of the geodetic moment accumulation rate calculated by the approach suggested by Anderson (1979). Based on the coherence between the graphs of the rates of geodetic moment accumulation and seismic moment release rate by the earthquakes with M ≥ 5.0 during the historical and instrumental observation periods, the contemporary seismic hazard for the South Baikal Basin could be assessed at a level of seismic event with M = 7.5–7.6.     

A study of the atmospheric circulation between equator and 60oN during the winter and summer seasons

Summary The mean zonal and meridional wind components and the mean mass circulation in different latitudes are discussed in relation to previous studies. Divergence and vertical motion are calculated for various latitude belts. There is evidence for a strong tropical Hadley cell with a temperate latitude indirect circulation during the winter season. During summer, the northern Hadley cell is weaker and displaced poleward; a circulation in the opposite sense appears in equatorial latitudes.The regional patterns of divergence and vertical motion appear related particularly to the position of the subtropical high pressure cells. Subsidence and lower-layer divergence are characteristic of the eastern flanks of the subtropical anticyclones, while the opposite pattern prevails on its western flanks. These longitudinal contrasts appear particularly pronounced during the summer season. The three-dimensional flow pattern in the tropics is illustrated by selected trajectories for the winter and summer seasons.     

Application of ridge-regression in inversion of low-latitude magnetic anomalies derived from space measurements

Anomalies in total field, horizontal, and vertical components over the Indian region derived from MAGSAT measurements have been inverted through the ridge-regression method, basically to test: (1) the application of the method in deriving a stable estimate of crustal magnetisation, and (2) the relative amount of information on crustal magnetisation contained in scalar vis-a`-vis vector data. Results show that the instabilities in magnetisation solution that appear when Mayhew's conventional method is applied in low latitudes could be removed through the ridge-regression technique. It was also noticed that magnetisation distribution estimated through the inversion of the total field(B) does not relate well with the geological features in the equatorial region. Inversion of theZ-anomaly alone gives realistic results for the equatorial region but not over higher latitudes. We conclude that a joint inversion ofX- andZ-anomalies provides a magnetisation estimate consistent with known geological features both for equatorial and higher latitudes.     

Observational evidence of deep convection over Indonesian sector in relation with major stratospheric warming events of 2003–04 and 2005–06

The major sudden stratospheric warming (SSW) events of 2003–04 and 2005–06 are considered to investigate changes in equatorial convection due to circulation changes associated with the SSW events. It is observed that the SSW events are accompanied by a considerable decrease in Outgoing Longwave Radiation (OLR), a proxy for tropical convection, over equatorial latitudes (15°N–15°S) in the Indonesian sector (90°E–150°E). However, unlike noted by earlier observations, the zonal mean OLR does not show any notable relationship with the SSW events. It can be explained from the latitude–longitude map of potential vorticity (PV) at 100 hPa, which shows a tongue of high PV emanating from high latitudes towards equator and converges in the longitude band of 90°E–150°E on the day of peak warming at 1 hPa in the case of 2003–04 and 10 hPa in the case of 2005–06. The latitude-height map of Eliassen–Palm (EP) vector and its divergence show convergence of EP flux in the upper troposphere at latitudes even lower than 20°N on these days. Further, vertical winds computed from the convergence of momentum flux are upward indicating convective activity at low-latitudes and downward at mid-latitudes.     

A modelling study of the latitudinal variations in the nighttime plasma temperatures of the equatorial topside ionosphere during northern winter at solar maximum

Latitudinal variations in the nighttime plasma temperatures of the equatorial topside ionosphere during northern winter at solar maximum have been examined by using values modelled by SUPIM (Sheffield University Plasmasphere Ionosphere Model) and observations made by the DMSP F10 satellite at 21.00 LT near 800 km altitude. The modelled values confirm that the crests observed near 15° latitude in the winter hemisphere are due to adiabatic heating and the troughs observed near the magnetic equator are due to adiabatic cooling as plasma is transported along the magnetic field lines from the summer hemisphere to the winter hemisphere. The modelled values also confirm that the interhemispheric plasma transport needed to produce the required adiabatic heating/cooling can be induced by F-region neutral winds. It is shown that the longitudinal variations in the observed troughs and crests arise mainly from the longitudinal variations in the magnetic meridional wind. At longitudes where the magnetic declination angle is positive the eastward geographic zonal wind combines with the northward (summer hemisphere to winter hemisphere) geographic meridional wind to enhance the northward magnetic meridional wind. This leads to deeper troughs and enhanced crests. At longitudes where the magnetic declination angle is negative the eastward geographic zonal wind opposes the northward geographic meridional wind and the trough depth and crest values are reduced. The characteristic features of the troughs and crests depend, in a complicated manner, on the field-aligned flow of plasma, thermal conduction, and inter-gas heat transfer. At the latitudes of the troughs/crests, the low/high plasma temperatures lead to increased/decreased plasma concentrations.     

Poleward expansion of the westward electrojet depending on the solar wind and IMF parameters

The effect of the interplanetary parameters on the latitudinal position of the substorm westward electrojet is studied in the work. The data from the IMAGE chain of magnetic stations and POLAR and WIND satellites for the period close to the solar activity minimum (1995–1996) and for the period of the solar activity maximum (2000) have been used for this purpose. It has been indicated that the electrojet poleward edge reaches, on average, higher latitudes at a higher solar wind velocity and at a larger (B _s ) IMF southward component. It has been indicated that the average latitude of the westward electrojet center increases with increasing solar wind velocity and decreases with increasing IMF southward component, as a result of which the electrojet center is, specifically, not observed at high geomagnetic latitudes at large values of the IMF southward component.     

On the exact shape of the horizontal profile of a topographically rectified tidal flow

Abstract

Starting from the nonlinear shallow water equations of a homogeneous rotating fluid we derive the equation describing the evolution of vorticity by a fluctuating bottom topography of small amplitude, using a multiple scale expansion in a small parameter, which is the topographic length scale relative to the tidal wave length. The exact response functions of residual vorticity for a sinusoidal bottom topography are compared with those obtained by a primitive perturbation series and by harmonic truncation, showing the former to be invalid for small topographic length scales and the latter to be only a fair approximation for vorticity produced by planetary vortex stretching. In deriving the exact shape of the horizontal residual velocity profile at a step-like break in the bottom topography, it is shown that the Lagrangian profile only exists in a strip having the width of the amplitude of the tidal excursion at both sides of the break, and that it vanishes outside that interval. Moreover, in the limit of small amplitude topography at least, it vanishes altogether for the generation mechanism by means of planetary vortex stretching. The Eulerian profile is shown to extend over twice the interval of the Lagrangian profile both for production by vortex stretching and by differential bottom friction. These finite intervals over which the residual velocity profiles exist for a step-like topography are not reproduced by harmonic truncation of the basic equation. This method gives exponentially decaying profiles, indicating spurious horizontal diffusion of vorticity. In terms of orders of magnitude, the method of harmonic truncation is reliable for residual velocity produced by vortex stretching but it overestimates the residual velocity produced by differential bottom friction by a factor 2.