Some numerical experiments on the effect of the variation of static stability in two-layer quasi-geostrophic models

A method to solve a quasi-geostrophic two-layer model including the variation of static stability is presented. The divergent part of the wind is incorporated by means of an iterative procedure. The procedure is rather fast and the time of computation is only 60–70% longer than for the usual two-layer model. The method of solution is justified by the conservation of the difference between the gross static stability and the kinetic energy. To eliminate the side-boundary conditions the experiments have been performed on a zonal channel model. The investigation falls mainly into three parts: The first part (section 5) contains a discussion of the significance of some physically inconsistent approximations. It is shown that physical inconsistencies are rather serious and for these inconsistent models which were studied the total kinetic energy increased faster than the gross static stability. In the next part (section 6) we are studying the effect of a Jacobian difference operator which conserves the total kinetic energy. The use of this operator in two-layer models will give a slight improvement but probably does not have any practical use in short periodic forecasts. It is also shown that the energy-conservative operator will change the wave-speed in an erroneous way if the wave-number or the grid-length is large in the meridional direction. In the final part (section 7) we investigate the behaviour of baroclinic waves for some different initial states and for two energy-consistent models, one with constant and one with variable static stability. According to the linear theory the waves adjust rather rapidly in such a way that the temperature wave will lag behind the pressure wave independent of the initial configuration. Thus, both models give rise to a baroclinic development even if the initial state is quasi-barotropic. The effect of the variation of static stability is very small, qualitative differences in the development are only observed during the first 12 hours. For an amplifying wave we will get a stabilization over the troughs and an instabilization over the ridges.

Supersonic aeroelastic effects on static stability and control. Flight Control Laboratory. Contract nos. AF33 (616)-3577 and AF33(616)-6067. ARDC Project no. 8219. Task no. 82158.

pt. 3. Aeroelastic interaction, by V. W. Donato.

A physical packing sequence algorithm for the container loading problem with static mechanical equilibrium conditions

The container loading problem (CLP) is a combinatorial optimization problem for the spatial arrangement of cargo inside containers so as to maximize the usage of space. The algorithms for this problem are of limited practical applicability if real-world constraints are not considered, one of the most important of which is deemed to be stability. This paper addresses static stability, as opposed to dynamic stability, looking at the stability of the cargo during container loading. This paper proposes two algorithms. The first is a static stability algorithm based on static mechanical equilibrium conditions that can be used as a stability evaluation function embedded in CLP algorithms (e.g. constructive heuristics, metaheuristics). The second proposed algorithm is a physical packing sequence algorithm that, given a container loading arrangement, generates the actual sequence by which each box is placed inside the container, considering static stability and loading operation efficiency constraints.

On the role of the ocean in projected atmospheric stability changes in the Atlantic polar low region

The occurrence of destructive mesoscale ‘polar low’ cyclones in the subpolar North Atlantic is projected to decline under anthropogenic change, due to an increase in atmospheric static stability. This letter reports on the role of changes in ocean circulation in shaping the atmospheric stability. In particular, the Atlantic Meridional Overturning Circulation (AMOC) is projected to weaken in response to anthropogenic forcing, leading to a local minimum in warming in this region. The reduced warming is restricted to the lower troposphere, hence contributing to the increase in static stability. Linear correlation analysis of the CMIP3 climate model ensemble suggests that around half of the model uncertainty in the projected stability response arises from the varied response of the AMOC between models.

Dynamic stability of long axisymmetric liquid bridges

This paper deals with the non-linear forced oscillations of axisymmetric long liquid bridges between equal disks. The dynamics of the liquid bridge has been analyzed by using a self-similar, one-dimensional model already used in similar problems. The influence of the dynamics on the static stability limits, as well as the main characteristics of the non-linear behaviour of long liquid bridges, have been studied with in the range of validity of the mathematical model used here.

On the stability and spatiotemporal variance distribution of salinity in the upper ocean

Despite recent advances in ocean observing arrays and satellite sensors, there remains great uncertainty in the large-scale spatial variations of upper ocean salinity on the interannual to decadal timescales. Consonant with both broad-scale surface warming and the amplification of the global hydrological cycle, observed global multidecadal salinity changes typically have focussed on the linear response to anthropogenic forcing but not on salinity variations due to changes in the static stability and or variability due to the intrinsic ocean or internal climate processes. Here, we examine the static stability and spatiotemporal variability of upper ocean salinity across a hierarchy of models and reanalyses. In particular, we partition the variance into time bands via application of singular spectral analysis, considering sea surface salinity (SSS), the Brunt Väisälä frequency (N2), and the ocean salinity stratification in terms of the stabilizing effect due to the haline part of N2 over the upper 500m. We identify regions of significant coherent SSS variability, either intrinsic to the ocean or in response to the interannually varying atmosphere. Based on consistency across models (CMIP5 and forced experiments) and reanalyses, we identify the stabilizing role of salinity in the tropics—typically associated with heavy precipitation and barrier layer formation, and the role of salinity in destabilizing upper ocean stratification in the subtropical regions where large-scale density compensation typically occurs.

Kinematics and Local Motion Planning for Quasi-static Whole-body Mobile Manipulation

This thesis studies mobile robotic manipulators, where one or more robot manipulator arms are integrated with a mobile robotic base. The base could be a wheeled or tracked vehicle, or it might be a multi-limbed locomotor. As robots are increasingly deployed in complex and unstructured environments, the need for mobile manipulation increases. Mobile robotic assistants have the potential to revolutionize human lives in a large variety of settings including home, industrial and outdoor environments.

Mobile Manipulation is the use or study of such mobile robots as they interact with physical objects in their environment. As compared to fixed base manipulators, mobile manipulators can take advantage of the base mechanism’s added degrees of freedom in the task planning and execution process. But their use also poses new problems in the analysis and control of base system stability, and the planning of coordinated base and arm motions. For mobile manipulators to be successfully and efficiently used, a thorough understanding of their kinematics, stability, and capabilities is required. Moreover, because mobile manipulators typically possess a large number of actuators, new and efficient methods to coordinate their large numbers of degrees of freedom are needed to make them practically deployable. This thesis develops new kinematic and stability analyses of mobile manipulation, and new algorithms to efficiently plan their motions.

I first develop detailed and novel descriptions of the kinematics governing the operation of multi- limbed legged robots working in the presence of gravity, and whose limbs may also be simultaneously used for manipulation. The fundamental stance constraint that arises from simple assumptions about friction and the ground contact and feasible motions is derived. Thereafter, a local relationship between joint motions and motions of the robot abdomen and reaching limbs is developed. Baseeon these relationships, one can define and analyze local kinematic qualities including limberness, wrench resistance and local dexterity. While previous researchers have noted the similarity between multi- fingered grasping and quasi-static manipulation, this thesis makes explicit connections between these two problems.

The kinematic expressions form the basis for a local motion planning problem that that determines the joint motions to achieve several simultaneous objectives while maintaining stance stability in the presence of gravity. This problem is translated into a convex quadratic program entitled the balanced priority solution, whose existence and uniqueness properties are developed. This problem is related in spirit to the classical redundancy resoxlution and task-priority approaches. With some simple modifications, this local planning and optimization problem can be extended to handle a large variety of goals and constraints that arise in mobile-manipulation. This local planning problem applies readily to other mobile bases including wheeled and articulated bases. This thesis describes the use of the local planning techniques to generate global plans, as well as for use within a feedback loop. The work in this thesis is motivated in part by many practical tasks involving the Surrogate and RoboSimian robots at NASA/JPL, and a large number of examples involving the two robots, both real and simulated, are provided.

Finally, this thesis provides an analysis of simultaneous force and motion control for multi- limbed legged robots. Starting with a classical linear stiffness relationship, an analysis of this problem for multiple point contacts is described. The local velocity planning problem is extended to include generation of forces, as well as to maintain stability using force-feedback. This thesis also provides a concise, novel definition of static stability, and proves some conditions under which it is satisfied.

How may tropical cyclones change in a warmer climate?

Tropical Cyclones (TC) under different climate conditions in the Northern Hemisphere have been investigated with the Max Planck Institute (MPI) coupled (ECHAM5/MPIOM) and atmosphere (ECHAM5) climate models. The intensity and size of the TC depend crucially on resolution with higher wind speed and smaller scales at the higher resolutions. The typical size of the TC is reduced by a factor of 2.3 from T63 to T319 using the distance of the maximum wind speed from the centre of the storm as a measure. The full three dimensional structure of the storms becomes increasingly more realistic as the resolution is increased. For the T63 resolution, three ensemble runs are explored for the period 1860 until 2100 using the IPCC SRES scenario A1B and evaluated for three 30 year periods at the end of the 19th, 20th and 21st century, respectively. While there is no significant change between the 19th and the 20th century, there is a considerable reduction in the number of the TC by some 20% in the 21st century, but no change in the number of the more intense storms. Reduction in the number of storms occurs in all regions. A single additional experiment at T213 resolution was run for the two latter 30-year periods. The T213 is an atmospheric only experiment using the transient Sea Surface Temperatures (SST) of the T63 resolution experiment. Also in this case, there is a reduction by some 10% in the number of simulated TC in the 21st century compared to the 20th century but a marked increase in the number of intense storms. The number of storms with maximum wind speeds greater than 50ms-1 increases by a third. Most of the intensification takes place in 2 the Eastern Pacific and in the Atlantic where also the number of storms more or less stays the same. We identify two competing processes effecting TC in a warmer climate. First, the increase in the static stability and the reduced vertical circulation is suggested to contribute to the reduction in the number of storms. Second, the increase in temperature and water vapor provide more energy for the storms so that when favorable conditions occur, the higher SST and higher specific humidity will contribute to more intense storms. As the maximum intensity depends crucially on resolution, this will require higher resolution to have its full effect. The distribution of storms between different regions does not, at first approximation, depend on the temperature itself but on the distribution of the SST anomalies and their influence on the atmospheric circulation. Two additional transient experiments at T319 resolution where run for 20 years at the end of the 20th and 21st century, respectively using the same conditions as in the T213 experiments. The results are consistent with the T213 study. The total number of tropical cyclones were similar to the T213 experiment but were generally more intense. The change from the 20th to the 21st century was also similar with fewer TC in total but with more intense cyclones.

Solar influences on dynamical coupling between the stratosphere and troposphere

We use a simplified atmospheric general circulation model (AGCM) to investigate the response of the lower atmosphere to thermal perturbations in the lower stratosphere. The results show that generic heating of the lower stratosphere tends to weaken the sub-tropical jets and the tropospheric mean meridional circulations. The positions of the jets, and the extent of the Hadley cells, respond to the distribution of the stratospheric heating, with low latitude heating displacing them poleward, and uniform heating displacing them equatorward. The patterns of response to the low latitude heating are similar to those found to be associated with solar variability in previous observational data analysis, and to the effects of varying solar UV radiation in sophisticated AGCMs. In order to investigate the chain of causality involved in converting the stratospheric thermal forcing to a tropospheric climate signal we conduct an experiment which uses an ensemble of model spin-ups to analyse the time development of the response to an applied stratospheric perturbation. We find that the initial effect of the change in static stability at the tropopause is to reduce the eddy momentum flux convergence in this region. This is followed by a vertical transfer of the momentum forcing anomaly by an anomalous mean circulation to the surface, where it is partly balanced by surface stress anomalies. The unbalanced part drives the evolution of the vertically integrated zonal flow. We conclude that solar heating of the stratosphere may produce changes in the circulation of the troposphere even without any direct forcing below the tropopause. We suggest that the impact of the stratospheric changes on wave propagation is key to the mechanisms involved.

Numerical simulation of baroclinic waves with a parameterized boundary layer

A dry three-dimensional baroclinic life cycle model is used to investigate the role of turbulent fluxes of heat and momentum within the boundary layer on mid-latitude cyclones. Simulations are performed of life cycles for two basic states, both with and without turbulent fluxes. The different basic states produce cyclones with contrasting frontal and mesoscale-flow structures. The analysis focuses on the generation of potential-vorticity (PV) in the boundary layer and its subsequent transport into the free troposphere. The dynamic mechanism through which friction mitigates a barotropic vortex is that of Ekman pumping. This has often been assumed to be also the dominant mechanism for baroclinic developments. The PV framework highlights an additional, baroclinic mechanism. Positive PV is generated baroclinically due to friction to the north-east of a surface low and is transported out of the boundary layer by a cyclonic conveyor belt flow. The result is an anomaly of increased static stability in the lower troposphere which restricts the growth of the baroclinic wave. The reduced coupling between lower and upper levels can be sufficient to change the character of the upper-level evolution of the mature wave. The basic features of the baroclinic damping mechanism are robust for different frontal structures, with and without turbulent heat fluxes, and for the range of surface roughness found over the oceans.

The triggering of orographic rainbands by small-scale topography

The triggering of convective orographic rainbands by small-scale topographic features is investigated through observations of a banded precipitation event over the Oregon Coastal Range and simulations using a cloud-resolving numerical model. A quasi-idealized simulation of the observed event reproduces the bands in the radar observations, indicating the model’s ability to capture the physics of the band-formation process. Additional idealized simulations reinforce that the bands are triggered by lee waves past small-scale topographic obstacles just upstream of the nominal leading edge of the orographic cloud. Whether a topographic obstacle in this region is able to trigger a strong rainband depends on the phase of its lee wave at cloud entry. Convective growth only occurs downstream of obstacles that give rise to lee-wave-induced displacements that create positive vertical velocity anomalies w_c and nearly zero buoyancy anomalies b_c as air parcels undergo saturation. This relationship is quantified through a simple analytic condition involving w_c, b_c, and the static stability N_m^2 of the cloud mass. Once convection is triggered, horizontal buoyancy gradients in the cross-flow direction generate circulations that align the bands parallel to the flow direction.

Boundary-layer friction in midlatitude cyclone

Results from an idealized three-dimensional baroclinic life-cycle model are interpreted in a potential vorticity (PV) framework to identify the physical mechanisms by which frictional processes acting in the atmospheric boundary layer modify and reduce the baroclinic development of a midlatitude storm. Considering a life cycle where the only non-conservative process acting is boundary-layer friction, the rate of change of depth-averaged PV within the boundary layer is governed by frictional generation of PV and the flux of PV into the free troposphere. Frictional generation of PV has two contributions: Ekman generation, which is directly analogous to the well-known Ekman-pumping mechanism for barotropic vortices, and baroclinic generation, which depends on the turning of the wind in the boundary layer and low-level horizontal temperature gradients. It is usually assumed, at least implicitly, that an Ekman process of negative PV generation is the mechanism whereby friction reduces the strength and growth rates of baroclinic systems. Although there is evidence for this mechanism, it is shown that baroclinic generation of PV dominates, producing positive PV anomalies downstream of the low centre, close to developing warm and cold fronts. These PV anomalies are advected by the large-scale warm conveyor belt flow upwards and polewards, fluxed into the troposphere near the warm front, and then advected westwards relative to the system. The result is a thin band of positive PV in the lower troposphere above the surface low centre. This PV is shown to be associated with a positive static stability anomaly, which Rossby edge wave theory suggests reduces the strength of the coupling between the upper- and lower-level PV anomalies, thereby reducing the rate of baroclinic development. This mechanism, which is a result of the baroclinic dynamics in the frontal regions, is in marked contrast with simple barotropic spin-down ideas. Finally we note the implications of these frictionally generated PV anomalies for cyclone forecasting.

Multimodel assessment of the upper troposphere and lower stratosphere: Extratropics

A multimodel assessment of the performance of chemistry-climate models (CCMs) in the extratropical upper troposphere/lower stratosphere (UTLS) is conducted for the first time. Process-oriented diagnostics are used to validate dynamical and transport characteristics of 18 CCMs using meteorological analyses and aircraft and satellite observations. The main dynamical and chemical climatological characteristics of the extratropical UTLS are generally well represented by the models, despite the limited horizontal and vertical resolution. The seasonal cycle of lowermost stratospheric mass is realistic, however with a wide spread in its mean value. A tropopause inversion layer is present in most models, although the maximum in static stability is located too high above the tropopause and is somewhat too weak, as expected from limited model resolution. Similar comments apply to the extratropical tropopause transition layer. The seasonality in lower stratospheric chemical tracers is consistent with the seasonality in the Brewer-Dobson circulation. Both vertical and meridional tracer gradients are of similar strength to those found in observations. Models that perform less well tend to use a semi-Lagrangian transport scheme and/or have a very low resolution. Two models, and the multimodel mean, score consistently well on all diagnostics, while seven other models score well on all diagnostics except the seasonal cycle of water vapor. Only four of the models are consistently below average. The lack of tropospheric chemistry in most models limits their evaluation in the upper troposphere. Finally, the UTLS is relatively sparsely sampled by observations, limiting our ability to quantitatively evaluate many aspects of model performance.

A global view of the extratropical tropopause transition layer from Atmospheric Chemistry Experiment Fourier Transform Spectrometer O3, H2O, and CO

The global behavior of the extratropical tropopause transition layer (ExTL) is investigated using O3, H2O, and CO measurements from the Atmospheric Chemistry Experiment Fourier Transform Spectrometer (ACE-FTS) on Canada’s SCISAT-1 satellite obtained between February 2004 and May 2007. The ExTL depth is derived using H2O-O3 and CO-O3 correlations. The ExTL top derived from H2O-O3 shows an increase from roughly 1–1.5 km above the thermal tropopause in the subtropics to 3–4 km (2.5–3.5 km) in the north (south) polar region, implying somewhat weaker tropospherestratosphere- transport in the Southern Hemisphere. The ExTL bottom extends ~1 km below the thermal tropopause, indicating a persistent stratospheric influence on the troposphere at all latitudes. The ExTL top derived from the CO-O3 correlation is lower, at 2 km or ~345 K (1.5 km or ~335 K) in the Northern (Southern) Hemisphere. Its annual mean coincides with the relative temperature maximum just above the thermal tropopause. The vertical CO gradient maximizes at the thermal tropopause, indicating a local minimum in mixing within the tropopause region. The seasonal changes in and the scales of the vertical H2O gradients show a similar pattern as the static stability structure of the tropopause inversion layer (TIL), which provides observational support for the hypothesis that H2O plays a radiative role in forcing and maintaining the structure of the TIL.

Asymptotic gravity wave drag expressions for non-hydrostatic rotating flow over a ridge

Asymptotic expressions are derived for the mountain wave drag in flow with constant wind and static stability over a ridge when both rotation and non-hydrostatic effects are important. These expressions, which are much more manageable than the corresponding exact drag expressions (when these do exist) are found to provide accurate approximations to the drag, even when non-hydrostatic and rotation effects are strong, despite having been developed for cases where these effects are weak. The derived expressions are compared with approximations to the drag found previously, and their asymptotic behaviour in various limits is studied.