scholarly journals A Stochastic Model for the Angular Momentum Budget of Latitude Belts

2005 ◽  
Vol 62 (7) ◽  
pp. 2592-2601 ◽  
Author(s):  
Joseph Egger
Keyword(s):  
Angular Momentum ◽  
Stochastic Model ◽  
Stochastic Models ◽  
Friction Torque ◽  
Decay Rates ◽  
Model Parameters ◽  
Flux Divergence ◽  
Covariance Functions ◽  
Momentum Budget ◽  
The Tropics

Abstract The stochastic model of Weickmann et al. for the global angular momentum budget is modified to become applicable to latitude belts. In particular, a Langevin equation is added for the flux divergence of angular momentum in a belt. The friction torque Tf is assumed to be purely damping with respect to angular momentum M. The mountain torque To is generated by red noise but also damps angular momentum directly as suggested by recent stochastic models. The model parameters are tuned such that the variances of all model variables come close to the observations. The corresponding equations for the covariance functions of all variables are solved analytically. The results are compared to observations for selected belts. It is found that the model captures the observed decay rates of all covariance functions. The covariance of the flux divergence and the angular momentum is simulated successfully for positive lags but rarely for negative ones. The covariance of friction torque and angular momentum is reproduced reasonably well. The model is also successful with respect to the covariance of mountain torque and M in the Tropics, but there are large discrepancies at midlatitudes because the observed mountain torque events are accompanied by flux divergences in these belts.

scholarly journals The Annual Cycle of the Axial Angular Momentum of the Atmosphere

2005 ◽  
Vol 18 (6) ◽  
pp. 757-771 ◽  
Author(s):  
Joseph Egger ◽  
Klaus-Peter Hoinka
Keyword(s):  
Angular Momentum ◽  
Northern Hemisphere ◽  
Annual Cycle ◽  
Lower Troposphere ◽  
Mass Term ◽  
Friction Torque ◽  
Hadley Cell ◽  
Trade Winds ◽  
Latitude Belt ◽  
The Tropics

Abstract Earlier analyses of the annual cycle of the axial angular momentum (AAM) are extended to include mass flows and vertical transports as observed, and to establish angular momentum budgets for various control volumes, using the European Centre for Medium-Range Forecasts (ECMWF) Re-Analyses (ERA) for the years 1979–92, transformed to height coordinates. In particular, the role of the torques is examined. The annual cycle of the zonally averaged angular momentum is large in the latitude belt 20° ⩽ |ϕ| ⩽ 45°, with little attenuation in the vertical up to a height of ∼12 km. The oscillation of the mass term (AAM due to the earth’s rotation) dominates in the lower troposphere, but that of the wind term (relative AAM) is more important elsewhere. The cycle of the friction torque as related to the trade winds prevails in the Tropics. Mountain torque and friction torque are equally important in the extratropical latitudes of the Northern Hemisphere. The annual and the semiannual cycle of the global angular momentum are in good balance with the global mountain and friction torques. The addition of the global gravity wave torque destroys this agreement. The transports must be adjusted if budgets of domains of less than global extent are to be considered. Both a streamfunction, representing the nondivergent part of the fluxes, and a flux potential, describing the divergences/convergences, are determined. The streamfunction pattern mainly reflects the seasonal shift of the Hadley cell. The flux potential links the annual oscillations of the angular momentum with the torques. It is concluded that the interaction of the torques with the angular momentum is restricted to the lower troposphere, in particular, in the Tropics. The range of influence is deeper in the Northern Hemisphere than in the Southern Hemisphere, presumably because of the mountains. The angular momentum cycle in the upper troposphere and stratosphere is not affected by the torques and reflects interhemispheric flux patterns. Budgets for the polar as well as for the midlatitude domains show that fluxes in the stratosphere are important.

scholarly journals Wave Forcing of Zonal Mean Angular Momentum in Various Coordinate Systems

2014 ◽  
Vol 71 (6) ◽  
pp. 2221-2229
Author(s):  
Joseph Egger ◽  
Klaus-Peter Hoinka
Keyword(s):  
Angular Momentum ◽  
Weighted Averaging ◽  
Coordinate Systems ◽  
Mean Flow ◽  
Flux Divergence ◽  
Standard Case ◽  
Wave Forcing ◽  
Momentum Budget ◽  
Flow Part ◽  
Isentropic Coordinates

Abstract The wave forcing of the atmospheric mean flow in isentropic coordinates has been investigated intensively in the past with the divergence of the Eliassen–Palm flux playing a dominating role. These concepts are reviewed briefly and it is pointed out that angular momentum is attractive in this context because the wave driving can be written in the form of a flux divergence. This helps to evaluate the wave forcing in other coordinate systems with a different separation of waves and mean flow. The following coordinates are chosen: (λ, φ, z), (λ, φ, θ), and (λ, θ, z). To be consistent, only one type of zonal averaging should be used. Mass-weighted averaging is applied in the isentropic standard case and simple averaging is applied in the others. The wave driving is presented for all three systems. It has to balance essentially the mean-flow part of the “Coriolis term” in the angular momentum budget in (φ, z) and (θ, z) coordinates but not in the (φ, θ) system where the form drag is a mean-flow term and, therefore, the forcing pattern differs from what has been published so far.

scholarly journals Torques and the Related Meridional and Vertical Fluxes of Axial Angular Momentum

2005 ◽  
Vol 133 (3) ◽  
pp. 621-633 ◽  
Author(s):  
Joseph Egger ◽  
Klaus-Peter Hoinka
Keyword(s):  
Angular Momentum ◽  
Rapid Change ◽  
Friction Torque ◽  
Meridional Plane ◽  
Flux Divergence ◽  
Vertical Fluxes ◽  
Momentum Fluxes ◽  
Order Of Magnitude ◽  
Budget Equation ◽  
Mass Circulation

Abstract The budget equation of the zonally averaged angular momentum is analyzed by introducing belts of 1000-km width to cover the meridional plane from pole to pole up to an altitude of 28 km. Using ECMWF Re-Analysis (ERA) data the fluxes of angular momentum are evaluated as well as the mountain and friction torques per belt. Generalized streamfunctions and velocity potentials are introduced to better depict the fluxes related to the angular momentum transferred at the ground during an event of mountain or friction torque. The variance of the total flux divergence per belt is one order of magnitude larger than those of the torques. All variances peak at midlatitudes. As a rule, the structure of the generalized streamfunctions changes little during an event; that is, the structure of the nondivergent part of the fluxes is stable. That of the divergent part, as represented by the velocity potential, undergoes a rapid change near the peak of a torque event. Positive friction torque events in midlatitude belts are preceded by a divergence of angular momentum fluxes in that belt, which is linked to the anticyclonic mass circulation needed to induce the positive torque. The divergence in the belt breaks down shortly before the torque is strongest. Angular momentum is transported upward from the ground after that. Much of the angular momentum generated in a midlatitude belt by positive mountain torques is transported out of the domain, but there is also a short burst of upward transports. Angular momentum anomalies linked to torque events near the equator tend to be symmetric with respect to the equator. Related fluxes affect the midlatitudes of both hemispheres.

scholarly journals The Angular Momentum Budget of the Transformed Eulerian Mean Equations

2008 ◽  
Vol 65 (10) ◽  
pp. 3305-3314 ◽  
Author(s):  
Joseph Egger ◽  
Klaus-Peter Hoinka
Keyword(s):  
Angular Momentum ◽  
Flux Divergence ◽  
Additional Insight ◽  
Momentum Budget ◽  
Residual Difference ◽  
Transformed Eulerian Mean ◽  
Upper Boundary

The axial angular momentum (AAM) budget of zonal atmospheric annuli extending from the surface to a given height and over meridional belts is discussed within the framework of conventional and transformed Eulerian mean (TEM) theory. Conventionally, it is only fluxes of AAM through the boundaries and/or torques at the surface that are able to change the AAM of an annulus. TEM theory introduces new torques in the budget related to the vertically integrated Eliassen–Palm flux divergence and also new AAM fluxes of the residual difference circulation. Some of these torques are displayed for various annuli. In particular, the application of TEM theory generates a large positive torque at tropospheric upper boundaries in the global case. This torque is much larger than the global mountain and friction torques but is cancelled exactly by the new vertical AAM fluxes through the upper boundary. It is concluded that the TEM approach complicates the analysis of AAM budgets but does not provide additional insight. Isentropic pressure torques are believed to be similar to the TEM torques at the upper boundary of an annulus. The isentropic pressure torques are evaluated from data and found to differ in several respects from the TEM torques.

GPS-BDS-Galileo double-differenced stochastic model refinement based on least-squares variance component estimation

2021 ◽  
pp. 1-16
Author(s):  
Hong Hu ◽  
Xuefeng Xie ◽  
Jingxiang Gao ◽  
Shuanggen Jin ◽  
Peng Jiang
Keyword(s):  
Stochastic Model ◽  
Least Squares ◽  
Stochastic Models ◽  
Variance Component ◽  
Satellite System ◽  
Variance Component Estimation ◽  
Short Baseline ◽  
Component Estimation ◽  
Zero Baseline ◽  
Global Navigation Satellite

Abstract Stochastic models are essential for precise navigation and positioning of the global navigation satellite system (GNSS). A stochastic model can influence the resolution of ambiguity, which is a key step in GNSS positioning. Most of the existing multi-GNSS stochastic models are based on the GPS empirical model, while differences in the precision of observations among different systems are not considered. In this paper, three refined stochastic models, namely the variance components between systems (RSM1), the variances of different types of observations (RSM2) and the variances of observations for each satellite (RSM3) are proposed based on the least-squares variance component estimation (LS-VCE). Zero-baseline and short-baseline GNSS experimental data were used to verify the proposed three refined stochastic models. The results show that, compared with the traditional elevation-dependent model (EDM), though the proposed models do not significantly improve the ambiguity resolution success rate, the positioning precision of the three proposed models has been improved. RSM3, which is more realistic for the data itself, performs the best, and the precision at elevation mask angles 20°, 30°, 40°, 50° can be improved by 4⋅6%, 7⋅6%, 13⋅2%, 73⋅0% for L1-B1-E1 and 1⋅1%, 4⋅8%, 16⋅3%, 64⋅5% for L2-B2-E5a, respectively.

Generalised DOPs with Consideration of the Influence Function of Signal-in-Space Errors

2011 ◽  
Vol 64 (S1) ◽  
pp. S3-S18 ◽  
Author(s):  
Yuanxi Yang ◽  
Jinlong Li ◽  
Junyi Xu ◽  
Jing Tang
Keyword(s):  
Least Squares ◽  
Stochastic Models ◽  
Influence Function ◽  
A Priori ◽  
Functional Model ◽  
Global Navigation Satellite Systems ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Integrated Navigation ◽  
Satellite Systems

Integrated navigation using multiple Global Navigation Satellite Systems (GNSS) is beneficial to increase the number of observable satellites, alleviate the effects of systematic errors and improve the accuracy of positioning, navigation and timing (PNT). When multiple constellations and multiple frequency measurements are employed, the functional and stochastic models as well as the estimation principle for PNT may be different. Therefore, the commonly used definition of “dilution of precision (DOP)” based on the least squares (LS) estimation and unified functional and stochastic models will be not applicable anymore. In this paper, three types of generalised DOPs are defined. The first type of generalised DOP is based on the error influence function (IF) of pseudo-ranges that reflects the geometry strength of the measurements, error magnitude and the estimation risk criteria. When the least squares estimation is used, the first type of generalised DOP is identical to the one commonly used. In order to define the first type of generalised DOP, an IF of signal–in-space (SIS) errors on the parameter estimates of PNT is derived. The second type of generalised DOP is defined based on the functional model with additional systematic parameters induced by the compatibility and interoperability problems among different GNSS systems. The third type of generalised DOP is defined based on Bayesian estimation in which the a priori information of the model parameters is taken into account. This is suitable for evaluating the precision of kinematic positioning or navigation. Different types of generalised DOPs are suitable for different PNT scenarios and an example for the calculation of these DOPs for multi-GNSS systems including GPS, GLONASS, Compass and Galileo is given. New observation equations of Compass and GLONASS that may contain additional parameters for interoperability are specifically investigated. It shows that if the interoperability of multi-GNSS is not fulfilled, the increased number of satellites will not significantly reduce the generalised DOP value. Furthermore, the outlying measurements will not change the original DOP, but will change the first type of generalised DOP which includes a robust error IF. A priori information of the model parameters will also reduce the DOP.

scholarly journals Mechanisms of Jet Formation on the Giant Planets

2010 ◽  
Vol 67 (11) ◽  
pp. 3652-3672 ◽  
Author(s):  
Junjun Liu ◽  
Tapio Schneider
Keyword(s):  
Angular Momentum ◽  
Rossby Wave ◽  
Momentum Flux ◽  
Wave Generation ◽  
Heat Fluxes ◽  
Giant Planets ◽  
Radiative Heating ◽  
Flux Divergence ◽  
Low Latitude ◽  
Flow Configurations

Abstract The giant planet atmospheres exhibit alternating prograde (eastward) and retrograde (westward) jets of different speeds and widths, with an equatorial jet that is prograde on Jupiter and Saturn and retrograde on Uranus and Neptune. The jets are variously thought to be driven by differential radiative heating of the upper atmosphere or by intrinsic heat fluxes emanating from the deep interior. However, existing models cannot account for the different flow configurations on the giant planets in an energetically consistent manner. Here a three-dimensional general circulation model is used to show that the different flow configurations can be reproduced by mechanisms universal across the giant planets if differences in their radiative heating and intrinsic heat fluxes are taken into account. Whether the equatorial jet is prograde or retrograde depends on whether the deep intrinsic heat fluxes are strong enough that convection penetrates into the upper troposphere and generates strong equatorial Rossby waves there. Prograde equatorial jets result if convective Rossby wave generation is strong and low-latitude angular momentum flux divergence owing to baroclinic eddies generated off the equator is sufficiently weak (Jupiter and Saturn). Retrograde equatorial jets result if either convective Rossby wave generation is weak or absent (Uranus) or low-latitude angular momentum flux divergence owing to baroclinic eddies is sufficiently strong (Neptune). The different speeds and widths of the off-equatorial jets depend, among other factors, on the differential radiative heating of the atmosphere and the altitude of the jets, which are vertically sheared. The simulations have closed energy and angular momentum balances that are consistent with observations of the giant planets. They exhibit temperature structures closely resembling those observed and make predictions about as yet unobserved aspects of flow and temperature structures.

scholarly journals Impacts of stochastic models on real-time 3D UAV mapping

2014 ◽  
Vol XL-1 ◽  
pp. 35-44
Author(s):  
M. Alqurashi ◽  
J. Wang
Keyword(s):  
Stochastic Model ◽  
Real Time ◽  
Stochastic Models ◽  
Feature Matching ◽  
Critical Role ◽  
Image Feature ◽  
Mapping Process ◽  
Camera Orientation ◽  
Camera Position

In UAV mapping using direct geo-referencing, the formation of stochastic model generally takes into the account the different types of measurements required to estimate the 3D coordinates of the feature points. Such measurements include image tie point coordinate measurements, camera position measurements and camera orientation measurements. In the commonly used stochastic model, it is commonly assumed that all tie point measurements have the same variance. In fact, these assumptions are not always realistic and thus, can lead to biased 3D feature coordinates. Tie point measurements for different image feature objects may not have the same accuracy due to the facts that the geometric distribution of features, particularly their feature matching conditions are different. More importantly, the accuracies of the geo-referencing measurements should also be considered into the mapping process. In this paper, impacts of typical stochastic models on the UAV mapping are investigated. It has been demonstrated that the quality of the geo-referencing measurements plays a critical role in real-time UAV mapping scenarios.

scholarly journals Disease control as an optimization problem

PLoS ONE ◽  
2021 ◽  
Vol 16 (9) ◽  
pp. e0257958
Author(s):  
Miguel Navascués ◽  
Costantino Budroni ◽  
Yelena Guryanova
Keyword(s):  
Disease Control ◽  
Stochastic Models ◽  
Optimization Problem ◽  
Initial Conditions ◽  
Optimization Theory ◽  
Model Parameters ◽  
Grid Search ◽  
Brute Force ◽  
Time Required ◽  
Policy Optimization

In the context of epidemiology, policies for disease control are often devised through a mixture of intuition and brute-force, whereby the set of logically conceivable policies is narrowed down to a small family described by a few parameters, following which linearization or grid search is used to identify the optimal policy within the set. This scheme runs the risk of leaving out more complex (and perhaps counter-intuitive) policies for disease control that could tackle the disease more efficiently. In this article, we use techniques from convex optimization theory and machine learning to conduct optimizations over disease policies described by hundreds of parameters. In contrast to past approaches for policy optimization based on control theory, our framework can deal with arbitrary uncertainties on the initial conditions and model parameters controlling the spread of the disease, and stochastic models. In addition, our methods allow for optimization over policies which remain constant over weekly periods, specified by either continuous or discrete (e.g.: lockdown on/off) government measures. We illustrate our approach by minimizing the total time required to eradicate COVID-19 within the Susceptible-Exposed-Infected-Recovered (SEIR) model proposed by Kissler et al. (March, 2020).

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