Initial Latitude Research Articles

Influence of mesoscale eddies on the cross-shelf phosphate transport of the Kuroshio Current northeast of Taiwan: A modeling study

The Kuroshio Current flows northeastward along the East China Sea (ECS) shelf break, carrying a large amount of nutrients, and is thus an important source of nutrients for the ECS. The mainstream and transport of the Kuroshio Current are significantly affected by mesoscale eddies. However, the influence of mesoscale eddies on the Kuroshio nutrient input into the ECS is unknown. We add constructed cyclonic and anticyclonic eddies to a hydrodynamic model to explore the influence of mesoscale eddies on cross-shelf Kuroshio phosphate input into the ECS. This model suitably reproduces the fate of mesoscale eddies and the variation in the Kuroshio Current during eddy-current interactions. The simulation results reveal that during the strong interaction between the Kuroshio Current and mesoscale eddy east of Taiwan, the cyclonic eddy reduces the on-shelf phosphate flux, while the anticyclonic eddy increases the Kuroshio phosphate input to the ECS. When the anticyclonic eddy moves to the Okinawa Trough, it reduces the Kuroshio phosphate input into the ECS.These basic features are not sensitive to the initial latitude of the eddy center east of Taiwan. The change in cross-shelf phosphate flux is caused by the changes in cross-shelf velocity and phosphate concentration along the shelf. Momentum balance analyses suggest that the change in cross-shelf velocity is mainly caused by the change in the pressure gradient term due to eddy-induced changes in sea surface height in the horizontal direction and isotherm tilting in the vertical direction. The advection-diffusion equation analysis shows that the change in phosphate concentration along the shelf is attributed to changes in the upper horizontal advection and lower vertical advection of phosphate, which are induced by the upper phosphate change and vertical velocity change along the shelf, respectively. This study has important implications for the possible response of the ECS ecosystem to mesoscale eddies that are partly triggered by enhanced typhoons east of Taiwan under global warming.

Wavelet DE-noising and Kalman Filtering of MEMS Sensors for Autonomous Latitude Determination

Background: There is a task of autonomous determination of the position latitude of unmoved vehicles. Also, there is another task of the initial value latitude determination as a prepared operation of gimbaled and strap-down inertial navigation systems. For both cases, it is necessary to have an inertial measurement unit (IMU) with triad gyroscopes and triad accelerometers. The output signals of micromechanical gyroscopes and accelerometers have large noise components when using the IMU in the micromachined electromechanical systems (MEMS) technology. Objective: Normally to filter output signals of MEMS sensors, averaging and filtering are used. However, for Kalman filtering, it is necessary to find the exact mathematical model of the sensors and a lot of their initial random characteristics. The study of the possibility of the wavelet transform usage to filter the output signals MEMS accelerometers and gyroscopes for the latitude autonomous determination was conducted in the paper. Method: The wavelet transform approach was used to filter the output signals of MEMS accelerometers and gyroscopes in order to improve the accuracy of the autonomous position latitude determination. The autonomous latitude determination efficiency of IMU based on MEMS gyroscopes and accelerometers has been experimentally confirmed. The projections of the Earth’s angular rate and gravitational acceleration were obtained from the MEMS IMU. After that, the signals of the IMU gyroscopes and accelerometers were filtered, using the wavelet ‘Daubechies’ in decomposition, and averaged. These signals were used in a computational algorithm to determine the latitude. Results: The results showed that Unlike the well-known Kalman filter wavelet de-noising reduced calculation error by almost twice. Conclusion: Wavelet de-noising could be used for output signals filtering of micromechanical gyroscopes and accelerometers for the autonomous determination of position latitude.

A Prediction Model of Online Car-Hailing Demand Based on K-means and SVR

The paper proposed a prediction model of online car-hailing demand based on K-means and support vector regression (SVR) methods. In the past few years, online car-hailing market demand has grown rapidly, and prediction of rapid demand growth has become a hot topic. This study takes the initial longitude and latitude of online car-hailing orders as the eigenvalues for K-means clustering. The clustering results are taken as the result of area division. The number and size of potential demand areas could be determined automatically. This method of area division solves the shortcomings of traditional artificial meshing division and existing administrative division methods. The model takes a small-sample data set as the application object and uses the SVR method for data regression. Finally, we conduct an empirical study on Didi’s real data set in the core area of Chengdu City, China. The final experimental results suggest that the area division method based on K-means is reasonable and that the demand prediction model based on K-means and SVR is effective.

Latitude Determination and Error Analysis for Stationary SINS in Unknow-Position Condition.

The initial geographic latitude information is the key to the self-alignment of the strapdown inertial navigation system (SINS), but how to determine the latitude when the latitude cannot be obtained directly or in a short time? The latitude determination (LD) methods are introduced, including magnitude method, geometric method, and analytical methods 1 and 2, to solve this situation only by the output of the SINS itself. Simulation and experimental test results validate the efficiency of these LD methods. In order to improve the accuracy of the LD, the error of the LD method is derived through comparative analysis. Based on the relationship between LD error and inertial measurement unit (IMU) bias. Partial bias estimation method is introduced and executed during latitude determination. After compensating the estimated IMU bias, the accuracy of the LD will be further improved. Latitude errors are also affected by the latitude where SINS is located. Comprehensive simulation and experimental tests verify the effectiveness of the method. The IMU determined latitude can not only be used to achieve the self-alignment of the SINS, but also to correct the navigation latitude of the long-term SINS, thereby improving the autonomy and positioning accuracy of the navigation system.

Improved specular point prediction precision using gradient descent algorithm

Global Navigation Satellite Systems Reflectometry (GNSS-R) utilizes GNSS signals reflected off the Earth surface for remote sensing applications. Due to weak power of reflected signals, GNSS-R receiver needs to track reflected signals by open loop. The first step is to calculate the position of specular point. The specular point position error of the existing algorithm—Quasi-Spherical Earth (QSE) Approach—is about 3 km which may cause troubles in data post-processing. In this paper, gradient descent algorithm is applied to calculate position of specular point and the calculation is based on World Geodetic System 1984 (WGS 84) ellipsoid in geodetic coordinate. The benefit of this coordinate is that it is easy to investigate the effect of real surface’s altitude. Learning rate—the key parameter of the algorithm—is adaptively adjusted according to initial error, latitude and gradient descent rate. With self-adaptive learning rate strategy, the algorithm converges fast. Through simulation and test on Global Navigation Satellite System Occultation Sounder II (GNOS II), the performances of the algorithm are validated. The specular point position error of the proposed algorithm is about 10 m. The speed of the proposed algorithm is competitive compared with the existing algorithm. The test on GNOS II shows that the proposed algorithm has good real-time performance.

Changes in topsoil organic carbon from 1986 to 2010 in a mountainous plateau region in Southwest China

AbstractThe carbon cycle and underlying environmental drivers are not yet fully understood, and whether climate warming is inducing soil carbon loss remains controversial, largely due to limited evidence from large‐scale observations. With relatively less human disturbance, Yunnan Province, a typical mountainous plateau region in Southwest China, is a favorable place to evaluate environmental effects on soil organic carbon (SOC) dynamics. In this study, soil sampling of the upper 20‐cm soil layer was conducted at sites across Yunnan Province in 1986 and 2010 to estimate topsoil SOC density (SOCD). The changes in SOCD and environmental factors, including initial SOCD value, temperature, precipitation, longitude, latitude, elevation, and slope gradient, were analyzed. The results indicated that the topsoil of Yunnan Province mainly acted as a carbon source during the study period. The topsoil SOCD in 1986 averaged 5.82 kg C m−2 and was higher than that of 2010 (5.45 kg C m−2), corresponding to a 0.14 Pg loss in SOC stock over the 25 years. The northwestern subregion experienced the most drastic SOCD changes, and the SOCD decreased most notably in areas with higher initial SOCD values. Compared with cropland and grassland, more significant SOCD reductions were observed in forest. Among the studied environmental factors, initial SOCD was the main factor associated with SOCD variations. The next most important factor was temperature, followed by precipitation. With high elevation and initial SOCD, the northwestern subregion of Yunnan Province had the most sensitive SOCD changes, underscoring the need for further protection and appropriate management.

Incorporation of Heliospheric Imagery Into the CME Analysis Tool for Improvement of CME Forecasting

AbstractCoronal mass ejections (CMEs) cause the largest geomagnetic disturbances at Earth, which impact satellites, wired communication systems, and power grids. The CME Analysis Tool (CAT) is used to determine a CME's initial longitude, latitude, angular width, and radial speed from coronagraph images. These are the initial conditions for the Wang‐Sheeley‐Arge Enlil solar wind model, along with the ambient solar wind properties derived from magnetograms. However, the coronagraph imagery is limited by field of view. We have incorporated heliospheric imagery (HI) from the Solar Terrestrial Relations Observatory into CAT to create the CME Analysis Tool with Heliospheric Imagery (CAT‐HI). These HI images have a larger field of view, allowing tracking of CMEs to greater distances from the Sun. We have compared the performances of CAT and CAT‐HI by examining the expected arrival times of CMEs at the L1 Lagrange point and found them to be consistent. However, CAT‐HI is advantageous because it could be used to prune ensemble forecasts and issue routine updates for CME arrival time forecasts. Finally, we discuss CAT‐HI in the context of an operational mission at the L4 or L5 Lagrange points.

Earth System Model Response to Large Midlatitude and High‐latitude Volcanic Eruptions

AbstractWe used the Meteorological Research Institute Earth System Model to simulate the climate response to massive sulfur dioxide (SO2) emission from the volcanic eruptions of Paektusan (China/North Korea) and Eldgjá (Iceland) into the stratosphere in the tenth century Common Era (CE). Assuming 3 times the SO2 emission of the 1883 Krakatau eruption, as recorded by Greenland ice core sulfate concentrations, simulations of Paektusan and Eldgjá had roughly similar global mean impacts within 2 years of erupting: decreases in surface insolation (−10 W/m2, −5%), surface air temperature (−1 °C), land net primary production (NPP; −3 GtC/year, −5%), and soil respiration (−5 GtC/year, −10%). While both simulations had severe impacts on the extratropical Northern Hemisphere, the simulated response to Paektusan is twice as strong as Eldgjá in the tropics (cooling [1 °C], precipitation decrease [10%], and NPP increase [7%]). Simulation‐Eldgjá had almost no impact on the extratropical Southern Hemisphere because of its initial latitude. These regional differences combine so that Simulation‐Paektusan has slightly larger global mean impacts, including an atmospheric CO2 decrease of ~2 ppm. Tropical NPP primarily increases due to the fact that photosynthesis maximizes at temperatures below the tropical mean temperature and secondarily to the cooling‐induced decrease in respiration, which indicates relatively rich tropical harvests despite large volcanic eruptions. In contrast, the severe cooling (−2.5 °C) and decreased NPP (−20%) in the northern extratropics could mean poor harvests and famines, which can lead to social turmoil such as a rebellion in northeast Japan around the same time as the eruptions.

The Effects of Uncertainty in Initial CME Input Parameters on Deflection, Rotation, Bz, and Arrival Time Predictions

AbstractUnderstanding the effects of coronal mass ejections (CMEs) requires knowing if and when they will impact and their properties upon impact. Of particular importance is the strength of a CME's southward magnetic field component (Bz). Kay et al. (2013, https://doi:10.1088/0004-637X/775/1/5, 2015, https://doi:10.1088/948 0004-637X/805/2/168) have shown that the simplified analytic model Forecasting a CME's Altered Trajectory (ForeCAT) can reproduce the deflection and rotation of CMEs. Kay, Gopalswamy, Reinard, and Opher (2017, https://doi.org/10.3847/1538-4357/835/2/117) introduced ForeCAT In situ Data Observer, which uses ForeCAT results to simulate magnetic field profiles. ForeCAT In situ Data Observer reproduces the in situ observations on roughly hourly time scales, suggesting that these models could be extremely useful for predictions of Bz. However, as with all models, both models are sensitive to their input parameters, which may not be precisely known for predictions. We explore this sensitivity using ensembles having small changes in the initial latitude, longitude, and orientation of the erupting CME. We explore the effects of different background magnetic field models and find that the changes in deflection and rotation resulting from the uncertainty in the initial parameters tend to exceed the changes from different magnetic backgrounds. The range in the in situ profiles tends to scale with the range in the deflection and rotation. We also consider a simple arrival time model using ForeCAT results and find an average absolute error of only 3 hr. We show that an uncertainty in the CME position of 8.1° ± 6.9° leads to variations of 6 hr in the arrival time. This measure depends strongly on the location of impact within the CME with the arrival time changing less for impacts near the nose.

Autonomous Determination of Initial Latitude with an Inertial Measuring Unit

A new method for determining the latitude of a fixed base is presented. This method is based on the strapdown inertial navigation technology using an inertial measurement unit (IMU) consisting of three accelerometers, three gyroscopes, and a processing board. It is shown that constant inclination of the base does not affect the latitude determination. The experiments conducted validate this method. The experimental equipment consists of an IMU with laser gyroscopes and accelerometers. A mathematical model of the error in the latitude that depends on the errors of gyroscopes and accelerometers is developed. The results that demonstrate the requirements to the latitude determination method are presented.

Basic dynamic and scale study of quasi-spherical Z-pinch implosion

Unlike cylindrical Z pinch, a quasi-spherical implosion enables load plasma to implode inward spherically and concentrate its kinetic energy toward the center. This helps to improve the energy-transport efficiency and increase the shock-induced radiation intensity of the foam convertor, when the quasi-spherical implosion is used to drive a dynamic hohlraum (DH). In previous work, it has been proved that a spherical metal shell with an exact mass-distribution can implode spherically by the nonuniform magnetic field, whose magnitude increases with the load latitude, Bφ~cos-1θ. However, this ‘mass-redistribution’ method is hard to realize on the fast pulse power generator widely used in today's Z-pinch study. The rise time of the facility is only ~100 ns, and the load is wire arrays with typical weight about 1 mg/cm. We develop a method of gaining quasi-spherical implosion with wire arrays by adjusting their initial shape, and it proves feasible on the 1.5 MA Qiangguang-I facility. Recently, we try to realize the quasi-spherical dynamic hohlraum (QSDH) implosion on generator with higher current, such as the 4.5 MA Angara5-I or the 8 MA PTS facility, and to make a direct compare with its cylindrical equivalence. But first of all, a basic but relatively comprehensive study on the quasi-spherical implosion dynamics is necessary and useful for the future QSDH load design and optimization.#br#Comparing with the device for classical cylindrical Z-pinch implosions, the load and electrodes structures of quasi-spherical implosions are complex, which leads to distinct implosion dynamics and scale rules. In this paper, we develop a thin shell model for the quasi-spherical implosion, from which the movement equation, as well as the energy scale relation is derived analytically. It is found that under the same drive condition, the implosion velocity and total kinetic energy of cylindrical load are higher than those of quasi-spherical one. However, as we expected, the quasi-spherical implosion has larger kinetic energy density, which is important for the applications such as driving a dynamic holhraum. Besides the peak current, the kinetic energy of quasi-spherical implosion also depends on the initial size of the load. By increasing the initial radius and maximum latitude angle moderately, one can obtain higher kinetic energy and energy density of the implosion, which is crucial for the load design. The theoretical study is supported by simulation results. It is found that under a drive condition close to that of the ZR facility, a quasi-spherical load with an initial radius of 5 cm will reach a peak kinetic energy density of 3.2 MJ/cm, which is about 3 times those from the cylindrical ones.

Underwater explosion induced shock loading of structures: Influence of water depth, salinity and temperature

Most of the literature available for determination of the response of underwater explosion induced shock loading on structures considers free surface of water, no salinity in the water and also no special effects of initial temperature and latitude. Thereby question naturally arises as to whether these theoretical researches can directly be applied to practical situations in various seas/oceans around the world. A framework is prescribed in this manuscript through which designers can evaluate coefficient of reflection, a major factor for design of marine vessels and offshore structures for protection against blast loads, in different conditions considering water depth, salinity, temperature and also latitude. The manuscript illustrates variability in response with discussion of some idealized cases.

Interannual Variability in North Atlantic Weather: Data Analysis and a Quasigeostrophic Model

Abstract This paper addresses the effect of interannual variability in jet stream orientation on weather systems over the North Atlantic basin (NAB). The observational analysis relies on 65 yr of NCEP–NCAR reanalysis (1948–2012). The total daily kinetic energy of the geostrophic wind (GTKE) is taken as a measure of storm activity over the North Atlantic. The NAB is partitioned into four rectangular regions, and the winter average of GTKE is calculated for each quadrant. The spatial GTKE average over all four quadrants shows striking year-to-year variability and is strongly correlated with the North Atlantic Oscillation (NAO). The GTKE strength in the northeast quadrant is closely related to the diffluence angle of the jet stream in the northwest quadrant. To gain insight into the relationship between the diffluence angle and its downstream impact, a quasigeostrophic baroclinic model is used. The results show that an initially zonal jet persists at its initial latitude over 30 days or longer, while a tilted jet propagates meridionally according to the Rossby wave group velocity, unless kept stationary by external forcing. A Gulf Stream–like narrow sea surface temperature (SST) front provides the requisite forcing for an analytical steady-state solution to this problem. This SST front influences the atmospheric jet in the northwest quadrant: it both strengthens the jet and tilts it northward at higher levels, while its effect is opposite at lower levels. Reanalysis data confirm these effects, which are consistent with thermal wind balance. The results suggest that the interannual variability found in the GTKE may be caused by intrinsic variability of the thermal Gulf Stream front.

On the Validity of the β-Plane Approximation in the Dynamics and the Chaotic Advection of a Point Vortex Pair Model on a Rotating Sphere

Abstract The dynamics of modulated point vortex pairs is investigated on a rotating sphere, where modulation is chosen to reflect the conservation of angular momentum (potential vorticity). In this setting the authors point out a qualitative difference between the full spherical dynamics and the one obtained in a β-plane approximation. In particular, dipole trajectories starting at the same location evolve to completely different directions under these two treatments, despite the fact that the deviations from the initial latitude remain small. This is a strong indication for the mathematical inconsistency of the traditional β-plane approximation. At the same time, a consistently linearized set of equations of motion leads to trajectories agreeing with those obtained under the full spherical treatment. The β-plane advection patterns due to chaotic advection in the velocity field of finite-sized vortex pairs are also found to considerably deviate from those of the full spherical treatment, and quantities characterizing transport properties (e.g., the escape rate from a given region) strongly differ.

A novel self-alignment method for SINS based on three vectors of gravitational apparent motion in inertial frame

Based on the alignment idea of tracing gravitational apparent motion in inertial frame, a novel self-alignment and latitude calculation method for Strapdown Inertial Navigation System (SINS) is designed. In this method, the problem of acquiring attitude matrix between body frame and navigation frame is attributed to acquiring the matrix between initial body frame and current navigation frame, and the gravitational apparent motion vectors at three moments are used to construct corresponding vectors and matrix through vector-operation. Meanwhile, the latitude information can be obtained by virtue of the geometric relationships among gravitational apparent vectors. Furthermore, the validity of the proposed method is proved by mathematical proof, and the theoretical expressions for evaluating accuracies of initial alignment and latitude calculation are deduced detailedly. Simulation and turntable results indicate that the proposed method can fulfill self-alignment and latitude calculation under a swinging condition without translational motion.

Latitudinal dependence of nonlinear interaction between electromagnetic ion cyclotron wave and terrestrial ring current ions

Electromagnetic ion cyclotron (EMIC) waves can lead to the rapid decay (on a timescale of hours) of the terrestrial ring current. Such decay process is usually investigated in the framework of quasi-linear theory. Here, both theoretical analysis and test-particle simulation are performed to understand the nonlinear interaction between ring current ions and EMIC waves. In particular, the dependence of the nonlinear wave-particle interaction processes on the ion initial latitude is investigated in detail. These nonlinear processes are classified into the phase trapping and phase bunching, and the phase bunching is further divided into the channel and cluster effects. Compared to the prediction of the quasi-linear theory, the ring current decay rate can be reduced by the phase trapping, increased by the channel effect phase bunching, but non-deterministically influenced by the cluster effect phase bunching. The ion initial latitude changes the occurrence of the phase trapping, modulates the transport direction and strength of the cluster effect phase bunching, and only slightly affects the channel effect phase bunching. The current results suggest that the latitudinal dependence of these nonlinear processes should be considered in the evaluation of the ring current decay induced by EMIC waves.

Test particle simulation of resonant interaction between energetic electrons in the magnetosphere and ELF/VLF waves generated by ionospheric modification

Ionospheric modulation can artificially trigger ELF/VLF whistler waves, which can leak into the inner magnetosphere and contribute to resonant interactions with energetic electrons. Combining the ray tracing method and test particle simulations, we investigate the propagation of these artificially generated ELF/VLF waves through the high ionosphere into the inner magnetosphere, and evaluate the subsequent effects of resonant scattering energetic electrons near the heart of the outer radiation belt. The results show that the artificially triggered ELF/VLF waves become highly oblique in the magnetosphere and their spatial extent of L shell and magnetic latitude can be significantly controlled by the initial launch latitude. Corresponding to the principal first-order resonance, the energetic electrons from ～ 100 keV to 3 MeV can resonate with the artificial VLF waves with frequency above 10 kHz in the inner radiation belt, while in the outer radiation belt these hazardous electrons can resonate with ELF waves from ～100 Hz to 1 kHz. At L=4.5 as the focus in this study, the artificial ELF waves can resonate with 1 MeV electron at the harmonics N=-1, 1, 2. In contrast, the Landau resonance rarely occurs for these energetic electrons. The results of test particle simulations indicate that while wave-induced changes in pitch angle and kinetic energy of a single electron are stochastic, the change averaged over all test electrons increases monotonically within the resonance timescale, which implies that resonant scattering is an overall characteristic of energetic electrons under the influence of the artificial whistler waves. Computed resonant scattering rates based on the test particle simulations indicate that aritificial ELF/VLF waves with an observable in situ wave amplitude of ～ 10 pT can drive efficient local pitch angle scattering of energetic electrons at the magnetic equator, thereby contributing considerably to their precipitation loss and magnetospheric electron dynamics. When the waves become highly oblique during the propagation, besides the fundamental first order resonance, higher order resonances can also drive efficient electron scattering. The results support the feasibility of generating artificially ELF/VLF whistler waves for controlled removal of energetic electrons in the Earth radiation belts.

Latitudinal dependence of nonlinear interaction between electromagnetic ion cyclotron wave and radiation belt relativistic electrons

Electromagnetic ion cyclotron (EMIC) waves are long suggested to account for the rapid loss of radiation belt relativistic electrons. Here we perform both theoretical analysis and numerical simulation to comprehensively investigate the nonlinear interaction between EMIC wave and relativistic electrons. In particular, we emphasize the dependence of nonlinear processes on the electron initial latitude. The nonlinear phase trapping yields negative equatorial pitch angle transport, with efficiency varying over the electron initial latitude, implying that it can increase the loss rate predicted by quasilinear theory. The nonlinear channel effect phase bunching produces positive equatorial pitch angle transport, less dependent on the electron initial latitude, suggesting that it can decrease the loss rate predicted by quasilinear theory. The nonlinear cluster effect phase bunching alternately causes positive and negative equatorial pitch angle transport, quasi‐periodically dependent on the electron initial latitude, suggesting that it can either decrease or increase the loss rate predicted by the quasilinear theory. Such latitudinal dependence of nonlinear processes should be taken into account in the evaluation of radiation belt electron loss rate driven by EMIC waves.

Comparing Simulations of Rising Flux Tubes Through the Solar Convection Zone with Observations of Solar Active Regions: Constraining the Dynamo Field Strength

We study how active-region-scale flux tubes rise buoyantly from the base of the convection zone to near the solar surface by embedding a thin flux tube model in a rotating spherical shell of solar-like turbulent convection. These toroidal flux tubes that we simulate range in magnetic field strength from 15 kG to 100 kG at initial latitudes of 1 degree to 40 degrees in both hemispheres. This article expands upon Weber, Fan, and Miesch (Astrophys. J., 741, 11, 2011) (Article 1) with the inclusion of tubes with magnetic flux of 10^20 Mx and 10^21 Mx, and more simulations of the previously investigated case of 10^22 Mx, sampling more convective flows than the previous article, greatly improving statistics. Observed properties of active regions are compared to properties of the simulated emerging flux tubes, including: the tilt of active regions in accordance with Joy's Law as in Article 1, and in addition the scatter of tilt angles about the Joy's Law trend, the most commonly occurring tilt angle, the rotation rate of the emerging loops with respect to the surrounding plasma, and the nature of the magnetic field at the flux tube apex. We discuss how these diagnostic properties constrain the initial field strength of the active region flux tubes at the bottom of the solar convection zone, and suggest that flux tubes of initial magnetic field strengths of \geq 40 kG are good candidates for the progenitors of large (10^21 Mx to 10^22 Mx) solar active regions, which agrees with the results from Article 1 for flux tubes of 10^22 Mx. With the addition of more magnetic flux values and more simulations, we find that for all magnetic field strengths, the emerging tubes show a positive Joy's Law trend, and that this trend does not show a statistically significant dependence on the magnetic flux.

Long-term polar motion on a quasi-fluid planetary body with an elastic lithosphere: Semi-analytic solutions of the time-dependent equation

In order to understand long-term polar motion (so-called true polar wander), I present a large-scale and time-dependent solution of the Liouville equation based on the quasi-fluid approximation. The formulation includes the stabilizing effect of an oblate fossil shape memorized in an elastic lithosphere. Reorientation is assumed to be driven by a surface mass excess that is axi-symmetric and grows linearly with time. Without a fossil bulge, the time scale of true polar wander (specifically the time scale to settle to an equilibrium state) depends mainly on the time to build the load and its final magnitude. A fossil bulge works against reorientation such that the initial latitude of load emplacement now also influences the time scale. I conclude that it is necessary to consider where a load is emplaced in order to reconstruct paleo-poles on a planetary body with a remnant rotational bulge.