Spherical Harmonic Model Research Articles

Anomaly in the earth magnetic field at north provinces of Najaf city

This paper investigated in the numerical simulation model to calculate the Earth magnetic field components at north provinces of Najaf city (Longitude 44.316 o -44.3592o E and Latitude 32.0508o - 32.0256o N). The components of the Earth magnetic field (total intensity (F), horizontal intensity (H), declination (D), inclination (I), the north component(X), the east component(Y), and Down component(Z)) were found by using spherical harmonic world magnetic model (WMM2010). A great deal of anomaly has been discovered in all components of the Earth magnetic field at the selected region (Long. 44.345o-44.335o E, Lat.32.042o-32.032o N) using Kriging method. This anomaly can be attributed either to oil rich region or cracking in the Earth crust.

Numerical study of chemical kinetics and radiation heat transfer characteristics on the temperature distribution in the oxy-fuel combustion

In this study, The IFRF methane-oxygen combustion furnace is used to investigate the effect of the radiation model, the method of evaluated absorption and emission coefficients and the different chemical mechanisms. The simulations are performed with OpenFOAM open source software by using of PaSR (partially stirred reactor) combustion model. The numerical investigations are carried out without radiative heat transfer and with the modeling of the radiation source term using the P1 (spherical harmonic radiation model) and DO (discrete ordinate) models. To evaluate the absorption and emission coefficients used from the constant coefficients, the grey mean gases model in terms of temperature polynomial, the WSGGM (weighted sum of grey gases model) and refined WSGGM models. The investigation of the global mechanism effect on the temperature distribution in the oxy-fuel combustion is performed by the modified 2-step Westbrook-Dryer mechanism by Yin and modified 4-step Jones-Lindstedt mechanisms by Yin and Andersen. The results indicate that the lack of consideration of radiation heat transfer in the oxy-fuel combustion leads to a large error in the prediction of the maximum and average temperature distributions inside the furnace. Also, the DO model has less error than P1 model due to more heat loss prediction by P1 model in the low optical thickness. The WSGGM model for calculating of absorption and emission coefficients provide the best result in comparison with other methods. The refined 4-step Jones-Lindstedt mechanism by Andersen has best prediction of on the basis of numerical simulations.

Analysis of the data processing strategies of spherical harmonic expansion model on global ionosphere mapping for moderate solar activity

Spherical harmonic (SH) expansion is widely used to model the global ionosphere map (GIM) of vertical total electron content (VTEC). According to the impact of different data processing methods of the SH expansion model on the VTEC maps, we specifically performed comprehensive analysis in terms of the data sampling rate, the time resolution, the spherical harmonic degree, and the relative constraint. One month of GPS data (January in 2016) from the International GNSS (Global Navigation Satellite System) Service (IGS) network in a moderate ionospheric activity period at the descending phase of Solar Cycle 24 was processed. To improve the computational efficiency of the daily GIM generation, the data sampling rate of 5 min was recommended allowing the GIM precision loss within 0.10 TECU (total electron content unit). The global VTEC map could be better represented in temporal and spatial domains with higher time resolution and higher spherical harmonic degree, especially at low latitude bands and in the southern hemisphere. The GIM precision improvement was about 10.91% for 1-h and about 15.15% for 0.5-h compared with the commonly used 2-h time resolution. The use of spherical harmonic degree 17 or 20 instead of 15 could improve the precision by 3.19% or 6.06%. We also found that an optimal relative constraint had to be found experimentally considering both the GIM precision and the GIM root mean square (RMS) map.

Divergence-free spherical harmonic gravity field modelling based on the Runge–Krarup theorem: a case study for the Moon

Recent numerical studies on external gravity field modelling show that external spherical harmonic series may diverge near or on planetary surfaces. This paper investigates an alternative solution that is still based on external spherical harmonic series, but capable of avoiding the divergence effect. The approach relies on the Runge–Krarup theorem and the iterative downward continuation. In theory, Runge–Krarup-type solutions are able to approximate the true potential within the entire space external to the masses with an arbitrary $$\varepsilon $$ -accuracy, $$\varepsilon >0$$ . Using gravity implied by the lunar topography, we show numerically that this technique avoids indeed the divergence effect, at least at the studied 5 arc-min resolution. In the context of the iterative scheme, we show that a function expressed as a truncated solid spherical harmonic expansion on a general star-shaped surface possesses an infinite surface spherical harmonic spectrum after it is mapped onto a sphere. We also study the convergence of the gradient approach, which is a technique for efficient grid-wise synthesis on irregular surfaces. We show that the resulting Taylor series may converge slowly when analytically upward continuing from points inside the masses. The continuation from the mass-free space should therefore be preferred. As an underlying topic of the paper, spherical harmonic coefficients from spectral gravity forward modelling and their Runge–Krarup counterpart are numerically studied. Regarding their different nature, we formulate some research topics that might contribute to a deeper understanding of the current methodologies used to develop combined high-degree spherical harmonic gravity models.

A New Lunar DEM Based on the Calibrated Chang’E-1 Laser Altimeter Data

To improve the lunar DEM accuracy derived from CE-1 altimeter data, CE-1 laser altimeter data are calibrated in this paper. Orbit accuracy and ranging accuracy are the two most important factors to affect the application of altimeter data in the lunar topography. An empirical method is proposed to calibrate CE-1 altimeter data, using gridded LOLA DEM to correct systematic errors of CE-1 altimeter data, and the systematic bias is about -139.52 m. A new lunar DEM grid model based on calibrated CE-1 altimeter data with the spatial resolution of 0.0625° × 0.0625° is obtained as well as a spherical harmonic model at 1400th order. Furthermore, the DEM accuracy is assessed through the comparison with the nearside landmarks of the Moon, and the results show that the DEM accuracy is improved from 127.3 m to 48.7 m after the calibration of laser altimeter data.

Global Climate and Atmospheric Composition of the Ultra-hot Jupiter WASP-103b from HST and Spitzer Phase Curve Observations

Abstract We present thermal phase curve measurements for the hot Jupiter WASP-103b observed with Hubble/WFC3 and Spitzer/IRAC. The phase curves have large amplitudes and negligible hotspot offsets, indicative of poor heat redistribution to the nightside. We fit the phase variation with a range of climate maps and find that a spherical harmonics model generally provides the best fit. The phase-resolved spectra are consistent with blackbodies in the WFC3 bandpass, with brightness temperatures ranging from 1880 ± 40 K on the nightside to 2930 ± 40 K on the dayside. The dayside spectrum has a significantly higher brightness temperature in the Spitzer bands, likely due to CO emission and a thermal inversion. The inversion is not present on the nightside. We retrieved the atmospheric composition and found that it is moderately metal-enriched ( ) and the carbon-to-oxygen ratio is below 0.9 at 3σ confidence. In contrast to cooler hot Jupiters, we do not detect spectral features from water, which we attribute to partial H2O dissociation. We compare the phase curves to 3D general circulation models and find that magnetic drag effects are needed to match the data. We also compare the WASP-103b spectra to brown dwarfs and young, directly imaged companions. We find that these objects have significantly larger water features, indicating that surface gravity and irradiation environment play an important role in shaping the spectra of hot Jupiters. These results highlight the 3D structure of exoplanet atmospheres and illustrate the importance of phase curve observations for understanding their complex chemistry and physics.

Global and Regional Assessments of Paleosecular Variation Activity Over the Past 100 ka

AbstractWe present a global compilation of paleomagnetic data spanning the past 100 ka. Sediment data comprise 61,687 declinations, 70,936 inclinations, and 69,596 relative paleointensities. Many sites are located in the northern Atlantic and western Pacific, with approximately twice as many data from the Northern Hemisphere as from the Southern Hemisphere. The 14,954 volcanic and archeomagnetic data are sparse, especially in the Southern Hemisphere. Directional and intensity information are aggregated under the paleosecular variation (PSV) index to assess occurrence of excursions over the past 100 ka. The Laschamp excursion (∼41 ka) is clearly defined across globally distributed sediment records with an average duration of 1,300 years. Regional stacks obtained using bootstrap resampling show a more pronounced Laschamp excursion in the Northern Hemisphere than in the Southern, and in the Atlantic Hemisphere compared with the Pacific. No anomalous indices occurred around the Mono Lake excursion or other periods in the bootstrap curves. This may result from low sedimentation rates, discrepancies in age scales, large age errors, and/or the lack of global character of any transitional events. These data and associated new uncertainty estimates for the sediment records provide a good foundation for global, time‐dependent, spherical harmonic field modeling for the past 100 ka.

A high resolution Mars surface gravity grid

We have developed a new model of the gravitational acceleration vector at the surface of Mars, and present it on an equal area grid covering the surface of Mars, with a 1.73 km resolution. The long wavelength part of the model is adopted from MRO120d, which is a spherical harmonic model of the potential derived from Doppler tracking data of spacecraft in orbit about Mars. The short wavelength part is derived from convolution of appropriate Green's functions with the surface mass distribution associated with the MOLA topography, assuming a uniform mass density. The density was selected to be 2782kg/m3, which yields surface gravity values, from that approach, which match those from the spacecraft-derived model at the transition wavelength, which is taken to be degree 80. Our estimate of the error in the radial component is 11 mGal, with a larger contribution from long wavelength sources than from short wavelengths.

A Computational Fluid Dynamics Study of Turbulence, Radiation, and Combustion Models for Natural Gas Combustion Burner

This paper presents a Computational Fluid Dynamics (CFD) study of a natural gas combustion burner focusing on the effect of combustion, thermal radiation and turbulence models on the temperature and chemical species concentration fields. The combustion was modelled using the finite rate/eddy dissipation (FR/EDM) and partially premixed flame models. Detailed chemistry kinetics CHEMKIN GRI-MECH 3.0 consisting of 325 reactions was employed to model the methane combustion. Discrete ordinates (DO) and spherical harmonics (P1) model were employed to predict the thermal radiation. The gas absorption coefficient dependence on the wavelength is resolved by the weighted-sum-of-gray-gases model (WSGGM). Turbulence flow was simulated using Reynolds-averaged Navier-Stokes (RANS) based models. The findings showed that a combination of partially premixed flame, P1 and standard k-ε (SKE) gave the most accurate prediction with an average deviation of around 7.8% of combustion temperature and 15.5% for reactant composition (methane and oxygen). The results show the multi-step chemistry in the partially premixed model is more accurate than the two-step FR/EDM. Meanwhile, inclusion of thermal radiation has a minor effect on the heat transfer and species concentration. SKE turbulence model yielded better prediction compared to the realizable k-ε (RKE) and renormalized k-ε (RNG). The CFD simulation presented in this work may serve as a useful tool to evaluate a performance of a natural gas combustor.

A New Model of Jupiter's Magnetic Field From Juno's First Nine Orbits

AbstractA spherical harmonic model of the magnetic field of Jupiter is obtained from vector magnetic field observations acquired by the Juno spacecraft during its first nine polar orbits about the planet. Observations acquired during eight of these orbits provide the first truly global coverage of Jupiter's magnetic field with a coarse longitudinal separation of ~45° between perijoves. The magnetic field is represented with a degree 20 spherical harmonic model for the planetary (“internal”) field, combined with a simple model of the magnetodisc for the field (“external”) due to distributed magnetospheric currents. Partial solution of the underdetermined inverse problem using generalized inverse techniques yields a model (“Juno Reference Model through Perijove 9”) of the planetary magnetic field with spherical harmonic coefficients well determined through degree and order 10, providing the first detailed view of a planetary dynamo beyond Earth.

A Model of Gravity Vector Measurement Noise for Estimating Accelerometer Bias in Gravity Disturbance Compensation.

Compensation of gravity disturbance can improve the precision of inertial navigation, but the effect of compensation will decrease due to the accelerometer bias, and estimation of the accelerometer bias is a crucial issue in gravity disturbance compensation. This paper first investigates the effect of accelerometer bias on gravity disturbance compensation, and the situation in which the accelerometer bias should be estimated is established. The accelerometer bias is estimated from the gravity vector measurement, and a model of measurement noise in gravity vector measurement is built. Based on this model, accelerometer bias is separated from the gravity vector measurement error by the method of least squares. Horizontal gravity disturbances are calculated through EGM2008 spherical harmonic model to build the simulation scene, and the simulation results indicate that precise estimations of the accelerometer bias can be obtained with the proposed method.

Archeomagnetic Intensity Spikes: Global or Regional Geomagnetic Field Features?

Variations of the geomagnetic field prior to direct observations are inferred from archeo- and paleomagnetic experiments. Seemingly unusual variations not seen in the present day and historical field are of particular interest to constrain the full range of core dynamics. Recently, archeomagnetic intensity spikes, characterised by very high field values that appear to be associated with rapid secular variation rates, have been reported from several parts of the world. They were first noted in data from the Levant at around 900~BCE. A recent re-assessment of previous and new Levantine data, involving a rigorous quality assessment, interprets the observations as an extreme local geomagnetic high with at least two intensity spikes between the 11$^{\rm th}$ and 8$^{\rm th}$ centuries BCE. Subsequent reports of similar features from Asia, the Canary Islands and Texas raise the question of whether such features might be common occurrences, or whether they might even be part of a global magnetic field feature. Here we use spherical harmonic modelling to test two hypotheses: firstly, whether the Levantine and other potential spikes might be associated with higher dipole field intensity than shown by existing global field models around 1000~BCE, and secondly, whether the observations from different parts of the world are compatible with a westward drifting intense flux patch. Our results suggest that the spikes originate from intense flux patches growing and decaying mostly in situ, combined with stronger and more variable dipole moment than shown by previous global field models. Axial dipole variations no more than 60\% higher than observed in the present field, probably within the range of normal geodynamo behaviour, seem sufficient to explain the observations.

A Computational Study of Swirl Number Effects on Entropy Generation in Gas Turbine Combustors

ABSTRACTIn this paper, local and global entropy generation features are studied numerically in two research flames and a real combustor problem. The research flames are the well-known Burner Engineering Research Laboratory and Sandia flame D experimental flame databases and the real combustor is a gas-turbine can-type combustor. The main focus is on investigating the effect of the swirl number, in the range 0.0–2.4, on entropy generation characteristics due to different phenomena, including viscous, mass transfer, heat transfer, heat-mass coupling, reaction, and specifically radiation. For this purpose, the surface and volumetric local entropy generation rates are formulated based on the first-order spherical harmonics model known as “P1,” a frequently used model in combustion applications. It is observed that heat transfer and reactions are dominant causes of entropy generation with the leading contribution of reaction at lower swirl numbers and heat transfer at higher swirl values. The radiation entropy generation is slightly affected by the swirl number and is of prime importance only in near stoichiometric conditions. Moreover, it is indicated how this local entropy generation analysis can be used to discover the weaknesses in the design of a real combustor.

Harmonic analysis of surface instability patterns on colloidal particles.

Wrinkling of colloidal particles alter a wide variety of interfacial properties but quantitative topographical descriptions have been explored experimentally to a very limited extent. In this study, we present a harmonic analysis of surface wrinkles and folds on submicron colloidal particles, obtained using an aerosol flow route, with small radius (<300 nm) and high crust thickness-to-radius ratio (>0.1). The particle surface coordinates were mapped in their entirety using cryo-electron tomography and subsequently reconstructed using spherical harmonics, allowing a spectral topographical description of the instability patterns and the identification of their surface modes by lateral wavelength. Wrinkled and crumpled particles showed a similar surface roughness spectrum, wherein differences were found most noticeable in the large wavelength region. The analysis of preferred directions of harmonic frequencies indicated a possible axial or planar alignment attributed to the directionality of the surface corrugations. The employed characterization methodology can further the study of topographical influences on colloidal interactions.

The Optimal Degree of Gravity Spherical Harmonic Model Calculation for Gravity Disturbance Compensation in Inertial Navigation

In recent years, the significant improvement of inertial navigation, leaves the gravity disturbance as the important factor which affects the accuracy of inertial navigation. This paper focus on the compensation for gravity disturbance with gravity spherical harmonic model, especially the optimal degree of gravity spherical harmonic model with which to calculate the gravity disturbance. The effect of gravity disturbance on inertial navigation is analysed based on the amplitude-frequency response characteristics of inertial navigation error differential equation, then the dominantly influential frequency band of gravity disturbance can be found which is the target of compensation. Combination the dominantly influential frequency band with the spatial resolution of the Earth’s gravity spherical harmonic model EGM2008 which is used to calculate the gravity disturbance, the optimal degree can be determined based on an algorithm proposed in this paper. Finally, shipborne inertial navigation experiment confirms the correctness and effectiveness of the proposed algorithm.

Analysis of the lithospheric magnetic anomalies and tectonics in continental China and the adjacent regions using CHAMP satellite data

In this paper, the CHAMP satellite data from the last decade are used to map the lithospheric magnetic field in continental China at altitudes of 300 and 400 km using the spline function model technique. The results show that our model has higher amplitude than the spherical harmonic magnetic field model MF7. The resulting lithospheric anomaly distribution of continental China agrees with the geotectonic structure and crustal thermal structure. The magnetic anomaly distribution clearly indicates extrusion of the Tibetan Plateau towards the northeast and northwest directions. Northward movement is impeded by the relative rigid Tarim Basin featured with positive magnetic anomalies. The positive magnetic anomalies in Tarim basin extend to the northern Tibetan Plateau, suggesting that the southern part of Tarim Basin underthrusted the northern Tibetan Plateau.

Combined multi-spectrum and orthogonal Laplacianfaces for fast CB-XLCT imaging with single-view data

Cone-beam X-ray luminescence computed tomography (CB-XLCT) is an attractive hybrid imaging modality, which has the potential of monitoring the metabolic processes of nanophosphors-based drugs in vivo. Single-view data reconstruction as a key issue of CB-XLCT imaging promotes the effective study of dynamic XLCT imaging. However, it suffers from serious ill-posedness in the inverse problem. In this paper, a multi-spectrum strategy is adopted to relieve the ill-posedness of reconstruction. The strategy is based on the third-order simplified spherical harmonic approximation model. Then, an orthogonal Laplacianfaces-based method is proposed to reduce the large computational burden without degrading the imaging quality. Both simulated data and in vivo experimental data were used to evaluate the efficiency and robustness of the proposed method. The results are satisfactory in terms of both location and quantitative recovering with computational efficiency, indicating that the proposed method is practical and promising for single-view CB-XLCT imaging.

Combining virtual observatory and equivalent source dipole approaches to describe the geomagnetic field with Swarm measurements

A detailed description of the main geomagnetic field and of its temporal variations (i.e., the secular variation or SV) is crucial to understanding the geodynamo. Although the SV is known with high accuracy at ground magnetic observatory locations, the globally uneven distribution of the observatories hampers the determination of a detailed global pattern of the SV. Over the past two decades, satellites have provided global surveys of the geomagnetic field which have been used to derive global spherical harmonic (SH) models through some strict data selection schemes to minimise external field contributions. However, discrepancies remain between ground measurements and field predictions by these models; indeed the global models do not reproduce small spatial scales of the field temporal variations. To overcome this problem we propose to directly extract time series of the field and its temporal variation from satellite measurements as it is done at observatory locations. We follow a Virtual Observatory (VO) approach and define a global mesh of VOs at satellite altitude. For each VO and each given time interval we apply an Equivalent Source Dipole (ESD) technique to reduce all measurements to a unique location. Synthetic data are first used to validate the new VO-ESD approach. Then, we apply our scheme to data from the first two years of the Swarm mission. For the first time, a 2.5° resolution global mesh of VO time series is built. The VO-ESD derived time series are locally compared to ground observations as well as to satellite-based model predictions. Our approach is able to describe detailed temporal variations of the field at local scales. The VO-ESD time series are then used to derive global spherical harmonic models. For a simple SH parametrization the model describes well the secular trend of the magnetic field both at satellite altitude and at the surface. As more data will be made available, longer VO-ESD time series can be derived and consequently used to study sharp temporal variation features, such as geomagnetic jerks.

The analysis of initial Juno magnetometer data using a sparse magnetic field representation

AbstractThe Juno spacecraft, now in polar orbit about Jupiter, passes much closer to Jupiter's surface than any previous spacecraft, presenting a unique opportunity to study the largest and most accessible planetary dynamo in the solar system. Here we present an analysis of magnetometer observations from Juno's first perijove pass (PJ1; to within 1.06 RJ of Jupiter's center). We calculate the residuals between the vector magnetic field observations and that calculated using the VIP4 spherical harmonic model and fit these residuals using an elastic net regression. The resulting model demonstrates how effective Juno's near‐surface observations are in improving the spatial resolution of the magnetic field within the immediate vicinity of the orbit track. We identify two features resulting from our analyses: the presence of strong, oppositely signed pairs of flux patches near the equator and weak, possibly reversed‐polarity patches of magnetic field over the polar regions. Additional orbits will be required to assess how robust these intriguing features are.

Study on ionosphere change over Shandong based from SDCORS in 2012

Temporal and spatial variation of ionosphere can influence our daily communication activities. By solving the one-year global positioning system (GPS) data of Shandong Continuous Operational Reference System (SDCORS) in 2012, we modeled the single-layer spherical harmonic model of vertical total electron content (TEC) over Shandong Province, China, and analyzed the time series of TEC in 2012. The ionosphere over Shandong in 2012 was in the peak year of solar activity. The ionospheric model over Shandong was calibrated and verified using data of the Center for Orbit Determination in Europe (CODE) and the Crustal Movement Observation Network of China (CMONOC), respectively. The ionosphere is greatly influenced by latitude and solar activity and has the phenomenon of Winter anomaly and semi-annual anomaly as well as the session change, diurnal variation, monthly change and seasonal variations. So we can grasp the regularity of temporal and spatial distribution of ionosphere over Shandong, China.