Computer programs for spherical cap harmonic analysis of potential and general fields

Haines, G. V.

doi:10.1016/0098-3004(88)90027-1

Cited by 93 publications

(81 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Crustal and measurement standard deviations, and areal elements over which original data is considered to apply before spatial averaging in bins. Haines (1988) have been modified to allow the use of totalfield data in the modelling process. Since total field is non-linear in the coefficients used to express vector components, the expression for total field must be linearized.…”

Section: Weightingmentioning

confidence: 99%

The Canadian Geomagnetic Reference Field 1995

Haines

Newitt

1997

J. geomagn. geoelec

View full text Add to dashboard Cite

Several innovations have been introduced in the production of the Canadian Geomagnetic Reference Field (CGRF) for 1995. The secular variation and main field were modelled simultaneously using the recently developed method of main field differences. The degree of the temporal polynomial was varied depending on the spherical cap harmonic spatial degree. Modifications were made to allow the use of scalar, as well as vector, data in the analysis. Use was made of several data sets not used in previous versions of the CGRF, including Project Magnet data, POGS data, low-level scalar aeromagnetic data, and scalar marine data. A spherical cap harmonic model was produced for a spherical cap of 30° radius centred at 65°N, 85°W. The maximum spatial index of expansion was K= 16, and the maximum temporal expansion was 7. The CGRF results in an error variance to the data over the modelling area that is 19% lower for the main field data and 55% lower for secular variation data than does the IGRF.

show abstract

Section: Weightingmentioning

confidence: 99%

The Canadian Geomagnetic Reference Field 1995

Haines

Newitt

1997

J. geomagn. geoelec

View full text Add to dashboard Cite

show abstract

“…(14) depend on m, Haines (1985) denoted the degree by n k (m), where k is an integer that can be used much like l in the full sphere spherical harmonics for defining the latitudinal resolution of the functions. Numerical calculation of the non-integral functions becomes increasingly difficult as k increases due to limitations in computational precision (Haines, 1988). The algorithm provided by Haines for the calculation of non-integral Legendre functions requires special extended precision hardware or a reduction in accuracy when computing k>12 Legendre functions.…”

Section: Numerical Evaluation Of Jmentioning

confidence: 99%

“…However, since only cross-track data are used in the fitting process the reconstructed b may exhibit unphysical features in the south component and still be divergenceless. To avoid this problem the SCHA was modified according to the suggestion of Haines (1988). The construction of the scalar potential, Q, was limited to one set of spherical harmonic functions.…”

Section: Numerical Evaluation Of Jmentioning

confidence: 99%

“…Spherical Cap Harmonic Analysis (SCHA) described by Haines (1985Haines ( , 1988) is used as the basis of the numerical approach. Haines showed that to model a vector field over a spherical cap the scalar potential function (Q in this case) should only be constructed from spherical harmonic functions that satisfy one of two boundary conditions at the cap edge (θ c ).…”

Section: Numerical Evaluation Of Jmentioning

confidence: 99%

See 1 more Smart Citation

Comparison of large-scale Birkeland currents determined from Iridium and SuperDARN data

Green¹,

Waters²,

Anderson

et al. 2006

Ann. Geophys.

View full text Add to dashboard Cite

Abstract. The Birkeland currents, J , electrically couple the high latitude ionosphere with the near Earth space environment. Approximating the spatial distribution of the Birkeland currents may be achieved using the divergence of the ionospheric electric field, E ⊥ , assuming zero conductance gradients such that J ≈ p ∇·E ⊥ . In this paper, electric field data derived from the Super Dual Auroral Radar Network (SuperDARN) are used to calculate p ∇·E ⊥ , which is compared with the Birkeland current distribution derived globally from the constellation of Iridium satellites poleward of 60 • magnetic latitude. We find that the assumption of zero conductance gradients is often a poor approximation. On the dayside, in regions where the SuperDARN electric field is constrained by radar returns, the agreement in the locations of regions of upward and downward current between p ∇·E ⊥ and J obtained from Iridium data is reasonable with differences of less than 3 • in the latitudinal location of major current features. It is also shown that away from noon, currents arising from conductance gradients can be larger than the p ∇·E ⊥ component. By combining the p ∇·E ⊥ estimate in regions of radar coverage with in-situ estimates of conductance gradients from DMSP satellite particle data, the agreement with the Iridium derived J is considerably improved. However, using an empirical model of ionospheric conductance did not account for the conductance gradient current terms. In regions where radar data are sparse or nonexistent and therefore constrained by the statistical potential model the p ∇·E ⊥ approximation does not agree with J calculated from Iridium data.

show abstract

“…By visual inspection of magnetograms from the year 1976 a number of quiet or slightly unsettled days were chosen. Data for the same day from the neighbouring observatories were used to correct the component values at the "repeat station" using each of the following six methods: 5) In this method, the external and induced disturbance field for each component is modelled over Canada for each hour of the day using spherical cap harmonic analysis (HAINES, 1988;WALKER, 1989). The harmonic expansion index for the model was 11 and the F level of significance for the coefficients was 3.0.…”

Section: Correcting High Latitude Repeat Station Data For Magnetic Acmentioning

confidence: 99%

Removing magnetic activity from high latitude magnetic repeat station observations.

Newitt

Walker

1990

J. geomagn. geoelec

View full text Add to dashboard Cite

The temporal magnetic disturbances which occur during magnetic repeat station surveys cause errors in the determination of the main field secular variation. However, their effects can be significantly reduced by optimizing the survey period and by modelling and subtracting the disturbance field. An analysis of data from five Canadian observatories, which form a meridional line from midlatitudes (Victoria) across the auroral zone to the polar cap (Resolute), shows that simple linear techniques for correcting the observations at a repeat station were generally unsuccessful. However, the subtraction of perturbations obtained by modelling data from 19 North American observatories using the new method of spherical cap harmonic analysis removed most of the temporal variations. After the removal of such fields, 80% of the errors at auroral zone locations were generally less than 10 nT. If repeat station surveys in high latitude regions are extended to several days, in order to increase the probability of observing a quiet or unsettled interval, and the disturbance field is modelled and removed from the observations, the errors in the secular variation are comparable to those obtained using observatory data.

show abstract

Computer programs for spherical cap harmonic analysis of potential and general fields

Cited by 93 publications

References 6 publications

The Canadian Geomagnetic Reference Field 1995

The Canadian Geomagnetic Reference Field 1995

Comparison of large-scale Birkeland currents determined from Iridium and SuperDARN data

Removing magnetic activity from high latitude magnetic repeat station observations.

Contact Info

Product

Resources

About