Evaluation of candidate geomagnetic field models for IGRF-11
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Abstract
The eleventh generation of the International Geomagnetic Reference Field (IGRF) was agreed in December 2009 by a task force appointed by the International Association of Geomagnetism and Aeronomy (IAGA) Division V Working Group V-MOD. New spherical harmonic main field models for epochs 2005.0 (DGRF-2005) and 2010.0 (IGRF-2010), and predictive linear secular variation for the interval 2010.0–2015.0 (SV-2010-2015) were derived from weighted averages of candidate models submitted by teams led by DTU Space, Denmark (team A); NOAA/NGDC, U.S.A. (team B); BGS, U.K. (team C); IZMIRAN, Russia (team D); EOST, France (team E); IPGP, France (team F); GFZ, Germany (team G) and NASA-GSFC, U.S.A. (team H). Here, we report the evaluations of candidate models carried out by the IGRF-11 task force during October/November 2009 and describe the weightings used to derive the new IGRF-11 model. The evaluations include calculations of root mean square vector field differences between the candidates, comparisons of the power spectra, and degree correlations between the candidates and a mean model. Coefficient by coefficient analysis including determination of weighting factors used in a robust estimation of mean coefficients is also reported. Maps of differences in the vertical field intensity at Earth’s surface between the candidates and weighted mean models are presented. Candidates with anomalous aspects are identified and efforts made to pinpoint both troublesome coefficients and geographical regions where large variations between candidates originate. A retrospective analysis of IGRF-10 main field candidates for epoch 2005.0 and predictive secular variation candidates for 2005.0–2010.0 using the new IGRF-11 models as a reference is also reported. The high quality and consistency of main field models derived using vector satellite data is demonstrated; based on internal consistency DGRF-2005 has a formal root mean square vector field error over Earth’s surface of 1.0 nT. Difficulties nevertheless remain in accurately forecasting field evolution only five years into the future.
Key words
Geomagnetism field modelling reference field secular variation1. Introduction
The IGRF is an internationally agreed spherical harmonic reference model describing the largest scales of the internal part of the Earth’s magnetic field. It is widely used by scientists studying local and regional crustal magnetic anomalies, by those studying space weather and solar-terrestrial magnetic interactions, and it is also sometimes used by individuals and commercial organizations for navigational purposes. Under normal circumstances the IGRF is updated every 5 years; for a history of IGRF and further background information consult Barton (1997), or Macmillan and Finlay (2010). An IGRF update involves collaboration between institutes collecting and disseminating geomagnetic measurements derived from satellites and ground-based observatories, and between teams of geomagnetic field modellers, making it a truly international enterprise.
Ultimate responsibility for producing an updated IGRF model lies with IAGA. At a business meeting of IAGA Division V Working Group V-MOD (hereafter referred to as IAGA Div V, WG V-MOD) in Perugia in July 2007, a task force with responsibility for the production of IGRF-11 was elected. This consisted of C. Finlay (Chair, ETHZ), S. Maus/S. McLean (NGDC), F. Lowes (Univ. Newcastle), N. Olsen (DTU Space), A. Chambodut (EOST), V. Lesur (GFZ), E. Thébault (IPGP), T. Sabaka (NASA), T. Bondar (IZMIRAN) and S. Macmillan (BGS). The task force included only one voting member from each institution contributing candidate models; this permitted the operation of a democratic voting system to make the necessary collective decisions. For example, in April 2009 the task force voted to retain a spherical harmonic truncation degree of 8 for the predictive secular variation (SV) in IGRF-11. In May 2009 a call for IGRF-11 candidate models was agreed on by the task force and issued. This requested main field (MF) candidate models for the Definitive Geomagnetic Reference Field for epoch 2005.0 (DGRF-2005), for a provisional IGRF model for epoch 2010.0 (IGRF-2010) both to spherical harmonic degree 13, and for a prediction of the average SV over the upcoming five years (SV-2010-2015) to degree 8. An update of progress towards IGRF-11 was given by the task force chair at a business meeting of IAGA Div V, WG V-MOD in Sopron in August 2009.
At the start of October 2009, seven MF candidate models were submitted for DGRF-2005 and IGRF-2010, while eight candidates were submitted for SV-2010-2015. Following a vote by the task force it was decided to allow teams to resubmit revised candidate models before the end of October 2009, due to problems with some initial candidates. BGS submitted revised candidate models for all three products, EOST submitted a revised DGRF candidate and IZMIRAN submitted a late DGRF candidate during this period. During November 2009 members of the task force and other interested parties carried out evaluations of the candidate models and submitted proposals concerning how the candidates should be weighted in the derivation of IGRF-11. Ten independent evaluations were received and posted online for consideration by the task force members. Following internal discussions within the task force, the task force chair (in consultation with the IAGA Div V, WG V-MOD chair) prepared a ballot paper containing various weighting options. This was voted on by the task force and the results announced on 7th December 2009. The final coefficients were prepared and checked, before being made available to the public through the IAGA Div V, WG V-MOD webpage http://www. ngdc.noaa.gov/IAGA/vmod/igrf.html on 24th December 2009. A summary of the construction of IGRF-11 will be presented at the next business meeting of IAGA Div V, WG V-MOD in Melbourne in July 2011. Further details about the process including progress reports, candidate models and descriptions provided by the authors, original evaluations and test models designed to aid decisions regarding IGRF-12, can be found at http://www. ngdc.noaa.gov/IAGA/vmod/candidatemodels.html.
The primary sources of data employed by the modelling teams to produce candidate models were from the German satellite CHAMP, the Danish satellite Ørsted and the Argentine-U.S.-Danish satellite SAC-C, along with data from the international network of geomagnetic observatories. The teams adopted a variety of data selection and processing procedures. Furthermore, the required single epoch spherical harmonic model coefficients were derived from parent models that used a range of time durations (1 month to 12 years), temporal parameterizations (including Taylor series of degree 0 to 2, splines of order 1 to 6), and external field parameterizations of varying complexity. The parent models also used a number of alternative parameter estimation schemes (including least-squares, least absolute deviations, robust estimation based on Huber’s distribution and natural orthogonal analysis). Further details concerning the techniques used to derive the individual candidate models can be found in the papers appearing in this special issue (Chambodut et al., 2010; Hamilton et al., 2010; Kuang et al., 2010; Lesur et al., 2010; Maus et al., 2010; Olsen et al., 2010; Thébault et al., 2010). The different strategies adopted naturally lead to differences in the submitted candidate models. As described above, the task force therefore undertook testing and inter-comparison of the candidates to produce the information required for decisions on the weights to be used in the construction of IGRF-11.
The purpose of the present article is to summarize the evaluations of candidate models carried out in October/November 2009 by the IGRF-11 task force, and to report the final weighting of the candidate models used to derive IGRF-11. We follow closely the strategy adopted in previous evaluations (see, for example, Maus et al., 2005) focusing on statistical comparisons between the candidate models and various mean models, and utilizing well-established diagnostic tools in both the spectral and physical domains. One limitation of this approach is that a good statistical agreement between models does not necessarily mean these models are the most realistic; it can also be a consequence of the use of very similar data selection or modelling techniques. Model evaluations would ideally be based not only upon statistical analysis of candidates, but also on comparisons with independent data that accurately measured the relevant field (the internal magnetic field at Earth’s surface) at the epochs of interest. Unfortunately such ideal evaluation data did not exist for the future epochs of 2010.0 and 2010.0–2015.0 at the time of the evaluations, and it is even troublesome to obtain high quality independent data for the retrospective epoch 2005.0. Attempts to assess the candidate models using either observatory or satellite data are thus complicated by the necessity of propagating the models to suitable comparison epochs as well as with difficulties in separating internal and external field contributions in the observed data. Nonetheless, some workers have made interesting attempts at such comparisons, see for example the study by Chulliat and Thébault (2010) in this issue.
As a mathematical preliminary, we begin in Section 2 by providing the formulae defining the analysis tools employed. In Section 3 MF candidates are studied, while Section 4 presents evaluations of SV candidates. In Section 3.1 we analyze the candidate models for DGRF-2005, then in Section 3.2 a retrospective evaluation of the IGRF-10 candidates for epoch 2005 in comparison with the new DGRF-2005 model is carried out. In Section 3.3 evaluations of the candidates for IGRF-2010 are presented, followed in Section 4.1 by a retrospective analysis of the predictive SV candidates for the epoch 2005-2010 from IGRF-10. Finally in Section 4.2 the IGRF-11 predictive SV candidates for epoch 2010–2015 are analyzed. In each case global comparisons of root mean square (RMS) vector field differences are made first, then comparisons in the spectral domain, per degree and then coefficient by coefficient; finally maps of differences between candidate models and a weighted mean model are presented. Discussion of the evaluation results and a summary of the decision of the task force is provided for each IGRF-11 product. We conclude with an overall summary and some remarks on the implications of these evaluations for the future of the IGRF.
2. Mathematical Definitions and Formulae Used in Evaluations
Having defined the tools used in the evaluations, we now proceed to present the results of the analysis, together with related discussion of the weightings allocated to candidates in the final IGRF-11 models.
3. Evaluation of Main Field Candidate Models
3.1 Analysis of IGRF-11 DGRF-2005 candidate models
Summary of DGRF-2005 candidate models submitted to IGRF-11.
DGRF candidate models for main field epoch 2005 | |||||
---|---|---|---|---|---|
Team | Model | Organization | Data | Comments (parent model etc.) | |
A | DGRF-2005-A | DTU Space / IPGP / GSFC-NASA | Ørsted, CHAMP, SAC-C revised observatory monthly means | Based on CHAOS-3α in 2005.0 (6th order splines for parent) | |
B | DGRF-2005-B | NGDC-NOAA / GFZ | CHAMP 2003.5–2006.5 | Based on POMME 6 2nd order Taylor series | |
C | DGRF-2005-C2 | BGS | Ørsted, CHAMP and observatory hourly means for 01:00–02:00 LT, 1999.0–2009.5 | Revised submission: parent model linear splines (400 day knots spacing) | |
D | DGRF-2005-D | IZMIRAN | CHAMP 2004.0–2006.0 no data selection | Natural Orthogonal Components (NOC) method with 5 terms | |
E | DGRF-2005-E2 | EOST / LPGN / / LATMOS / IPGP | CHAMP & Ørsted 2004.5–2005.5 | Revised submission: based on 12 month model with linear SV | |
F | DGRF-2005-F | IPGP / EOST / LPGN / LATMOS | CHAMP 2004.4–2005.7 | 2nd order Taylor series (to n = 5) | |
G | DGRF-2005-G | GFZ | CHAMP 2001–2009.6 observatory hourly means | Based on GRIMM2 (6th order splines for parent) averaged over 1 yr. |
3.1.1 RMS vector field differences for DGRF-2005 candidate models
RMS vector field differences _{i, j}R in units nT between DGRF-2005 candidate models and also between candidates and the arithmetic mean reference models M, M_{noD} and M_{ABG} shown in the rightmost columns. The bottom three rows are arithmetic means Open image in new window of the_{i,j}R where the means include respectively all candidates, exclude candidate D, and use only models A, B and G.
_{i,j}R/nT | A | B | C2 | D | E2 | F | G | M | M_{noD} | M_{ABG} | |
---|---|---|---|---|---|---|---|---|---|---|---|
A | 0.0 | 2.3 | 4.3 | 14.9 | 5.4 | 4.6 | 2.9 | 3.1 | 2.0 | 1.6 | |
B | 2.3 | 0.0 | 4.8 | 14.5 | 5.2 | 3.8 | 2.2 | 2.6 | 1.7 | 1.2 | |
C2 | 4.3 | 4.8 | 0.0 | 15.2 | 6.8 | 6.5 | 5.2 | 4.6 | 4.0 | 4.6 | |
D | 14.9 | 14.5 | 15.2 | 0.0 | 14.6 | 15.0 | 14.4 | 12.4 | 14.4 | 14.5 | |
E2 | 5.4 | 5.2 | 6.8 | 14.6 | 0.0 | 5.6 | 5.6 | 4.5 | 4.2 | 5.2 | |
F | 4.6 | 3.8 | 6.5 | 15.0 | 5.6 | 0.0 | 4.4 | 4.1 | 3.4 | 4.0 | |
G | 2.9 | 2.2 | 5.2 | 14.4 | 5.6 | 4.4 | 0.0 | 3.0 | 2.4 | 1.6 | |
Mean Diff | 5.7 | 5.5 | 7.1 | 14.7 | 7.2 | 6.6 | 5.8 | 4.9 | 4.6 | 4.7 | |
Mean Diff noD | 3.9 | 3.7 | 5.5 | 17.7 | 5.7 | 5.0 | 4.1 | 3.7 | 3.0 | 3.0 | |
Mean Diff ABG | 2.6 | 2.2 | 4.8 | 14.6 | 5.4 | 4.2 | 2.6 | 2.9 | 2.0 | 1.4 |
The final three rows of Table 2 involve the arithmetic means of the RMS vector field differences of _{i, j}R of model i from the other models j. The third from last row is Open image in new window, the penultimate row is the same calculation excluding candidate D while the final row involves only _{i, j}R from candidates A, B and G. Candidates A, B and G have the smallest Open image in new window and the mean of the _{i, j}R becomes smaller when only candidates A, B and G are retained.
3.1.2 Spectral analysis of DGRF-2005 candidate models
3.1.3 Spatial analysis of DGRF-2005 candidate models
Studying differences between the candidate models and a reference model in space yields insight into the geographical locations where disparities in the candidates are located. Visual inspection of Fig. 3 reveals that candidate D involves the most striking deviations from M_{ABG} that are locally as large as 50 nT. The differences are scattered over the globe and not confined to any particular geographical location, though the largest discrepancies occur in the polar regions and in the mid-Atlantic. Candidates C2 and E2 display largest deviations from A, B and G in the polar regions (particularly in the Arctic). Model E2 shows one localized anomalous region in the equatorial Pacific while model F shows rather minor differences at high latitudes and at mid-latitudes in the northern hemisphere. Candidates A, B and G exhibit only minor differences to the reference model M_{ABG} demonstrating once more that they are consistent with each other.
3.1.4 Choice of numerical precision for DGRF-2005
3.1.5 Discussion and summary for DGRF-2005
Based on the tests presented above, candidate D appears consistently different in both the spectral domain (with certain spherical harmonic coefficients apparently anomalous—see Fig. 2) as well as in physical space where global problems are observed. In addition candidates E2, C2 and to lesser extent F were observed to have some problems, particularly at high degrees in the spectral domain and at high latitudes in space. In contrast candidates A, B and G were very similar despite being derived using different data selection criteria and using different modelling procedures. The task force therefore voted that DGRF-2005 be derived from a simple arithmetic mean of candidates A, B and G (i.e. model M_{ABG} as discussed above).
3.2 Retrospective analysis of IGRF-10 MF candidate models for epoch 2005
RMS vector field differences _{i,j}R in units of nT between candidate models for IGRF-10 epoch 2005.0, the IGRF-2005 from IGRF-10 and the DGRF-2005 from IGRF-11. Note the symmetry about the diagonal, included as a check on the calculations.
_{i,j}R | IGRF-2005-A1 | IGRF-2005-B3 | IGRF-2005-C1 | IGRF-2005-D1 | IGRF-2005 | DGRF-2005 | |
---|---|---|---|---|---|---|---|
IGRF-2005-A1 | 0.0 | 8.0 | 14.6 | 15.8 | 7.0 | 9.9 | |
IGRF-2005-B3 | 8.0 | 0.0 | 11.4 | 15.6 | 4.6 | 10.9 | |
IGRF-2005-C1 | 14.6 | 11.4 | 0.0 | 20.4 | 8.3 | 18.5 | |
IGRF-2005-D1 | 15.7 | 15.6 | 20.4 | 0.0 | 16.1 | 14.0 | |
IGRF-2005 | 7.0 | 4.6 | 8.3 | 16.1 | 0.0 | 12.0 | |
DGRF-2005 | 9.9 | 10.9 | 18.5 | 14.0 | 12.0 | 0.0 |
3.3 Analysis of IGRF-11 MF candidate models for epoch 2010
Summary of IGRF-2010 candidate models submitted for consideration in IGRF-11.
IGRF candidate models for main field epoch 2010 | |||||
---|---|---|---|---|---|
Team | Model | Organization | Data | Comments (parent model, fwd propagation etc.) | |
A | IGRF-2010-A | DTU Space / IPGP / NASA-GSFC | Ørsted, CHAMP, SAC-C revised observatory monthly means | Based on CHAOS-3α evaluated in 2010.0 | |
B | IGRF-2010-B | NGDC-NOAA / GFZ | CHAMP 2006.5–2009.7 | Based on POMME 6: 2nd order Taylor series SV & SA used for 2010.0 estimate | |
C | IGRF-2010-C2 | BGS | Ørsted, CHAMP, observatory hourly means for 01:00–02:00 LT, 1999.0–2009.5 | Revised sub: model evaluated 2009.0 MF and linear SV used to predict 2010.0 field. | |
D | IGRF-2010-D | IZMIRAN | CHAMP 2004.0–2009.2 no data selection | NOC method with extrapolation to 2010 using NOC1, 2 | |
E | IGRF-2010-E | EOST / LPGN / LATMOS / IPGP | CHAMP June/July 2009 | Model at 2009.5 extrapolated to 2010.0 using SV models for 2009, 2010. | |
F | IGRF-2010-F | IPGP / EOST / / LPGN / LATMOS | CHAMP 2008.5–2009.6 | 2nd order Taylor series (to n = 5 in quadratic) extrapolated to 2010.0 | |
G | IGRF-2010-G | GFZ | CHAMP 2001–2009.6 observatory hourly means | Based on GRIMM2 MF and SV in 2009 extrapolated to 2010.0 |
3.3.1 RMS vector field differences for IGRF-2010 candidate models
RMS vector field differences _{i,j}R in units of nT between IGRF-2010 candidates and also between them and the arithmetic mean of all candidates M and the weighted mean M_{w} (see text). The bottom row displays the mean of the RMS vector field differences between each candidate model and all other candidate models Open image in new window from (7) labelled ‘Mean Diff’.
_{i,j}R | A | B | C2 | D | E | F | G | M | M_{w} | |
---|---|---|---|---|---|---|---|---|---|---|
A | 0.0 | 6.3 | 10.6 | 14.2 | 14.8 | 8.2 | 8.2 | 6.3 | 6.4 | |
B | 6.3 | 0.0 | 8.1 | 13.9 | 13.4 | 5.2 | 5.4 | 3.8 | 3.0 | |
C2 | 10.6 | 8.1 | 0.0 | 16.9 | 11.8 | 10.0 | 8.9 | 7.1 | 6.8 | |
D | 14.2 | 13.9 | 16.9 | 0.0 | 19.4 | 15.0 | 14.2 | 12.3 | 13.4 | |
E | 14.8 | 13.4 | 11.8 | 19.4 | 0.0 | 14.0 | 12.4 | 10.9 | 12.0 | |
F | 8.2 | 5.2 | 10.0 | 15.0 | 14.0 | 0.0 | 6.6 | 5.8 | 5.3 | |
G | 8.2 | 5.4 | 8.9 | 14.2 | 12.4 | 6.6 | 0.0 | 4.6 | 4.4 | |
Mean Diff | 10.4 | 8.7 | 11.1 | 15.6 | 14.3 | 9.8 | 9.3 | 7.3 | 7.3 |
As anticipated, the differences between the IGRF-2010 candidates are larger than between the DGRF-2005 candidates, with the mean of the differences between the candidates and the mean model (i.e. the mean of _{i,M}R) being 7.3 nT here for epoch 2010.0 compared to 4.9 nT for epoch 2005.0. Candidates D and E display the largest differences from the other candidates and to the mean models M and M_{w}. Candidate B is most similar to M and it also agrees reasonably closely with candidates F and G (differences less than 5.5 nT) and slightly less well with candidates A and C2 (differences of less than 8.5 nT).
3.3.2 Spectral analysis of IGRF-2010 candidate models
Figure 6 (right) shows the degree correlation per degree _{i,M}ρ_{n} from (9) between the candidates and the arithmetic mean model M. Candidates E and especially D show the largest differences above degree 10; candidates C2, F and G show smaller deviations from M while candidates A and B are closest to M.
3.3.3 Spatial analysis of IGRF-2010 candidate models
3.3.4 Discussion and summary for IGRF-2010
The evaluations of the IGRF-2010 candidates presented above suggest that candidates D and E have some problems, particularly at spherical harmonic degree greater than 10. Consequently the task force voted to allocate these candidates weight 0.25 while candidates A, B, C2, F, G were allocated weight 1.0 in the determination of the new IGRF-11 model for epoch 2010. In addition the task force voted to disregard coefficients Open image in new window and Open image in new window from candidate A since these were thought to be suspect. Subsequent analysis has shown that a model that includes more recent data but is otherwise similar to the parent model for candidate A results in values of Open image in new window and Open image in new window 11 that are in much better agreement with model M (Olsen et al., 2010). The final IGRF-2010 was therefore fixed to be the model discussed above as M_{w}.
4. Evaluation of Predictive SV Candidate Models
4.1 Retrospective analysis of IGRF-10 SV-2005-2010 candidate models
With the evaluations of the main field candidates for epoch 2005.0 and 2010.0 complete we now move on to consider evaluations of predictive SV models. First we present a retrospective analysis of the predictive average SV-2005-2010 candidates (with central epoch 2007.5) used in IGRF-10. We treat as a reference SV model IGRF-2010 minus DGRF-2005 divided by 5 years—this provides the required coefficients in nT/yr centered on epoch 2007.5.
We refer to this model in the following discussion as SV-2007.5-G11. The predictive SV from IGRF-10 (a weighted mean of IGRF-10 candidates A3, C1 and D1 with weight 1.0, and B1 and B2 with weight 0.5) is referred to in the following as SV-2007.5-G10. Candidate A1 was from DSRI/NASA/Newcastle, candidates B1, B2 were models from NGDC/GFZ, candidate C1 was a model from BGS and candidate D1 was produced by IZMIRAN. For further details on the IGRF-10 candidate models readers should consult Maus et al. (2005).
RMS vector field differences _{ij}R in units of nT/yr between SV candidate models from IGRF-10 for epoch 2007.5, their weighted mean SV-2007.5-G10 and the mean SV between 2005 and 2010 as determined from IGRF-11, using DGRF-2005 and IGRF-2010, SV-2007.5-G11. Note the symmetry about the diagonal, again included as a check on the calculations.
_{i, j}R | SV-2007.5-A3 | SV-2007.5-B1 | SV-2007.5-B2 | SV-2007.5-C1 | SV-2007.5-D1 | SV-2007.5-G10 | SV-2007.5-G11 | |
---|---|---|---|---|---|---|---|---|
SV-2007.5-A3 | 0.0 | 11.1 | 6.7 | 11.8 | 16.9 | 6.0 | 21.9 | |
SV-2007.5-B1 | 11.1 | 0.0 | 12.2 | 17.4 | 19.5 | 11.3 | 21.3 | |
SV-2007.5-B2 | 6.7 | 12.2 | 0.0 | 10.3 | 16.6 | 5.9 | 23.8 | |
SV-2007.5-C1 | 11.8 | 17.4 | 10.3 | 0.0 | 19.1 | 9.4 | 28.4 | |
SV-2007.5-D1 | 16.9 | 19.5 | 16.6 | 19.1 | 0.0 | 12.6 | 20.3 | |
SV-2007.5-G10 | 6.0 | 11.3 | 5.9 | 9.4 | 12.6 | 0.0 | 21.5 | |
SV-2007.5-G11 | 21.9 | 21.3 | 23.8 | 28.4 | 20.3 | 21.5 | 0.0 |
4.2 Analysis of IGRF-11 SV-2010–2015 candidate models
Summary of SV-2010-2015 candidate models submitted to IGRF-11.
Predictive SV candidate models for epoch 2010–2015 | |||||
---|---|---|---|---|---|
Team | Model | Organization | Data | Comments (parent model etc.) | |
A | SV-2010-2015-A | DTU Space / IPGP / NASA-GSFC | Ørsted, CHAMP, SAC-C revised observatory monthly means | Based on CHAOS-3α SV at 2010.0 | |
B | SV-2010-2105-B | NGDC-NOAA / GFZ | CHAMP 2006.5–2009.7 | Based on POMME 6: 2nd order Taylor SV at 2009.7 used. | |
C | SV-2010-2015-C2 | BGS | Ørsted, CHAMP and observatory hourly means | Revised sub: Av. SV 2005.0–2009.0 from parent model used | |
D | SV-2010-2105-D | IZMIRAN | CHAMP 2004.0–2009.25 | Based on linear NOC extrapolated | |
E | SV-2010-2015-E2 | EOST / LPGN / LATMOS / IPGP | Observatory hourly mean used to derive monthly means 1980–1998 | Extrap. gives 1st diff of ann. means 1981–2015: SV models is averaged over last 6 yrs | |
F | SV-2010-2015-F | IPGP / EOST / / LPGN / LATMOS | CHAMP 2008.5–2009.6 | 2nd order Taylor series (to n = 5): used slope at 2009.0. | |
G | SV-2010-2015-G | GFZ | CHAMP 2001-2009.6 Observatory hourly means | Based on GRIMM2: linear fit. SV 2001.0–2009.5, extrapolated to 2012.5. | |
H | SV-2010-2015-H | NASA GSFC / UMBC / Univ. Liverpool | Geodynamo simulation, with assimilation from CALS7K.2, gufm1, CM4, CHAOS-2s |
4.2.1 RMS vector field differences for SV-2010–2015 candidate models
RMS vector field differences _{ij}R in units nT/yr between SV-2010-2015 candidate models and between these and the mean model M and the weighted mean model M_{w} in the rightmost columns. The final row labelled ‘Mean Diff’ is the mean _{i}Open image in new window of the _{ij}R for each candidate or mean model.
_{i, j}R | A | B | C2 | D | E | F | G | H | M | M_{w} | |
---|---|---|---|---|---|---|---|---|---|---|---|
A | 0.0 | 10.0 | 20.2 | 15.9 | 22.2 | 11.4 | 21.0 | 18.1 | 12.8 | 13.8 | |
B | 10.0 | 0.0 | 15.4 | 10.2 | 18.3 | 5.1 | 18.1 | 12.5 | 7.4 | 7.8 | |
C2 | 20.2 | 15.4 | 0.0 | 8.0 | 11.0 | 11.4 | 24.2 | 6.5 | 9.7 | 8.6 | |
D | 15.9 | 10.2 | 8.0 | 0.0 | 12.7 | 6.7 | 18.2 | 4.7 | 4.1 | 3.5 | |
E | 22.2 | 18.3 | 11.0 | 12.7 | 0.0 | 15.3 | 26.3 | 11.6 | 12.9 | 12.6 | |
F | 11.4 | 5.1 | 11.4 | 6.7 | 15.3 | 0.0 | 18.1 | 9.0 | 4.1 | 4.3 | |
G | 21.0 | 18.1 | 24.2 | 18.2 | 26.3 | 18.1 | 0.0 | 20.7 | 16.9 | 17.8 | |
H | 18.1 | 12.5 | 6.5 | 4.7 | 11.6 | 9.0 | 20.7 | 0.0 | 6.6 | 5.7 | |
Mean Diff | 17.0 | 12.8 | 13.8 | 10.9 | 16.8 | 11.0 | 21.0 | 11.9 | 9.3 | 9.3 |
4.2.2 Spectral analysis of SV-2010-2015 candidate models
4.2.3 Spatial analysis of SV-2010–2015 candidate models
We remark that the differences between SV candidates are often most striking at low latitudes; this becomes even more obvious when the models are analyzed at the core-mantle boundary. These differences amount to different predictions concerning the evolution (especially westward drift) of high amplitude flux features that are found at low latitudes at the core-mantle boundary and are responsible for a large amount of the present secular variation. Accurate determination of the evolution of these low latitude features is crucial for accurate SV predictions—it will be of great interest in the upcoming five years to see whether any of the candidates (including H which is based on an approximation of core physics) performs better in this regard than the weighted mean of the candidates M_{w}—it is unfortunately not currently possible to make a prior judgment on this matter.
4.2.4 Discussion and summary for SV-2010-2015
The analyses presented earlier in this section, in both the physical and spectral domains, suggested that candidate E (which may have problems at degrees greater than 5), candidate G (which made predictions for the sectoral harmonic different from other candidates) and candidate A (which possessed anomalous dipole terms) were consistently different from the other candidates. The task force therefore voted to allocated weights of 0.5 to A, E and G with the remaining candidates B, C, D, F, H allocated weights of 1.0 for the construction of final IGRF-11 SV-2010-2015 model. The SV-2010-2015 model for IGRF-11 is thus identical to the model M_{w} discussed previously in this section. We emphasize that in the case of SV models it is much more difficult to be certain that a particular candidate is in error simply because it differs from a mean model, because there are non-random difficulties in field forecasting, and because it is not obvious that a mean model is more likely to be correct. Further study of how best to propagate forward information from accurate MF and SV models at the current epoch is urgently needed.
5. Conclusion
In this article we have described some of the statistical tests carried out by the IGRF-11 task force in order to evaluate candidate models for DGRF-2005, IGRF-2010 and SV-2010–2015. As a result of these tests, the task force voted in December 2009 that DGRF-2005 be composed of an unweighted combination of candidates A, B and G; that IGRF-2010 be composed of candidates A, B, C2, F, G with weight 1.0 and candidates D, E with weight 0.25 with Open image in new window and Open image in new window of candidate A discarded; and that SV-2010–2015 be composed from candidates B, C2, D, F, H with weight 1.0 and candidates A, E and G with weight 0.5, with the Open image in new window and Open image in new window SV predictions of candidate A discarded. The model coefficients for IGRF-11 can be found in electronic form online at http://www.ngdc.noaa.gov/IAGA/vmod/igrf.html and are also published in print in the article by Finlay et al. (2010).
The retrospective MF models submitted for DGRF-2005 were found to largely be in good agreement. Candidates A, B and G, based on parent models from the established series of models CHAOS, POMME and GRIMM, were found to agree particularly well, with the formal RMS vector field error in their mean being only 1.0 nT. This close agreement is a consequence of the advances in main field modelling that have occurred in the past decade, in particular thanks to the availability of high quality satellite data from the CHAMP mission. Differences in the MF models to degree 13 are now primarily due to differences in the data selection and pre-processing strategies employed by the various teams, as well as in their choice of parameterization of external field variations. We note however that it remains possible that minor systematic errors (common to all or many candidates) could remain, for example, due to limitations in common techniques used to account for the external field variations. Improved knowledge of external fields (particularly those originating in ionospheric current systems) can be anticipated from ESA’s multi-satellite constellation mission Swarm (Friis-Christensen et al., 2006) that is expected to be underway before the next IGRF revision in 2015.
Concerning the provisional IGRF model for epoch 2010.0, differences in how teams forward propagated their estimates from mid-2009 to 2010.0, depending on the nature of the time-dependence of their parent models, was an additional source of variation between the candidates. It is clear (see Fig. 13) that accurate determination of predictive SV remains the major challenge in the IGRF process; a noticeable scatter in the submitted candidate models was again present in the IGRF-11 SV candidates and it was not possible to clearly identify one group of candidates that were demonstrably of superior quality. These difficulties were further underlined by retrospective analysis of IGRF-10 SV candidates centered in 2007.5 which differed by 20 to 30 nT/yr from the retrospective IGRF-11 estimate for the same interval. It will be of considerable interest over the next 5 years to discover whether data assimilation methods utilizing approximations of core physics to forward propagate information (see Beggan and Whaler, 2010; Kuang et al., 2010, this issue) are yet at the stage where they can provide better forecasts than the traditional statistical extrapolation strategies.
Notes
Acknowledgments
We thank the institutes responsible for supporting the CHAMP, Ørsted and SAC-C missions for operating the satellites and making the data available. We also thank the national institutes that support ground magnetic observatories and INTER-MAGNET for promoting high standards of practise. Vincent Lesur is thanked for his help in producing Fig. 13. This is IPGP contribution no. 3108.
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