Restricciones sobre las generalizaciones Para modelar una empresa más exactamente, el diseña-

In our study of the comprehensive model (CM4) as a model for predicting the magnetic observatory data (chapter 3), we find that the CM4 model is predicting the daily variation of the parameterized fields during quiet periods, outside the timespan of the CM4 model. The profile plots obtained using the CM4 model (section 3.3.1) comparing the model and the observatory data reflects the Sq diurnal variations expected for the different geographical regions and latitudes. Away from quiet time, despite the lack of active data in the original CM4 model dataset, we find the CM4 model predicting the regional type features of the observatory data. It is in predicting the short term features of the rapid variations that the model is not doing well in its prediction (figures 3.7-3.12). This is particularly more evident in the X component where we see the greatest misfit between the CM4 model and the observatory data. This is in part because Dst is not parameterized for short-time variation.

The comparison of the modelled diurnal maps of the CM4 model and the observatory data shows that increasing the spherical harmonic degree decreases the residuals and reduces the misfit of the CM4 model to the observatory data i.e. the CM4 model appears to do reasonably well in predicting the diurnal field (away from quiet time) as we move to higher degree of harmonics. This produces a

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better coherence and close match between the CM4 model and observatory data (figures 3.13- 3.17). This is instructive as it shows that as we move from lower to higher harmonic degree, more small scale features are revealed and the similarity between the CM4 model and the observatory data is seen in the comparison.

This motivates delving into the nature of the signals that we are seeing, particularly in the X component, since this may be the reason for the misfit between the CM4 model and the observatory data comparison. In order to identify the nature of the rapid variation, we investigated its relationship with the external fields using the RC index. This becomes necessary as our results show that the external field descriptions included in the CM4 model (F10.7 and 𝐷𝑠𝑡) could not sufficiently

explain the field contributions for days away from quiet time. 𝐷𝑠𝑡 as a global index measuring the

disturbances in the magnetic field, and describing the time-space structure of the magnetospheric ring current, does not provide a high enough time resolution. As a result the CM4 model is hampered in its bid to fully describe the external field variations for days away from quiet time. So we deemed it advantageous to make use of the new RC index which provides a higher time resolution and may not suffer from baseline instabilities like the 𝐷𝑠𝑡 index, in order to investigate the

rapid variation nature of the property seen in the X component of our data.

Our observatory data show coherent structure that is essentially Sq diurnal variation, with most of the observatory locations, particularly the European ones, showing very strong coherence between the same components of the field at different observatory locations. When comparing individual days against the comprehensive model, they show deviations of two kinds: long period variations that show variations between days of slowly varying feature, and more rapid variations, particularly for the data for days away from quiet time.

Using eigenanalysis and detrending the data sequences with spline fits, we compared these against the RC index. When comparing the observatory data residuals with the RC index we find that the RC index residual is doing a reasonably good job fitting the time variations. Taking the ionosphere/magnetosphere stated from CM4 away from the observatory data, the ionosphere clearly does a good job of removal (section 4.5.5). There are definitely coherent features showing up in the rapid variation, not only for the single observatory locations, but also seen in the combined observatory locations (i.e. between Niemegk and Mbour, and Budkov and Bangui in figure 4.13 and 4.14 respectively). In this comparison, we only considered the X component residuals against the RC index, because it is the component that is most easily influenced by the external field sources of ionospheric and magnetospheric origin. The different results show clearly that external influences dominate the observatory data residual variations for days away from quiet time.

In trying to establish the nature of these rapid variations for days away from quiet time seen in our noisier data, and to see how well we can understand them, we tried to establish the link between the RC index and the rapid variations observed. Are they related to the ring current effect (in which case such variations would be fully explainable by the RC index)? Or are they related to changes in the pattern of Sq – slightly different structure for S_not_so_q?

Looking at the coherence and correlation between small scale features, and trying to establish whether these coherence and correlation between the components of the observatory data residuals and the RC index have a global spread, we took the path of a simple running average of one hour, then the difference between the running average and what is left (chapter 5). We clearly observe that there is a general coherence and agreement between the RC index and the residuals of

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the X component of the observatory data. This coherence and agreement is seen in observatory locations in all the geographical regions of the globe. This suggests a global phenomenon. This trend is replicated in all the different field contributions, for both raw data and when the ionospheric/magnetospheric fields are corrected with CM4 model. However, this was not the case for the Y and Z components of the field. Here there are no clear trends, as they show a mixture of low correlation/coherence and anti-correlation against the RC index. But the Z component shows more correlation and coherence with the RC index than the Y component. This lack of substantial agreement/coherence between the Y and Z components and the RC index show the clear lack of influence of the external field variations of ionospheric and magnetospheric origins compared to the X component.

Looking at observatory locations which show strong equatorial electrojet (EEJ) influences e.g. Huancayo observatory, we observe some coherence in the Y and Z components unlike what obtains in other observatory locations. Here the coherence/agreement between the Z component and the RC index is almost as good as that of the X component against the RC index.

To substantiate the level of coherence and correlation or lack of it observed in the profile plots comparison between the observatory data residuals and RC index, we looked at the cross- correlation coefficients for the different observatory components with RC index. The cross- correlation coefficient between the X component residuals of the observatory locations and the RC index is generally higher in almost all the observatory locations in all geographical regions of the globe, ranging from 0.70-0.85 (section 5.4.1), confirming the strong coherence between the X component and the RC index seen in our correlation comparison profile plots. For the Y and Z components, the cross-correlation coefficients show that these components are not generally well correlated with the RC index, having cross-correlation coefficients ranging from -0.55-0.50 in most observatory locations. However, some exceptional cases are seen in the cross-correlation coefficients in the Z component, which confirms the earlier suggestion that the Z component has a better coherence with RC index than the Y component. Here we recorded cross-correlation coefficient as high as 0.70 in the Z component with RC index for some observatory locations (HUA, VSS, and KAK) (table 5.1).

In addition, we also investigated the correlation between the X component residuals between the different observatory locations, both within the same geographical locations, and situated at different geographical locations. The profile plots show strong coherence and correlation between the X components of the field at different observatory stations within the same geographical location. This is confirmed in the cross-correlation coefficients with values ranging from 0.80-0.95. This is also seen in some of the cross-correlation coefficients across different geographical regions, except those between North America and those of South America and Oceania observatory stations, i.e. VSS and DLR, GNA and DLR, etc. (section 5.4.2).

The comparison of the RC index and the observatory residual components for both single and combined observatory locations characterise the RC index as a good representation of most of the observatory stations for rapid variations, particularly for the X component. This tells us that the rapid variations we see in our observatory data, showing Sq diurnal variation, for days away from quiet time are coming from a large scale source (magnetospheric ring current). Therefore, corrections for exploration activities conducted during disturbed times maybe considered to be global, particularly

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for X component. Also, looking at rapid variation observatory data results for combined locations (more than one base station) might be a good remote referencing technique.