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Baumjohann & Kamide 1984
Baumjohann, W. and Kamide, Y. (1984). Hemispherical Joule heating and the AE indices. Journal of Geophysical Research 89: doi: 10.1029/JA089iA01p00383. issn: 0148-0227.

A linear regression analysis of Joule energy deposition rates integrated over the northern hemisphere as a function of the standard auroral elecctrojet indices yields a correlation coefficient of r=0.7--0.9. Except for very disturbed times, when the A(E)12) index tends to underestimate the electrojet current, the hemispherical Joule heating rate can be calculated by substituting 1 nT in the AE index by approximately 0.3 GW. This scale factor is appreciably larger than those employed in earlier energy coupling studies. A higher-scale factor is found for the regression between Joule heating caused by eastward current versus AU than for that caused by the westward electrojet versus AL. This is consistent with typically lower ionospheric conductivity values in the eastward electrojet region which require higher electric fields and thus more Joule heating for a given eastward current or AU value than for the same intensity of the westward electrojet.

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Journal
Journal of Geophysical Research
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American Geophysical Union
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