Originally complied for 1868-1967 and subsequently continued so that it now covers 150 years, the $aa$ index has become a vital resource for studying space climate change. However, there have been debates about the inter-calibration of data from the different stations. In addition, the effects of secular change in the geomagnetic field have not previously been allowed for. As a result, the components of the classical $aa$ index for the southern and northern hemispheres ($aa_S$ and $aa_N$) have drifted apart. We here separately correct both $aa_S$ and $aa_N$ for both these effects using the same method as used to generate the classic $aa$ values but allowing ${delta}$, the minimum angular separation of each station from a nominal auroral oval, to vary as calculated using the IGRF-12 and gufm1 models of the intrinsic geomagnetic field. Our approach is to correct the quantized aK-values for each station, originally scaled on the assumption that ${delta}$ values are constant, with time-dependent scale factors that allow for the drift in ${delta}$. This requires revisiting the intercalibration of successive stations used in making the $aa_S$ and $aa_N$ composites. These intercalibrations are defined using independent data and daily averages from 11 years before and after each station change and it is shown that they depend on the time of year. This procedure produces new homogenized hemispheric aa indices, $aa_{HS}$ and $aa_{HN}$, which show centennial-scale changes that are in very close agreement. Calibration problems with the classic $aa$ index are shown to have arisen from drifts in ${delta}$ combined with simpler corrections which gave an incorrect temporal variation and underestimate the rise in $aa$ during the 20th century by about 15%.
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