  We prove that on a compact almost Hermitian 4-manifold the space of
$\bar\partial$-harmonic $(1,1)$-forms always has dimension
$h_{\bar\partial}^{1,1} = b_- +1$ or $b_-$, whilst the space of Bott-Chern
harmonic $(1,1)$-forms always has dimension $h_{BC}^{1,1} = b_- +1$. We also
perform calculations of $h^{2,1}_{BC}$ and $h^{1,2}_{BC}$ on the
Kodaira-Thurston manifold, thereby providing a full account of when
$h^{p,q}_{BC}$ is or is not invariant of the choice of almost Hermitian metric.
Finally, we introduce a decomposition of the space of $L^2$ functions on all
torus bundles over $S^1$, which has proven useful for solving linear PDEs, and
we demonstrate its use in the calculation of $h^{p,q}_{\bar\partial}$.
