  I provide a construction of intrinsic weakly Ulrich bundles of large rank on
any smooth complete surface in ${\bf P}^3$ over fields of characteristic $p>0$
and also for some classes of surfaces of general type in ${\bf P}^n$. I also
construct intrinsic weakly Ulrich bundles on any Frobenius split variety of
dimension at most three. The bundles constructed here are in fact ACM and
weakly Ulrich bundles and so I call them almost Ulrich bundles. Frobenius split
varieties in dimension three include as special cases: (1) smooth hypersurfaces
in ${\bf P}^4$ of degree at most four, (2) Frobenius split, smooth quintics in
${\bf P}^4$ (3) Frobenius split Calabi-Yau varieties of dimension at most three
(4) Frobenius split (i.e ordinary) abelian varieties of dimension at most
three.
