Effective divisors in the projectivized Hodge bundle

We compute the class of the closure of the locus of canonical divisors in the projectivization of the Hodge bundle $\mathbb{P}{\bar{\mathcal{H}}}_g$ over ${\bar{\mathcal{M}}}_g$ which have a zero at a Weierstrass point. We also show that the strata of canonical and bicanonical divisors with a double zero span extremal rays of the respective pseudoeffective cones.