  Central WENO reconstruction procedures have shown very good performances in
finite volume and finite difference schemes for hyperbolic conservation and
balance laws in one and more space dimensions, on different types of meshes.
Their most recent formulations include WENOZ-type nonlinear weights, but in
this context a thorough analysis of the global smoothness indicator $\tau$ is
still lacking.
  In this work we first prove results on the asymptotic expansion of one- and
multi-dimensional Jiang-Shu smoothness indicators that are useful for the
rigorous design of a CWENOZ schemes, also beyond those considered in this
paper. Next, we introduce the optimal definition of $\tau$ for the
one-dimensional CWENOZ schemes and for one example of two-dimensional CWENOZ
reconstruction.
  Numerical experiments of one and two dimensional test problems show the
correctness of the analysis and the good performance of the new schemes.
