Advances in techniques of data assimilation in meteorology and oceanography and continuing improvements in the scope and reliability of numerical simulations of motions in atmospheres and oceans and other rotating fluid systems offer opportunities for experimenting with novel diagnostic schemes for elucidating basic dynamical processes. Here attention is drawn to the likely diagnostic value of determinations of the fields of certain pseudoscalar quantities, namely helicity, superhelicity and weighted relative potential vorticity. Copyright © 2002 Royal Meteorological Society.