StoredProcedureQuery spq = ...;
spq.registerStoredProcedureParameter( 1, Calendar.class, ParameterMode.IN );
spq.setParameter( 1, aGregorianCalendar, TemporalType.DATE ); 

Started a discussion on the dev mailing list about whether it makes sense to leverage Statement#setDate(int,Date,Calendar) e.g. in such cases to leverage TZ. That may not be what the user intended is my concern.