«If we know the wave field, we can identify immediately what would be the critical length scale that one has to observe, and then identify spatial regions with high probability for a rare event,» Sapsis says. (sciencedaily.com)
The «velocity» therefore has to be an average taken over some defined spatial region and interval of time, and to get a smooth function we can work with we have to blur the scale a little and obtain a statistical distribution. (planet3.org)