Doppler radar cannot 'see' a tornado within a thunderstorm cluster. The radar instead detects winds which are blowing toward the radar site and winds blowing away from the radar site. These opposing winds may represent a developing tornado on the radar screen and sometimes a tornado warning is issued. This is the main reason why we depend so heavily upon storm chasers and other Skywarn spotters when determining whether or not there is an actual tornado cloud.
These 'radar indicated tornadoes' rarely actually develop into true funnel clouds and/or tornadoes. The vast majority of tornado warnings which are issued never actually verify. This is why there is such a high percentage of "false alarms" from the National Weather Serice. Ken Barlow, KARE 11.