My first tornado was one I did not chase. I was an undergraduate at the University of Iowa on 13 April 2006 when an F2 went right through the middle of town after dark on an exceptionally hot and humid day for early-mid April in Iowa. The event seemed to go on for a long time, too, since this was actually part of a small outbreak across C/E IA and into N IL, with several closely spaced tornadic supercells (one hit near my parents' house in Marion, IA, also).
I still remember watching the storm come in while standing out in the open near the Iowa River as it goes through campus near my dorm (I had no idea how to read clouds, so to me it was a nebulous, ominous mess).
Then I remember hearing the sirens go off, still well before the tornado struck, as I had KCRG-TV9 out of Cedar Rapids now wall-to-wall about all of the storms (not just the Iowa City one) and had some idea something bad was coming.
Then I remember the hail storm that preceded the tornado. Heavy golf balls. I stood in one of the foyers of my dorm building with the doors open watching the hail crack down. Stones were bouncing off the pavement and through the door, piling up in the foyer. Kinda funny watching students outside scrambling to run for cover.
What has been particularly indelible for me was the feeling in the air after the hail abated. It was dead quiet and still warm and humid, something that really perked me up (even in my ignorance in those days I still knew enough that something was up when a heavy precip core was not followed by a cool sensation). That's when I walked outside the other end of the building and onto a parking garage that sat on the side of the hill by my dorm (right next to the river, too).
That's when I saw it, illuminated only by lightning (frequently enough). I was totally mesmerized. Someone else had walked out with me to that same spot, but took off at some point while I was gawking. I could tell it was kind of moving towards me, but not directly. I figured in my head I needed about 30 seconds to run for the door to the dorm for cover if it threatened me, but alas it did not.
I watched it tear through campus and through downtown (the campus of U of I basically is fused with part of downtown Iowa City). I remember the sounds of debris crashing into stuff against downtown buildings. From eight blocks north of it at closest, it was a sound I had never heard before.
A few minutes after I was sure it had exited town, I raced up a set of metal stairs that served as an external fire escape for the next dorm building over and watched it rope out east of town (there was little cloud material between me and the tornado at that time). Normally, such an action would be severely frowned upon, but by this time people were now milling about, some combination of confused and excited, so I wasn't worried about getting in trouble.
I think a lot of people were still unaware that more storms were behind this first one. The sirens went off again less than an hour later as another, briefly tornadic supercell skirted just north of town. I remember seeing what I now know was the inside of the RFD clear slot, but at the time just seemed very eerie. I could not see below the trees to determine a tornado, but there very well may have been. Later still I remember looking over the river to the northwest and seeing a plume of something (smoke, vapor, I'll never know) angled off to the right several miles away. It was directly in front of another heavy precip core with frequent lightning, so at the time I thought it might be another tornado. Someone else mentioned it could have been a smoke plume from something struck by lightning.
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My first tornado while chasing is a bit more nebulous. I kind of saw things happening in Kearney, NE when it was getting hit on 29 May 2008, but I never saw the tornado itself, just some power flashes. However, I definitely saw the tornado that TWISTEX got a direct media probe hit on later that evening near Tipton, KS. That is likely my first official "chased" tornado. Thanks to
@Tony Laubach I still have a copy of the video from that hit!