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Looking at the ashfall distribution map from the 1980 eruption of Mt. St. Helens (below), there is a measured 'patch' of ash depth significant enough to be measured occurring in Oklahoma.

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What caused a measurable patch of Mt. St. Helens' ash to be deposited across Oklahoma?

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I will propose an explanation. From experience I would say it have something to do with the US meteorological systems (systems as in masses of air) active the 18th of May 1980 and the week(s) after.

A bit of background : air masses can be high pressure (cool, and stable) or low pressure (warmer, more energy, more volatile, less stable). The next figure show in red a low unstable and warm system, and in blue a cool, stable system. (full website here)

air-systems

Further, let's take into account the meteorological nature of Oklahoma - as an area in a volatile sector, where warm wet air masses from the gulf collide with colder, dryer masses from the west and the north - area part of what is broadly know as the tornado alley. On the wiki page for OK we see a typical system condition favorable for volatile weather. Green masses are warm, blue are cold and red is where the action is likely to occur.

Tornado Alley

Tornado or other frequent wild weather events are the result of a clash between those widely different air masses, temperature, moisture and pressures often leading to storm cells or other unpleasant windy/stormy situations.

Now let's get back to our volcano. I found those daily meteorological maps from the NOAA. When entering the proper dates, let's say 18th of May 1980 and the week after, we see the various systems in action. To keep things simple, I picked the 18th of May, and the 21st.

18thofmay1980

The 18th of May there was a low pressure system about right over the volcano - which was ideal to transport and displace a lot of ashes very far. The 20th, at 7:00 am, there was a Low in formation over Oklahoma which would become full fledged the 21st (see figure) and there was bad weather that day over Oklahoma City because of clashing cell. Eventually causing precipitation (rain and ash?).

21thofmay1980

I am not a climate-meteo-specialist, but I have good confidence that this scenario could explain a part of the reason why there is ash in Oklahoma.

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    $\begingroup$ Sounded very logical to me. One of the best answers I've seen. $\endgroup$
    – JeopardyTempest
    Commented Sep 30, 2021 at 5:08
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    $\begingroup$ The split flow in the latter maps certainly shows why it went both east and southeast. Though the rainfall maps from the weather maps are a little less square than I'd have through, over a lot of the region that wasn't in the dust map they gave. And the GOES satellite animation at youtube.com/watch?v=AMxLBWAetfY (unfortunately with many gaps) hints maybe it was a bit more that a leading burst that got higher in the atmosphere and so descended in a different area than the rest... but guess that's science, even the best reasoning sometimes doesn't pan out, but your answer was great $\endgroup$
    – JeopardyTempest
    Commented Sep 30, 2021 at 5:14
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    $\begingroup$ Great animation: we see already the lows (clouds) in the animation same as in the pressure maps. And also that things are moving quite fast, each hour ash is moving east and reach OK already the 19th. $\endgroup$
    – marsisalie
    Commented Oct 2, 2021 at 19:59
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    $\begingroup$ Yeah I certainly was surprised by how quickly it progressed, I figured it might have been many days. But I guess jet stream speeds over 100 mph can move things along quite quickly. $\endgroup$
    – JeopardyTempest
    Commented Oct 3, 2021 at 4:08

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