"Based on" vs. "based upon"

Usage note from Thefreedictionary:

In their uses to indicate spatial relations, on and upon are often interchangeable.

It was resting on (or upon) two supports.
We saw a finch light on (or upon) a bough.

To indicate a relation between two things, however, instead of between an action and an end point, upon cannot always be used.

Hand me the book on (not upon) the table.
It was the only town on (not upon) the main line.

Similarly, upon cannot always be used in place of on when the relation is not spatial.

He wrote a book on (not upon) alchemy.
She will be here on (not upon) Tuesday.

on, not upon.

Based upon might have been used in the past.

(src: Google nGrams)

Should I use on or upon in the following sentence?

I remembered the story years later when I investigated the incident it was based on.

In this particular case, it makes no real difference. And if you’re one of those who feels that whenever you have the choice of two words of unequal lengths, indistinguishable in meaning, that you should always select the shorter of the two, then the choice is clear.

Others have noted that despite claims that on and upon are completely interchangeable, that there many places where you cannot use upon at all. It turns out there are also a few places where the reverse is true, that you cannot use on and must upon.

One such place is with phrasal verbs involving upon; there are also several non-verbal formulaic constructs associated with upon. Here are some of them:

• to come upon

  • 1827     Scott Tales of Grandfather 1st Ser. viii,     To come upon him suddenly and by night.
  • 1832     Tennyson Lady of Shalott iii, in Poems (new ed.) 15     ‘The curse is come upon me,’ cried The Lady of Shalott.
  • 1886     J. McCarthy & R. C. Praed Right Hon'ble III. xxviii. 39     It came upon her now that something subtler‥lay at the root.
  • 1850     Tait's Edinb. Mag. Dec. 725/2     They might come upon me afterward, and make me pay up.
  • 1820     Examiner No. 637. 414/2     She came upon us by surprise.
  • 1849     T*ait's Edinb. Mag.* 16 154/1     The travellers soon came upon a village.
  • 1865     J. W. Carlyle Lett. III. 256,     I came upon Geraldine in Cheyne Row.

• to fall upon

  • 1858     E. H. Sears Athanasia III. v. 297     The church‥had fallen upon the belief that he [Christ] was soon to appear again.
  • Also, to fall upon the enemy is not the same as to fall on the enemy.

• to set upon (to attack, assail, fall violently upon)

  • 1875     Jowett Plato (ed. 2) I. 356     This is the reason why my three accusers..have set upon me.

• to stand upon

  • 1854     Poultry Chron. 2 206     ‘Faint heart ne'er won fair lady’ is a good motto to stand upon.
  • 1828     E. Bulwer-Lytton Pelham III. xii. 209     Lady Glanville was a woman of the good old school, and stood somewhat upon forms and ceremonies.
  • 1889     ‘M. Gray’ Reproach of Annesley I. ii. i. 145     You stand upon a fanciful punctilio.
  • 1889     F. Barrett Under Strange Mask II. x. 2     We were real friends, and only stood upon ceremony in our business relations.

• to feel put-upon by an imposition

  • 1996     Daily Express 1 Mar. 47/5     Dolores is revealed‥as a put-upon drudge who slaved for her employer.
  • 2005     Observer 18 Sept. i. 23/3     Wallace's‥poor put-upon dog, Gromit.

• upon a wind (a nautical term)

  • 1810     Scott Let. 18 Mar. (1932) II. 313,     I would‥endeavour to go as the sailors express it upon a wind i.e. make use of it to carry me my own way.
  • 1846     H. Raikes Life Sir J. Brenton 328     Every ship‥made all the sail she could carry upon a wind.

• once upon (a time)

  • 1854     Poe The Raven     Once upon a midnight dreary, while I pondered, weak and weary,
  • Once upon a time, there lived ...
  • Once upon an autumn eve, a wounded knight named Sieur Luc ...