"Whereäs" as an alternative spelling of "whereas"

Wiktionary shows whereäs as a valid alternative spelling of the word whereas (see here).

It gives the following quotations to illustrate the usage:

1 Permanent International Association of Navigation Congresses, Report of Proceedings — Milan (1905)

After a dry season, the influence of heavy rains becomes manifest more quickly and more progressively in the less wooded basin, whereäs the reverse is found in the basin which has a larger forest area.

2 Friedrich-Schiller-Universität Jena, Wissenschaftliche Zeitschrift (1984)

Notice that since the range of χ is limited by (5), whereäs that of x is unlimited, the transformation (6) does not cover the whole of the space-time represented by (1).

3 Hiroyuki Sonoki et alii, Heart and Vessels — Nipradilol, a new β-adrenergic blocker, reduces left ventricular remodeling following myocardial infarction in spontaneously hypertensive rats (1997)

...after MI, whereäs propranolol promotes it.

That was the only dictionary where I found the word (with that spelling) though. And a Google search for whereäs returns only 209 pages.

Is that really a valid spelling of the word whereas? If yes, where did it come from?

English occasionally uses a trema (the two-dot diacritical mark over the "a" in whereäs) to signify diaeresis. Diaeresis means that a vowel combination that normally would form a digraph is instead pronounced as two separate vowels. In the case of "whereäs", the additional trema gives us the familiar where-as pronunciation, rather than were-ease which would be suggested by the "ea" digraph.

Like so many aspects of English, usage of trema disappears as the original word becomes so commonly used that the diaeresis is understood. Thus whereas is now the typical spelling, rendering whereäs extremely uncommon, as you discovered.

The canonical example of an English word which includes a trema in the "standard" spelling is naïve.

Even a century ago, it seems that the diaeresis wasn't necessarily favoured. For what it's worth, in his "Modern English Usage" (late 1920s), Fowler has this to say:

There are three ways of writing cooperate (coop-, co-op-, coöp-). The diaeresis should at once be rejected as possible only in some words (those in which co- is followed by a vowel), whereas the hyphen is possible in all. Next it should be recognised that hyphens in the middle of words are no ornament, & admittance should be refused to all that cannot prove their usefulness.

He then goes on to give a list of a small number of words beginning with co- with his "recommended" spellings. In some cases he advocates a hyphen and no case does he recommend the diaeresis. He writes e.g. coordinate, coopt with neither hyphen nor diaeresis, the argument being that they are "so common or so analysable at a glance that the hyphen, though sometimes used, is entirely superfluous".

In other words, as of 100 years ago, inasmuch as we can take Fowler's opinion as being representative of "prescriptive opinion" (and with the caveat that in some cases his opinion wasn't very representative), it doesn't seem as though there was much of a consensual rule in favour of the diaeresis, but possibly even the opposite.

The dieresis (two dots over a vowel) is used to distinguish pronunciation when two vowels together might be blended into a single phoneme, as in cooperate / coöperate. Theoretically it can be used in any such instance, but in practice it is rarely seen and has an archaic feel to it.