There is no mystery about the 'required additional information'.

The nearest the so-called SWR meter ever gets to measuring anything is
the "magnitude of the reflection coefficient", MRC, which arises due
to the impedance of whatever is presented to the meter's output
terminals. (Recall, this impedance is the 4th variable arm of the
meter's RF resistance bridge.)

This impedance can have an angle anywhere between 90 and -90 degrees.
And the MRC can have an angle in any of the 4 quadrants, ie., anywhere
between 0 and 360 degrees.

But the meter is capable of indicating ONLY the MRC. All the angle
information is lost and gone forever. This is equivalent to losing
information about the location along the line of the peaks and troughs
in the standing wave. That is, of course, if a long line extending
back from the input of the meter to the transmitter actually exists.

Now, if the line with standing wave exists, the magnitude of the SWR
can be calculated from -

SWR = (1 + MRC) / (1 - MRC)

or the meter scale can be calibrated in terms of SWR.

It is frequently thought the SWR can be used to calculate the power
lost in the line. But, particularly when the the line is less than
1/4-wavelength long, this is not so. It requires the location of peaks
and troughs to be known - which they are not.

It is also thought that by rearranging the equation it is possible to
calculate the reflection coefficient from the indicated SWR. Wrong
again - can't be done, and in any case the reflection coefficient is
useless without an angle.

So the indicated SWR is not of much use except to provide a topic of
conversation. On the other hand, just by recalibrating the meter
scale, you can have a valuable, indispensible TLI.

By the way, I hear Californian wine makers have been hijacking the
names of French grape-growing districts and have been obliged to
re-calibrate their bottles. Ah well, back to the Chilian stuff.
----
Reg.