visibility Visibility Questions

[Hazed]

Hello everybody!
I'm a new member of the netweather forum; interested in a number of, perhaps, niche metrological effects, as part of a project with my son who is studying engineering.

The viewing site is an Etang in Southern France (a sea water lake).
Depending upon the forecaster, for the 3 experiments, visibility was stated as being 15km or 35km.

The first trip went well, and we witnessed reflection in what we believe to be, a temperature layer in the atmosphere.

We called this image 'The Floating House'

If you draw a horizontal line through the windows, you will see that the lower half is a reflection of the upper half.

However, our scope was not excellent.
Consequently, the scope was improved.

The second trip also went well, with greatly improved images.

This one is the Petanque Club

(note - the obstacles beneath the club are mussel posts in the etang)

Here it is from google-earth:

Geodetic surveying methodology tells us that refraction occurs according primarily to temperature gradient.
We judged that the mural of the tree was stretched, and of course we have the appearance of the houses towering above the club house (around 1km distant), which we believe are also slightly stretched.

While this seems to merely confirm geodetic methodology ... we had gained a great subject for further studies during Uni holidays
... and what a great subject for 'father & son' common endeavour (rather than being a freebie hotel hahaha!)
... and there was the unanswered question concerning temperature layer reflection.

You can imagine the pleasure to be gained from working together, rather than drifting apart...
So I bit the bullet, and redesigned the scope, in preparation for the next holiday, bumping it up to 90mm, damping the resonance, and adding baffles and flocking (to control stray light).

What a job
... but it was a succesful build.
Only that the holidays were upon us ... so options for the 3rd trip were limited (lots of bad weather predicted).

Saturday 29th was forecast to be variable cloud cover (cloud and sun), but with a rising temperature gradient from around 10 deg climbing to 15 deg, with visibility listed as 15km or 35km depending upon the forecaster.
... that was the same prediction as the two previous visits.

We figured that the light might not be great, but hey ... we'd see what we would see
... and with more than double the scope light aperture, we should be fine.

We arose at 4.45am, to get to the site in time for first light and sunrise, hoping to capture the images of the buildings stretching upwards, as the temperature increased.

Ha!
We may as well have stayed in bed.
There was a band of white cloud (from the ground up), above which could be seen blue sky (when the higher clouds broke).

Sorry ... I should have photographed the sky.
I didn't think to do this, until we got back, when I began thinking about weather forecasting.

I don't know whether this was haze or an inversion.
Either way, we could not gain focus ... it was all a shimmering blur.
We stuck it out till 1.00pm and then chucked in the towel.

Here are the 3 weather pages from DarkSky.net

Dark Sky - Friday, Nov 1st, 2019

DARKSKY.NET

Dark Sky - Sunday, Dec 29th, 2019

DARKSKY.NET

Dark Sky - Saturday, Feb 29th, 2020

DARKSKY.NET

The problem is the visibility forecast.
It seems to be meaningless (and other sites had visibilty at 35km!).

Is there any way to predict good visibilty?
... because, we need to set off in the dark
... and it is a major event, pulling everything together
... and the next day must be written off to physical recovery (wiped out )

We could really benefit from some advice