Elevation measures

The 245 doesn't have a barometer.  It uses GPS to track your route and then calculates elevation using geographical surveys.  Garmin states their GPS is within 3M (10 feet) 95% of the time.  I suspect this is standing still in perfect conditions.  Movement, weather and available satellites and their location will affect this track.  Therefore, your track may have you running next to a hill when you're actually ascending or descending that hill.  If ascent and descent is important to you, get a watch that has a barometer which will detect those elevation changes more precisely even if the GPS plot is off.

Can 245 measure acent and descent using only GPS, does it have that option in general. I've seen some other watches have ascent and descent measurements using only GPS,but I like Garmin. I see that the Garmin vivoactive 4 has a barometer, but what is it for running ?

I don't own a 245.  I had a 235 which didn't have a barometer either and elevation gain/loss was based of the GPS geographical surveys.  Using a watch with a barometer is much better at collecting this data.  The Vivo series do have barometers, but the lack a lot of running features.  If you want a watch with all the running features that will measure ascent/descent more precisely, I recommend the 945, 935 or 645.  The latter two are older models, but will fit your needs.  The 935 is the oldest, but you'll find many that will say it's the best watch Garmin ever released.  I use a 945 now and my 935 as a back-up.

Thank you !

Today I tested the 245 in a route with descent hills: 15km with 285m of ascent. Then compared to previous results of my Suunto 9 (with barometer which works as an altimeter) and I have to say that there is an almost perfect match.  The test was in Madrid at around 700m altitude.  

I will test again in higher altitudes and in more remote areas to see if it is still a good match.  

So. The 245 is a great one with its GPS.