Welcome to the Forums!
First off, thanks for being a HAM volunteer if your club supports the community. What HAM operators do during disasters is a godsend for the communities you support,
so thank you!
Sadly, the answer is, it depends. The
FAQ section probably has all the information you want, but here are some quick thoughts.
A 12V battery with 100 ah, is 1200 watt-hours.
You won't want to run the battery below 90% (80% to be safe), so you really only have ~960 Wh available.
Say 95% efficient on the charger and 95% efficient on the battery and a 1200 Wh battery needs 1200 / .95 / .95 ~= 1330 Wh to fully recharge. Or if you're only running to 80% then 1064 Wh to fully charge it. The efficiencies are just examples, plug in your actual numbers for better values.
IF 100 ah battery can run the repeater for 30 hours, then the repeater is consuming 1200 Wh / 30h = ~40 watts.
Now for the part you're not going to like. Sunshine is highly variable day to day, you never know what you're going to get.
If the insolation is 6 (average long summer day) then a 400W panel will generate 400 x 6 = 2400 Wh/d.
If it's a average winter day the insolation might be 3.0, in which case a 400W solar panel will generate 1200 Wh/d.
Panels are pretty good even during moderately cloudy weather, but on dark gloomy days it's possible to get nothing from them.
Don't forget that the repeater will run off solar during the day normally, so the battery only operates at night (and when a cloud floats over), which means the battery will last longer than 30 hours. If there's enough sun it might never run out.
Does the repeater only get deployed during a disaster?
If so, then something else to think about is 400W panels are heavy and easier to break just because they're bulky. For a deployment use-case you might find light-weight panels (say two
9 lb 200 watt panels) are far easier to handle, practically indestructible and far easier to transport. If you can, get the latest generation flexible solar panels with 25 year warranties. Well, actually, since your use-case might not have them in the sun day-in/day-out, you can probably go with the cheap ones. If you need super-rugged flexible panels that can survive being shot (possibly tree branch penetration), you want CIG panels.
If it sits year round in one spot a rigid panel is fine... but if the battery is subject to freezing it might need to be in a heated space, have a safety shut off (more common in BMSes these days), or buried below the frost line so it won't get too cold. Lithium batteries can die the first time they are charged below zero.
Hope that helps!