The answer to this question will surprise you as well. The answer is: Lots more. Well, this, assuming you want to store enough energy to be reasonably self-sufficient during weather events.
The shape of a perfect solar energy day approximates an inverted parabola. The integral of an inverted parabola is the energy you produce. This turns out to be 2/3 of the enclosing rectangle. The height of that enclosing rectangle would be the constant peak power output (think of a nuclear power plant, which is constant power).
Not too long ago, we had a period of about four months of fairly consistent mid to heavy rain. That meant heavy cloud cover even when it wasn't raining. If you want to plan for such events and perhaps, assume you might have to deal with the grid going down due to emergencies, you'll need a massive amount of batteries to store the energy. If you depend on an electric car for transportation it's even worse.
I installed a 13 kW system. That was nearly five years ago. In other words, I have years of looking at this data and navigating various hypothetical and real scenarios. My conclusion is that I would need to triple my system and have somewhere beyond 300 kWh of storage if I wanted to be self-sufficient enough for a two week event without grid power, particularly with electric vehicles.
I'm in CA, so a two week outage, while definitely black swan, is just one earthquake away. During the Northridge quake (I lived less than a mile from the epicenter then) we were without power for three days.
Anyhow, I like having solar. I just wish the people pushing it as the solution to the problems of the universe would understand the difference between solar reality and fantasy. Most of my neighbors were sold these small arrays (3 to 5 kW), have expensive leases and are in absolute pain right now as rates have more than doubled and the solar array turns out to be far from an idealized power source.