When a weather forecast goes up on the web, or out over the radio or tv, it represents considerable effort by human forecasters. They've spent hours poring over various weather models, applying their knowledge of how weather works to determine which model, or perhaps combination of models, they trust most to properly represent how the weather will develop over the hours and days to come. Because of the chaotic nature of weather, these models are re-run every six hours (or sometimes even more frequently), so the forecast is tweaked and adjusted on that same schedule, just to be sure that it is based on the most up-to-date information.
Computer weather models are loaded with some of the most complex mathematical equations that have been developed in science. Just a small sampling of these give us best estimates of how air flows, how moisture condenses into clouds and precipitation, how heat radiates and is transferred between parts of the atmosphere, and even how the atmosphere interacts with the land and with the oceans. The models take the information they're given, sections off the atmosphere into 'blocks' and moves those blocks around, having them interact with each other to produce a forecast of where those blocks will be in the future. However, no matter how powerful the computers that run these models get - even if we actually achieve practical quantum computing - there is still one aspect of all of this that will always limit the ability of computers to forecast weather.
The aspects of Autor's study - creativity and common sense - certainly play a part. Humans definitely add these two factors to any forecast, as they are what enables us to make the right judgments about the computer model results. However, the issue goes back further than that, to a much more fundamental level, and it involves exactly how small those 'blocks' can get, and thus how fine the resolution of the models can get.
This limits the ability of computer models even now, and it will continue to limit their performance going forward.
The issue is that we will never, ever be able to gather enough information about the atmosphere to make those 'blocks' small enough to get an accurate enough forecast. To accurately represent the atmosphere at any point in time, and be able to model how conditions will change over time, we would need to gather basic data (temperature, humidity, wind speed & direction) for every point in the atmosphere, from the ground up to the point where it phases with the solar wind, and ranging down to the very smallest scales, and from all the way around the planet, all at the same time. That's not even counting the fact that the motion of every living creature, every plant or tree branch swaying in the wind, every vehicle on the ground and in the air, and the motions of waves and vessels travelling on those waves, has an effect (however tiny) on how the atmosphere behaves. Factor in cloud cover, dust and particles in the air, and patterns of heat in the ocean, and the problem becomes even more complicated.
Consider just one small storm cloud, containing roughly a billion litres worth of water droplets. All those droplets are swirling around on the winds, merging to form raindrops that eventually fall to the ground when they become large enough that gravity 'pulls' it to the ground, all the while exchanging electrons with each other to produce charge differences that spark lightning flashes, and some even swirling around to freeze and grow bigger to produce hail. Try taking a snapshot of all that, at exactly one moment, and account for the size, position, speed and direction of motion, heat content, etc, of every one of those water droplets, rain drops and hail stones, not to mention the exchange of even smaller effects like electric charge. If you could, a powerful enough computer would probably be able to accurately model what happens from that point on. The problem is that we'll never be able to capture that snapshot accurately, not for that one small storm cloud, and definitely not for the entire atmosphere.
That's what it really comes down to. We will no doubt eventually create computers that are so powerful that they could produce accurate forecasts, if we were able to supply enough information to them. However, since the amount of information we can gather will always be limited, that will put a limit on the resolution of the models, and thus we'll always have enough uncertainty that we'll need human forecasters, with all their common sense and creativity, to interpret the models and decide which ones are performing best.