I've read that the solar constant, or energy output from the sun is approximately 1366 kilowatts per meter squared (1366 kW/m2). One half of a percent should be about 68 kW/m2. Maybe I'm missing something, but why is this considered a small change when magnified on a global level?
So 0.5% is ~1380 divided by 4 (re-radiating area) divided by 100 (percent) divided by 2 (half a percent) or ~1.7 watts per square meter. That is roughly the same order of magnitude as the predicted change in direct greenhouse effect from observed past changes in atmospheric CO2. So yes, it is the right order of magnitude for explanations about these things.
However, it is not the right order of magnitude for the predictions the scaremongers are interested in. Because the change in equilibrium mean temperature goes as the one-fourth power of the change in the power term. As per Boltzman's law, literally true for black bodies, the right first order approximation for most other things. E.g. the earth's albedo is on the order of 0.8, 1 being black-body.
So, change solar input to 1.005 of previously, and the equilibrium temperature goes 1.001247663, in degrees Kelvin. Or about 0.36 degrees C. Geez Louise, same order of magnitude as observed changes in mean temperture over century time scales. But the scaremonger predictions are changes of 3-5 degrees C, so they need 8-14 times as large a temperature change.
Meaning they need power changes on the order of 4-7%, or 14-24 watts per re-radiating square meter. They think they can get ~4W from direct greenhouse if they predict doubling of CO2 levels (along with other twiddles about other gases, because the latest on CO2 alone, in the UN's own climate report, is only about 2.4W even if it happens).
So they need amplifiers somewhere that take input power signal and boost its climatic effect 5 fold - by changing overall planetary albedo/blackness, or increasing water vapor based greenhouse, or anything else they can dream up (e.g. wetness to dust to cloud, here).
So the important thing to realize is that solar variation is big enough to explain observed *past* temperature changes on time scales of order 50 to a few hundred years - which have been minor. But it is not large enough to predict large *future* changes, which is what a lot of these characters want. So "not useful" has two meanings. Scientifically, solar variation explains quite a bit of past temperature change (though probably nothing like all - maybe half). But it doesn't help the scaremongers.
But amplifiers, in whatever context first "found"/invented, can help the scaremongers. Because they don't have a coherent power budget. Their own predictions of power effects from the greenhouse gas changes they decide to predict (which they mostly pick out of the air, but have to keep reasonably plausible) aren't sufficient to account for the temperature changes they also predict. They need 4/5ths of the power to pop out of the complexity of the climate system somewhere, "sensitively".
But, you will wonder, if they don't have 4/5ths of the needed power and don't know where it would come from, why in heck to they make that prediction? Because the prediction is practically constant; it is the theory that moves to save the prediction, not the other way around.
CO2 warming was originally proposed as a possible explanation for ice ages. Which show temperature changes on the order of 5 degrees C. The prediction that CO2 variation might cause temperature changes of that scale was first made more than 100 years ago, in the late 1800s, when effects like greenhouse could first be modeled theoretically (though still crudely - they knew nothing of quantum mechanics and little of energy levels etc).
Global climate models based on that idea were first built in the late 1960s and early 1970s. But shortly afterward, in the mid 1970s, the real explanation of ice ages was re-discovered (one fellow had figured in out much earlier, but his ideas had been overlooked). Long time scale variations in the earth's orbit around the sun (eccentricity changes, tilt shifts, precession, etc) lead to changes in total solar radiation received on the order of 7% over time scales of 10s of thousands of years.
So there was no 7% overall power change left in ice ages to be explained by CO2 variation. The original late 1800s idea was wrong as a solution to ice ages. But the idea still existed, some scale of greenhouse effect from CO2 variation was perfectly plausible, and models had been built based on it. The right way to proceed therefore would have been to accept the orbital explanation of ~5C changes - the largest seen in the past records - and then to expect CO2 changes to be smaller, second order terms explaining minor subvariations.
But there was no potential scaremongering it that. It was not done. Instead, they kept the scale of prediction from when CO2 variation was supposed to cause ice ages. Which means ice ages are "overexplained", twice. Meanwhile physicists went out and measured the scale of effect you could expect from direct CO2 greenhouse, and it was on the order 1-3 watts per re-radiating square meter. Exactly what you'd expect from a second order correction to the orbital variation model of ice ages. But not enough to save the 5C prediction.
So they kept the prediction instead of accepting what the physicist's data ought to have told them. And realized they'd need some mysterious twiddle of an amplifier somewhere, to turn small but real and verifiable power changes from direct greenhouse, into their hackneyed old predictions. Since the climate is complicated, they thought they might be able to do this.
They ran off looking for epicycle amplifiers in every complicated subsystem of the global climate. Maybe this, maybe that, maybe 4/5ths of the needed power will pop out through the vengeance of offended mother earth. It was generalized water vapor, then it was clouds, then it was seeding of clouds, then clouds were two varieties, then in was sulphates, aerosols, dust, volcanoes, ice caps, ozone - on and on, trying to spin out new explanations faster than they could be investigated and shot down.
They still don't have an energy budget. They just wave their hands and gesture toward some version of that complexity, and then say "well, it pops out of our models". That is, their models predict a temperature response to their own power terms 4 times as large as it should be, on the "naive" simple physics of it.
For all the world like they forgot Boltzman's law, maybe because a linear model is "simpler". For small changes, even a linear model would have been fine, if they had replaced the fourth root with a 1/4 times coefficient. (Since 1.0n ^ .25 is about 1.0n/4). But why put that in, when you are just going to do a regression to find all the coefficients in the linear model anyway? That their model thus predicts a linear relationship (with coefficient near 1) between power term and equilibrium temperature is can thus be explained, but as a gross error.
Complicated climatic twiddles are supposed to fill in between the simple physics screaming "you dropped a fourth root" and their old ice-age scale prediction.