The natural carbon cycle cannot absorb all that we are putting out, which is why the amount in the atmosphere is climbing. The ocean is the biggest absorber but it will spit CO2 back out as it warms, regardless of whether or not the warming is natural or AGW, we are overloading the planet with CO2. I don't think the deserts absorb much CO2, but they do hold more heat now thanks to more CO2.
550 Million years ago, the co2 level was 20 times higher than it is now, at around 8000 parts per million. The natural carbon cycle absorbed nearly all of it. We are currently near the all time low for airborne co2. During the last glacial period, the level dropped to around 170ppm. Below 150ppm all the trees die and it's game over for most of the higher order animals on Earth.
Evidence falsifying the enhanced greenhouse effect theory - item #1.
When the ice cores were drilled in Antarctica and Greenland, and the cores analysed and matched with changes in temperature, it was discovered that changes in co2 lag behind changes in temperature during glacial/interglacial cycles by 800 to 2800 years. The law of cause and effect should have put an end to the co2 driven climate theory at this point, bu because so much is invested in continuing the co2 scare, ludicrous and unphysical post hoc explanations were invented to save the theory.
Co2 changes lag behind temperature change at all timescales, the longer the timescale of change, the longer the lag. So, at interannual timescales the lag is around 9 months, up to the 2800 year lag for the multi-thousand year timescale of glacial/interglacial change.
Effect can't drive cause, therefore something else drives both temperature change and co2 response. That something else, at the timescale of glacial/interglacial change is the changes in Earth's orbital parameters known as the Milankovitch cycles. The first of these is the gradual changes in the shape of Earth's orbit from near circular to more elliptical. This cycle is ~100,000 years long, the same periodicity as the last ten glacial-interglacial cycles on Earth. The second of the three Milankovitch cycles is the change in axial tilt, which varies between around 3 and 30 degrees. The periodicity of this cycle is ~42,000 years, which matches the length of the glacial-interglacial cycles prior to their shift to 100,000 years. The third Milankovitch cycle is the precession of the equinox. This cycle of around 20 to 25,000 years determines which pole of the Earth is tilted towards the Sun during closest approach (perihelion). Because the Earth is asymmetrical in the distribution of land mass versus open ocean (more land in the northern hemisphere, more ocean in the south), there is a profound effect on climate, because of the different ways land and ocean absorb and emit the Sun's energy.
The ways in which these three periodic changes interact with Earth's physical attributes to cause change in Earth's climate is as yet poorly understood, but the coincidence of the cycle length with major change is undeniable. The co2 theory proponents try to dismiss their importance by saying that the change in the overall average number of watts per square metre from the Sun is too small to cause the big changes from glacial to interglacial conditions. This facile argument doesn't take into account the changes in the distribution of the Sun's energy on the Earth's surface.