Erosion rate of regolith is taken as the outgoing flux from a grid cell, assuming that Be-10 erosion rates are not measured in depositional environments.
Solutes in the upper right: solid is flow to the right (Amazon), open is Andean.
Lithium isotopes fractionate between Mg-Beidellite and solution. I'm assuming that Li does go into kaolinite but with no fractionation. The part I had to invent was to use the observed Li / Mg ratio from river waters to determine the partitioning between dissolved and reprecpitated Li. There are no Mg carbonates in the bedrock, so the porewater Mg concentrations are too low, which would affect the flux balance of the Li.
For reference, here are the sensitivity of end-states to runoff rate, groundwater fraction of runoff, basalt fraction of bedrock, saprolite thickness, saprolite fluid stagnation parameter, erosion rate parameter, erosion rate 1/e dropoff depth, regolith transport parameter, and the reaction rate scale parameter.
The steady state takes millions of years to achieve and is not necessarily relevant to a short-term perturbation, but it is the way to start to understand the model. CO2 uptake rates are limited by availability of source rock, not CO2 concentration or many of the other model parameters. In particular, the erosion rate is taken as a pre-exponential multiplier and an e-folding depth scale parameter, neither of which has much impact on CO2 uptake rates, because the thickness of the regolith cell in an eroding grid point responds quickly and adjusts to the dynamics of the system, which is regulated ultimately by the regoith tranport parameter.
CO2 uptake flux is much less sensitive to most parameters in the initial response, although the reaction rate parameter has more impact than in the long term. In general the feedback takes time to grow in.
It seems odd that CO2 uptake rate in the long term responds to precipitation rates and groundwater fraction parameters, if the dissolution is independent of porewater concentrations. The next two plots explain why this is.
The above plot shows that primary mineral dissolution is independent of water flushing, as expected from the model formulation, while the plot below shows that the budget for the CaO component among all minerals does show flushing sensitivity. Flushing drives CO2 uptake by changing the mineralogy of the precipitating secondary minerals.
The model response to a persistent doubling of CO2, projected on its potential effect on model parameters. Climate sensitivity is 4 degrees / doubling; precipitation goes as 2% / degree C, probably a high estimate; parameters associated with erosion and regolith transport scale with precipitation; soil CO2 is 4000 ppm in the pre-spike and 4250 in the spike, so probably a low estimate of the relative change. Dissolution rate constants increase by 40%, consistent with a doubling of rates in 10 degrees C.
The effect of temperature on the equilibrium constants is actually to suppress CO2 uptake! The erosion rate constant is impotent as before, and the dissolution rate constants also don't get much traction. The change in soil pCO2, small relative change as it is, has a significant impact, as does the precipitation rate. The land transport parameter takes time to start to take out CO2.
The total response (red line, upper left) is compared with the response expected from BLAG in the lower right.
First attempt to close the carbon budget in the model. CO2 uptake rates from an initial steady state are scaled to global volcanic emissions. A CO2 release of 1,200 Gton reaches doubled atmospheric concentrations at the peak (airborn fraction 50%), but on the time scale of this model the airborn fraction is assusmed to be 10% (equilibrium with the ocean buffered by CaCO3). Climate-sensitive parameters scale to CO2 as above. The BLAG curve is a 400-kyr drawdown; the new model looks more like 2 million years. Perhaps a smaller continent would have a faster equilibration time, but there doesn't seem to be much other wiggle room to drive the model more quickly. And the basis for the existing estimates has completely fallen apart.