$\mathrm{CO2\_o}=\begin{cases}0.0 & \text{if $t< 100$}\\ 1.1877 & \text{if $t< 2800$}\\ 0.0 & \text{otherwise}\end{cases}\mathrm{rho}=\frac{2}{r}\mathrm{HCO3\_o}=\frac{\mathrm{K\_HA}\mathrm{CO2\_o}}{\mathrm{H\_o}}\mathrm{epsilon}=e^{\frac{-\mathrm{V\_m}F}{RT}}\mathrm{pH\_Lim}=-\lg (1E-3\mathrm{H\_Lim})\mathrm{pH\_i}=-\lg (1E-3\mathrm{H\_i})\mathrm{pH\_o}=-\lg (1E-3\mathrm{H\_o})\mathrm{J\_CO2}=\mathrm{P\_CO2}(\mathrm{CO2\_o}-\mathrm{CO2\_i})\mathrm{J\_HCO3}=\frac{\frac{\mathrm{P\_HCO3}\mathrm{V\_m}F}{RT}(\mathrm{HCO3\_o}-\mathrm{HCO3\_i}\mathrm{epsilon})}{1-\mathrm{epsilon}}\mathrm{J\_H}=\begin{cases}\frac{k}{\mathrm{rho}}(\mathrm{H\_i}-\mathrm{H\_Lim}) & \text{if $\mathrm{pH\_i}< \mathrm{pH\_Lim}$}\\ 0.0 & \text{otherwise}\end{cases}\mathrm{alpha}=\frac{\mathrm{H\_i}}{\mathrm{H\_i}+\mathrm{K\_HA}}\mathrm{CO2\_i}=\mathrm{alpha}\mathrm{TA\_i}\mathrm{HCO3\_i}=(1-\mathrm{alpha})\mathrm{TA\_i}\frac{d \mathrm{TA\_i}}{d t}=\mathrm{rho}(\mathrm{J\_CO2}+\mathrm{J\_HCO3})\frac{d \mathrm{H\_i}}{d t}=\frac{2.303\mathrm{H\_i}}{\mathrm{beta}}\mathrm{rho}((1-\mathrm{alpha})\mathrm{J\_CO2}-\mathrm{alpha}\mathrm{J\_HCO3}-\mathrm{J\_H})$