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We present a new semi-analytic formalism for modeling metal absorption linesthat emerge from a clumpy galactic environment, ALPACA. We predict the''down-the-barrel'' (DTB) metal absorption line profiles and the EW ofabsorption at different impact parameters as a function of the properties ofthe clumps, including the clump kinematics, the clump volume filling factor,the clump number density profile and the clump ion column densities. WithALPACA, we jointly model the stacked DTB CII$\lambda$1334 spectrum of a sampleof $z \sim$ 3 Lyman break galaxies and the EW v.s. $b$ profile of a sample of$z \sim$ 2 star-forming galaxy-galaxy pairs. ALPACA successfully reproduced twodatasets simultaneously, and the best-fit prefers a low clump volume fillingfactor ($\sim 3 \times 10^{-3}$). The radial velocities of the clumps are asuperposition of a rapidly accelerated outflow with a maximum velocity of $\sim400\,\rm km\,s^{-1}$ and a velocity dispersion of $\sigma_{\rm cl} \sim\,120\rm km\,s^{-1}$. The joint modeling reveals a physical scenario where theabsorption observed at a particular velocity is contributed by the clumpsdistributed over a fairly broad range of radii. We also find that the commonlyadopted Sobolev approximation is at best only applicable within a narrow rangeof radii where the clumps are undergoing rapid acceleration in anon-volume-filling clumpy medium. Lastly, we find that the clump radialvelocity profile may not be fully constrained by the joint modeling andspatially-resolved Ly$\alpha$ emission modeling may help break the degeneracy.

ALPACA: A New Semi-Analytic Model for Metal Absorption Lines Emerging from Clumpy Galactic Environments