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We present ultra-violet to mid-infrared observations of the long-lasting TypeIIn supernova (SN) 2013L obtained by the Carnegie Supernova Project II(CSP-II). The spectra of SN 2013L are dominated by H emission featurescharacterized by three components attributed to different regions. A uniquefeature of this Type IIn SN is that the blue shifted line profile is dominatedby the macroscopic velocity of the expanding shock wave of the SN. We aretherefore able to trace the evolution of the shock velocity in the dense andpartially opaque circumstellar medium (CSM), from $\sim 4800~km~s^{-1}$ at +48d, decreasing as $t^{-0.23}$ to $\sim 2700~km~s^{-1}$ after a year. We performspectral modeling of both the broad- and intermediate-velocity components ofthe H$\alpha$ line profile. The high-velocity component is consistent withemission from a radially thin, spherical shell located behind the expandingshock with emission wings broadened by electron scattering. We propose that theintermediate component originates from pre-ionized gas from the unshocked denseCSM with the same velocity as the narrow component, $\sim 100~km~s^{-1}$, butalso broadened by electron scattering. The spectral energy distributions (SEDs)of SN 2013L after +132 d are well reproduced by a two-component black-body (BB)model. The circumstellar-interaction model of the bolometric light curvereveals a mass-loss rate history with large values ($1.7\times 10^{-2} -0.15~M_\odot~yr^{-1}$) over the $\sim $25 - 40 years before explosion. The dropin the light curve at $\sim 350$ days and presence of electron scattering wingsat late epochs indicate an anisotropic CSM. The mass-loss rate values and theunshocked CSM velocity are consistent with the characteristics of a massivestar, such as a luminous blue variable (LBV) undergoing strong eruptions,similar to $\eta$ Carina.

The Carnegie Supernova Project II. The shock wave revealed through the fog: The strongly interacting Type IIn SN 2013L