The Cornell Electron Storage Ring Test Accelerator (CesrTA) program has included extensive measurements of coherent betatron tune shifts for a variety of electron and positron beam energies, bunch population levels, and bunch train configurations. The tune shifts have been shown to result primarily from the interaction of the beam with the space-charge field of the beam-induced low-energy electron cloud in the vacuum chamber. Comparison to several advanced electron cloud simulation codes has allowed determination of the sensitivity of these measurements to physical parameters characterizing the synchrotron radiation flux, the production of photo-electrons on the vacuum chamber wall, the beam emittance, lattice optics, and the secondary-electron yield model. We report on progress in understanding the cloud buildup and decay mechanisms in magnetic fields and in field-free regions, addressing quantitatively the precise determination of the physical parameters of the modeling. Validation of these models will serve as essential input in the design of damping rings for future high-energy linear colliders.