  Type Ia Supernovae (SNe Ia) are widely used to measure the expansion of the
Universe. Improving distance measurements of SNe Ia is one technique to better
constrain the acceleration of expansion and determine its physical nature. This
document develops a new SNe Ia spectral energy distribution (SED) model, called
the SUpernova Generator And Reconstructor (SUGAR), which improves the spectral
description of SNe Ia, and consequently could improve the distance
measurements. This model is constructed from SNe Ia spectral properties and
spectrophotometric data from The Nearby Supernova Factory collaboration. In a
first step, a PCA-like method is used on spectral features measured at maximum
light, which allows us to extract the intrinsic properties of SNe Ia. Next, the
intrinsic properties are used to extract the average extinction curve. Third,
an interpolation using Gaussian Processes facilitates using data taken at
different epochs during the lifetime of a SN Ia and then projecting the data on
a fixed time grid. Finally, the three steps are combined to build the SED model
as a function of time and wavelength. This is the SUGAR model. The main
advancement in SUGAR is the addition of two additional parameters to
characterize SNe Ia variability. The first is tied to the properties of SNe Ia
ejecta velocity, the second is correlated with their calcium lines. The
addition of these parameters, as well as the high quality the Nearby Supernova
Factory data, makes SUGAR an accurate and efficient model for describing the
spectra of normal SNe Ia as they brighten and fade. The performance of this
model makes it an excellent SED model for experiments like ZTF, LSST or WFIRST.
