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Type Ia Supernovae (SNe Ia) are widely used to measure the expansion of theUniverse. Improving distance measurements of SNe Ia is one technique to betterconstrain the acceleration of expansion and determine its physical nature. Thisdocument develops a new SNe Ia spectral energy distribution (SED) model, calledthe SUpernova Generator And Reconstructor (SUGAR), which improves the spectraldescription of SNe Ia, and consequently could improve the distancemeasurements. This model is constructed from SNe Ia spectral properties andspectrophotometric data from The Nearby Supernova Factory collaboration. In afirst step, a PCA-like method is used on spectral features measured at maximumlight, which allows us to extract the intrinsic properties of SNe Ia. Next, theintrinsic properties are used to extract the average extinction curve. Third,an interpolation using Gaussian Processes facilitates using data taken atdifferent epochs during the lifetime of a SN Ia and then projecting the data ona fixed time grid. Finally, the three steps are combined to build the SED modelas a function of time and wavelength. This is the SUGAR model. The mainadvancement in SUGAR is the addition of two additional parameters tocharacterize SNe Ia variability. The first is tied to the properties of SNe Iaejecta velocity, the second is correlated with their calcium lines. Theaddition of these parameters, as well as the high quality the Nearby SupernovaFactory data, makes SUGAR an accurate and efficient model for describing thespectra of normal SNe Ia as they brighten and fade. The performance of thismodel makes it an excellent SED model for experiments like ZTF, LSST or WFIRST.

SUGAR: An improved empirical model of Type Ia Supernovae based on spectral features