Type Ia Supernovae provided the first strong evidence of dark energy and are still an important tool for measuring the accelerated expansion of the universe. However, future improvements will be limited by systematic uncertainties in our use of Type Ia supernovae as standard candles. Using Type Ia supernovae for cosmology relies on our ability to standardize their absolute magnitudes, but this relies on imperfect models of supernova spectra time series. This thesis is focused on using data from the Nearby Supernova Factory both to understand current sources of uncertainty in standardizing Type Ia supernovae and to develop techniques that can be used to limit uncertainty in future analyses.

Part I of this thesis is concerned with studying systematic errors that occur in the current generation of supernova lightcurve models. Lightcurve models are used to fit photometric supernova data, generating a small number of parameters that can then be used to `correct' the supernova magnitude to a standard value. The analysis presented here estimates systematic errors due to K-corrections that occur when using such lightcurve models to fit high-redshift supernovae. These errors occur when the spectral template underlying the lightcurve fitter poorly matches the actual supernova spectral energy distribution and also if the model fit is dependent on the spectral coverage of the photometric filters used to observe the supernova.

In order to quantify this effect, synthetic photometry is performed on artificially redshifted spectrophotometric data from the Nearby Supernova Factory, simulating having photometric data for the same supernovae with a range of filter positions. The resulting lightcurves are fit with a conventional lightcurve fitter and the variation is measured in the resulting standardized magnitudes. We find significant variation in the measurements of the same supernovae placed at different redshifts regardless of filters used, which causes dispersion greater than $\sim 0.05$ mag for measurements of photometry using Sloan-like filters and a bias that corresponds to a 0.03 shift in $w$ when applied to an outside data set. We also test the effect of population changes at high redshift and measure the resulting bias for the average of the supernova magnitudes. Lastly, methods are discussed for mitigating bias and dispersion due to K-corrections.

Part II presents an alternative to current lightcurve models. The supernovae from the Nearby Supernova Factory are used to develop an empirical model that will be able to more fully describe the variety of supernova behavior. The spectrophotometric time series for over 200 supernova are used to fit linear principal components that will be able to be used as a lightcurve model. This is done by first using Gaussian Processes to model the true spectral time series for each supernova and make a prediction for it on a regular grid in time and wavelength space. Once this has been done, principal components are calculated that describe the full set of supernovae using a method that incorporates the variance in the data. K-fold cross-validation is used to determine how many components best describe the full population without over-training on noise in the data. In the final version of the analysis, three different models are presented: one simple model that can be compared to the current generation of lightcurve models; one model that is the best for performing a linear standardization of supernova magnitudes following current standardization methods, at least when spectra for the supernova are available; and one complex model that provides the most complete model of spectral time series for the full population.