This dissertation investigates and describes several ways of using spectral analysis as a frequency domain approach for mathematical hydrological modeling. Hydrologists have used spectral analysis for modeling in the past in various ways. However, one of the novelties of this research is that it is a simplification of previous techniques, which involved acquiring information about several parameters. Many of these parameters are time consuming to collect as data or are only estimated using intricate mathematical equations. In the first chapter the relationship between stream discharge and wetland water elevations in a watershed located in North Madison, CT was successfully modeled using exclusively independent measurements of discharge and wetland water elevations. This relationship was previously modeled using six parameters, three of which had to be estimated for their instantaneous behavior. Using the methods developed in this study conserved time and effort and produced the same results. The second chapter describes how to model discharge with measures of water table elevations in a runoff source area using the same techniques described in the first chapter. Using water table elevations across a lower part of the hillslope and in a near stream area of Townbrook watershed in the Catskills of New York, spectral analysis was used to determine the rate of water transport at these various locations and to successfully model stream discharge. The third chapter describes a method of using spectral analysis to determine chemical transport throughout a catchment area. Three watersheds were analyzed to describe a relationship between wet deposition and stream water concentrations of chloride (Cl) and nitrate (NO3). Spectral analysis was also used to define a distribution of travel times associated with the transport of input concentrations of Cl, NO3, ammonium (NH4), total Phosphorus (TP), total dissolved phosphorus (TDP), total particulate phosphorus (TPP), soluble reactive phosphorus (SRP) suspended solids (SS), total kjeldahl nitrogen (TKN), and total organic carbon (TOC). All of these studies combined indicate that spectral analysis is a tool than can be of further use in many aspects of hydrology and in studies of water quality and chemical transport.