I applied empirical mode decomposition (EMD) and the Hilbert-Herbert transforms, as tools to analyze streamflow data. I used the EMD method to extract and analyze periodic processes and trends in several environmental datasets including daily stream flow, daily precipitation, and daily temperature on data from the watersheds of two rivers in the Upper Colorado River Basin, the Yampa and the Upper-Green rivers. I used these data to identify forcing functions governing streamflow. Forcing functions include environmental factors such as temperature and precipitation and anthropogenic factors such as dams or diversions. The Green and Yampa Rivers have similar headwaters, but the Yampa has minimal diversions or controls while Flaming George Dam on the Green river significantly affects flow. This provides two different flow regimes with similar large watersheds. In addition to flow data, I analyzed several time series data sets, including temperature and precipitation from Northeast Utah, North Western Colorado, and Southern Wyoming. These data are from the area that defines the Yampa River and Green River watersheds, which stretch from Flaming Gorge Dam to Ouray Colorado. The EMD method is a relatively new technique that allows any time series data set, including non-linear and non-stationary datasets that are common in earth observation data, to be decomposed into a small quantity of composite finite data series, called intrinsic mode functions (IMFs). The EMD method can decompose any complicated data into several IMFs that represent independent signals in the original data. These IMFs may represent periodic forcing functions, such as environmental conditions or dam operations, or they may be artifacts of the decomposition method and not have an associated physical meaning. This study attempts to assign physical meaning to some IMFs resulting from the decomposition of the Green and Yampa flows where possible. To assign physical meaning to the IMFs, I analyzed frequencies of each IMF using the Hilbert-Hung transform, part of the Empirical Mode Decomposition method, and then compared frequencies of the IMFs with the known frequencies of physical processes. I performed these calculations on both flow, temperature, and precipitation. I found significant correlation between IMF components of flow, precipitation, and temperature data with El Niño Southern Oscillation (ENSO) events. The EMD process also extracts the long-term trend in non-linear data sets that can provide insights into the effects of climate change on the flow system. Though in preliminary stages of research, these analysis methods may lead to further understanding the availability of water within the upper Yampa and Green River Watersheds.

We analyzed long-term temperature trends in Utah using a relatively new signal processing method called Empirical Mode Decomposition (EMD). We evaluated the available weather records in Utah and selected 52 stations, which had records longer than 60 years, for analysis. We analyzed daily temperature data, both minimum and maximums, using the EMD method that decomposes non-stationary data (data with a trend) into periodic components and the underlying trend. Most decomposition algorithms require stationary data (no trend) with constant periods and temperature data do not meet these constraints. In addition to identifying the long-term trend, we also identified other periodic processes in the data. While the immediate goal of this research is to characterize long-term temperature trends and identify periodic processes and anomalies, these techniques can be applied to any time series data to characterize trends and identify anomalies. For example, this approach could be used to evaluate flow data in a river to separate the effects of dams or other regulatory structures from natural flow or to look at other water quality data over time to characterize the underlying trends and identify anomalies, and also identify periodic fluctuations in the data. If these periodic fluctuations can be associated with physical processes, the causes or drivers might be discovered helping to better understand the system. We used EMD to separate and analyze long-term temperature trends. This provides awareness and support to better evaluate the extremities of climate change. Using these methods we will be able to define many new aspects of nonlinear and nonstationary data. This research was successful and identified several areas in which it could be extended including data reconstruction for time periods missing data. This analysis tool can be applied to various other time series records.