| Mode Functions (IMFs) using a technique known as Empirical Mode Decomposition (EMD). Unlike an infinite Fourier series expansion, the EMD always yields a finite number of IMFs, whose sum is equal to the original time series exactly. Two datasets are used for this thesis: (i) a set of solutions for the Lorenz equations, and (ii) the reconstructed time series of the global-average monthly precipitation anomalies generated by a technique known as Spectral Optimal Gridding of Precipitation (SOGP). SOGP is a multivariate regression model that computes the monthly quasi-global (75°S-75°N) precipitation reconstructed by an Empirical Orthogonal Function (EOF) expansion. First we apply the HHT technique to the Lorenz equations as a proof of concept that this technique is successful at analyzing non-linear and non-stationary processes. We then apply the HHT to monthly precipitation time series data for the Tibetan Plateau region. Using the HHT, we were able to obtain the signal representing the annual cycle for the time series data, and a cycle every 4.7 years which may represent the El Nino oscillation patterns and monsoonal variation for the region. Using the SOGP technique, we generated 2.5° and 5.0° historical global reconstructions. A comparison between the two reconstructions shows that the coefficient of determination was r 2 = 0.5360, indicating a strong relationship between the reconstructed datasets. The 2.5° reconstruction tends to underestimate the anomaly values as compared to the 5.0° reconstruction. A further comparison of the variance and EOF patterns between this study's 2.5° reconstruction and the existing 5.0° reconstructions shows that the patterns are very similar, and that the new, higher resolution 2.5° data is a valid reconstruction. The final part of this thesis is the creation of a user interface for the SOGP software, which allows the general public to perform precipitation reconstruction back to 1900 and generate various graphics for applications. |
