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On the Application of Low Wavenumber Fourier Filtering To the Estimation of System Predictability in Northern Winter
AdvisorLewis, John M.
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In this dissertation’s second chapter, a brief survey is made of the history of long-range weather forecasting (LRF), or forecasting on the seasonal timescale. The contrast between empirical/statistical and physical/theoretical forecasting methods is traced, from the time of Halley, through Walker and Indian monsoon prediction, and through pre- and post-World War II forecasting milieus. Moving into the modern era, a brief review of modern LRF methods and skill is made. Based upon the evidence presented, conclusions are offered that: (1) neither the modern appropriations of empirical methods (i.e., teleconnections) nor modern GCMs are effective at providing accurate temperature and precipitation LRF results; (2) the implications of the canonical 10- to 14-day Lorenzian limit on exact predictions should be understood as providing a necessary constraint on forecasting model design; (3) the time evolution of large-scale atmospheric structures, such as low wavenumber planetary waves, might provide a basis for LRF model design consistent with restrictions imposed by the Lorenzian limit.In the second chapter, Rex blocks were characterized using Fourier decomposition. A three stage model of Rex block structure was proposed, using specific tendencies among component wavenumbers 2, 3, and 5 to pinpoint onset, persistence, and dissolution of a Rex block (research ongoing). In the predictability study, geopotential height reanalysis data over the northern hemisphere for 90-day winter, 1979-2016, were compared over all non-intra-winter two-day comparisons by RMS differencing, to establish a roster of Lorenzian analogue pairs of similar atmospheric states. These analogue pairs were then decomposed by Fourier analysis. The resulting Fourier wavenumber 2-8 components’ phase angles and amplitudes were evaluated for similarity with respect to ridging about the -140° line of longitude, consistent with eastern Pacific high amplitude ridging. The resulting comparisons of phase angle and amplitude between analogue pairs were used to populate a 21-day progression of those analogue pairs forward in time. Both a single latitude circle (40°N) and a large latitude swath (20°-80°N) were used separately to establish analogue pair progressions. These progressions showed gradual diminishment in similarity as phase angle and amplitude differences grew between the pairs. The consequent aggregate pattern of difference growth showed a range of limiting values, with lower wavenumbers exhibiting larger values in general than higher wavenumbers. For wavenumbers 2 and 3, these values exceeded 21 days in some permutations of our method. Our interpretation of these values suggests that modeling low wavenumber wave structures has the potential to move well past the canonical 10- to 14-day Lorenzian predictability limit for exact forecasting results, consistent with the hypothesis that the limit of predictability increases as model resolution decreases.We believe this is the first use of Fourier analysis to be applied to the problem of system predictability via analogue pair progressions.