Fading pdf of free-space optical communication system with pointing error

A free-space optical (FSO) laser communication system with perfect fast-tracking experiences random power fading due to atmospheric turbulence. For a FSO communication system without fast-tracking or with imperfect fast-tracking, the fading probability density function (pdf) is also affected by the pointing error. In this thesis, the overall fading pdfs of FSO communication system with pointing errors are calculated using an analytical method based on the fast-tracked on-axis and off-axis fading pdfs and the fast-tracked beam profile of a turbulence channel. The overall fading pdf is firstly studied for the FSO communication system with collimated laser beam. Large-scale numerical wave-optics simulations are performed to verify the analytically calculated fading pdf with collimated beam under various turbulence channels and pointing errors. The calculated overall fading pdfs are almost identical to the directly simulated fading pdfs. The calculated overall fading pdfs are also compared with the gamma-gamma (GG) and the log-normal (LN) fading pdf models. They fit better than both the GG and LN fading pdf models under different receiver aperture sizes in all the studied cases. Further, the analytical method is expanded to the FSO communication system with beam diverging angle case. It is shown that the gamma pdf model is still valid for the fast-tracked on-axis and off-axis fading pdfs with point-like receiver aperture when the laser beam is propagated with beam diverging angle. Large-scale numerical wave-optics simulations prove that the analytically calculated fading pdfs perfectly fit the overall fading pdfs for both focused and diverged beam cases. The influence of the fast-tracked on-axis and off-axis fading pdfs, the fast-tracked beam profile, and the pointing error on the overall fading pdf is also discussed. At last, the analytical method is compared with the previous heuristic fading pdf models proposed since 1970s. Although some of previously proposed fading pdf models provide close fit to the experiment and simulation data, these close fits only exist under particular conditions. Only analytical method shows accurate fit to the directly simulated fading pdfs under different turbulence strength, propagation distances, receiver aperture sizes and pointing errors.

Golden-winged Warbler habitat model validation for northern Wisconsin and central Minnesota

Between 1966 and 2003, the Golden-winged Warbler (Vermivora chrysoptera) experienced declines of 3.4% per year in large parts of the breeding range and has been identified by Partners in Flight as one of 28 land birds requiring expedient action to prevent its continued decline. It is currently being considered for listing under the Endangered Species Act. A major step in advancing our understanding of the status and habitat preferences of Golden-winged Warbler populations in the Upper Midwest was initiated by the publication of new predictive spatially explicit Golden-winged Warbler habitat models for the northern Midwest. Here, I use original data on observed Golden-winged Warbler abundances in Wisconsin and Minnesota to compare two population models: the hierarchical spatial count (HSC) model with the Habitat Suitability Index (HSI) model. I assessed how well the field data compared to the model predictions and found that within Wisconsin, the HSC model performed slightly better than the HSI model whereas both models performed relatively equally in Minnesota. For the HSC model, I found a 10% error of commission in Wisconsin and a 24.2% error of commission for Minnesota. Similarly, the HSI model has a 23% error of commission in Minnesota; in Wisconsin due to limited areas where the HSI model predicted absences, there was incomplete data and I was unable to determine the error of commission for the HSI model. These are sites where the model predicted presences and the Golden-winged Warbler did not occur. To compare predicted abundance from the two models, a 3x3 contingency table was used. I found that when overlapped, the models do not complement one another in identifying Golden-winged Warbler presences. To calculate discrepancy between the models, the error of commission shows that the HSI model has only a 6.8% chance of correctly classifying absences in the HSC model. The HSC model has only 3.3% chance of correctly classifying absences in the HSI model. These findings highlight the importance of grasses for nesting, shrubs used for cover and foraging, and trees for song perches and foraging as key habitat characteristics for breeding territory occupancy by singing males.

Numerical solutions of elliptic inverse problems via the equation error method

To estimate a parameter in an elliptic boundary value problem, the method of equation error chooses the value that minimizes the error in the PDE and boundary condition (the solution of the BVP having been replaced by a measurement). The estimated parameter converges to the exact value as the measured data converge to the exact value, provided Tikhonov regularization is used to control the instability inherent in the problem. The error in the estimated solution can be bounded in an appropriate quotient norm; estimates can be derived for both the underlying (infinite-dimensional) problem and a finite-element discretization that can be implemented in a practical algorithm. Numerical experiments demonstrate the efficacy and limitations of the method.

Modeling and classifying variable width riparian zones utilizing digital elevation models, flood height data, digital soil data and national wetlands inventory : a new approach for riparian zone delineation

Riparian zones are dynamic, transitional ecosystems between aquatic and terrestrial ecosystems with well defined vegetation and soil characteristics. Development of an all-encompassing definition for riparian ecotones, because of their high variability, is challenging. However, there are two primary factors that all riparian ecotones are dependent on: the watercourse and its associated floodplain. Previous approaches to riparian boundary delineation have utilized fixed width buffers, but this methodology has proven to be inadequate as it only takes the watercourse into consideration and ignores critical geomorphology, associated vegetation and soil characteristics. Our approach offers advantages over other previously used methods by utilizing: the geospatial modeling capabilities of ArcMap GIS; a better sampling technique along the water course that can distinguish the 50-year flood plain, which is the optimal hydrologic descriptor of riparian ecotones; the Soil Survey Database (SSURGO) and National Wetland Inventory (NWI) databases to distinguish contiguous areas beyond the 50-year plain; and land use/cover characteristics associated with the delineated riparian zones. The model utilizes spatial data readily available from Federal and State agencies and geospatial clearinghouses. An accuracy assessment was performed to assess the impact of varying the 50-year flood height, changing the DEM spatial resolution (1, 3, 5 and 10m), and positional inaccuracies with the National Hydrography Dataset (NHD) streams layer on the boundary placement of the delineated variable width riparian ecotones area. The result of this study is a robust and automated GIS based model attached to ESRI ArcMap software to delineate and classify variable-width riparian ecotones.