Remote sensing studies and morphotectonic investigations in an arid rift setting, Baja California, Mexico

The Gulf of California and its surrounding land areas provide a classic example of recently rifted continental lithosphere. The recent tectonic history of eastern Baja California has been dominated by oblique rifting that began at ~12 Ma. Thus, extensional tectonics, bedrock lithology, long-term climatic changes, and evolving surface processes have controlled the tectono-geomorphological evolution of the eastern part of the peninsula since that time. In this study, digital elevation data from the Shuttle Radar Topography Mission (SRTM) from Baja California were corrected and enhanced by replacing artifacts with real values that were derived using a series of geostatistical techniques. The next step was to generate accurate thematic geologic maps with high resolution (15-m) for the entire eastern coast of Baja California. The main approach that we used to clearly represent all the lithological units in the investigated area was objectoriented classification based on fuzzy logic theory. The area of study was divided into twenty-two blocks; each was classified independently on the basis of its own defined membership function. Overall accuracies were 89.6 %, indicating that this approach was highly recommended over the most conventional classification techniques. The third step of this study was to assess the factors that affected the geomorphologic development along the eastern side of Baja California, where thirty-four drainage basins were extracted from a 15-m-resolution absolute digital elevation model (DEM). Thirty morphometric parameters were extracted; these parameters were then reduced using principal component analysis (PCA). Cluster analysis classification defined four major groups of basins. We extracted stream length-gradient indices, which highlight the differential rock uplift that has occurred along fault escarpments bounding the basins. Also, steepness and concavity indices were extracted for bedrock channels within the thirty-four drainage basins. The results were highly correlated with stream length-gradient indices for each basin. Nine basins, exhibiting steepness index values greater than 0.07, indicated a strong tectonic signature and possible higher uplift rates in these basins. Further, our results indicated that drainage basins in the eastern rift province of Baja California could be classified according to the dominant geomorphologic controlling factors (i.e., faultcontrolled, lithology-controlled, or hybrid basins)

Optimization Methods and Algorithms for Classes of Black-Box and Grey-Box Problems

There are many optimization problems in physics, chemistry, finance, computer science, engineering and operations research for which the analytical expressions of the objective and/or the constraints are unavailable. These are black-box problems where the derivative information are often not available or too expensive to approximate numerically. When the derivative information is absent, it becomes challenging to optimize and guarantee optimality of the solution. The objective of this Ph.D. work is to propose methods and algorithms to address some of the challenges of blackbox optimization (BBO). A top-down approach is taken by first addressing an easier class of black-box and then the difficulty and complexity of the problems is gradually increased. In the first part of the dissertation, a class of grey-box problems is considered for which the closed form of the objective and/or constraints are unknown, but it is possible to obtain a global upper bound on the diagonal Hessian elements. This allows the construction of an edge-concave underestimator with vertex polyhedral solution. This lower bounding technique is implemented within a branch-and-bound framework with guaranteed convergence to global optimality. The technique is applied for the optimization of problems with embedded system of ordinary differential equations (ODEs). Time dependent bounds on the state variables and the diagonal elements of the Hessian are computed by solving auxiliary set of ODEs that are derived using differential inequalities. In the second part of the dissertation, general box-constrained black-box problems are addressed for which only simulations can be performed. A novel optimization method, UNIPOPT (Univariate Projection-based Optimization) based on projection onto a univariate space is proposed. A special function is identified in this space that also contains the global minima of the original function. Computational experiments suggest that UNIPOPT often have better space exploration features compared to other approaches. The third part of the dissertation addresses general black-box problems with constraints of both known and unknown algebraic forms. An efficient two-phase algorithm based on trust-region framework is proposed for problems particularly involving high function evaluation cost. The performance of the approach is illustrated through computational experiments which evaluate its ability to reduce a merit function and find the optima

Predicting glacier accumulation area distributions

A mass balance model based on energy balance at the terrain surface was developed and used to predict glacier accumulation areas in the Jotunheimen, Norway. Spatially distributed melt modelling used local climate and energy balance surfaces to drive predictions, derived from regional climate and topographic data. Predictions had a temporal resolution of 1 month and a spatial resolution of 100 m, which were able to simulate observed glacier accumulation area distributions. Data were stored and manipulated within a GIS and spatial trends and patterns within the data were explored. These trends guided the design of a suite of geomorphologically and climatologically significant variables which were used to simulate the observed spatial organisation of climatic variables, specifically temperature, precipitation and wind speed and direction. DEM quality was found as a critical factor in minimising error propagation. A new method of removing spatially and spectrally organised DEM error is presented using a fast Fourier transformation. This was successfully employed to remove error within the DEM minimising error propagation into model predictions. With no parameter fitting the modeled spatial distribution of snowcover showed good agreement with observed distributions. Topographic maps and a Landsat ETM+ image are used to validate the predictions and identify areas of over or under prediction. Topographically constrained glaciers are most effectively simulated, where aspect, gradient and altitude impose dominant controls on accumulation. Reflections on the causes of over or under prediction are presented and future research directions to address these are outlined. Sensitivity of snow accumulation to climatic and radiative variables was assessed. Results showed the mass balance of accumulation areas is most sensitive to air temperature and cloud cover parameterisations. The model was applied to reconstruct snow accumulation at the last glacial maximum and under IPCC warming scenarios to assess the sensitivity of melt to changing environmental conditions, which showed pronounced sensitivity to summer temperatures Low data requirements: regional climate and elevation data identify the model as a powerful tool for predicting the onset, duration and rate of melt for any geographical area

The Detection of Change in Spatial Processes With Environmental Applications

Ever since Halley (1686) superimposed onto a map of land forms, the direction of trade winds and monsoons between and near the tropics and attempted to assign them a physical cause, homo-sapiens has attempted to develop procedures which quantify the level of change in a spatial process, or assess the relationship between associated spatially measured variables. Most spatial data, whether it be originally point, linear or areal in nature, can be converted by a suitable procedure into a continuous form and plotted as an isarithmic map i.e. points of equal height are joined. Once in that form it may be regarded as a statistical surface in which height varies over area in much the same way as the terrain varies on topographic maps. Particularly in environmental statistics, the underlying shape of the surface is unknown, and hence the use of non-parametric techniques is wholly appropriate. For most applications, the location of data points is beyond the control of the map-maker hence the analyst must cope with irregularly spaced data points. A variety of possible techniques for describing a surface are given in chapter two, with attention focusing on the methodology surrounding kernel density estimation. Once a surface has been produced to describe a set of data, a decision concerning the number of contours and how they should be selected has to be taken. When comparing two sets of data, it is imperative that the contours selected are chosen using the same criteria. A data based procedure is developed in chapter three which ensures comparability of the surfaces and hence spurious conclusions are not reached as a result of inconsistencies between surfaces. Contained within this chapter is a discussion of issues which relate to other aspects of how a contour should be drawn to minimise the potential for inaccuracies in the surface fitting methodology. Chapter four focuses on a whole wealth of techniques which are currently available for comparing surfaces. These range from the simplest method of overlaying two maps and visually comparing them to more involved techniques which require intensive numerical computation. It is the formalisation of the former of these techniques which forms the basis of the methodology developed in the following two chapters to discern whether change/association has materialised between variables. One means of quantifying change between two surfaces, represented as a contoured surface, is in terms of the transformation which would be required for the two surfaces to be matched. Mathematically, transformations are described in terms of rotation, translation and scalar change. Chapter five provides a geometrical interpretation of the three transformations in terms of area, perimeter, orientation and the centre of gravity of the contour of interest and their associated properties. Although grid resolution is fundamentally a secondary level of smoothing, this aspect of surface fitting has generally been ignored. However to ensure consistency across surfaces, it is necessary to decide firstly, whether data sets of different sizes should be depicted using different mesh resolutions and secondly, how fine a resolution provides optimal results, both in terms of execution time and inherent surface variability. This aspect is examined with particular reference to the geometric descriptors used to quantify change. The question of random noise contained within a measurement process has been ignored in the analysis to this point. However in practice, some form of noise will always be contained within a process. Quantifying the level of noise attributable to a process can prove difficult since the scientist may be over optimistic in his evaluation of the noise level. In developing a suitable set of test statistics, four situations were examined, firstly when no noise was present and then for three levels of noise, the upper bounds of which were 5,15 and 25%. Based on these statistics, a series of hypothesis tests were developed to look at the question of change for individual contour levels i.e. local analysis, or alternatively for a whole surface by combining the statistics and effectively performing a multivariate test