Nutrient supply regulates the activity of phytoplankton, but the global biogeography of nutrient limitation and co-limitation are poorly understood. Bottle incubation experiments have revealed patterns of nutrient limitation but have limited spatial coverage, and surface nutrient concentrations are below detection limits in much of the oligotrophic ocean. In my first chapter I used genomic changes as an indicator of adaptation to nutrient stress. We collected 909 surface metagenomes from the Atlantic, Pacific, and Indian Ocean, quantified the global genome content of Prochlorococcus and inferred local nutrient stress based on shifts in nitrogen, phosphorus, and iron assimilation genes. Our ‘omics-based description of phytoplankton resource use provided a nuanced and highly resolved quantification of nutrient stress in the global ocean.We see a clear association between genome content and nutrient limitation, but the underlying population genetics of these genomic differences and the mechanisms by which they arise are unknown. In my second chapter, I described the functional diversity found within Prochlorococcus and captured the link between low nutrient adaptation and phylogeography. I analyzed 630 surface ocean metagenomes and quantified global variation in gene abundance, phylogeny, and genomic structure through consensus marker genes and metagenomically assembled genomes (MAGs). The analysis of functional diversity and phylogeography revealed widespread flexibility in genomic content, with a phylogenetically conserved haplotype driven by P limitation. While omics-based analysis can give a detailed representation of a microbial community, these methods are spatially and temporally limited to the time and location of sampling. Remote sensing-based descriptions of microbial nutrient limitation have been proposed but have never been validated in situ. For my third chapter, I combined remote sensing and metagenomically derived estimates of nutrient limitation to expand both the temporal and spatial extent of our characterization of nutrient limitation. Based on this in situ validation of the remote sensing products I analyzed the past 10 years of data and captured novel seasonal variation and a recent reduction in global nutrient limitation.

Water use estimation is central to managing most water problems. To better understand water use in California’s Sacramento–San Joaquin Delta, a collaborative, integrated approach was used to predict Delta island diversion, consumption, and return of water on a more detailed temporal and spatial resolution. Fabian Tract and Staten Island were selected for this pilot study based on available data and island accessibility. Historical diversion and return location data, water rights claims, LiDAR digital elevation model data, and Google Earth were used to predict island diversion and return locations, which were tested and improved through ground-truthing. Soil and land-use characteristics as well as weather data were incorporated with the Integrated Water Flow Model Demand Calculator to estimate water use and runoff returns from input agricultural lands. For modeling, the islands were divided into grid cells forming subregions, representing fields, levees, ditches, and roads. The subregions were joined hydrographically to form diversion and return watersheds related to return and diversion locations. Diversions and returns were limited by physical capacities. Differences between initial model and measured results point to the importance of seepage into deeply subsided islands. The capabilities of the models presented far exceeded current knowledge of agricultural practices within the Delta, demonstrating the need for more data collection to enable improvements upon current Delta Island Consumptive Use estimates.

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The generalized Radon (or Hough) transform is a well-known tool for detecting parameterized shapes in an image. The Radon transform is a mapping between the image space and a parameter space. The coordinates of a point in the latter correspond to the parameters of a shape in the image. The amplitude at that point corresponds to the amount of evidence for that shape. In this paper we discuss three important aspects of the Radon transform. The first aspect is discretization. Using concepts from sampling theory we derive a set of sampling criteria for the generalized Radon transform. The second aspect is accuracy. For the specific case of the Radon transform for spheres, we examine how well the location of the maxima matches the true parameters. We derive a correction term to reduce the bias in the estimated radii. The third aspect concerns a projection-based algorithm to reduce memory requirements.