The watersheds in which we live are comprised of a complex set of physical and social systems that interact over a range of spatial and temporal scales. These systems are continually evolving in response to changing climatic patterns, land use practices and the increasing intervention of humans. Management of these watersheds benefits from the development and application of models that offer a comprehensive and integrated view of these complex systems and the demands placed upon them. The utility of these models is greatly enhanced if they are developed in a participatory process that incorporates the views and knowledge of relevant stakeholders. System dynamics provides a unique mathematical framework for integrating the physical and social Aquatic Sciences processes important to watershed management, and for providing an interactive interface for engaging the public. We have employed system dynamics modeling to assist in community-based water planning for a three-county region in north-central New Mexico. The planning region is centered on a ~165-km reach of the Rio Grande that includes the greater Albuquerque metropolitan area. The challenge, which is common to other arid/semi-arid environments, is to balance a highly variable water supply among the demands posed by urban development, irrigated agriculture, river/reservoir evaporation and riparian/in-stream uses. A description of the model and the planning process are given along with results and perspectives drawn from both.

Absorption spectra and induced fluorescence excitation emission matrices of colored dissolved organic matter were measured in water samples collected along the Atlantic Meridional Transect in different bio-geographic provinces of the Atlantic Ocean from October-November 2010. The highest values of CDOM absorption coefficient at 305 nm (a CDOM (305)), were recorded at the continental margins of the English Channel and Patagonian Shelf. The lowest values of a CDOM (305) were observed in the mixed layer of both North and South Atlantic subtropical oligotrophic gyres. The DOM composition was assessed using fluorescence spectroscopy, Excitation Emission Matrix spectra (EEMs) and the Parallel Factor Analysis (PARAFAC) model in addition to spectral indices calculated from CDOM absorption spectrum and EEMs spectra. Six different components were identified in the EEMs by PARAFAC: Two components were similar to the humic-like fraction of DOM, associated with basin scale microbial mineralization processes. These components represent allochthonous DOM in the biogeographic provinces studied. One component of marine humic-like material of autochthonous origin, associated with DOM production from marine phytoplankton. Three components were associated with protein-like DOM. Two protein-like components had the spectral characteristics of pure tryptophan and tyrosine. There was a significant difference in DOM composition both between bio-geographical provinces and above and below the mixed layer. In the mixed layer in all provinces, except the waters of the Western European Shelf, the DOM was dominated by protein-like components. At the Western European Shelf, it was dominated by humic-like components. Fluorescence intensities of humic-like components were high at the Patagonian Shelf, but were up to 40% lower compared to Northern Hemisphere shelf waters. Humic-like components made a significant contribution to the DOM composition of the upper mesopelagic layer in all provinces, with the highest values at the Equatorial Upwelling zone. There was a significant inverse relationship between humic-like components and salinity and temperature and a positive relationship with Apparent Oxygen Utilization. The humification index (HIX) was linearly correlated with the intensity of the humic-like DOM components. These trends suggest that the humic-like components are in dynamic equilibrium between likely microbial production in the deep ocean and photochemical degradation in the mixed layer.

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Borisov-Joyce constructed a real virtual cycle on compact moduli spaces of stable sheaves on Calabi-Yau 4-folds, using derived differential geometry.We construct an algebraic virtual cycle. A key step is a localisation of Edidin-Graham's square root Euler class for SOpr, Cq bundles to the zero locus of an isotropic section, or to the support of an isotropic cone.We prove a torus localisation formula, making the invariants computable and extending them to the noncompact case when the fixed locus is compact.We give a K-theoretic refinement by defining K-theoretic square root Euler classes and their localised versions.In a sequel we prove our invariants reproduce those of Borisov-Joyce. Contents 1. Introduction 1 2. (Special) orthogonal bundles 7 3. Localised Edidin-Graham class 10 4. Moduli of sheaves on CY 4 via orthogonal bundles 21 5. K-theoretic virtual class 34 6. Riemann-Roch 41 7. Torus localisation 43 8. Local Calabi-Yau 4-folds 49 9. Gauge theoretic motivation 51 References 54 32 This gives both the quadratic form (114) and the Serre duality Ext i pE, Eq ˚-Ext 4´i pE, Eq so crucial to this paper.

In [MT2] the Vafa-Witten theory of complex projective surfaces is lifted to oriented C * -equivariant cohomology theories. Here we study the K-theoretic refinement. It gives rational functions in t 1/2 invariant under t 1/2 ↔ t −1/2 which specialise to numerical Vafa-Witten invariants at t = 1.On the "instanton branch" the invariants give the virtual χ −t -genus refinement of Göttsche-Kool, extended to allow for strictly semistable sheaves. Applying modularity to their calculations gives predictions for the contribution of the "monopole branch". We calculate some cases and find perfect agreement. We also do calculations on K3 surfaces, finding Jacobi forms refining the usual modular forms, proving a conjecture of Göttsche-Kool.We determine the K-theoretic virtual classes of degeneracy loci using Eagon-Northcott complexes, and show they calculate refined Vafa-Witten invariants. Using this Laarakker [La1] proves universality results for the invariants.