Toric K\"ahler metrics seen from infinity, quantization and compact tropical amoebas

We consider the metric space of all toric K\"ahler metrics on a compact toric manifold; when "looking at it from infinity" (following Gromov), we obtain the tangent cone at infinity, which is parametrized by equivalence classes of complete geodesics. In the present paper, we study the associated limit for the family of metrics on the toric variety, its quantization, and degeneration of generic divisors. The limits of the corresponding K\"ahler polarizations become degenerate along the Lagrangian fibration defined by the moment map. This allows us to interpolate continuously between geometric quantizations in the holomorphic and real polarizations and show that the monomial holomorphic sections of the prequantum bundle converge to Dirac delta distributions supported on Bohr-Sommerfeld fibers. In the second part, we use these families of toric metric degenerations to study the limit of compact hypersurface amoebas and show that in Legendre transformed variables they are described by tropical amoebas. We believe that our approach gives a different, complementary, perspective on the relation between complex algebraic geometry and tropical geometry.Comment: v1: 32 pages, 5 figures; v2: 1 figure added; v3: 1 reference added; v4: some reorganization, 1 theorem (now 1.1) added; v5: final version, to appear in JD

Climate change impacts on water resources and reservoir management: uncertainty and adaptation for a mountain catchment in Northeast Portugal

Reservoirs often play an important role in mitigating water supply problems. However, the implications of climate change are not always considered in reservoir planning and management. This study aimed to address this challenge in the Alto Sabor watershed, northeast Portugal. The study analysed whether or not the shortage of water supply can be effectively addressed through the construction of a new reservoir (two-reservoir system) by considering future climate projections. The hydrological model Soil and Water Assessment Tool (SWAT) was calibrated and validated against daily-observed discharge and reservoir volume, with a good agreement between model predictions and observations. Outputs from four General Circulation Models (GCM) for two scenarios (RCP 4.5 and 8.5) were statistically downscaled and bias-corrected with ground observations. A general increase in temperature is expected in the future while the change in precipitation is more uncertain as per the differences among climatic models. In general, annual precipitation would slightly decrease while seasonal changes would be more significant, with more precipitation in winter and much less in spring and summer. SWAT simulations suggest that the existence of two-reservoir will better solve the water supply problems under current climate conditions compared to a single-reservoir system. However in the future, the reliability of this solution will decrease, especially due to the variability of projections from the different climatic models. The solution to water supply problems in this region, adopted taking only present-day climate into account, will likely be inefficient for water supply management under future climate conditions.This work was funded by FEDER funds through the Operational Programme for Competitiveness Factors - COMPETE and by National Funds through FCT - Foundation for Science and Technology under the project PTDC/AAG-MAA/4539/2012 / FCOMP-01-0124-FEDER-027863 (IND_CHANGE). J.P. Nunes was financially supported by FCT (Portuguese Science Foundation), and the European Social Fund through post-doctoral grant (SFRH/BPD/87571/2012). A.T. Monteiro is supported by FEDER funds through the Operational Programme for Competitiveness Factors - COMPETE and by National Funds through FCT - Foundation for Science and Technology under the UID/BIA/50027/2013 and POCI-01-0145-FEDER-006821. The authors would like to thank the Municipality of Bragança for the datasets on water inflows.info:eu-repo/semantics/publishedVersio

Approaches and methods for ecosystem services assessment in the North of Portugal: from supply modeling to land management optimization

In the last decades, ecosystems services (ES) in the North of Portugal have been assessed typically for sets of ES addressed individually based on indicators (e.g., LULC) but also through mechanistic and non-mechanistic modeling (e.g., hydrological modeling, InVEST). Economic evaluation has been applied based mostly on the combination of ES supply in biophysical units with market prices or value attributed by other techniques (e.g., avoided cost, unit value transfer). Such studies, and the approaches and methods involved, have been helpful in demonstrating the magnitude and dynamics of the supply of a series of ES in the region, both in biophysical and monetary units, and to inform regional planning and management of natural resources, such as forests. These studies have been changing the perception of stakeholders regarding forest systems and their management. Despite the importance of ES research conducted so far, there is an ongoing effort to further develop ES assessment in the region, conceptually and methodologically, namely by overcoming some of the intrinsic constraints of the approaches and methods used. Improvements intend to better integrate different ecosystem functions and services, to eliminate double counting, and to address the interactions between supply and demand of ES at several scales. The incorporation of capabilities of land-use and management optimization based on the supply and value of ES is also currently a research goal in the region. Recent developments have been based on operational research tools developed for the forest sector in the region of Bragan ça addressing ecosystem services from heuristics, multi-criteria and linear programming perspectives, expecting to solve complex spatially explicit management alternatives problems based on ES. In this presentation we will introduce these tools and their adjustment and applications in the assessment of ES in the region.info:eu-repo/semantics/publishedVersio