The canonical 8-form on manifolds with holonomy group Spin(9)

An explicit expression of the canonical 8-form on a Riemannian manifold with a Spin(9)-structure, in terms of the nine local symmetric involutions involved, is given. The list of explicit expressions of all the canonical forms related to Berger's list of holonomy groups is thus completed. Moreover, some results on Spin(9)-structures as G-structures defined by a tensor and on the curvature tensor of the Cayley planes, are obtained

The role of surface roughness, albedo, and Bowen ratio on ecosystem energy balance in the Eastern United States

Land cover and land use influence surface climate through differences in biophysical surface properties, including partitioning of sensible and latent heat (e.g., Bowen ratio), surface roughness, and albedo. Clusters of closely spaced eddy covariance towers (e.g., \u3c10 \u3ekm) over a variety of land cover and land use types provide a unique opportunity to study the local effects of land cover and land use on surface temperature. We assess contributions albedo, energy redistribution due to differences in surface roughness and energy redistribution due to differences in the Bowen ratio using two eddy covariance tower clusters and the coupled (land-atmosphere) Variable-Resolution Community Earth System Model. Results suggest that surface roughness is the dominant biophysical factor contributing to differences in surface temperature between forested and deforested lands. Surface temperature of open land is cooler (−4.8 °C to −0.05 °C) than forest at night and warmer (+0.16 °C to +8.2 °C) during the day at northern and southern tower clusters throughout the year, consistent with modeled calculations. At annual timescales, the biophysical contributions of albedo and Bowen ratio have a negligible impact on surface temperature, however the higher albedo of snow-covered open land compared to forest leads to cooler winter surface temperatures over open lands (−0.4 °C to −0.8 °C). In both the models and observation, the difference in mid-day surface temperature calculated from the sum of the individual biophysical factors is greater than the difference in surface temperature calculated from radiative temperature and potential temperature. Differences in measured and modeled air temperature at the blending height, assumptions about independence of biophysical factors, and model biases in surface energy fluxes may contribute to daytime biases

Constraining the date of a seasonally ice-free Arctic using a simple model

State-of-the-art climate models simulate a large spread in the projected decline of Arctic sea-ice area (SIA) over the 21st century. Here we diagnose causes of this intermodel spread using a model that approximates future SIA based on present SIA and the sensitivity of SIA to Arctic temperatures. This model accounts for 70-95% of the intermodel variance, with the majority of the spread arising from present-day biases. The remaining spread arises from model differences in Arctic warming, with some contribution from the local sea-ice sensitivity. Using observations to constrain the projections moves the probability of an ice-free Arctic forward by 10-35 years. Under a high-emissions scenario, an ice-free Arctic will likely (66% probability) occur in September around 2046 and from July-October around 2059. Under a medium-emissions scenario, this date occurs around 2051 in September and 2080 from July-October. These observation-based constraints imply ice-free Arctic summers are approaching faster than previously thought

Moduli spaces of G2 manifolds

This paper is a review of current developments in the study of moduli spaces of G2 manifolds. G2 manifolds are 7-dimensional manifolds with the exceptional holonomy group G2. Although they are odd-dimensional, in many ways they can be considered as an analogue of Calabi-Yau manifolds in 7 dimensions. They play an important role in physics as natural candidates for supersymmetric vacuum solutions of M-theory compactifications. Despite the physical motivation, many of the results are of purely mathematical interest. Here we cover the basics of G2 manifolds, local deformation theory of G2 structures and the local geometry of the moduli spaces of G2 structures.Comment: 31 pages, 2 figure

Influence of Vertical Heterogeneities in the Canopy Microenvironment on Interannual Variability of Carbon Uptake in Temperate Deciduous Forests

Vegetation structure and function are key design choices in terrestrial models that affect the relationship between carbon uptake and environmental drivers. Here, we investigate how representing canopy vertical structure in a terrestrial biosphere model- that is, micrometeorological, leaf area, and leaf water profiles- influences carbon uptake at five U.S. temperate deciduous forest sites in July. Specifically, we test whether the interannual variability (IAV) of gross primary productivity (GPP) responds differently to four abiotic environmental drivers- air temperature, relative humidity, incoming shortwave radiation, and soil moisture- using either a Community Land Model multilayer canopy model (CLM- ml) or a big- leaf model (CLM4.5/CLM5). We conclude that vertical leaf area and microclimatic profiles (temperature, humidity, and wind) do not impact GPP IAV compared to a single- layer model when plant hydraulics is excluded. However, with a mechanistic representation of plant hydraulics there is vertically varying water stress in CLM- ml, and the sensitivity of carbon uptake to particular climate variables changes with height, resulting in dampened canopy- scale GPP IAV relative to CLM4.5. Dampening is due to both a reduced dependence on soil moisture and opposing climatic forcing on different leaf layers. Such dampening is not evident in the single- layer representation of plant hydraulic water stress implemented in the recently released CLM5. Overall, both model representations of the canopy fail to accurately simulate observed GPP IAV and this may be related by their inability to capture the upper range of observed hourly GPP and diffuse light- GPP relationships that cannot be resolved by canopy structure alone.Key PointsExplicitly simulated leaf area and microclimatic profiles do not affect gross primary productivity (GPP) interannual variability compared to a - big- leaf- simplificationMultilayer plant hydraulics lead to vertically varying water stress, altering leaf- layer responses to interannual climate variationsAll model simulations underestimate hourly GPP compared to FLUXNET estimates, adversely impacting simulated GPP interannual variabilityPeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/156484/2/jgrg21710_am.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/156484/1/jgrg21710.pd

The streamwater microbiome encodes hydrologic data across scales

Many fundamental questions in hydrology remain unanswered due to the limited information that can be extracted from existing data sources. Microbial communities constitute a novel type of environmental data, as they are comprised of many thousands of taxonomically and functionally diverse groups known to respond to both biotic and abiotic environmental factors. As such, these microscale communities reflect a range of macroscale conditions and characteristics, some of which also drive hydrologic regimes. Here, we assess the extent to which streamwater microbial communities (as characterized by 16S gene amplicon sequence abundance) encode information about catchment hydrology across scales. We analyzed 64 summer streamwater DNA samples collected from subcatchments within the Willamette, Deschutes, and John Day river basins in Oregon, USA, which range 0.03–29,000 km2 in area and 343–2334 mm/year of precipitation. We applied information theory to quantify the breadth and depth of information about common hydrologic metrics encoded within microbial taxa. Of the 256 microbial taxa that spanned all three watersheds, we found 9.6 % (24.5/256) of taxa, on average, shared information with a given hydrologic metric, with a median 15.6 % (range = 12.4–49.2 %) reduction in uncertainty of that metric based on knowledge of the microbial biogeography. All of the hydrologic metrics we assessed, including daily discharge at different time lags, mean monthly discharge, and seasonal high and low flow durations were encoded within the microbial community. Summer microbial taxa shared the most information with winter mean flows. Our study demonstrates quantifiable relationships between streamwater microbial taxa and hydrologic metrics at different scales, likely resulting from the integration of multiple overlapping drivers of each. Streamwater microbial communities are rich sources of information that may contribute fresh insight to unresolved hydrologic questions

Active Amplification of the Terrestrial Albedo to Mitigate Climate Change: An Exploratory Study

This study explores the potential to enhance the reflectance of solar insolation by the human settlement and grassland components of the Earth's terrestrial surface as a climate change mitigation measure. Preliminary estimates derived using a static radiative transfer model indicate that such efforts could amplify the planetary albedo enough to offset the current global annual average level of radiative forcing caused by anthropogenic greenhouse gases by as much as 30 percent or 0.76 W/m2. Terrestrial albedo amplification may thus extend, by about 25 years, the time available to advance the development and use of low-emission energy conversion technologies which ultimately remain essential to mitigate long-term climate change. However, additional study is needed to confirm the estimates reported here and to assess the economic and environmental impacts of active land-surface albedo amplification as a climate change mitigation measure.Comment: 21 pages, 3 figures. In press with Mitigation and Adaptation Strategies for Global Change, Springer, N

Self-Duality in D <= 8-dimensional Euclidean Gravity

In the context of D-dimensional Euclidean gravity, we define the natural generalisation to D-dimensions of the self-dual Yang-Mills equations, as duality conditions on the curvature 2-form of a Riemannian manifold. Solutions to these self-duality equations are provided by manifolds of SU(2), SU(3), G_2 and Spin(7) holonomy. The equations in eight dimensions are a master set for those in lower dimensions. By considering gauge fields propagating on these self-dual manifolds and embedding the spin connection in the gauge connection, solutions to the D-dimensional equations for self-dual Yang-Mills fields are found. We show that the Yang-Mills action on such manifolds is topologically bounded from below, with the bound saturated precisely when the Yang-Mills field is self-dual. These results have a natural interpretation in supersymmetric string theory.Comment: 9 pages, Latex, factors in eqn. (6) corrected, acknowledgement and reference added, typos fixe

The G_2 sphere over a 4-manifold

We present a construction of a canonical G_2 structure on the unit sphere tangent bundle S_M of any given orientable Riemannian 4-manifold M. Such structure is never geometric or 1-flat, but seems full of other possibilities. We start by the study of the most basic properties of our construction. The structure is co-calibrated if, and only if, M is an Einstein manifold. The fibres are always associative. In fact, the associated 3-form results from a linear combination of three other volume 3-forms, one of which is the volume of the fibres. We also give new examples of co-calibrated structures on well known spaces. We hope this contributes both to the knowledge of special geometries and to the study of 4-manifolds.Comment: 13 page