Localization for nonabelian group actions

Suppose $X$ is a compact symplectic manifold acted on by a compact Lie group $K$ (which may be nonabelian) in a Hamiltonian fashion, with moment map $\mu: X \to {\rm Lie}(K)^*$ and Marsden-Weinstein reduction \xred = \mu^{-1}(0)/K. There is then a natural surjective map $\kappa_0$ from the equivariant cohomology $H^*_K(X)$ of $X$ to the cohomology H^*(\xred). In this paper we prove a formula (Theorem 8.1, the residue formula) for the evaluation on the fundamental class of \xred of any \eta_0 \in H^*(\xred) whose degree is the dimension of \xred, provided that $0$ is a regular value of the moment map $\mu$ on $X$. This formula is given in terms of any class $\eta \in H^*_K(X)$ for which $\kappa_0(\eta ) = \eta_0$, and involves the restriction of $\eta$ to $K$-orbits $KF$ of components $F \subset X$ of the fixed point set of a chosen maximal torus $T \subset K$. Since $\kappa_0$ isComment: 42 pages, LaTex version no. 2.09, Introduction and Section 8 have been rewritten in revised versio

Restoring the Chesapeake--A Watershed Education and Restoration Project for Virginia Youth

A watershed education and restoration project was started in the Virginia portion of the Chesapeake Bay watershed in 2002. Over 37,000 hardwood seedlings were distributed to school groups and 4-H leaders in 19 counties. A geographic information system (GIS) identified subwatersheds in greatest need of riparian restoration. A Web site provided educational material and facilitated communication. Results indicate 3 years are needed to develop partnerships necessary for large-scale projects such as this one. Hands-on activities like planting trees result in large knowledge gains. Use of land-use maps and a Web site also result in knowledge gain about watershed

Sea-level driven land conversion and the formation of ghost forests

Ghost forests created by the submergence of low-lying land are one of the most striking indicators of climate change along the Atlantic coast of North America. Although dead trees at the margin of estuaries were described as early as 1910, recent research has led to new recognition that the submergence of terrestrial land is geographically widespread, ecologically and economically important, and globally relevant to the survival of coastal wetlands in the face of rapid sea level rise. This emerging understanding has in turn generated widespread interest in the physical and ecological mechanisms influencing the extent and pace of upland to wetland conversion. Choices between defending the coast from sea level rise and facilitating ecosystem transgression will play a fundamental role in determining the fate and function of low-lying coastal land

The effect of a small vegetation dieback event on salt marsh sediment transport

Vegetation is a critical component of the ecogeomorphic feedbacks that allow a salt marsh to build soil and accrete vertically. Vegetation dieback can therefore have detrimental effects on marsh stability, especially under conditions of rising sea levels. Here, we report a variety of sediment transport measurements associated with an unexpected, natural dieback in a rapidly prograding marsh in the Altamaha River Estuary, Georgia. We find that vegetation mortality led to a significant loss in elevation at the dieback site as evidenced by measurements of vertical accretion, erosion, and surface topography compared to vegetated refer- ence areas. Below-ground vegetation mortality led to reduced soil shear strength. The dieback site displayed an erosional, concave-up topographic profile, in contrast to the reference sites. At the location directly impacted by the dieback, there was a reduction in flood dominance of suspended sediment concentration. Our work illustrates how a vegetation disturbance can at least temporarily reverse the local trajectory of a prograding marsh and produce complex patterns of sediment transport

Sea Level-Driven Marsh Migration Results in Rapid Net Loss of Carbon

Sea level rise alters coastal carbon cycling by driving the rapid migration of coastal ecosystems, salinization of freshwater systems, and replacement of terrestrial forests with tidal wetlands. Wetland soils accumulate carbon (C) at faster rates than terrestrial soils, implying that sea level rise may lead to enhanced carbon accumulation. Here, we show that carbon stored in tree biomass greatly exceeds carbon stored in adjacent marsh soils so that marsh migration reduces total carbon stocks by 50% in less than 100years. Continued marsh soil carbon accumulation may eventually offset forest carbon loss, but we estimate that the time for replacement is similar to estimates of marsh survival (i.e., centuries), which suggests that forest C may never be replaced. These findings reveal a critical C source not included in coastal C budgets driven by migrating ecosystems and rapidly shifting allocations between carbon stored in soils and biomasS

Optimal hurricane overwash thickness for maximizing marsh resilience to sea level rise

The interplay between storms and sea level rise, and between ecology and sediment transport governs the behavior of rapidly evolving coastal ecosystems such as marshes and barrier islands. Sediment deposition during hurricanes is thought to increase the resilience of salt marshes to sea level rise by increasing soil elevation and vegetation productivity. We use mesocosms to simulate burial of Spartina alterniflora during hurricane-induced overwash events of various thickness (0-60 cm), and find that adventitious root growth within the overwash sediment layer increases total biomass by up to 120%. In contrast to most previous work illustrating a simple positive relationship between burial depth and vegetation productivity, our work reveals an optimum burial depth (510 cm) beyond which burial leads to plant mortality. The optimum burial depth increases with flooding frequency, indicating that storm deposition ameliorates flooding stress, and that its impact on productivity will become more important under accelerated sea level rise. Our results suggest that frequent, low magnitude storm events associated with naturally migrating islands may increase the resilience of marshes to sea level rise, and in turn, slow island migration rates. Synthesis: We find that burial deeper than the optimum results in reduced growth or mortality of marsh vegetation, which suggests that future increases in overwash thickness associated with more intense storms and artificial heightening of dunes could lead to less resilient marshes

Integrable Unsteady Motion With an Application to Ocean Eddies

Application of the Brown-Samelson theorem, which shows that particle motion is integrable in a class of vorticity-conserving, two-dimensional incompressible hows, is extended here to a class of explicit time dependent dynamically balanced flows in multilayered systems. Particle motion for nonsteady two-dimensional flows with discontinuities in the vorticity or potential vorticity fields (modon solutions) is shown to be integrable. An example of a two-layer modon solution constrained by observations of a Gulf Stream ring system is discussed

Spatio-temporal development of vegetation die-off in a submerging coastal marsh

In several places around the world, coastal marsh vegetation is converting to open water through the formation of pools. This is concerning, as vegetation die-off is expected to reduce the marshes\u27 capacity to adapt to sea level rise by vegetation-induced sediment accretion. Quantitative analyses of the spatial and temporal development of marsh vegetation die-off are scarce, although these are needed to understand the bio-geomorphic feedback effects of vegetation die-off on flow, erosion, and sedimentation. In this study, we quantified the spatial and temporal development of marsh vegetation die-off with aerial images from 1938 to 2010 in a submerging coastal marsh along the Blackwater River (Maryland, U.S.A). Our results indicate that die-off begins with conversion of marsh vegetation into bare open water pools that are relatively far (\u3e 75 m) from tidal channels. As vegetation die-off continues, pools expand, and new pools emerge at shorter and shorter distances from channels. Consequently larger pools are found at larger distances from the channels. Our results suggest that the size of the pools and possibly the connection of pools with the tidal channel system have important bio-geomorphic implications and aggravate marsh deterioration. Moreover, we found that the temporal development of vegetation die-off in moderately degraded marshes is similar as the spatial die-off development along a present-day gradient, which indicates that the contemporary die-off gradient might be considered a chronosequence that offers a unique opportunity to study vegetation die-off processes

Inferring tidal wetland stability from channel sediment fluxes: Observations and a conceptual model

Anthropogenic and climatic forces have modified the geomorphology of tidal wetlands over a range of timescales. Changes in land use, sediment supply, river flow, storminess, and sea level alter the layout of tidal channels, intertidal flats, and marsh plains; these elements define wetland complexes. Diagnostically, measurements of net sediment fluxes through tidal channels are high-temporal resolution, spatially integrated quantities that indicate (1) whether a complex is stable over seasonal timescales and (2) what mechanisms are leading to that state. We estimated sediment fluxes through tidal channels draining wetland complexes on the Blackwater and Transquaking Rivers, Maryland, USA. While the Blackwater complex has experienced decades of degradation and been largely converted to open water, the Transquaking complex has persisted as an expansive, vegetated marsh. The measured net export at the Blackwater complex (1.0kg/s or 0.56kg/m(2)/yr over the landward marsh area) was caused by northwesterly winds, which exported water and sediment on the subtidal timescale; tidally forced net fluxes were weak and precluded landward transport of suspended sediment from potential seaward sources. Though wind forcing also exported sediment at the Transquaking complex, strong tidal forcing and proximity to a turbidity maximum led to an import of sediment (0.031kg/s or 0.70kg/m(2)/yr). This resulted in a spatially averaged accretion of 3.9mm/yr, equaling the regional relative sea level rise. Our results suggest that in areas where seaward sediment supply is dominant, seaward wetlands may be more capable of withstanding sea level rise over the short term than landward wetlands. We propose a conceptual model to determine a complex\u27s tendency toward stability or instability based on sediment source, wetland channel location, and transport mechanisms. Wetlands with a reliable portfolio of sources and transport mechanisms appear better suited to offset natural and anthropogenic loss