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Richard McGehee

Publications and source records attributed to Richard McGehee.

7 recordsLinked to original sources

Nitrogen-induced hysteresis in grassland biodiversity: a theoretical test of litter-mediated mechanisms

The global rise in anthropogenic reactive nitrogen (N) and the negative impacts of N deposition on terrestrial plant diversity are well-documented. The R* theory of resource competition predicts reversible decreases in plant diversity in response to N loading. However, empirical evidence for the reversibility of N-induced biodiversity loss is mixed. In a long-term N-enrichment experiment in Minnesota, a low-diversity state that emerged during N addition has persisted for decades after additions ceased. Hypothesized mechanisms preventing recovery of biodiversity include nutrient recycling, insufficient external seed supply, and litter inhibition of plant growth. Here we present an ODE model that unifies these mechanisms, produces bistability at intermediate N inputs, and qualitatively matches the observed hysteresis at Cedar Creek. Key features of the model, including native species' growth advantage in low-N conditions and limitation by litter accumulation, generalize from Cedar Creek to North American grasslands. Our results suggest that effective biodiversity restoration in these systems may require management beyond reducing N inputs, such as burning, grazing, haying, and seed additions. By coupling resource competition with an additional inter-specific inhibitory process, the model also illustrates a general mechanism for bistability and hysteresis that may occur in multiple ecosystem types.

q-bio.PE

A new method of carbon budget analysis with application to present and paleo atmospheric concentration data sets

We introduce a new method for analyzing the carbon budget using box models and a mass balance approach. The method describes the net flow of carbon between the atmosphere and other reservoirs. The method assumes that the data can be explained by having the carbon move in and out of the atmosphere through two reservoirs, one consisting of isotopically light carbon (biotic) and the other consisting of isotopically heavy carbon (abiotic). The systems are underdetermined from the data, so the Occam's razor approach is to assume that the least amount of carbon moves between the atmosphere and the reservoirs. As data from known sources and sinks are added to the model, one can determine the constraints on the unknown sources and sinks. To illustrate the method, we analyze data from the Mauna Loa Observatory and data from Antarctic ice cores.

q-bio.QM

Approximating Annual Mean Incoming Solar Radiation

We derive the Legendre series expansion for the insolation distribution on rapidly rotating planets as a function of sine of the latitude and the planet's obliquity. We give an explicit formula for the coefficients of this series as it depends on the obliquity and approximate the convergence rate. We determine the optimal truncation of the series for use in climate models and compare this approximation to other approximations in the literature.

astro-ph.EP

Heat conduction through permafrost and its potential for explosive behavior

The recent widespread thaw of permafrost has led to observations of explosive gas emissions, which expel ice and soil debris and leave behind large craters. This phenomenon appears to be caused by a buildup of pressure from below the permafrost, possibly due to gas released as permafrost melts, followed by a sudden emission of gas through the surface. Although there have been some studies modeling the processes involved in crater formation using computationally complex models, we propose that these explosive events can be attributed to a simple heat diffusion-based process. Under certain boundary conditions and parameters, this may be sufficient to describe the explosive behavior observed. We demonstrate this effect by linearly increasing surface temperature from average monthly values (1961-1990) at an example latitude, which causes more dramatic melting from below the permafrost than above. This may lead to a buildup of gas pressure, if the permafrost is both continuous and has a high ice saturation, and has the potential for sudden gas release.

physics.geo-ph

A simple formula for a planet's mean annual insolation by latitude

In this paper, we use a sixth order Legendre series expansion to approximate the mean annual insolation by latitude of a planet with obliquity angle $β$, leading to faster computations with little loss in the accuracy of results. We discuss differences between our method and selected computational results for insolation found in the literature.

astro-ph.EP

Nonsmooth frameworks for an extended Budyko model

In latitude-dependent energy balance models, ice-free and ice-covered conditions form physical boundaries of the system. With carbon dioxide treated as a bifurcation parameter, the resulting bifurcation diagram is nonsmooth with curves of equilibria and boundaries forming corners at points of intersection. Over long time scales, atmospheric carbon dioxide varies dynamically and the nonsmooth diagram becomes a set of quasi-equilibria. {However, when introducing carbon dynamics, care must be taken with the physical boundaries and appropriate boundary motion specified. In this article, we extend an energy balance model to include slowly varying carbon dioxide and develop a nonsmooth framework based on physically relevant boundary dynamics. Within this framework, we prove existence and uniqueness of solutions, as well as invariance of the region of phase space bounded by ice-free and ice-covered states.

math.DS

Periodic Orbits for a Discontinuous Vector Field Arising from a Conceptual Model of Glacial Cycles

Conceptual climate models provide an approach to understanding climate processes through a mathematical analysis of an approximation to reality. Recently, these models have also provided interesting examples of nonsmooth dynamical systems. Here we discuss a conceptual model of glacial cycles consisting of a system of three ordinary differential equations defining a discontinuous vector field. We show that this system has a large periodic orbit crossing the discontinuity boundary. This orbit can be interpreted as an intrinsic cycling of the Earth's climate giving rise to alternating glaciations and deglaciations.

math.DS