Coupling the PLANKTOM5.0 marine ecosystem model to the OCCAM 1º ocean general circulation model for investigation of the sensitivity of global biogeochemical cycles to variations in ecosystem complexity and physical environment

The earliest marine ecosystem models consisted of a simple representation of the main features of marine ecosystems, including, typically, variables for phytoplankton, zooplankton, nutrient and detritus (NPZD models). These have been incorporated into ocean general circulation models to give a basic representation of ecosystem function, providing predictions of bulk quantities such as global primary production, export and biomass which can be compared with available observations. A recent trend has been to increase the number of phytoplankton and zooplankton groups modelled, as analogues of different plankton groups observed to exist in the ocean, for example diatoms and cocolithophores (the so-called plankton functional type or PFT approach). It is usually assumed that the increase in complexity of the model will result in simulated ecosystems which more faithfully reproduce observations than NPZD models, but this has not been demonstrated systematically. The robustness of the PFT models to changes in model parameters and to changes to the physical environment in which it is embedded, have not been investigated. As a first step towards these goals, we incorporate a state-of-the-art PFT model, PLANKTOM5.0 into the OCCAM ocean general circulation model. A 6 year simulation is performed, covering the years 1989-1994 with identical parameter choices to an existing run of PLANKTOM5.0 coupled to the OPA general circulation model. This document describes the development of the coupled model and the 6 year simulation. Comparison with the OPA model and sensitivity of the solution to parameter choices will be described in a forthcoming journal paper

Third Order Trace Formula

In (J. Funct. Anal. 257, 1092-1132 (2009)), Dykema and Skripka showed the existence of higher order spectral shift functions when the unperturbed self-adjoint operator is bounded and the perturbations is Hilbert-Schmidt. In this article, we give a different proof for the existence of spectral shift function for the third order when the unperturbed operator is self-adjoint (bounded or unbounded, but bounded below).Comment: 26 page

Robust Emergent Activity in Dynamical Networks

We study the evolution of a random weighted network with complex nonlinear dynamics at each node, whose activity may cease as a result of interactions with other nodes. Starting from a knowledge of the micro-level behaviour at each node, we develop a macroscopic description of the system in terms of the statistical features of the subnetwork of active nodes. We find the asymptotic characteristics of this subnetwork to be remarkably robust: the size of the active set is independent of the total number of nodes in the network, and the average degree of the active nodes is independent of both the network size and its connectivity. These results suggest that very different networks evolve to active subnetworks with the same characteristic features. This has strong implications for dynamical networks observed in the natural world, notably the existence of a characteristic range of links per species across ecological systems.Comment: 4 pages, 5 figure