Sequential Monte Carlo with Highly Informative Observations

We propose sequential Monte Carlo (SMC) methods for sampling the posterior distribution of state-space models under highly informative observation regimes, a situation in which standard SMC methods can perform poorly. A special case is simulating bridges between given initial and final values. The basic idea is to introduce a schedule of intermediate weighting and resampling times between observation times, which guide particles towards the final state. This can always be done for continuous-time models, and may be done for discrete-time models under sparse observation regimes; our main focus is on continuous-time diffusion processes. The methods are broadly applicable in that they support multivariate models with partial observation, do not require simulation of the backward transition (which is often unavailable), and, where possible, avoid pointwise evaluation of the forward transition. When simulating bridges, the last cannot be avoided entirely without concessions, and we suggest an epsilon-ball approach (reminiscent of Approximate Bayesian Computation) as a workaround. Compared to the bootstrap particle filter, the new methods deliver substantially reduced mean squared error in normalising constant estimates, even after accounting for execution time. The methods are demonstrated for state estimation with two toy examples, and for parameter estimation (within a particle marginal Metropolis--Hastings sampler) with three applied examples in econometrics, epidemiology and marine biogeochemistry.Comment: 25 pages, 11 figure

Parameterizing the microbial loop: an experiment in reducing model complexity

The structure of the plankton food web in the upper mixed layer has important implications for the export of biogenic material from the euphotic zone. While the action of the microbial loop causes material to be recycled near the surface, activity of the larger zooplankton leads to a significant downward flux of material. The balance between these pathways must be properly represented in climate models to predict carbon export. However, the number of biogeochemical compartments available to represent the food web is limited by the need to couple biogeochemical models with general circulation models. A structurally simple model is therefore sought, with a number of free parameters, which can be constrained by available observations to produce reliable estimates of export.A step towards addressing this aim is described: an attempt is made to emulate the behavior of an 11 compartment model with an explicit microbial loop, using a 4 compartment model. The latter, incorporating a basic microbial loop parameterization, is derived directly from the 'true' model. The results are compared with equivalent results for a 4 compartment model with no representation of the microbial loop. These non-identical twin experiments suggest that export estimates from 4 compartment models are prone to serious biases in regions where the action of the microbial loop is significant. The basic parameterization shows some promise in addressing the problem but a more sophisticated parameterization would be needed to produce reliable estimates. Some recommendations are made for future research

Shnol's theorem and the spectrum of long range operators

We extend some basic results known for finite range operators to long range operators with off-diagonal decay. Namely, we prove an analogy of Sch'nol's theorem. We also establish the connection between the almost sure spectrum of long range random operators and the spectra of deterministic periodic operators.Comment: To appear in Proc. AMS. Referee's comments incorporate

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

Modular System for Shelves and Coasts (MOSSCO v1.0) - a flexible and multi-component framework for coupled coastal ocean ecosystem modelling

Shelf and coastal sea processes extend from the atmosphere through the water column and into the sea bed. These processes are driven by physical, chemical, and biological interactions at local scales, and they are influenced by transport and cross strong spatial gradients. The linkages between domains and many different processes are not adequately described in current model systems. Their limited integration level in part reflects lacking modularity and flexibility; this shortcoming hinders the exchange of data and model components and has historically imposed supremacy of specific physical driver models. We here present the Modular System for Shelves and Coasts (MOSSCO, http://www.mossco.de), a novel domain and process coupling system tailored---but not limited--- to the coupling challenges of and applications in the coastal ocean. MOSSCO builds on the existing coupling technology Earth System Modeling Framework and on the Framework for Aquatic Biogeochemical Models, thereby creating a unique level of modularity in both domain and process coupling; the new framework adds rich metadata, flexible scheduling, configurations that allow several tens of models to be coupled, and tested setups for coastal coupled applications. That way, MOSSCO addresses the technology needs of a growing marine coastal Earth System community that encompasses very different disciplines, numerical tools, and research questions.Comment: 30 pages, 6 figures, submitted to Geoscientific Model Development Discussion

Transport, species-specific resource competition, and shallow water effects in coupled bio-physical ecosystem models for C. polykrikoides harmful algal blooms off the coast of Korea

This thesis examines the role of transport and environmental variables in determining the occurrence or suppression of harmful algal blooms (HABs). In the first part, a simple 2-D diagnostic model is used to hindcast HABs occurring off the coast of Korea using observations of averaged environmental factors including nutrient concentration. Hindcasting results using the model show that physical transport of HABs is of the same order of importance as the environmental conditions in controlling HABs. The model reproduces the interannual variability of the observe HABs off the coast of Korea. The relative importance of the environmental factors based on limiting functional analysis suggest that phosphate, ammonium, and temperature are the most important (in that order), and that nitrate and light limitations have very little influence on the behavior of HABs.In the second part, a modified version of the NPZD ecosystem model is used to examine the effects of species competition and nutrient limitation in the development of HABs. Solutions to the NPZD system of equations show that steady state (equilibrium) conditions cannot occur for two phytoplankton groups (one normal and one HAB) without the presence of zooplankton which effectively acts to replenish the nitrogen pool. When the zooplankton prefer different phytoplankton groups, different equilibrium states are found and depend on a threshold for nitrogen level that depends on functional group parameters (like growth and mortality rates). Solutions explain details of population dynamics underlying HABs and should be useful to find best-fit mode coefficients. In the third part, the NPZD model is modified to include a bottom boundary condition describing sediment nitrification-denitrification process that necessitates both the inclusion of a functional phytoplankton group that fixes nitrogen, and the phosphorus cycle. The model shows why previous models that do not include specified bottom boundary conditions unrealistically predict oligotrophic water in coastal regions, whereas inclusions of denitrification and nitrogen fixing group lead to phytoplankton spatial distributions consistent with observations