Stochastic climate theory and modeling

Stochastic methods are a crucial area in contemporary climate research and are increasingly being used in comprehensive weather and climate prediction models as well as reduced order climate models. Stochastic methods are used as subgrid-scale parameterizations (SSPs) as well as for model error representation, uncertainty quantification, data assimilation, and ensemble prediction. The need to use stochastic approaches in weather and climate models arises because we still cannot resolve all necessary processes and scales in comprehensive numerical weather and climate prediction models. In many practical applications one is mainly interested in the largest and potentially predictable scales and not necessarily in the small and fast scales. For instance, reduced order models can simulate and predict large-scale modes. Statistical mechanics and dynamical systems theory suggest that in reduced order models the impact of unresolved degrees of freedom can be represented by suitable combinations of deterministic and stochastic components and non-Markovian (memory) terms. Stochastic approaches in numerical weather and climate prediction models also lead to the reduction of model biases. Hence, there is a clear need for systematic stochastic approaches in weather and climate modeling. In this review, we present evidence for stochastic effects in laboratory experiments. Then we provide an overview of stochastic climate theory from an applied mathematics perspective. We also survey the current use of stochastic methods in comprehensive weather and climate prediction models and show that stochastic parameterizations have the potential to remedy many of the current biases in these comprehensive models.

Bifurcations and state changes in the human alpha rhythm: Theory and experiment

Despite many decades investigating scalp recordable 8–13-Hz (alpha) electroencephalographic activity, no consensus has yet emerged regarding its physiological origins nor its functional role in cognition. Here we outline a detailed, physiologically meaningful, theory for the genesis of this rhythm that may provide important clues to its functional role. In particular we find that electroencephalographically plausible model dynamics, obtained with physiological admissible parameterisations, reveals a cortex perched on the brink of stability, which when perturbed gives rise to a range of unanticipated complex dynamics that include 40-Hz (gamma) activity. Preliminary experimental evidence, involving the detection of weak nonlinearity in resting EEG using an extension of the well-known surrogate data method, suggests that nonlinear (deterministic) dynamics are more likely to be associated with weakly damped alpha activity. Thus rather than the “alpha rhythm” being an idling rhythm it may be more profitable to conceive it as a readiness rhythm.

Theory and observations of ice particle evolution in cirrus using Doppler radar: evidence for aggregation

Vertically pointing Doppler radar has been used to study the evolution of ice particles as they sediment through a cirrus cloud. The measured Doppler fall speeds, together with radar-derived estimates for the altitude of cloud top, are used to estimate a characteristic fall time tc for the `average' ice particle. The change in radar reflectivity Z is studied as a function of tc, and is found to increase exponentially with fall time. We use the idea of dynamically scaling particle size distributions to show that this behaviour implies exponential growth of the average particle size, and argue that this exponential growth is a signature of ice crystal aggregation.

MEASUREMENT AND MODELING OF THE TOXICITY OF BINARY MIXTURES IN THE NEMATODE CAENORHABDITIS ELEGANS-A TEST OF INDEPENDENT ACTION

Ecological risk assessments must increasingly consider the effects of chemical mixtures on the environment as anthropogenic pollution continues to grow in complexity. Yet testing every possible mixture combination is impractical and unfeasible; thus, there is an urgent need for models that can accurately predict mixture toxicity from single-compound data. Currently, two models are frequently used to predict mixture toxicity from single-compound data: Concentration addition and independent action (IA). The accuracy of the predictions generated by these models is currently debated and needs to be resolved before their use in risk assessments can be fully justified. The present study addresses this issue by determining whether the IA model adequately described the toxicity of binary mixtures of five pesticides and other environmental contaminants (cadmium, chlorpyrifos, diuron, nickel, and prochloraz) each with dissimilar modes of action on the reproduction of the nematode Caenorhabditis elegans. In three out of 10 cases, the IA model failed to describe mixture toxicity adequately with significant or antagonism being observed. In a further three cases, there was an indication of synergy, antagonism, and effect-level-dependent deviations, respectively, but these were not statistically significant. The extent of the significant deviations that were found varied, but all were such that the predicted percentage effect seen on reproductive output would have been wrong by 18 to 35% (i.e., the effect concentration expected to cause a 50% effect led to an 85% effect). The presence of such a high number and variety of deviations has important implications for the use of existing mixture toxicity models for risk assessments, especially where all or part of the deviation is synergistic.

Reconciling internalization theory and the eclectic paradigm

The eclectic paradigm of Dunning (1980) (with its OLI and four motives for FDI framework) can be reconciled with the firm and country matrix of Rugman (1981). However, the fit is not perfect. The main reason for misalignment is that Dunning is focused upon outward FDI into host economies, whereas Rugman’s matrix is for firm-level strategy covering MNE activity in both home and host countries.