PRACTICAL STOCHASTIC MODEL FOR CHEMICAL KINETICS

The Practical Stochastic Model is a simple and robust method to describe coupled chemical reactions. The connection between this stochastic method and a deterministic method was initially established to understand how the parameters and variables that describe the concentration in both methods were related. It was necessary to define two main concepts to make this connection: the filling of compartments or dilutions and the rate of reaction enhancement. The parameters, variables, and the time of the stochastic methods were scaled with the size of the compartment and were compared with a deterministic method. The deterministic approach was employed as an initial reference to achieve a consistent stochastic result. Finally, an independent robust stochastic method was obtained. This method could be compared with the Stochastic Simulation Algorithm developed by Gillespie, 1977. The Practical Stochastic Model produced absolute values that were essential to describe non-linear chemical reactions with a simple structure, and allowed for a correct description of the chemical kinetics.

Hysteresis and avalanches in the T=0 random field ising model with 2-spin flip dynamics

We study the nonequilibrium behavior of the three-dimensional Gaussian random-field Ising model at T=0 in the presence of a uniform external field using a two-spin-flip dynamics. The deterministic, history-dependent evolution of the system is compared with the one obtained with the standard one-spin-flip dynamics used in previous studies of the model. The change in the dynamics yields a significant suppression of coercivity, but the distribution of avalanches (in number and size) stays remarkably similar, except for the largest ones that are responsible for the jump in the saturation magnetization curve at low disorder in the thermodynamic limit. By performing a finite-size scaling study, we find strong evidence that the change in the dynamics does not modify the universality class of the disorder-induced phase transition.

A Computational Model for Observation in Quantum Mechanics

A computational model of observation in quantum mechanics is presented. The model provides a clean and simple computational paradigm which can be used to illustrate and possibly explain some of the unintuitive and unexpected behavior of some quantum mechanical systems. As examples, the model is used to simulate three seminal quantum mechanical experiments. The results obtained agree with the predictions of quantum mechanics (and physical measurements), yet the model is perfectly deterministic and maintains a notion of locality.

Comparison of stochastic parametrization approaches in a single-column model

We discuss and test the potential usefulness of single-column models (SCMs) for the testing of stchastic physics schemes that have been proposed for use in general circulation models (GCMs). We argue that although single column tests cannot be definitive in exposing the full behaviour of a stochastic method in the full GCM, and although there are differences between SCM testing of deterministic and stochastic methods, nonetheless SCM testing remains a useful tool. It is necessary to consider an ensemble of SCM runs produced by the stochastic method. These can be usefully compared to deterministic ensembles describing initial condition uncertainty and also to combinations of these (with structural model changes) into poor man's ensembles. The proposed methodology is demonstrated using an SCM experiment recently developed by the GCSS community, simulating the transitions between active and suppressed periods of tropical convection.

Comparison of stochastic parameterisation approaches in a single-column model

We discuss and test the potential usefulness of single-column models (SCMs) for the testing of stochastic physics schemes that have been proposed for use in general circulation models (GCMs). We argue that although single column tests cannot be definitive in exposing the full behaviour of a stochastic method in the full GCM, and although there are differences between SCM testing of deterministic and stochastic methods, SCM testing remains a useful tool. It is necessary to consider an ensemble of SCM runs produced by the stochastic method. These can be usefully compared to deterministic ensembles describing initial condition uncertainty and also to combinations of these (with structural model changes) into poor man's ensembles. The proposed methodology is demonstrated using an SCM experiment recently developed by the GCSS (GEWEX Cloud System Study) community, simulating transitions between active and suppressed periods of tropical convection.

Stochastic resonance in a nonlinear model of a rotating, stratified shear flow, with a simple stochastic inertia-gravity wave parameterization

We report on a numerical study of the impact of short, fast inertia-gravity waves on the large-scale, slowly-evolving flow with which they co-exist. A nonlinear quasi-geostrophic numerical model of a stratified shear flow is used to simulate, at reasonably high resolution, the evolution of a large-scale mode which grows due to baroclinic instability and equilibrates at finite amplitude. Ageostrophic inertia-gravity modes are filtered out of the model by construction, but their effects on the balanced flow are incorporated using a simple stochastic parameterization of the potential vorticity anomalies which they induce. The model simulates a rotating, two-layer annulus laboratory experiment, in which we recently observed systematic inertia-gravity wave generation by an evolving, large-scale flow. We find that the impact of the small-amplitude stochastic contribution to the potential vorticity tendency, on the model balanced flow, is generally small, as expected. In certain circumstances, however, the parameterized fast waves can exert a dominant influence. In a flow which is baroclinically-unstable to a range of zonal wavenumbers, and in which there is a close match between the growth rates of the multiple modes, the stochastic waves can strongly affect wavenumber selection. This is illustrated by a flow in which the parameterized fast modes dramatically re-partition the probability-density function for equilibrated large-scale zonal wavenumber. In a second case study, the stochastic perturbations are shown to force spontaneous wavenumber transitions in the large-scale flow, which do not occur in their absence. These phenomena are due to a stochastic resonance effect. They add to the evidence that deterministic parameterizations in general circulation models, of subgrid-scale processes such as gravity wave drag, cannot always adequately capture the full details of the nonlinear interaction.

Identifying the critical parameters of a cyanobacterial growth and movement model by using generalised sensitivity analysis

Bloom-forming and toxin-producing cyanobacteria remain a persistent nuisance across the world. Modelling of cyanobacteria in freshwaters is an important tool for understanding their population dynamics and predicting the location and timing of the bloom events in lakes and rivers. A new deterministic-mathematical model was developed, which simulates the growth and movement of cyanobacterial blooms in river systems. The model focuses on the mathematical description of the bloom formation, vertical migration and lateral transport of colonies within river environments by taking into account the major factors that affect the cyanobacterial bloom formation in rivers including, light, nutrients and temperature. A technique called generalised sensitivity analysis was applied to the model to identify the critical parameter uncertainties in the model and investigates the interaction between the chosen parameters of the model. The result of the analysis suggested that 8 out of 12 parameters were significant in obtaining the observed cyanobacterial behaviour in a simulation. It was found that there was a high degree of correlation between the half-saturation rate constants used in the model.

A policy model for secure information flow

When a computer program requires legitimate access to confidential data, the question arises whether such a program may illegally reveal sensitive information. This paper proposes a policy model to specify what information flow is permitted in a computational system. The security definition, which is based on a general notion of information lattices, allows various representations of information to be used in the enforcement of secure information flow in deterministic or nondeterministic systems. A flexible semantics-based analysis technique is presented, which uses the input-output relational model induced by an attacker's observational power, to compute the information released by the computational system. An illustrative attacker model demonstrates the use of the technique to develop a termination-sensitive analysis. The technique allows the development of various information flow analyses, parametrised by the attacker's observational power, which can be used to enforce what declassification policies.

Working Group 1: Future developments in deterministic and stochastic parametrizations

Our group considered the desirability of including representations of uncertainty in the development of parameterizations. (By ‘uncertainty’ here we mean the deviation of sub-grid scale fluxes or tendencies in any given model grid box from truth.) We unanimously agreed that the ECWMF should attempt to provide a more physical basis for uncertainty estimates than the very effective but ad hoc methods being used at present. Our discussions identified several issues that will arise.

Ensemble clustering in deterministic ensemble Kalman filters

Ensemble clustering (EC) can arise in data assimilation with ensemble square root filters (EnSRFs) using non-linear models: an M-member ensemble splits into a single outlier and a cluster of M−1 members. The stochastic Ensemble Kalman Filter does not present this problem. Modifications to the EnSRFs by a periodic resampling of the ensemble through random rotations have been proposed to address it. We introduce a metric to quantify the presence of EC and present evidence to dispel the notion that EC leads to filter failure. Starting from a univariate model, we show that EC is not a permanent but transient phenomenon; it occurs intermittently in non-linear models. We perform a series of data assimilation experiments using a standard EnSRF and a modified EnSRF by a resampling though random rotations. The modified EnSRF thus alleviates issues associated with EC at the cost of traceability of individual ensemble trajectories and cannot use some of algorithms that enhance performance of standard EnSRF. In the non-linear regimes of low-dimensional models, the analysis root mean square error of the standard EnSRF slowly grows with ensemble size if the size is larger than the dimension of the model state. However, we do not observe this problem in a more complex model that uses an ensemble size much smaller than the dimension of the model state, along with inflation and localisation. Overall, we find that transient EC does not handicap the performance of the standard EnSRF.

A unified neurofuzzy model for classification

This work proposes a unified neurofuzzy modelling scheme. To begin with, the initial fuzzy base construction method is based on fuzzy clustering utilising a Gaussian mixture model (GMM) combined with the analysis of covariance (ANOVA) decomposition in order to obtain more compact univariate and bivariate membership functions over the subspaces of the input features. The mean and covariance of the Gaussian membership functions are found by the expectation maximisation (EM) algorithm with the merit of revealing the underlying density distribution of system inputs. The resultant set of membership functions forms the basis of the generalised fuzzy model (GFM) inference engine. The model structure and parameters of this neurofuzzy model are identified via the supervised subspace orthogonal least square (OLS) learning. Finally, instead of providing deterministic class label as model output by convention, a logistic regression model is applied to present the classifier’s output, in which the sigmoid type of logistic transfer function scales the outputs of the neurofuzzy model to the class probability. Experimental validation results are presented to demonstrate the effectiveness of the proposed neurofuzzy modelling scheme.

Improving the evaluation of hydrological multi-model forecast performance in the Upper Danube Catchment

Medium range flood forecasting activities, driven by various meteorological forecasts ranging from high resolution deterministic forecasts to low spatial resolution ensemble prediction systems, share a major challenge in the appropriateness and design of performance measures. In this paper possible limitations of some traditional hydrological and meteorological prediction quality and verification measures are identified. Some simple modifications are applied in order to circumvent the problem of the autocorrelation dominating river discharge time-series and in order to create a benchmark model enabling the decision makers to evaluate the forecast quality and the model quality. Although the performance period is quite short the advantage of a simple cost-loss function as a measure of forecast quality can be demonstrated.

A mathematical model of the sterol regulatory element binding protein 2 cholesterol biosynthesis pathway

Cholesterol is one of the key constituents for maintaining the cellular membrane and thus the integrity of the cell itself. In contrast high levels of cholesterol in the blood are known to be a major risk factor in the development of cardiovascular disease. We formulate a deterministic nonlinear ordinary differential equation model of the sterol regulatory element binding protein 2 (SREBP-2) cholesterol genetic regulatory pathway in an hepatocyte. The mathematical model includes a description of genetic transcription by SREBP-2 which is subsequently translated to mRNA leading to the formation of 3-hydroxy-3-methylglutaryl coenzyme A reductase (HMGCR), a main precursor of cholesterol synthesis. Cholesterol synthesis subsequently leads to the regulation of SREBP-2 via a negative feedback formulation. Parameterised with data from the literature, the model is used to understand how SREBP-2 transcription and regulation affects cellular cholesterol concentration. Model stability analysis shows that the only positive steady-state of the system exhibits purely oscillatory, damped oscillatory or monotic behaviour under certain parameter conditions. In light of our findings we postulate how cholesterol homestasis is maintained within the cell and the advantages of our model formulation are discussed with respect to other models of genetic regulation within the literature.

Evaluation of the Plant–Craig stochastic convection scheme (v2.0) in the ensemble forecasting system MOGREPS-R (24 km) based on the Unified Model (v7.3)

The Plant–Craig stochastic convection parameterization (version 2.0) is implemented in the Met Office Regional Ensemble Prediction System (MOGREPS-R) and is assessed in comparison with the standard convection scheme with a simple stochastic scheme only, from random parameter variation. A set of 34 ensemble forecasts, each with 24 members, is considered, over the month of July 2009. Deterministic and probabilistic measures of the precipitation forecasts are assessed. The Plant–Craig parameterization is found to improve probabilistic forecast measures, particularly the results for lower precipitation thresholds. The impact on deterministic forecasts at the grid scale is neutral, although the Plant–Craig scheme does deliver improvements when forecasts are made over larger areas. The improvements found are greater in conditions of relatively weak synoptic forcing, for which convective precipitation is likely to be less predictable.

Flood Risk Assessment in Coastal Drainage Basins through a Multivariate Analysis within a GIS-Based Model

This paper presents a GIS-based multicriteria flood risk assessment and mapping approach applied to coastal drainage basins where hydrological data are not available. It involves risk to different types of possible processes: coastal inundation (storm surge), river, estuarine and flash flood, either at urban or natural areas, and fords. Based on the causes of these processes, several environmental indicators were taken to build-up the risk assessment. Geoindicators include geological-geomorphologic proprieties of Quaternary sedimentary units, water table, drainage basin morphometry, coastal dynamics, beach morphodynamics and microclimatic characteristics. Bioindicators involve coastal plain and low slope native vegetation categories and two alteration states. Anthropogenic indicators encompass land use categories properties such as: type, occupation density, urban structure type and occupation consolidation degree. The selected indicators were stored within an expert Geoenvironmental Information System developed for the State of Sao Paulo Coastal Zone (SIIGAL), which attributes were mathematically classified through deterministic approaches, in order to estimate natural susceptibilities (Sn), human-induced susceptibilities (Sa), return period of rain events (Ri), potential damages (Dp) and the risk classification (R), according to the equation R=(Sn.Sa.Ri).Dp. Thematic maps were automatically processed within the SIIGAL, in which automata cells (""geoenvironmental management units"") aggregating geological-geomorphologic and land use/native vegetation categories were the units of classification. The method has been applied to the Northern Littoral of the State of Sao Paulo (Brazil) in 32 small drainage basins, demonstrating to be very useful for coastal zone public politics, civil defense programs and flood management.