Impact of Resolution on the Tropical Pacific Circulation in a Matrix of Coupled Models

Results are presented from a matrix of coupled model integrations, using atmosphere resolutions of 135 and 90 km, and ocean resolutions of 1° and 1/3°, to study the impact of resolution on simulated climate. The mean state of the tropical Pacific is found to be improved in the models with a higher ocean resolution. Such an improved mean state arises from the development of tropical instability waves, which are poorly resolved at low resolution; these waves reduce the equatorial cold tongue bias. The improved ocean state also allows for a better simulation of the atmospheric Walker circulation. Several sensitivity studies have been performed to further understand the processes involved in the different component models. Significantly decreasing the horizontal momentum dissipation in the coupled model with the lower-resolution ocean has benefits for the mean tropical Pacific climate, but decreases model stability. Increasing the momentum dissipation in the coupled model with the higher-resolution ocean degrades the simulation toward that of the lower-resolution ocean. These results suggest that enhanced ocean model resolution can have important benefits for the climatology of both the atmosphere and ocean components of the coupled model, and that some of these benefits may be achievable at lower ocean resolution, if the model formulation allows.

A GIS-based empirical model for vegetation prediction in Lefka Ori, Crete

The aim of the study was to establish and verify a predictive vegetation model for plant community distribution in the alti-Mediterranean zone of the Lefka Ori massif, western Crete. Based on previous work three variables were identified as significant determinants of plant community distribution, namely altitude, slope angle and geomorphic landform. The response of four community types against these variables was tested using classification trees analysis in order to model community type occurrence. V-fold cross-validation plots were used to determine the length of the best fitting tree. The final 9node tree selected, classified correctly 92.5% of the samples. The results were used to provide decision rules for the construction of a spatial model for each community type. The model was implemented within a Geographical Information System (GIS) to predict the distribution of each community type in the study site. The evaluation of the model in the field using an error matrix gave an overall accuracy of 71%. The user's accuracy was higher for the Crepis-Cirsium (100%) and Telephium-Herniaria community type (66.7%) and relatively lower for the Peucedanum-Alyssum and Dianthus-Lomelosia community types (63.2% and 62.5%, respectively). Misclassification and field validation points to the need for improved geomorphological mapping and suggests the presence of transitional communities between existing community types.

A GIS-based empirical model for vegetation prediction in Lefka Ori, Crete

The aim of the study was to establish and verify a predictive vegetation model for plant community distribution in the alti-Mediterranean zone of the Lefka Ori massif, western Crete. Based on previous work three variables were identified as significant determinants of plant community distribution, namely altitude, slope angle and geomorphic landform. The response of four community types against these variables was tested using classification trees analysis in order to model community type occurrence. V-fold cross-validation plots were used to determine the length of the best fitting tree. The final 9node tree selected, classified correctly 92.5% of the samples. The results were used to provide decision rules for the construction of a spatial model for each community type. The model was implemented within a Geographical Information System (GIS) to predict the distribution of each community type in the study site. The evaluation of the model in the field using an error matrix gave an overall accuracy of 71%. The user's accuracy was higher for the Crepis-Cirsium (100%) and Telephium-Herniaria community type (66.7%) and relatively lower for the Peucedanum-Alyssum and Dianthus-Lomelosia community types (63.2% and 62.5%, respectively). Misclassification and field validation points to the need for improved geomorphological mapping and suggests the presence of transitional communities between existing community types.

Predicting the thermal inactivation of bacteria in a solid matrix: simulation studies on the relative effects of microbial thermal resistance parameters and process conditions

A combined mathematical model for predicting heat penetration and microbial inactivation in a solid body heated by conduction was tested experimentally by inoculating agar cylinders with Salmonella typhimurium or Enterococcus faecium and heating in a water bath. Regions of growth where bacteria had survived after heating were measured by image analysis and compared with model predictions. Visualisation of the regions of growth was improved by incorporating chromogenic metabolic indicators into the agar. Preliminary tests established that the model performed satisfactorily with both test organisms and with cylinders of different diameter. The model was then used in simulation studies in which the parameters D, z, inoculum size, cylinder diameter and heating temperature were systematically varied. These simulations showed that the biological variables D, z and inoculum size had a relatively small effect on the time needed to eliminate bacteria at the cylinder axis in comparison with the physical variables heating temperature and cylinder diameter, which had a much greater relative effect. (c) 2005 Elsevier B.V All rights reserved.

A tunable radial basis function model for nonlinear system identification using particle swarm optimisation

A tunable radial basis function (RBF) network model is proposed for nonlinear system identification using particle swarm optimisation (PSO). At each stage of orthogonal forward regression (OFR) model construction, PSO optimises one RBF unit's centre vector and diagonal covariance matrix by minimising the leave-one-out (LOO) mean square error (MSE). This PSO aided OFR automatically determines how many tunable RBF nodes are sufficient for modelling. Compared with the-state-of-the-art local regularisation assisted orthogonal least squares algorithm based on the LOO MSE criterion for constructing fixed-node RBF network models, the PSO tuned RBF model construction produces more parsimonious RBF models with better generalisation performance and is computationally more efficient.

Sparse model identification using orthogonal forward regression with basis pursuit and D-optimality

An efficient model identification algorithm for a large class of linear-in-the-parameters models is introduced that simultaneously optimises the model approximation ability, sparsity and robustness. The derived model parameters in each forward regression step are initially estimated via the orthogonal least squares (OLS), followed by being tuned with a new gradient-descent learning algorithm based on the basis pursuit that minimises the l(1) norm of the parameter estimate vector. The model subset selection cost function includes a D-optimality design criterion that maximises the determinant of the design matrix of the subset to ensure model robustness and to enable the model selection procedure to automatically terminate at a sparse model. The proposed approach is based on the forward OLS algorithm using the modified Gram-Schmidt procedure. Both the parameter tuning procedure, based on basis pursuit, and the model selection criterion, based on the D-optimality that is effective in ensuring model robustness, are integrated with the forward regression. As a consequence the inherent computational efficiency associated with the conventional forward OLS approach is maintained in the proposed algorithm. Examples demonstrate the effectiveness of the new approach.

A neurofuzzy network knowledge extraction and extended gram-Schmidt algorithm for model subspace decomposition

This paper introduces a new neurofuzzy model construction and parameter estimation algorithm from observed finite data sets, based on a Takagi and Sugeno (T-S) inference mechanism and a new extended Gram-Schmidt orthogonal decomposition algorithm, for the modeling of a priori unknown dynamical systems in the form of a set of fuzzy rules. The first contribution of the paper is the introduction of a one to one mapping between a fuzzy rule-base and a model matrix feature subspace using the T-S inference mechanism. This link enables the numerical properties associated with a rule-based matrix subspace, the relationships amongst these matrix subspaces, and the correlation between the output vector and a rule-base matrix subspace, to be investigated and extracted as rule-based knowledge to enhance model transparency. The matrix subspace spanned by a fuzzy rule is initially derived as the input regression matrix multiplied by a weighting matrix that consists of the corresponding fuzzy membership functions over the training data set. Model transparency is explored by the derivation of an equivalence between an A-optimality experimental design criterion of the weighting matrix and the average model output sensitivity to the fuzzy rule, so that rule-bases can be effectively measured by their identifiability via the A-optimality experimental design criterion. The A-optimality experimental design criterion of the weighting matrices of fuzzy rules is used to construct an initial model rule-base. An extended Gram-Schmidt algorithm is then developed to estimate the parameter vector for each rule. This new algorithm decomposes the model rule-bases via an orthogonal subspace decomposition approach, so as to enhance model transparency with the capability of interpreting the derived rule-base energy level. This new approach is computationally simpler than the conventional Gram-Schmidt algorithm for resolving high dimensional regression problems, whereby it is computationally desirable to decompose complex models into a few submodels rather than a single model with large number of input variables and the associated curse of dimensionality problem. Numerical examples are included to demonstrate the effectiveness of the proposed new algorithm.

Automatic nonlinear predictive model-construction algorithm using forward regression and the PRESS statistic

An automatic nonlinear predictive model-construction algorithm is introduced based on forward regression and the predicted-residual-sums-of-squares (PRESS) statistic. The proposed algorithm is based on the fundamental concept of evaluating a model's generalisation capability through crossvalidation. This is achieved by using the PRESS statistic as a cost function to optimise model structure. In particular, the proposed algorithm is developed with the aim of achieving computational efficiency, such that the computational effort, which would usually be extensive in the computation of the PRESS statistic, is reduced or minimised. The computation of PRESS is simplified by avoiding a matrix inversion through the use of the orthogonalisation procedure inherent in forward regression, and is further reduced significantly by the introduction of a forward-recursive formula. Based on the properties of the PRESS statistic, the proposed algorithm can achieve a fully automated procedure without resort to any other validation data set for iterative model evaluation. Numerical examples are used to demonstrate the efficacy of the algorithm.

Kinetic multi-layer model of aerosol surface and bulk chemistry (KM-SUB): the influence of interfacial transport and bulk diffusion on the oxidation of oleic acid by ozone

We present a novel kinetic multi-layer model that explicitly resolves mass transport and chemical reaction at the surface and in the bulk of aerosol particles (KM-SUB). The model is based on the PRA framework of gas-particle interactions (Poschl-Rudich-Ammann, 2007), and it includes reversible adsorption, surface reactions and surface-bulk exchange as well as bulk diffusion and reaction. Unlike earlier models, KM-SUB does not require simplifying assumptions about steady-state conditions and radial mixing. The temporal evolution and concentration profiles of volatile and non-volatile species at the gas-particle interface and in the particle bulk can be modeled along with surface concentrations and gas uptake coefficients. In this study we explore and exemplify the effects of bulk diffusion on the rate of reactive gas uptake for a simple reference system, the ozonolysis of oleic acid particles, in comparison to experimental data and earlier model studies. We demonstrate how KM-SUB can be used to interpret and analyze experimental data from laboratory studies, and how the results can be extrapolated to atmospheric conditions. In particular, we show how interfacial and bulk transport, i.e., surface accommodation, bulk accommodation and bulk diffusion, influence the kinetics of the chemical reaction. Sensitivity studies suggest that in fine air particulate matter oleic acid and compounds with similar reactivity against ozone (carbon-carbon double bonds) can reach chemical lifetimes of many hours only if they are embedded in a (semi-)solid matrix with very low diffusion coefficients (< 10(-10) cm(2) s(-1)). Depending on the complexity of the investigated system, unlimited numbers of volatile and non-volatile species and chemical reactions can be flexibly added and treated with KM-SUB. We propose and intend to pursue the application of KM-SUB as a basis for the development of a detailed master mechanism of aerosol chemistry as well as for the derivation of simplified but realistic parameterizations for large-scale atmospheric and climate models.

Kinetic multi-layer model of aerosol surface and bulk chemistry (KM-SUB): the influence of interfacial transport and bulk diffusion on the oxidation of oleic acid by ozone

We present a novel kinetic multi-layer model that explicitly resolves mass transport and chemical reaction at the surface and in the bulk of aerosol particles (KM-SUB). The model is based on the PRA framework of gas–particle interactions (P¨oschl et al., 5 2007), and it includes reversible adsorption, surface reactions and surface-bulk exchange as well as bulk diffusion and reaction. Unlike earlier models, KM-SUB does not require simplifying assumptions about steady-state conditions and radial mixing. The temporal evolution and concentration profiles of volatile and non-volatile species at the gas-particle interface and in the particle bulk can be modeled along with surface 10 concentrations and gas uptake coefficients. In this study we explore and exemplify the effects of bulk diffusion on the rate of reactive gas uptake for a simple reference system, the ozonolysis of oleic acid particles, in comparison to experimental data and earlier model studies. We demonstrate how KM-SUB can be used to interpret and analyze experimental data from laboratory stud15 ies, and how the results can be extrapolated to atmospheric conditions. In particular, we show how interfacial transport and bulk transport, i.e., surface accommodation, bulk accommodation and bulk diffusion, influence the kinetics of the chemical reaction. Sensitivity studies suggest that in fine air particulate matter oleic acid and compounds with similar reactivity against ozone (C=C double bonds) can reach chemical lifetimes of 20 multiple hours only if they are embedded in a (semi-)solid matrix with very low diffusion coefficients (10−10 cm2 s−1). Depending on the complexity of the investigated system, unlimited numbers of volatile and non-volatile species and chemical reactions can be flexibly added and treated with KM-SUB. We propose and intend to pursue the application of KM-SUB 25 as a basis for the development of a detailed master mechanism of aerosol chemistry as well as for the derivation of simplified but realistic parameterizations for large-scale atmospheric and climate models.

Nonlinear model structure design and construction using orthogonal least squares and D-optimality design

A very efficient learning algorithm for model subset selection is introduced based on a new composite cost function that simultaneously optimizes the model approximation ability and model robustness and adequacy. The derived model parameters are estimated via forward orthogonal least squares, but the model subset selection cost function includes a D-optimality design criterion that maximizes the determinant of the design matrix of the subset to ensure the model robustness, adequacy, and parsimony of the final model. The proposed approach is based on the forward orthogonal least square (OLS) algorithm, such that new D-optimality-based cost function is constructed based on the orthogonalization process to gain computational advantages and hence to maintain the inherent advantage of computational efficiency associated with the conventional forward OLS approach. Illustrative examples are included to demonstrate the effectiveness of the new approach.

The effect of nonlinearity on the variational assimilation of satellite observations using a simple column model

Cloud imagery is not currently used in numerical weather prediction (NWP) to extract the type of dynamical information that experienced forecasters have extracted subjectively for many years. For example, rapidly developing mid-latitude cyclones have characteristic signatures in the cloud imagery that are most fully appreciated from a sequence of images rather than from a single image. The Met Office is currently developing a technique to extract dynamical development information from satellite imagery using their full incremental 4D-Var (four-dimensional variational data assimilation) system. We investigate a simplified form of this technique in a fully nonlinear framework. We convert information on the vertical wind field, w(z), and profiles of temperature, T(z, t), and total water content, qt (z, t), as functions of height, z, and time, t, to a single brightness temperature by defining a 2D (vertical and time) variational assimilation testbed. The profiles of w, T and qt are updated using a simple vertical advection scheme. We define a basic cloud scheme to obtain the fractional cloud amount and, when combined with the temperature field, we convert this information into a brightness temperature, having developed a simple radiative transfer scheme. With the exception of some matrix inversion routines, all our code is developed from scratch. Throughout the development process we test all aspects of our 2D assimilation system, and then run identical twin experiments to try and recover information on the vertical velocity, from a sequence of observations of brightness temperature. This thesis contains a comprehensive description of our nonlinear models and assimilation system, and the first experimental results.

Breakdown of hydrostatic balance at convective scales in the forecast errors in the Met Office Unified Model

For data assimilation in numerical weather prediction, the initial forecast-error covariance matrix Pf is required. For variational assimilation it is particularly important to prescribe an accurate initial matrix Pf, since Pf is either static (in the 3D-Var case) or constant at the beginning of each assimilation window (in the 4D-Var case). At large scales the atmospheric flow is well approximated by hydrostatic balance and this balance is strongly enforced in the initial matrix Pf used in operational variational assimilation systems such as that of the Met Office. However, at convective scales this balance does not necessarily hold any more. Here we examine the extent to which hydrostatic balance is valid in the vertical forecast-error covariances for high-resolution models in order to determine whether there is a need to relax this balance constraint in convective-scale data assimilation. We use the Met Office Global and Regional Ensemble Prediction System (MOGREPS) and a 1.5 km resolution version of the Unified Model for a case study characterized by the presence of convective activity. An ensemble of high-resolution forecasts valid up to three hours after the onset of convection is produced. We show that at 1.5 km resolution hydrostatic balance does not hold for forecast errors in regions of convection. This indicates that in the presence of convection hydrostatic balance should not be enforced in the covariance matrix used for variational data assimilation at this scale. The results show the need to investigate covariance models that may be better suited for convective-scale data assimilation. Finally, we give a measure of the balance present in the forecast perturbations as a function of the horizontal scale (from 3–90 km) using a set of diagnostics. Copyright © 2012 Royal Meteorological Society and British Crown Copyright, the Met Office

A model-based PID controller for Hammerstein systems using B-spline neural networks

In this paper, a new model-based proportional–integral–derivative (PID) tuning and controller approach is introduced for Hammerstein systems that are identified on the basis of the observational input/output data. The nonlinear static function in the Hammerstein system is modelled using a B-spline neural network. The control signal is composed of a PID controller, together with a correction term. Both the parameters in the PID controller and the correction term are optimized on the basis of minimizing the multistep ahead prediction errors. In order to update the control signal, the multistep ahead predictions of the Hammerstein system based on B-spline neural networks and the associated Jacobian matrix are calculated using the de Boor algorithms, including both the functional and derivative recursions. Numerical examples are utilized to demonstrate the efficacy of the proposed approaches.

Integration of a 3D Variational data assimilation scheme with a coastal area morphodynamic model of Morecambe Bay

This paper describes the implementation of a 3D variational (3D-Var) data assimilation scheme for a morphodynamic model applied to Morecambe Bay, UK. A simple decoupled hydrodynamic and sediment transport model is combined with a data assimilation scheme to investigate the ability of such methods to improve the accuracy of the predicted bathymetry. The inverse forecast error covariance matrix is modelled using a Laplacian approximation which is calibrated for the length scale parameter required. Calibration is also performed for the Soulsby-van Rijn sediment transport equations. The data used for assimilation purposes comprises waterlines derived from SAR imagery covering the entire period of the model run, and swath bathymetry data collected by a ship-borne survey for one date towards the end of the model run. A LiDAR survey of the entire bay carried out in November 2005 is used for validation purposes. The comparison of the predictive ability of the model alone with the model-forecast-assimilation system demonstrates that using data assimilation significantly improves the forecast skill. An investigation of the assimilation of the swath bathymetry as well as the waterlines demonstrates that the overall improvement is initially large, but decreases over time as the bathymetry evolves away from that observed by the survey. The result of combining the calibration runs into a pseudo-ensemble provides a higher skill score than for a single optimized model run. A brief comparison of the Optimal Interpolation assimilation method with the 3D-Var method shows that the two schemes give similar results.