Internal model control of nonlinear systems through the inversion of recurrent neural networks

Recurrent neural networks can be used for both the identification and control of nonlinear systems. This paper takes a previously derived set of theoretical results about recurrent neural networks and applies them to the task of providing internal model control for a nonlinear plant. Using the theoretical results, we show how an inverse controller can be produced from a neural network model of the plant, without the need to train an additional network to perform the inverse control.

Exploring behavioural change through an agent-oriented system dynamics model: the use of personal protective equipment among pesticide applicators in Colombia

The misuse of Personal Protective Equipment results in health risk among smallholders in developing countries, and education is often proposed to promote safer practices. However, evidence point to limited effects of education. This paper presents a System Dynamics model which allows the identification of risk-minimizing policies for behavioural change. The model is based on the IAC framework and survey data. It represents farmers' decision-making from an agent-oriented standpoint. The most successful intervention strategy was the one which intervened in the long term, targeted key stocks in the systems and was diversified. However, the results suggest that, under these conditions, no policy is able to trigger a self sustaining behavioural change. Two implementation approaches were suggested by experts. One, based on constant social control, corresponds to a change of the current model's parameters. The other, based on participation, would lead farmers to new thinking, i.e. changes in their decision-making structure.

Investigation of the factors influencing the survival of Bifidobacterium longum in model acidic solutions and fruit juices

The survival of Bifidobacterium longum NCIMB 8809 was studied during refrigerated storage for 6 weeks in model solutions, based on which a mathematical model was constructed describing cell survival as a function of pH, citric acid, protein and dietary fibre. A Central Composite Design (CCD) was developed studying the influence of four factors at three levels, i.e., pH (3.2–4), citric acid (2–15 g/l), protein (0–10 g/l), and dietary fibre (0–8 g/l). In total, 31 experimental runs were carried out. Analysis of variance (ANOVA) of the regression model demonstrated that the model fitted well the data. From the regression coefficients it was deduced that all four factors had a statistically significant (P < 0.05) negative effect on the log decrease [log10N0 week−log10N6 week], with the pH and citric acid being the most influential ones. Cell survival during storage was also investigated in various types of juices, including orange, grapefruit, blackcurrant, pineapple, pomegranate and strawberry. The highest cell survival (less than 0.4 log decrease) after 6 weeks of storage was observed in orange and pineapple, both of which had a pH of about 3.8. Although the pH of grapefruit and blackcurrant was similar (pH ∼3.2), the log decrease of the former was ∼0.5 log, whereas of the latter was ∼0.7 log. One reason for this could be the fact that grapefruit contained a high amount of citric acid (15.3 g/l). The log decrease in pomegranate and strawberry juices was extremely high (∼8 logs). The mathematical model was able to predict adequately the cell survival in orange, grapefruit, blackcurrant, and pineapple juices. However, the model failed to predict the cell survival in pomegranate and strawberry, most likely due to the very high levels of phenolic compounds in these two juices.

The impact of resolution on the adjustment and decadal variability of the Atlantic Meridional Overturning Circulation in a coupled climate model

Variations in the Atlantic Meridional Overturning Circulation (MOC) exert an important influence on climate, particularly on decadal time scales. Simulation of the MOC in coupled climate models is compromised, to a degree that is unknown, by their lack of fidelity in resolving some of the key processes involved. There is an overarching need to increase the resolution and fidelity of climate models, but also to assess how increases in resolution influence the simulation of key phenomena such as the MOC. In this study we investigate the impact of significantly increasing the (ocean and atmosphere) resolution of a coupled climate model on the simulation of MOC variability by comparing high and low resolution versions of the same model. In both versions, decadal variability of the MOC is closely linked to density anomalies that propagate from the Labrador Sea southward along the deep western boundary. We demonstrate that the MOC adjustment proceeds more rapidly in the higher resolution model due the increased speed of western boundary waves. However, the response of the Atlantic Sea Surface Temperatures (SSTs) to MOC variations is relatively robust - in pattern if not in magnitude - across the two resolutions. The MOC also excites a coupled ocean-atmosphere response in the tropical Atlantic in both model versions. In the higher resolution model, but not the lower resolution model, there is evidence of a significant response in the extratropical atmosphere over the North Atlantic 6 years after a maximum in the MOC. In both models there is evidence of a weak negative feedback on deep density anomalies in the Labrador Sea, and hence on the MOC (with a time scale of approximately ten years). Our results highlight the need for further work to understand the decadal variability of the MOC and its simulation in climate models.

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

Advances in sequential data assimilation and numerical weather forecasting: an Ensemble Transform Kalman-Bucy Filter, a study on clustering in deterministic Ensemble Square Root Filters, and a test of a new time stepping scheme in an atmospheric model

This dissertation deals with aspects of sequential data assimilation (in particular ensemble Kalman filtering) and numerical weather forecasting. In the first part, the recently formulated Ensemble Kalman-Bucy (EnKBF) filter is revisited. It is shown that the previously used numerical integration scheme fails when the magnitude of the background error covariance grows beyond that of the observational error covariance in the forecast window. Therefore, we present a suitable integration scheme that handles the stiffening of the differential equations involved and doesn’t represent further computational expense. Moreover, a transform-based alternative to the EnKBF is developed: under this scheme, the operations are performed in the ensemble space instead of in the state space. Advantages of this formulation are explained. For the first time, the EnKBF is implemented in an atmospheric model. The second part of this work deals with ensemble clustering, a phenomenon that arises when performing data assimilation using of deterministic ensemble square root filters in highly nonlinear forecast models. Namely, an M-member ensemble detaches into an outlier and a cluster of M-1 members. Previous works may suggest that this issue represents a failure of EnSRFs; this work dispels that notion. It is shown that ensemble clustering can be reverted also due to nonlinear processes, in particular the alternation between nonlinear expansion and compression of the ensemble for different regions of the attractor. Some EnSRFs that use random rotations have been developed to overcome this issue; these formulations are analyzed and their advantages and disadvantages with respect to common EnSRFs are discussed. The third and last part contains the implementation of the Robert-Asselin-Williams (RAW) filter in an atmospheric model. The RAW filter is an improvement to the widely popular Robert-Asselin filter that successfully suppresses spurious computational waves while avoiding any distortion in the mean value of the function. Using statistical significance tests both at the local and field level, it is shown that the climatology of the SPEEDY model is not modified by the changed time stepping scheme; hence, no retuning of the parameterizations is required. It is found the accuracy of the medium-term forecasts is increased by using the RAW filter.

Likelihood-free estimation of model evidence

Statistical methods of inference typically require the likelihood function to be computable in a reasonable amount of time. The class of “likelihood-free” methods termed Approximate Bayesian Computation (ABC) is able to eliminate this requirement, replacing the evaluation of the likelihood with simulation from it. Likelihood-free methods have gained in efficiency and popularity in the past few years, following their integration with Markov Chain Monte Carlo (MCMC) and Sequential Monte Carlo (SMC) in order to better explore the parameter space. They have been applied primarily to estimating the parameters of a given model, but can also be used to compare models. Here we present novel likelihood-free approaches to model comparison, based upon the independent estimation of the evidence of each model under study. Key advantages of these approaches over previous techniques are that they allow the exploitation of MCMC or SMC algorithms for exploring the parameter space, and that they do not require a sampler able to mix between models. We validate the proposed methods using a simple exponential family problem before providing a realistic problem from human population genetics: the comparison of different demographic models based upon genetic data from the Y chromosome.

Aerosol forcing in the Climate Model Intercomparison Project (CMIP5) simulations by HadGEM2-ES and the role of ammonium nitrate

The latest Hadley Centre climate model, HadGEM2-ES, includes Earth system components such as interactive chemistry and eight species of tropospheric aerosols. It has been run for the period 1860–2100 in support of the fifth phase of the Climate Model Intercomparison Project (CMIP5). Anthropogenic aerosol emissions peak between 1980 and 2020, resulting in a present-day all-sky top of the atmosphere aerosol forcing of −1.6 and −1.4 W m−2 with and without ammonium nitrate aerosols, respectively, for the sum of direct and first indirect aerosol forcings. Aerosol forcing becomes significantly weaker in the 21st century, being weaker than −0.5 W m−2 in 2100 without nitrate. However, nitrate aerosols become the dominant species in Europe and Asia and decelerate the decrease in global mean aerosol forcing. Considering nitrate aerosols makes aerosol radiative forcing 2–4 times stronger by 2100 depending on the representative concentration pathway, although this impact is lessened when changes in the oxidation properties of the atmosphere are accounted for. Anthropogenic aerosol residence times increase in the future in spite of increased precipitation, as cloud cover and aerosol-cloud interactions decrease in tropical and midlatitude regions. Deposition of fossil fuel black carbon onto snow and ice surfaces peaks during the 20th century in the Arctic and Europe but keeps increasing in the Himalayas until the middle of the 21st century. Results presented here confirm the importance of aerosols in influencing the Earth's climate, albeit with a reduced impact in the future, and suggest that nitrate aerosols will partially replace sulphate aerosols to become an important anthropogenic species in the remainder of the 21st century.

The upper end of climate model temperature projections is inconsistent with past warming

Climate models predict a large range of possible future temperatures for a particular scenario of future emissions of greenhouse gases and other anthropogenic forcings of climate. Given that further warming in coming decades could threaten increasing risks of climatic disruption, it is important to determine whether model projections are consistent with temperature changes already observed. This can be achieved by quantifying the extent to which increases in well mixed greenhouse gases and changes in other anthropogenic and natural forcings have already altered temperature patterns around the globe. Here, for the first time, we combine multiple climate models into a single synthesized estimate of future warming rates consistent with past temperature changes. We show that the observed evolution of near-surface temperatures appears to indicate lower ranges (5–95%) for warming (0.35–0.82 K and 0.45–0.93 K by the 2020s (2020–9) relative to 1986–2005 under the RCP4.5 and 8.5 scenarios respectively) than the equivalent ranges projected by the CMIP5 climate models (0.48–1.00 K and 0.51–1.16 K respectively). Our results indicate that for each RCP the upper end of the range of CMIP5 climate model projections is inconsistent with past warming.

Associating spontaneous with evoked activity in a neural mass model of cat visual cortex

Spontaneous activity of the brain at rest frequently has been considered a mere backdrop to the salient activity evoked by external stimuli or tasks. However, the resting state of the brain consumes most of its energy budget, which suggests a far more important role. An intriguing hint comes from experimental observations of spontaneous activity patterns, which closely resemble those evoked by visual stimulation with oriented gratings, except that cortex appeared to cycle between different orientation maps. Moreover, patterns similar to those evoked by the behaviorally most relevant horizontal and vertical orientations occurred more often than those corresponding to oblique angles. We hypothesize that this kind of spontaneous activity develops at least to some degree autonomously, providing a dynamical reservoir of cortical states, which are then associated with visual stimuli through learning. To test this hypothesis, we use a biologically inspired neural mass model to simulate a patch of cat visual cortex. Spontaneous transitions between orientation states were induced by modest modifications of the neural connectivity, establishing a stable heteroclinic channel. Significantly, the experimentally observed greater frequency of states representing the behaviorally important horizontal and vertical orientations emerged spontaneously from these simulations. We then applied bar-shaped inputs to the model cortex and used Hebbian learning rules to modify the corresponding synaptic strengths. After unsupervised learning, different bar inputs reliably and exclusively evoked their associated orientation state; whereas in the absence of input, the model cortex resumed its spontaneous cycling. We conclude that the experimentally observed similarities between spontaneous and evoked activity in visual cortex can be explained as the outcome of a learning process that associates external stimuli with a preexisting reservoir of autonomous neural activity states. Our findings hence demonstrate how cortical connectivity can link the maintenance of spontaneous activity in the brain mechanistically to its core cognitive functions.

Potential role of the quasi-biennial oscillation in the stratosphere-troposphere exchange as found in water vapor in general circulation model experiments

The tropical tropopause is considered to be the main region of upward transport of tropospheric air carrying water vapor and other tracers to the tropical stratosphere. The lower tropical stratosphere is also the region where the quasi-biennial oscillation (QBO) in the zonal wind is observed. The QBO is positioned in the region where the upward transport of tropospheric tracers to the overworld takes place. Hence the QBO can in principle modulate these transports by its secondary meridional circulation. This modulation is investigated in this study by an analysis of general circulation model (GCM) experiments with an assimilated QBO. The experiments show, first, that the temperature signal of the QBO modifies the specific humidity in the air transported upward and, second, that the secondary meridional circulation modulates the velocity of the upward transport. Thus during the eastward phase of the QBO the upward moving air is moister and the upward velocity is less than during the westward phase of the QBO. It was further found that the QBO period is too short to allow an equilibration of the moisture in the QBO region. This causes a QBO signal of the moisture which is considerably smaller than what could be obtained in the limiting case of indefinitely long QBO phases. This also allows a high sensitivity of the mean moisture over a QBO cycle to the El Niño-Southern Oscillation (ENSO) phenomena or major tropical volcanic eruptions. The interplay of sporadic volcanic eruptions, ENSO, and QBO can produce low-frequency variability in the water vapor content of the tropical stratosphere, which renders the isolation of the QBO signal in observational data of water vapor in the equatorial lower stratosphere difficult.

Evaluation of the use of high-density SNP genotyping to implement UPOV Model 2 for DUS testing in barley

Developments in high-throughput genotyping provide an opportunity to explore the application of marker technology in distinctness, uniformity and stability (DUS) testing of new varieties. We have used a large set of molecular markers to assess the feasibility of a UPOV Model 2 approach: “Calibration of threshold levels for molecular characteristics against the minimum distance in traditional characteristics”. We have examined 431 winter and spring barley varieties, with data from UK DUS trials comprising 28 characteristics, together with genotype data from 3072 SNP markers. Inter varietal distances were calculated and we found higher correlations between molecular and morphological distances than have been previously reported. When varieties were grouped by kinship, phenotypic and genotypic distances of these groups correlated well. We estimated the minimum marker numbers required and showed there was a ceiling after which the correlations do not improve. To investigate the possibility of breaking through this ceiling, we attempted genomic prediction of phenotypes from genotypes and higher correlations were achieved. We tested distinctness decisions made using either morphological or genotypic distances and found poor correspondence between each method.

The simulation of the opposing fluxes of latent heat and CO2 over various land-use types: coupling a gas exchange model to a mesoscale atmospheric model

A mesoscale meteorological model (FOOT3DK) is coupled with a gas exchange model to simulate surface fluxes of CO2 and H2O under field conditions. The gas exchange model consists of a C3 single leaf photosynthesis sub-model and an extended big leaf (sun/shade) sub-model that divides the canopy into sunlit and shaded fractions. Simulated CO2 fluxes of the stand-alone version of the gas exchange model correspond well to eddy-covariance measurements at a test site in a rural area in the west of Germany. The coupled FOOT3DK/gas exchange model is validated for the diurnal cycle at singular grid points, and delivers realistic fluxes with respect to their order of magnitude and to the general daily course. Compared to the Jarvis-based big leaf scheme, simulations of latent heat fluxes with a photosynthesis-based scheme for stomatal conductance are more realistic. As expected, flux averages are strongly influenced by the underlying land cover. While the simulated net ecosystem exchange is highly correlated with leaf area index, this correlation is much weaker for the latent heat flux. Photosynthetic CO2 uptake is associated with transpirational water loss via the stomata, and the resulting opposing surface fluxes of CO2 and H2O are reproduced with the model approach. Over vegetated surfaces it is shown that the coupling of a photosynthesis-based gas exchange model with the land-surface scheme of a mesoscale model results in more realistic simulated latent heat fluxes.

European storminess and associated circulation weather types: future changes deduced from a multi-model ensemble of GCM simulations

A range of possible changes in the frequency and characteristics of European wind storms under future climate conditions was investigated on the basis of a multi-model ensemble of 9 coupled global climate model (GCM) simulations for the 20th and 21st centuries following the IPCC SRES A1B scenario. A multi-model approach allowed an estimation of the (un)certainties of the climate change signals. General changes in large-scale atmospheric flow were analysed, the occurrence of wind storms was quantified, and atmospheric features associated with wind storm events were considered. Identified storm days were investigated according to atmospheric circulation, associated pressure patterns, cyclone tracks and wind speed patterns. Validation against reanalysis data revealed that the GCMs are in general capable of realistically reproducing characteristics of European circulation weather types (CWTs) and wind storms. Results are given with respect to frequency of occurrence, storm-associated flow conditions, cyclone tracks and specific wind speed patterns. Under anthropogenic climate change conditions (SRES A1B scenario), increased frequency of westerly flow during winter is detected over the central European investigation area. In the ensemble mean, the number of detected wind storm days increases between 19 and 33% for 2 different measures of storminess, only 1 GCM revealed less storm days. The increased number of storm days detected in most models is disproportionately high compared to the related CWT changes. The mean intensity of cyclones associated with storm days in the ensemble mean increases by about 10 (±10)% in the Eastern Atlantic, near the British Isles and in the North Sea. Accordingly, wind speeds associated with storm events increase significantly by about 5 (±5)% over large parts of central Europe, mainly on days with westerly flow. The basic conclusions of this work remain valid if different ensemble contructions are considered, leaving out an outlier model or including multiple runs of one particular model.

Nonlinear saturation of baroclinic instability: part II: continuously stratified fluid

Rigorous upper bounds are derived that limit the finite-amplitude growth of arbitrary nonzonal disturbances to an unstable baroclinic zonal flow in a continuously stratified, quasi-geostrophic, semi-infinite fluid. Bounds are obtained bath on the depth-integrated eddy potential enstrophy and on the eddy available potential energy (APE) at the ground. The method used to derive the bounds is essentially analogous to that used in Part I of this study for the two-layer model: it relies on the existence of a nonlinear Liapunov (normed) stability theorem, which is a finite-amplitude generalization of the Charney-Stern theorem. As in Part I, the bounds are valid both for conservative (unforced, inviscid) flow, as well as for forced-dissipative flow when the dissipation is proportional to the potential vorticity in the interior, and to the potential temperature at the ground. The character of the results depends on the dimensionless external parameter γ = f02ξ/β0N2H, where ξ is the maximum vertical shear of the zonal wind, H is the density scale height, and the other symbols have their usual meaning. When γ ≫ 1, corresponding to “deep” unstable modes (vertical scale ≈H), the bound on the eddy potential enstrophy is just the total potential enstrophy in the system; but when γ≪1, corresponding to ‘shallow’ unstable modes (vertical scale ≈γH), the eddy potential enstrophy can be bounded well below the total amount available in the system. In neither case can the bound on the eddy APE prevent a complete neutralization of the surface temperature gradient which is in accord with numerical experience. For the special case of the Charney model of baroclinic instability, and in the limit of infinitesimal initial eddy disturbance amplitude, the bound states that the dimensionless eddy potential enstrophy cannot exceed (γ + 1)2/24&gamma2h when γ ≥ 1, or 1/6;&gammah when γ ≤ 1; here h = HN/f0L is the dimensionless scale height and L is the width of the channel. These bounds are very similar to (though of course generally larger than) ad hoc estimates based on baroclinic-adjustment arguments. The possibility of using these kinds of bounds for eddy-amplitude closure in a transient-eddy parameterization scheme is also discussed.