Design and analysis of climate model experiments for the efficient estimation of anthropogenic signals

Presented herein is an experimental design that allows the effects of several radiative forcing factors on climate to be estimated as precisely as possible from a limited suite of atmosphere-only general circulation model (GCM) integrations. The forcings include the combined effect of observed changes in sea surface temperatures, sea ice extent, stratospheric (volcanic) aerosols, and solar output, plus the individual effects of several anthropogenic forcings. A single linear statistical model is used to estimate the forcing effects, each of which is represented by its global mean radiative forcing. The strong colinearity in time between the various anthropogenic forcings provides a technical problem that is overcome through the design of the experiment. This design uses every combination of anthropogenic forcing rather than having a few highly replicated ensembles, which is more commonly used in climate studies. Not only is this design highly efficient for a given number of integrations, but it also allows the estimation of (nonadditive) interactions between pairs of anthropogenic forcings. The simulated land surface air temperature changes since 1871 have been analyzed. The changes in natural and oceanic forcing, which itself contains some forcing from anthropogenic and natural influences, have the most influence. For the global mean, increasing greenhouse gases and the indirect aerosol effect had the largest anthropogenic effects. It was also found that an interaction between these two anthropogenic effects in the atmosphere-only GCM exists. This interaction is similar in magnitude to the individual effects of changing tropospheric and stratospheric ozone concentrations or to the direct (sulfate) aerosol effect. Various diagnostics are used to evaluate the fit of the statistical model. For the global mean, this shows that the land temperature response is proportional to the global mean radiative forcing, reinforcing the use of radiative forcing as a measure of climate change. The diagnostic tests also show that the linear model was suitable for analyses of land surface air temperature at each GCM grid point. Therefore, the linear model provides precise estimates of the space time signals for all forcing factors under consideration. For simulated 50-hPa temperatures, results show that tropospheric ozone increases have contributed to stratospheric cooling over the twentieth century almost as much as changes in well-mixed greenhouse gases.

Design of a minimum variance multiple input-multiple output neuro self-tuning proportional-integral-derivative controller for non-linear dynamic systems

In this study a minimum variance neuro self-tuning proportional-integral-derivative (PID) controller is designed for complex multiple input-multiple output (MIMO) dynamic systems. An approximation model is constructed, which consists of two functional blocks. The first block uses a linear submodel to approximate dominant system dynamics around a selected number of operating points. The second block is used as an error agent, implemented by a neural network, to accommodate the inaccuracy possibly introduced by the linear submodel approximation, various complexities/uncertainties, and complicated coupling effects frequently exhibited in non-linear MIMO dynamic systems. With the proposed model structure, controller design of an MIMO plant with n inputs and n outputs could be, for example, decomposed into n independent single input-single output (SISO) subsystem designs. The effectiveness of the controller design procedure is initially verified through simulations of industrial examples.

A fast identification algorithm for Box-Cox transformation based radial basis function neural network

In this letter, a Box-Cox transformation-based radial basis function (RBF) neural network is introduced using the RBF neural network to represent the transformed system output. Initially a fixed and moderate sized RBF model base is derived based on a rank revealing orthogonal matrix triangularization (QR decomposition). Then a new fast identification algorithm is introduced using Gauss-Newton algorithm to derive the required Box-Cox transformation, based on a maximum likelihood estimator. The main contribution of this letter is to explore the special structure of the proposed RBF neural network for computational efficiency by utilizing the inverse of matrix block decomposition lemma. Finally, the Box-Cox transformation-based RBF neural network, with good generalization and sparsity, is identified based on the derived optimal Box-Cox transformation and a D-optimality-based orthogonal forward regression algorithm. The proposed algorithm and its efficacy are demonstrated with an illustrative example in comparison with support vector machine regression.

A neural network enhanced generalized minimum variance self-tuning proportional, integral and derivative control algorithm for complex dynamic systems

A neural network enhanced proportional, integral and derivative (PID) controller is presented that combines the attributes of neural network learning with a generalized minimum-variance self-tuning control (STC) strategy. The neuro PID controller is structured with plant model identification and PID parameter tuning. The plants to be controlled are approximated by an equivalent model composed of a simple linear submodel to approximate plant dynamics around operating points, plus an error agent to accommodate the errors induced by linear submodel inaccuracy due to non-linearities and other complexities. A generalized recursive least-squares algorithm is used to identify the linear submodel, and a layered neural network is used to detect the error agent in which the weights are updated on the basis of the error between the plant output and the output from the linear submodel. The procedure for controller design is based on the equivalent model, and therefore the error agent is naturally functioned within the control law. In this way the controller can deal not only with a wide range of linear dynamic plants but also with those complex plants characterized by severe non-linearity, uncertainties and non-minimum phase behaviours. Two simulation studies are provided to demonstrate the effectiveness of the controller design procedure.

Nonlinear saturation of baroclinic instability: part I: the two-layer model

A rigorous bound is derived which limits the finite-amplitude growth of arbitrary nonzonal disturbances to an unstable baroclinic zonal flow within the context of the two-layer model. The bound is valid for conservative (unforced) flow, as well as for forced-dissipative flow that when the dissipation is proportional to the potential vorticity. The method used to derive the bound relies on the existence of a nonlinear Liapunov (normed) stability theorem for subcritical flows, which is a finite-amplitude generalization of the Charney-Stern theorem. For the special case of the Philips model of baroclinic instability, and in the limit of infinitesimal initial nonzonal disturbance amplitude, an improved form of the bound is possible which states that the potential enstrophy of the nonzonal flow cannot exceed ϵβ2, where ϵ = (U − Ucrit)/Ucrit is the (relative) supereriticality. This upper bound turns out to be extremely similar to the maximum predicted by the weakly nonlinear theory. For unforced flow with ϵ < 1, the bound demonstrates that the nonzonal flow cannot contain all of the potential enstrophy in the system; hence in this range of initial supercriticality the total flow must remain, in a certain sense, “close” to a zonal state.

Balanced excitation and inhibition: Model based analysis of local field potentials

We have developed a model of the local field potential (LFP) based on the conservation of charge, the independence principle of ionic flows and the classical Hodgkin–Huxley (HH) type intracellular model of synaptic activity. Insights were gained through the simulation of the HH intracellular model on the nonlinear relationship between the balance of synaptic conductances and that of post-synaptic currents. The latter is dependent not only on the former, but also on the temporal lag between the excitatory and inhibitory conductances, as well as the strength of the afferent signal. The proposed LFP model provides a method for decomposing the LFP recordings near the soma of layer IV pyramidal neurons in the barrel cortex of anaesthetised rats into two highly correlated components with opposite polarity. The temporal dynamics and the proportional balance of the two components are comparable to the excitatory and inhibitory post-synaptic currents computed from the HH model. This suggests that the two components of the LFP reflect the underlying excitatory and inhibitory post-synaptic currents of the local neural population. We further used the model to decompose a sequence of evoked LFP responses under repetitive electrical stimulation (5 Hz) of the whisker pad. We found that as neural responses adapted, the excitatory and inhibitory components also adapted proportionately, while the temporal lag between the onsets of the two components increased during frequency adaptation. Our results demonstrated that the balance between neural excitation and inhibition can be investigated using extracellular recordings. Extension of the model to incorporate multiple compartments should allow more quantitative interpretations of surface Electroencephalography (EEG) recordings into components reflecting the excitatory, inhibitory and passive ionic current flows generated by local neural populations.

A model of the dynamic relationship between blood flow and volume changes during brain activation

The temporal relationship between changes in cerebral blood flow (CBF) and cerebral blood volume (CBV) is important in the biophysical modeling and interpretation of the hemodynamic response to activation, particularly in the context of magnetic resonance imaging and the blood oxygen level-dependent signal. Grubb et al. (1974) measured the steady state relationship between changes in CBV and CBF after hypercapnic challenge. The relationship CBV proportional to CBFPhi has been used extensively in the literature. Two similar models, the Balloon (Buxton et al., 1998) and the Windkessel (Mandeville et al., 1999), have been proposed to describe the temporal dynamics of changes in CBV with respect to changes in CBF. In this study, a dynamic model extending the Windkessel model by incorporating delayed compliance is presented. The extended model is better able to capture the dynamics of CBV changes after changes in CBF, particularly in the return-to-baseline stages of the response.

A statistical model for sea surface diurnal warming driven by numercial weather predictions fluxes and winds

A statistical model is derived relating the diurnal variation of sea surface temperature (SST) to the net surface heat flux and surface wind speed from a numerical weather prediction (NWP) model. The model is derived using fluxes and winds from the European Centre for Medium-Range Weather Forecasting (ECMWF) NWP model and SSTs from the Spinning Enhanced Visible and Infrared Imager (SEVIRI). In the model, diurnal warming has a linear dependence on the net surface heat flux integrated since (approximately) dawn and an inverse quadratic dependence on the maximum of the surface wind speed in the same period. The model coefficients are found by matching, for a given integrated heat flux, the frequency distributions of the maximum wind speed and the observed warming. Diurnal cooling, where it occurs, is modelled as proportional to the integrated heat flux divided by the heat capacity of the seasonal mixed layer. The model reproduces the statistics (mean, standard deviation, and 95-percentile) of the diurnal variation of SST seen by SEVIRI and reproduces the geographical pattern of mean warming seen by the Advanced Microwave Scanning Radiometer (AMSR-E). We use the functional dependencies in the statistical model to test the behaviour of two physical model of diurnal warming that display contrasting systematic errors.

The Joint UK Land Environment Simulator (JULES), model description – part 1: energy and water fluxes

This manuscript describes the energy and water components of a new community land surface model called the Joint UK Land Environment Simulator (JULES). This is developed from the Met Office Surface Exchange Scheme (MOSES). It can be used as a stand alone land surface model driven by observed forcing data, or coupled to an atmospheric global circulation model. The JULES model has been coupled to the Met Office Unified Model (UM) and as such provides a unique opportunity for the research community to contribute their research to improve both world-leading operational weather forecasting and climate change prediction systems. In addition JULES, and its forerunner MOSES, have been the basis for a number of very high-profile papers concerning the land-surface and climate over the last decade. JULES has a modular structure aligned to physical processes, providing the basis for a flexible modelling platform.

A multithickness sea ice model accounting for sliding friction

A multithickness sea ice model explicitly accounting for the ridging and sliding friction contributions to sea ice stress is developed. Both ridging and sliding contributions depend on the deformation type through functions adopted from the Ukita and Moritz kinematic model of floe interaction. In contrast to most previous work, the ice strength of a uniform ice sheet of constant ice thickness is taken to be proportional to the ice thickness raised to the 3/2 power, as is revealed in discrete element simulations by Hopkins. The new multithickness sea ice model for sea ice stress has been implemented into the Los Alamos “CICE” sea ice model code and is shown to improve agreement between model predictions and observed spatial distribution of sea ice thickness in the Arctic.

Avoiding a bad apple: insect pollination enhances fruit quality and economic value

Insect pollination is important for food production globally and apples are one of the major fruit crops which are reliant on this ecosystem service. It is fundamentally important that the full range of benefits of insect pollination to crop production are understood, if the costs of interventions aiming to enhance pollination are to be compared against the costs of the interventions themselves. Most previous studies have simply assessed the benefits of pollination to crop yield and ignored quality benefits and how these translate through to economic values. In the present study we examine the influence of insect pollination services on farmgate output of two important UK apple varieties; Gala and Cox. Using field experiments, we quantify the influence of insect pollination on yield and importantly quality and whether either may be limited by sub-optimal insect pollination. Using an expanded bioeconomic model we value insect pollination to UK apple production and establish the potential for improvement through pollination service management. We show that insects are essential in the production of both varieties of apple in the UK and contribute a total of £36.7 million per annum, over £6 million more than the value calculated using more conventional dependence ratio methods. Insect pollination not only affects the quantity of production but can also have marked impacts on the quality of apples, influencing size, shape and effecting their classification for market. These effects are variety specific however. Due to the influence of pollination on both yield and quality in Gala, there is potential for insect pollination services to improve UK output by up to £5.7 million per annum. Our research shows that continued pollinator decline could have serious financial implications for the apple industry but there is considerable scope through management of wild pollinators or using managed pollinator augmentation, to improve the quality of production. Furthermore, we show that it is critically important to consider all production parameters including quality, varietal differences and management costs when valuing the pollination service of any crop so investment in pollinator management can be proportional to its contribution.

Assimilation of sea-ice concentration in a global climate model — physical and statistical aspects

We investigate the initialization of Northern-hemisphere sea ice in the global climate model ECHAM5/MPI-OM by assimilating sea-ice concentration data. The analysis updates for concentration are given by Newtonian relaxation, and we discuss different ways of specifying the analysis updates for mean thickness. Because the conservation of mean ice thickness or actual ice thickness in the analysis updates leads to poor assimilation performance, we introduce a proportional dependence between concentration and mean thickness analysis updates. Assimilation with these proportional mean-thickness analysis updates significantly reduces assimilation error both in identical-twin experiments and when assimilating sea-ice observations, reducing the concentration error by a factor of four to six, and the thickness error by a factor of two. To understand the physical aspects of assimilation errors, we construct a simple prognostic model of the sea-ice thermodynamics, and analyse its response to the assimilation. We find that the strong dependence of thermodynamic ice growth on ice concentration necessitates an adjustment of mean ice thickness in the analysis update. To understand the statistical aspects of assimilation errors, we study the model background error covariance between ice concentration and ice thickness. We find that the spatial structure of covariances is best represented by the proportional mean-thickness analysis updates. Both physical and statistical evidence supports the experimental finding that proportional mean-thickness updates are superior to the other two methods considered and enable us to assimilate sea ice in a global climate model using simple Newtonian relaxation.

Assimilation of sea-ice concentration in a global climate model — physical and statistical aspects

We investigate the initialisation of Northern Hemisphere sea ice in the global climate model ECHAM5/MPI-OM by assimilating sea-ice concentration data. The analysis updates for concentration are given by Newtonian relaxation, and we discuss different ways of specifying the analysis updates for mean thickness. Because the conservation of mean ice thickness or actual ice thickness in the analysis updates leads to poor assimilation performance, we introduce a proportional dependence between concentration and mean thickness analysis updates. Assimilation with these proportional mean-thickness analysis updates leads to good assimilation performance for sea-ice concentration and thickness, both in identical-twin experiments and when assimilating sea-ice observations. The simulation of other Arctic surface fields in the coupled model is, however, not significantly improved by the assimilation. To understand the physical aspects of assimilation errors, we construct a simple prognostic model of the sea-ice thermodynamics, and analyse its response to the assimilation. We find that an adjustment of mean ice thickness in the analysis update is essential to arrive at plausible state estimates. To understand the statistical aspects of assimilation errors, we study the model background error covariance between ice concentration and ice thickness. We find that the spatial structure of covariances is best represented by the proportional mean-thickness analysis updates. Both physical and statistical evidence supports the experimental finding that assimilation with proportional mean-thickness updates outperforms the other two methods considered. The method described here is very simple to implement, and gives results that are sufficiently good to be used for initialising sea ice in a global climate model for seasonal to decadal predictions.

Fold-change detection in a whole-pathway model of Escherichia coli chemotaxis

There has been recent interest in sensory systems that are able to display a response which is proportional to a fold change in stimulus concentration, a feature referred to as fold-change detection (FCD). Here, we demonstrate FCD in a recent whole-pathway mathematical model of Escherichia coli chemotaxis. FCD is shown to hold for each protein in the signalling cascade and to be robust to kinetic rate and protein concentration variation. Using a sensitivity analysis, we find that only variations in the number of receptors within a signalling team lead to the model not exhibiting FCD. We also discuss the ability of a cell with multiple receptor types to display FCD and explain how a particular receptor configuration may be used to elucidate the two experimentally determined regimes of FCD behaviour. All findings are discussed in respect of the experimental literature.

Global forecasting of thermal health hazards: the skill of probabilistic predictions of the Universal Thermal Climate Index (UTCI)

Although over a hundred thermal indices can be used for assessing thermal health hazards, many ignore the human heat budget, physiology and clothing. The Universal Thermal Climate Index (UTCI) addresses these shortcomings by using an advanced thermo-physiological model. This paper assesses the potential of using the UTCI for forecasting thermal health hazards. Traditionally, such hazard forecasting has had two further limitations: it has been narrowly focused on a particular region or nation and has relied on the use of single ‘deterministic’ forecasts. Here, the UTCI is computed on a global scale,which is essential for international health-hazard warnings and disaster preparedness, and it is provided as a probabilistic forecast. It is shown that probabilistic UTCI forecasts are superior in skill to deterministic forecasts and that despite global variations, the UTCI forecast is skilful for lead times up to 10 days. The paper also demonstrates the utility of probabilistic UTCI forecasts on the example of the 2010 heat wave in Russia.