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.

Influence of drought-induced acidification on the mobility of dissolved organic carbon in peat soils

A strong relationship between dissolved organic carbon (DOC) and sulphate (SO42−) dynamics under drought conditions has been revealed from analysis of a 10-year time series (1993–2002). Soil solution from a blanket peat at 10 cm depth and stream water were collected at biweekly and weekly intervals, respectively, by the Environmental Change Network at Moor House-Upper Teesdale National Nature Reserve in the North Pennine uplands of Britain. DOC concentrations in soil solution and stream water were closely coupled, displaying a strong seasonal cycle with lowest concentrations in early spring and highest in late summer/early autumn. Soil solution DOC correlated strongly with seasonal variations in soil temperature at the same depth 4-weeks prior to sampling. Deviation from this relationship was seen, however, in years with significant water table drawdown (>−25 cm), such that DOC concentrations were up to 60% lower than expected. Periods of drought also resulted in the release of SO42−, because of the oxidation of inorganic/organic sulphur stored in the peat, which was accompanied by a decrease in pH and increase in ionic strength. As both pH and ionic strength are known to control the solubility of DOC, inclusion of a function to account for DOC suppression because of drought-induced acidification accounted for more of the variability of DOC in soil solution (R2=0.81) than temperature alone (R2=0.58). This statistical model of peat soil solution DOC at 10 cm depth was extended to reproduce 74% of the variation in stream DOC over this period. Analysis of annual budgets showed that the soil was the main source of SO42− during droughts, while atmospheric deposition was the main source in other years. Mass balance calculations also showed that most of the DOC originated from the peat. The DOC flux was also lower in the drought years of 1994 and 1995, reflecting low DOC concentrations in soil and stream water. The analysis presented in this paper suggests that lower concentrations of DOC in both soil and stream waters during drought years can be explained in terms of drought-induced acidification. As future climate change scenarios suggest an increase in the magnitude and frequency of drought events, these results imply potential for a related increase in DOC suppression by episodic acidification.

Meson properties in an extended nonlocal NJL model

We consider a non-local version of the NJL model, based on a separable quark-quark interaction. The interaction is extended to include terms that bind vector and axial-vector mesons. The non-locality means that no further regulator is required. Moreover the model is able to confine the quarks by generating a quark propagator without poles at real energies. Working in the ladder approximation, we calculate amplitudes in Euclidean space and discuss features of their continuation to Minkowski energies. Conserved currents are constructed and we demonstrate their consistency with various Ward identities. Various meson masses are calculated, along with their strong and electromagnetic decay amplitudes. We also calculate the electromagnetic form factor of the pion, as well as form factors associated with the processes γγ* → π0 and ω → π0γ*. The results are found to lead to a satisfactory phenomenology and lend some dynamical support to the idea of vector-meson dominance.

Fibrillar superstructure from extended nanotapes formed by a collagen-stimulating peptide

The nanostructure of a peptide amphiphile in commercial use in anti-wrinkle creams is investigated. The peptide contains a matrikine, collagen-stimulating, pentapeptide sequence. Selfassembly into giant nanotapes is observed and the internal structure was found to comprise bilayers parallel to the flat tape surfaces.

Meson properties in an extended nonlocal NJL model

A nonlocal version of the NJL model is investigated. It is based on a separable quark-quark interaction, as suggested by the instanton liquid picture of the QCD vacuum. The interaction is extended to include terms that bind vector and axial-vector mesons. The nonlocality means that no further regulator is required. Moreover the model is able to confine the quarks by generating a quark propagator without poles at real energies. Features of the continuation of amplitudes from Euclidean space to Minkowski energies are discussed. These features lead to restrictions on the model parameters as well as on the range of applicability of the model. Conserved currents are constructed, and their consistency with various Ward identities is demonstrated. In particular, the Gell-Mann-Oakes-Renner relation is derived both in the ladder approximation and at meson loop level. The importance of maintaining chiral symmetry in the calculations is stressed throughout. Calculations with the model are performed to all orders in momentum. Meson masses are determined, along with their strong and electromagnetic decay amplitudes. Also calculated are the electromagnetic form factor of the pion and form factors associated with the processes gamma gamma* --> pi0 and omega --> pi0 gamma*. The results are found to lead to a satisfactory phenomenology and demonstrate a possible dynamical origin for vector-meson dominance. In addition, the results produced at meson loop level validate the use of 1/Nc as an expansion parameter and indicate that a light and broad scalar state is inherent in models of the NJL type.

Cloud optical depth retrievals from the Aerosol Robotic Network (AERONET) cloud mode observations

Cloud optical depth is one of the most poorly observed climate variables. The new “cloud mode” capability in the Aerosol Robotic Network (AERONET) will inexpensively yet dramatically increase cloud optical depth observations in both number and accuracy. Cloud mode optical depth retrievals from AERONET were evaluated at the Atmospheric Radiation Measurement program’s Oklahoma site in sky conditions ranging from broken clouds to overcast. For overcast cases, the 1.5 min average AERONET cloud mode optical depths agreed to within 15% of those from a standard ground‐based flux method. For broken cloud cases, AERONET retrievals also captured rapid variations detected by the microwave radiometer. For 3 year climatology derived from all nonprecipitating clouds, AERONET monthly mean cloud optical depths are generally larger than cloud radar retrievals because of the current cloud mode observation strategy that is biased toward measurements of optically thick clouds. This study has demonstrated a new way to enhance the existing AERONET infrastructure to observe cloud optical properties on a global scale.

Idealized model for changes in equilibrium temperature, mixed layer depth, and boundary layer cloud over land in a doubled CO2 climate

An idealized equilibrium model for the undisturbed partly cloudy boundary layer (BL) is used as a framework to explore the coupling of the energy, water, and carbon cycles over land in midlatitudes and show the sensitivity to the clear‐sky shortwave flux, the midtropospheric temperature, moisture, CO2, and subsidence. The changes in the surface fluxes, the BL equilibrium, and cloud cover are shown for a warmer, doubled CO2 climate. Reduced stomatal conductance in a simple vegetation model amplifies the background 2 K ocean temperature rise to an (unrealistically large) 6 K increase in near‐surface temperature over land, with a corresponding drop of near‐surface relative humidity of about 19%, and a rise of cloud base of about 70 hPa. Cloud changes depend strongly on changes of mean subsidence; but evaporative fraction (EF) decreases. EF is almost uniquely related to mixed layer (ML) depth, independent of background forcing climate. This suggests that it might be possible to infer EF for heterogeneous landscapes from ML depth. The asymmetry of increased evaporation over the oceans and reduced transpiration over land increases in a warmer doubled CO2 climate.

Retrievals of thick cloud optical depth from the Geoscience Laser Altimeter System (GLAS) by calibration of solar background signal

Laser beams emitted from the Geoscience Laser Altimeter System (GLAS), as well as other spaceborne laser instruments, can only penetrate clouds to a limit of a few optical depths. As a result, only optical depths of thinner clouds (< about 3 for GLAS) are retrieved from the reflected lidar signal. This paper presents a comprehensive study of possible retrievals of optical depth of thick clouds using solar background light and treating GLAS as a solar radiometer. To do so one must first calibrate the reflected solar radiation received by the photon-counting detectors of the GLAS 532-nm channel, the primary channel for atmospheric products. Solar background radiation is regarded as a noise to be subtracted in the retrieval process of the lidar products. However, once calibrated, it becomes a signal that can be used in studying the properties of optically thick clouds. In this paper, three calibration methods are presented: (i) calibration with coincident airborne and GLAS observations, (ii) calibration with coincident Geostationary Opera- tional Environmental Satellite (GOES) and GLAS observations of deep convective clouds, and (iii) cali- bration from first principles using optical depth of thin water clouds over ocean retrieved by GLAS active remote sensing. Results from the three methods agree well with each other. Cloud optical depth (COD) is retrieved from the calibrated solar background signal using a one-channel retrieval. Comparison with COD retrieved from GOES during GLAS overpasses shows that the average difference between the two retriev- als is 24%. As an example, the COD values retrieved from GLAS solar background are illustrated for a marine stratocumulus cloud field that is too thick to be penetrated by the GLAS laser. Based on this study, optical depths for thick clouds will be provided as a supplementary product to the existing operational GLAS cloud products in future GLAS data releases.

Cloud optical depth retrievals from solar background "signals" of micropulse lidars

Pulsed lidars are commonly used to retrieve vertical distributions of cloud and aerosol layers. It is widely believed that lidar cloud retrievals (other than cloud base altitude) are limited to optically thin clouds. Here, we demonstrate that lidars can retrieve optical depths of thick clouds using solar background light as a signal, rather than (as now) merely a noise to be subtracted. Validations against other instruments show that retrieved cloud optical depths agree within 10%–15% for overcast stratus and broken clouds. In fact, for broken cloud situations, one can retrieve not only the aerosol properties in clear-sky periods using lidar signals, but also the optical depth of thick clouds in cloudy periods using solar background signals. This indicates that, in general, it may be possible to retrieve both aerosol and cloud properties using a single lidar. Thus, lidar observations have great untapped potential to study interactions between clouds and aerosols.

Using Doppler radar with a simple explicit microphysics model to diagnose problems with ice sublimation depth-scales in forecast models

Several previous studies have attempted to assess the sublimation depth-scales of ice particles from clouds into clear air. Upon examining the sublimation depth-scales in the Met Office Unified Model (MetUM), it was found that the MetUM has evaporation depth-scales 2–3 times larger than radar observations. Similar results can be seen in the European Centre for Medium-Range Weather Forecasts (ECMWF), Regional Atmospheric Climate Model (RACMO) and Météo-France models. In this study, we use radar simulation (converting model variables into radar observations) and one-dimensional explicit microphysics numerical modelling to test and diagnose the cause of the deep sublimation depth-scales in the forecast model. The MetUM data and parametrization scheme are used to predict terminal velocity, which can be compared with the observed Doppler velocity. This can then be used to test the hypothesis as to why the sublimation depth-scale is too large within the MetUM. Turbulence could lead to dry air entrainment and higher evaporation rates; particle density may be wrong, particle capacitance may be too high and lead to incorrect evaporation rates or the humidity within the sublimating layer may be incorrectly represented. We show that the most likely cause of deep sublimation zones is an incorrect representation of model humidity in the layer. This is tested further by using a one-dimensional explicit microphysics model, which tests the sensitivity of ice sublimation to key atmospheric variables and is capable of including sonde and radar measurements to simulate real cases. Results suggest that the MetUM grid resolution at ice cloud altitudes is not sufficient enough to maintain the sharp drop in humidity that is observed in the sublimation zone.

The climatology of the middle atmosphere in a vertically extended version of the Met Office's climate model. Part I: mean state

The climatology of a stratosphere-resolving version of the Met Office’s climate model is studied and validated against ECMWF reanalysis data. Ensemble integrations are carried out at two different horizontal resolutions. Along with a realistic climatology and annual cycle in zonal mean zonal wind and temperature, several physical effects are noted in the model. The time of final warming of the winter polar vortex is found to descend monotonically in the Southern Hemisphere, as would be expected for purely radiative forcing. In the Northern Hemisphere, however, the time of final warming is driven largely by dynamical effects in the lower stratosphere and radiative effects in the upper stratosphere, leading to the earliest transition to westward winds being seen in the midstratosphere. A realistic annual cycle in stratospheric water vapor concentrations—the tropical “tape recorder”—is captured. Tropical variability in the zonal mean zonal wind is found to be in better agreement with the reanalysis for the model run at higher horizontal resolution because the simulated quasi-biennial oscillation has a more realistic amplitude. Unexpectedly, variability in the extratropics becomes less realistic under increased resolution because of reduced resolved wave drag and increased orographic gravity wave drag. Overall, the differences in climatology between the simulations at high and moderate horizontal resolution are found to be small.

Bernoulli free-boundary problems in strip-like domains and a property of permanent waves on water of finite depth

We study weak solutions for a class of free-boundary problems which includes as a special case the classical problem of travelling gravity waves on water of finite depth. We show that such problems are equivalent to problems in fixed domains and study the regularity of their solutions. We also prove that in very general situations the free boundary is necessarily the graph of a function.

Minimum neighbour and extended Kalman filter estimator: a practical distributed channel assignment scheme for dense wireless local area networks

Dense deployments of wireless local area networks (WLANs) are becoming a norm in many cities around the world. However, increased interference and traffic demands can severely limit the aggregate throughput achievable unless an effective channel assignment scheme is used. In this work, a simple and effective distributed channel assignment (DCA) scheme is proposed. It is shown that in order to maximise throughput, each access point (AP) simply chooses the channel with the minimum number of active neighbour nodes (i.e. nodes associated with neighbouring APs that have packets to send). However, application of such a scheme to practice depends critically on its ability to estimate the number of neighbour nodes in each channel, for which no practical estimator has been proposed before. In view of this, an extended Kalman filter (EKF) estimator and an estimate of the number of nodes by AP are proposed. These not only provide fast and accurate estimates but can also exploit channel switching information of neighbouring APs. Extensive packet level simulation results show that the proposed minimum neighbour and EKF estimator (MINEK) scheme is highly scalable and can provide significant throughput improvement over other channel assignment schemes.

Operator performance evaluation of controlled depth of field in a stereographically displayed virtual environment

Retinal blurring resulting from the human eye's depth of focus has been shown to assist visual perception. Infinite focal depth within stereoscopically displayed virtual environments may cause undesirable effects, for instance, objects positioned at a distance in front of or behind the observer's fixation point will be perceived in sharp focus with large disparities thereby causing diplopia. Although published research on incorporation of synthetically generated Depth of Field (DoF) suggests that this might act as an enhancement to perceived image quality, no quantitative testimonies of perceptional performance gains exist. This may be due to the difficulty of dynamic generation of synthetic DoF where focal distance is actively linked to fixation distance. In this paper, such a system is described. A desktop stereographic display is used to project a virtual scene in which synthetically generated DoF is actively controlled from vergence-derived distance. A performance evaluation experiment on this system which involved subjects carrying out observations in a spatially complex virtual environment was undertaken. The virtual environment consisted of components interconnected by pipes on a distractive background. The subject was tasked with making an observation based on the connectivity of the components. The effects of focal depth variation in static and actively controlled focal distance conditions were investigated. The results and analysis are presented which show that performance gains may be achieved by addition of synthetic DoF. The merits of the application of synthetic DoF are discussed.