A combined statistical and dynamical approach for downscaling large-scale footprints of European windstorms

The occurrence of mid-latitude windstorms is related to strong socio-economic effects. For detailed and reliable regional impact studies, large datasets of high-resolution wind fields are required. In this study, a statistical downscaling approach in combination with dynamical downscaling is introduced to derive storm related gust speeds on a high-resolution grid over Europe. Multiple linear regression models are trained using reanalysis data and wind gusts from regional climate model simulations for a sample of 100 top ranking windstorm events. The method is computationally inexpensive and reproduces individual windstorm footprints adequately. Compared to observations, the results for Germany are at least as good as pure dynamical downscaling. This new tool can be easily applied to large ensembles of general circulation model simulations and thus contribute to a better understanding of the regional impact of windstorms based on decadal and climate change projections.

Superensembles of linear viscoelastic models of polymer melts

The idea of incorporating multiple models of linear rheology into a superensemble, to forge a consensus forecast from the individual model predictions, is investigated. The relative importance of the individual models in the so-called multimodel superensemble (MMSE) was inferred by evaluating their performance on a set of experimental training data, via nonlinear regression. The predictive ability of the MMSE model was tested by comparing its predictions on test data that were similar (in-sample) and dissimilar (out-of-sample) to the training data used in the calibration. For the in-sample forecasts, we found that the MMSE model easily outperformed the best constituent model. The presence of good individual models greatly enhanced the MMSE forecast, while the presence of some bad models in the superensemble also improved the MMSE forecast modestly. While the performance of the MMSE model on the out-of-sample training data was not as spectacular, it demonstrated the robustness of this approach.

Linear-wavelet models for non-linear identification applied to a pressure plant

A nonlinear regression structure comprising a wavelet network and a linear term is proposed for system identification. The theoretical foundation of the approach is laid by proving that radial wavelets are orthogonal to linear functions. A constructive procedure for building such models is described and the approach is tested with experimental data.

Linear-wavelet models applied to the identification of a two-link manipulator

This paper shows that a wavelet network and a linear term can be advantageously combined for the purpose of non linear system identification. The theoretical foundation of this approach is laid by proving that radial wavelets are orthogonal to linear functions. A constructive procedure for building such nonlinear regression structures, termed linear-wavelet models, is described. For illustration, sim ulation data are used to identify a model for a two-link robotic manipulator. The results show that the introduction of wavelets does improve the prediction ability of a linear model.

Inclusion of nonlinear demand-supply relationships within large-scale partial equilibrium linear programming models

This paper presents a new method for the inclusion of nonlinear demand and supply relationships within a linear programming model. An existing method for this purpose is described first and its shortcomings are pointed out before showing how the new approach overcomes those difficulties and how it provides a more accurate and 'smooth' (rather than a kinked) approximation of the nonlinear functions as well as dealing with equilibrium under perfect competition instead of handling just the monopolistic situation. The workings of the proposed method are illustrated by extending a previously available sectoral model for the UK agriculture.

Power properties if invariant tests for spatial autocorrelation in linear regression

This paper derives some exact power properties of tests for spatial autocorrelation in the context of a linear regression model. In particular, we characterize the circumstances in which the power vanishes as the autocorrelation increases, thus extending the work of Krämer (2005). More generally, the analysis in the paper sheds new light on how the power of tests for spatial autocorrelation is affected by the matrix of regressors and by the spatial structure. We mainly focus on the problem of residual spatial autocorrelation, in which case it is appropriate to restrict attention to the class of invariant tests, but we also consider the case when the autocorrelation is due to the presence of a spatially lagged dependent variable among the regressors. A numerical study aimed at assessing the practical relevance of the theoretical results is included

Linear-wavelet models for system identification

A model structure comprising a wavelet network and a linear term is proposed for nonlinear system identification. It is shown that under certain conditions wavelets are orthogonal to linear functions and, as a result, the two parts of the model can be identified separately. The linear-wavelet model is compared to a standard wavelet network using data from a simulated fermentation process. The results show that the linear-wavelet model yields a smaller modelling error when compared to a wavelet network using the same number of regressors.

The effect of nonlinearity in CO2 heating rates on the attribution of stratospheric ozone and temperature changes

An analysis of the attribution of past and future changes in stratospheric ozone and temperature to anthropogenic forcings is presented. The analysis is an extension of the study of Shepherd and Jonsson (2008) who analyzed chemistry-climate simulations from the Canadian Middle Atmosphere Model (CMAM) and attributed both past and future changes to changes in the external forcings, i.e. the abundances of ozone-depleting substances (ODS) and well-mixed greenhouse gases. The current study is based on a new CMAM dataset and includes two important changes. First, we account for the nonlinear radiative response to changes in CO2. It is shown that over centennial time scales the radiative response in the upper stratosphere to CO2 changes is significantly nonlinear and that failure to account for this effect leads to a significant error in the attribution. To our knowledge this nonlinearity has not been considered before in attribution analysis, including multiple linear regression studies. For the regression analysis presented here the nonlinearity was taken into account by using CO2 heating rate, rather than CO2 abundance, as the explanatory variable. This approach yields considerable corrections to the results of the previous study and can be recommended to other researchers. Second, an error in the way the CO2 forcing changes are implemented in the CMAM was corrected, which significantly affects the results for the recent past. As the radiation scheme, based on Fomichev et al. (1998), is used in several other models we provide some description of the problem and how it was fixed.

Ozone database in support of CMIP5 simulations: results and corresponding radiative forcing

A continuous tropospheric and stratospheric vertically resolved ozone time series, from 1850 to 2099, has been generated to be used as forcing in global climate models that do not include interactive chemistry. A multiple linear regression analysis of SAGE I+II satellite observations and polar ozonesonde measurements is used for the stratospheric zonal mean dataset during the well-observed period from 1979 to 2009. In addition to terms describing the mean annual cycle, the regression includes terms representing equivalent effective stratospheric chlorine (EESC) and the 11-yr solar cycle variability. The EESC regression fit coefficients, together with pre-1979 EESC values, are used to extrapolate the stratospheric ozone time series backward to 1850. While a similar procedure could be used to extrapolate into the future, coupled chemistry climate model (CCM) simulations indicate that future stratospheric ozone abundances are likely to be significantly affected by climate change, and capturing such effects through a regression model approach is not feasible. Therefore, the stratospheric ozone dataset is extended into the future (merged in 2009) with multimodel mean projections from 13 CCMs that performed a simulation until 2099 under the SRES (Special Report on Emission Scenarios) A1B greenhouse gas scenario and the A1 adjusted halogen scenario in the second round of the Chemistry-Climate Model Validation (CCMVal-2) Activity. The stratospheric zonal mean ozone time series is merged with a three-dimensional tropospheric data set extracted from simulations of the past by two CCMs (CAM3.5 and GISSPUCCINI)and of the future by one CCM (CAM3.5). The future tropospheric ozone time series continues the historical CAM3.5 simulation until 2099 following the four different Representative Concentration Pathways (RCPs). Generally good agreement is found between the historical segment of the ozone database and satellite observations, although it should be noted that total column ozone is overestimated in the southern polar latitudes during spring and tropospheric column ozone is slightly underestimated. Vertical profiles of tropospheric ozone are broadly consistent with ozonesondes and in-situ measurements, with some deviations in regions of biomass burning. The tropospheric ozone radiative forcing (RF) from the 1850s to the 2000s is 0.23Wm−2, lower than previous results. The lower value is mainly due to (i) a smaller increase in biomass burning emissions; (ii) a larger influence of stratospheric ozone depletion on upper tropospheric ozone at high southern latitudes; and possibly (iii) a larger influence of clouds (which act to reduce the net forcing) compared to previous radiative forcing calculations. Over the same period, decreases in stratospheric ozone, mainly at high latitudes, produce a RF of −0.08Wm−2, which is more negative than the central Intergovernmental Panel on Climate Change (IPCC) Fourth Assessment Report (AR4) value of −0.05Wm−2, but which is within the stated range of −0.15 to +0.05Wm−2. The more negative value is explained by the fact that the regression model simulates significant ozone depletion prior to 1979, in line with the increase in EESC and as confirmed by CCMs, while the AR4 assumed no change in stratospheric RF prior to 1979. A negative RF of similar magnitude persists into the future, although its location shifts from high latitudes to the tropics. This shift is due to increases in polar stratospheric ozone, but decreases in tropical lower stratospheric ozone, related to a strengthening of the Brewer-Dobson circulation, particularly through the latter half of the 21st century. Differences in trends in tropospheric ozone among the four RCPs are mainly driven by different methane concentrations, resulting in a range of tropospheric ozone RFs between 0.4 and 0.1Wm−2 by 2100. The ozone dataset described here has been released for the Coupled Model Intercomparison Project (CMIP5) model simulations in netCDF Climate and Forecast (CF) Metadata Convention at the PCMDI website (http://cmip-pcmdi.llnl.gov/).

Multivariate analysis of the dielectric response of materials modeled using networks of resistors and capacitors

We discuss the modeling of dielectric responses of electromagnetically excited networks which are composed of a mixture of capacitors and resistors. Such networks can be employed as lumped-parameter circuits to model the response of composite materials containing conductive and insulating grains. The dynamics of the excited network systems are studied using a state space model derived from a randomized incidence matrix. Time and frequency domain responses from synthetic data sets generated from state space models are analyzed for the purpose of estimating the fraction of capacitors in the network. Good results were obtained by using either the time-domain response to a pulse excitation or impedance data at selected frequencies. A chemometric framework based on a Successive Projections Algorithm (SPA) enables the construction of multiple linear regression (MLR) models which can efficiently determine the ratio of conductive to insulating components in composite material samples. The proposed method avoids restrictions commonly associated with Archie’s law, the application of percolation theory or Kohlrausch-Williams-Watts models and is applicable to experimental results generated by either time domain transient spectrometers or continuous-wave instruments. Furthermore, it is quite generic and applicable to tomography, acoustics as well as other spectroscopies such as nuclear magnetic resonance, electron paramagnetic resonance and, therefore, should be of general interest across the dielectrics community.

Analysis of the variability of auditory brainstem response components through linear regression

(ABR) is of fundamental importance to the investiga- tion of the auditory system behavior, though its in- terpretation has a subjective nature because of the manual process employed in its study and the clinical experience required for its analysis. When analyzing the ABR, clinicians are often interested in the identi- fication of ABR signal components referred to as Jewett waves. In particular, the detection and study of the time when these waves occur (i.e., the wave la- tency) is a practical tool for the diagnosis of disorders affecting the auditory system. In this context, the aim of this research is to compare ABR manual/visual analysis provided by different examiners. Methods: The ABR data were collected from 10 normal-hearing subjects (5 men and 5 women, from 20 to 52 years). A total of 160 data samples were analyzed and a pair- wise comparison between four distinct examiners was executed. We carried out a statistical study aiming to identify significant differences between assessments provided by the examiners. For this, we used Linear Regression in conjunction with Bootstrap, as a me- thod for evaluating the relation between the responses given by the examiners. Results: The analysis sug- gests agreement among examiners however reveals differences between assessments of the variability of the waves. We quantified the magnitude of the ob- tained wave latency differences and 18% of the inves- tigated waves presented substantial differences (large and moderate) and of these 3.79% were considered not acceptable for the clinical practice. Conclusions: Our results characterize the variability of the manual analysis of ABR data and the necessity of establishing unified standards and protocols for the analysis of these data. These results may also contribute to the validation and development of automatic systems that are employed in the early diagnosis of hearing loss.