Modelling and control of Hammerstein system using B-spline approximation and the inverse of De Boor algorithm

In this article a simple and effective controller design is introduced for the Hammerstein systems that are identified based on observational input/output data. The nonlinear static function in the Hammerstein system is modelled using a B-spline neural network. The controller is composed by computing the inverse of the B-spline approximated nonlinear static function, and a linear pole assignment controller. The contribution of this article is the inverse of De Boor algorithm that computes the inverse efficiently. Mathematical analysis is provided to prove the convergence of the proposed algorithm. Numerical examples are utilised to demonstrate the efficacy of the proposed approach.

A method for merging flow-dependent forecast error statistics from an ensemble with static statistics for use in high resolution variational data assimilation

The background error covariance matrix, B, is often used in variational data assimilation for numerical weather prediction as a static and hence poor approximation to the fully dynamic forecast error covariance matrix, Pf. In this paper the concept of an Ensemble Reduced Rank Kalman Filter (EnRRKF) is outlined. In the EnRRKF the forecast error statistics in a subspace defined by an ensemble of states forecast by the dynamic model are found. These statistics are merged in a formal way with the static statistics, which apply in the remainder of the space. The combined statistics may then be used in a variational data assimilation setting. It is hoped that the nonlinear error growth of small-scale weather systems will be accurately captured by the EnRRKF, to produce accurate analyses and ultimately improved forecasts of extreme events.

B-spline neural network based digital baseband predistorter solution using the inverse of De Boor algorithm

In this paper a new nonlinear digital baseband predistorter design is introduced based on direct learning, together with a new Wiener system modeling approach for the high power amplifiers (HPA) based on the B-spline neural network. The contribution is twofold. Firstly, by assuming that the nonlinearity in the HPA is mainly dependent on the input signal amplitude the complex valued nonlinear static function is represented by two real valued B-spline neural networks, one for the amplitude distortion and another for the phase shift. The Gauss-Newton algorithm is applied for the parameter estimation, in which the De Boor recursion is employed to calculate both the B-spline curve and the first order derivatives. Secondly, we derive the predistorter algorithm calculating the inverse of the complex valued nonlinear static function according to B-spline neural network based Wiener models. The inverse of the amplitude and phase shift distortion are then computed and compensated using the identified phase shift model. Numerical examples have been employed to demonstrate the efficacy of the proposed approaches.

Northern Hemisphere extratropical cyclones in a warming climate in the HiGEM high-resolution climate model

Changes to the Northern Hemisphere winter (December, January and February) extratropical storm tracks and cyclones in a warming climate are investigated. Two idealised climate change experiments with HiGEM1.1, a doubled CO2 and a quadrupled CO2 experiment, are compared against a present day control run. An objective feature tracking method is used and a focus given to regional changes. The climatology of extratropical storm tracks from the control run is shown to be in good agreement with ERA-40, while the frequency distribution of cyclone intensity also compares well. In both simulations the mean climate changes are generally consistent with the simulations of the IPCC AR4 models, with a strongly enhanced surface warming at the winter pole and the reduced lower tropospheric warming over the North Atlantic Ocean associated with the slowdown of the Meridional Overturning Circulation. The circulation changes in the North Atlantic are different between the two idealised simulations with different CO2 forcings. In the North Atlantic the storm tracks are influenced by the slowdown of the MOC, the enhanced surface polar warming, and the enhanced upper tropical troposphere warming, giving a north eastward shift of the storm tracks in the 2XCO2 experiment, but no shift in the 4XCO2 experiment. Over the Pacific, in the 2XCO2 experiment, changes in the mean climate are associated with local temperature changes, while in the 4XCO2 experiment the changes in the Pacific are impacted by the weakened tropical circulation. The storm track changes are consistent with the shifts in the zonal wind. Total cyclone numbers are found to decrease over the Northern Hemisphere with increasing CO2 forcing. Changes in cyclone intensity are found using 850hPa vorticity, mean sea level pressure, and 850hPa winds. The intensity of the Northern Hemisphere cyclones is found to decrease relative to the control.

Impact of increasing resolution and a warmer climate on extreme weather from NH extra-tropical cyclones

The effect of a warmer climate on the properties of extra-tropical cyclones is investigated using simulations of the ECHAM5 global climate model at resolutions of T213 (60 km) and T319 (40 km). Two periods representative of the end of the 20th and 21st centuries are investigated using the IPCC A1B scenario. The focus of the paper is on precipitation for the NH summer and winter seasons, however results from vorticity and winds are also presented. Similar number of events are identified at both resolutions. There are, however, a greater number of extreme precipitation events in the higher reso- lution run. The difference between maximum intensity distributions are shown to be statistically significant using a Kolmogorov-Smirnov test. A Generalised Pareto Distribution is used to analyse changes in extreme precipitation and wind events. In both resolutions, there is an increase in the number of ex- treme precipitation events in a warmer climate for all seasons, together with a reduction in return period. This is not associated with any increased verti- cal velocity, or with any increase in wind intensity in the winter and spring. However, there is an increase in wind extremes in the summer and autumn associated with tropical cyclones migrating into the extra-tropics.

Application of a hybrid tracking algorithm to motion analysis

An algorithm for tracking multiple feature positions in a dynamic image sequence is presented. This is achieved using a combination of two trajectory-based methods, with the resulting hybrid algorithm exhibiting the advantages of both. An optimizing exchange algorithm is described which enables short feature paths to be tracked without prior knowledge of the motion being studied. The resulting partial trajectories are then used to initialize a fast predictor algorithm which is capable of rapidly tracking multiple feature paths. As this predictor algorithm becomes tuned to the feature positions being tracked, it is shown how the location of occluded or poorly detected features can be predicted. The results of applying this tracking algorithm to data obtained from real-world scenes are then presented.

New fast SCFT algorithm applied to binary diblock copolymer/homopolymer blends

We present an efficient strategy for mapping out the classical phase behavior of block copolymer systems using self-consistent field theory (SCFT). With our new algorithm, the complete solution of a classical block copolymer phase can be evaluated typically in a fraction of a second on a single-processor computer, even for highly segregated melts. This is accomplished by implementing the standard unit-cell approximation (UCA) for the cylindrical and spherical phases, and solving the resulting equations using a Bessel function expansion. Here the method is used to investigate blends of AB diblock copolymer and A homopolymer, concentrating on the situation where the two molecules are of similar size.

Objective detection of sting jets in low-resolution datasets

Sting jets are transient coherent mesoscale strong wind features that can cause damaging surface wind gusts in extratropical cyclones. Currently, we have only limited knowledge of their climatological characteristics. Numerical weather prediction models require enough resolution to represent slantwise motions with horizontal scales of tens of kilometres and vertical scales of just a few hundred metres to represent sting jets. Hence, the climatological characteristics of sting jets and the associated extratropical cyclones can not be determined by searching for sting jets in low-resolution datasets such as reanalyses. A diagnostic is presented and evaluated for the detection in low-resolution datasets of atmospheric regions from which sting jets may originate. Previous studies have shown that conditional symmetric instability (CSI) is present in all storms studied with sting jets, while other, rapidly developing storms of a similar character but no CSI do not develop sting jets. Therefore, we assume that the release of CSI is needed for sting jets to develop. While this instability will not be released in a physically realistic way in low-resolution models (and hence sting jets are unlikely to occur), it is hypothesized that the signature of this instability (combined with other criteria that restrict analysis to moist mid-tropospheric regions in the neighbourhood of a secondary cold front) can be used to identify cyclones in which sting jets occurred in reality. The diagnostic is evaluated, and appropriate parameter thresholds defined, by applying it to three case studies simulated using two resolutions (with CSI-release resolved in only the higher-resolution simulation).

A comparison among four different retrieval methods for ice-cloud properties using data from CloudSat, CALIPSO, and MODIS

The A-Train constellation of satellites provides a new capability to measure vertical cloud profiles that leads to more detailed information on ice-cloud microphysical properties than has been possible up to now. A variational radar–lidar ice-cloud retrieval algorithm (VarCloud) takes advantage of the complementary nature of the CloudSat radar and Cloud–Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) lidar to provide a seamless retrieval of ice water content, effective radius, and extinction coefficient from the thinnest cirrus (seen only by the lidar) to the thickest ice cloud (penetrated only by the radar). In this paper, several versions of the VarCloud retrieval are compared with the CloudSat standard ice-only retrieval of ice water content, two empirical formulas that derive ice water content from radar reflectivity and temperature, and retrievals of vertically integrated properties from the Moderate Resolution Imaging Spectroradiometer (MODIS) radiometer. The retrieved variables typically agree to within a factor of 2, on average, and most of the differences can be explained by the different microphysical assumptions. For example, the ice water content comparison illustrates the sensitivity of the retrievals to assumed ice particle shape. If ice particles are modeled as oblate spheroids rather than spheres for radar scattering then the retrieved ice water content is reduced by on average 50% in clouds with a reflectivity factor larger than 0 dBZ. VarCloud retrieves optical depths that are on average a factor-of-2 lower than those from MODIS, which can be explained by the different assumptions on particle mass and area; if VarCloud mimics the MODIS assumptions then better agreement is found in effective radius and optical depth is overestimated. MODIS predicts the mean vertically integrated ice water content to be around a factor-of-3 lower than that from VarCloud for the same retrievals, however, because the MODIS algorithm assumes that its retrieved effective radius (which is mostly representative of cloud top) is constant throughout the depth of the cloud. These comparisons highlight the need to refine microphysical assumptions in all retrieval algorithms and also for future studies to compare not only the mean values but also the full probability density function.