Nonlinear system identification using particle swarm optimisation tuned radial basis function models

A novel particle swarm optimisation (PSO) tuned radial basis function (RBF) network model is proposed for identification of non-linear systems. At each stage of orthogonal forward regression (OFR) model construction process, PSO is adopted to tune one RBF unit's centre vector and diagonal covariance matrix by minimising the leave-one-out (LOO) mean square error (MSE). This PSO aided OFR automatically determines how many tunable RBF nodes are sufficient for modelling. Compared with the-state-of-the-art local regularisation assisted orthogonal least squares algorithm based on the LOO MSE criterion for constructing fixed-node RBF network models, the PSO tuned RBF model construction produces more parsimonious RBF models with better generalisation performance and is often more efficient in model construction. The effectiveness of the proposed PSO aided OFR algorithm for constructing tunable node RBF models is demonstrated using three real data sets.

The International Urban Energy Balance Models Comparison Project: First Results from Phase 1

A large number of urban surface energy balance models now exist with different assumptions about the important features of the surface and exchange processes that need to be incorporated. To date, no com- parison of these models has been conducted; in contrast, models for natural surfaces have been compared extensively as part of the Project for Intercomparison of Land-surface Parameterization Schemes. Here, the methods and first results from an extensive international comparison of 33 models are presented. The aim of the comparison overall is to understand the complexity required to model energy and water exchanges in urban areas. The degree of complexity included in the models is outlined and impacts on model performance are discussed. During the comparison there have been significant developments in the models with resulting improvements in performance (root-mean-square error falling by up to two-thirds). Evaluation is based on a dataset containing net all-wave radiation, sensible heat, and latent heat flux observations for an industrial area in Vancouver, British Columbia, Canada. The aim of the comparison is twofold: to identify those modeling ap- proaches that minimize the errors in the simulated fluxes of the urban energy balance and to determine the degree of model complexity required for accurate simulations. There is evidence that some classes of models perform better for individual fluxes but no model performs best or worst for all fluxes. In general, the simpler models perform as well as the more complex models based on all statistical measures. Generally the schemes have best overall capability to model net all-wave radiation and least capability to model latent heat flux.

Robots with a gentle touch: advances in assistive robotics and prosthetics

As healthcare costs rise and an aging population makes an increased demand on services, so new techniques must be introduced to promote an individuals independence and provide these services. Robots can now be designed so they can alter their dynamic properties changing from stiff to flaccid, or from giving no resistance to movement, to damping any large and sudden movements. This has some strong implications in health care in particular for rehabilitation where a robot must work in conjunction with an individual, and might guiding or assist a persons arm movements, or might be commanded to perform some set of autonomous actions. This paper presents the state-of-the-art of rehabilitation robots with examples from prosthetics, aids for daily living and physiotherapy. In all these situations there is the potential for the interaction to be non-passive with a resulting potential for the human/machine/environment combination to become unstable. To understand this instability we must develop better models of the human motor system and fit these models with realistic parameters. This paper concludes with a discussion of this problem and overviews some human models that can be used to facilitate the design of the human/machine interfaces.

On the response of the Antarctic Circumpolar Current transport to climate change in coupled climate models

The CMIP3 (IPCC AR4) models show a consistent intensification and poleward shift of the westerly winds over the Southern Ocean during the 21st century. However, the responses of the Antarctic Circumpolar Currents (ACC) show great diversity in these models, with many even showing reductions in transport. To obtain some understanding of diverse responses in the ACC transport, we investigate both external atmospheric and internal oceanic processes that control the ACC transport responses in these models. While the strengthened westerlies act to increase the tilt of isopycnal surfaces and hence the ACC transport through Ekman pumping effects, the associated changes in buoyancy forcing generally tend to reduce the surface meridional density gradient. The steepening of isopycnal surfaces induced by increased wind forcing leads to enhanced (parameterized) eddy-induced transports that act to reduce the isopycnal slopes. There is also considerable narrowing of the ACC that tends to reduce the ACC transport, caused mainly by the poleward shifts of the subtropical gyres and to a lesser extent by the equatorward expansions of the subpolar gyres in some models. If the combined effect of these retarding processes is larger than that of enhanced Ekman pumping, the ACC transport will be reduced. In addition, the effect of Ekman pumping on the ACC is reduced in weakly stratified models. These findings give insight into the reliability of IPCC-class model predictions of the Southern Ocean circulation, and into the observed decadal-scale steady ACC transport.

Daily precipitation statistics in regional climate models: evaluation and intercomparison for the European Alps

An evaluation is undertaken of the statistics of daily precipitation as simulated by five regional climate models using comprehensive observations in the region of the European Alps. Four limited area models and one variable-resolution global model are considered, all with a grid spacing of 50 km. The 15-year integrations were forced from reanalyses and observed sea surface temperature and sea ice (global model from sea surface only). The observational reference is based on 6400 rain gauge records (10–50 stations per grid box). Evaluation statistics encompass mean precipitation, wet-day frequency, precipitation intensity, and quantiles of the frequency distribution. For mean precipitation, the models reproduce the characteristics of the annual cycle and the spatial distribution. The domain mean bias varies between −23% and +3% in winter and between −27% and −5% in summer. Larger errors are found for other statistics. In summer, all models underestimate precipitation intensity (by 16–42%) and there is a too low frequency of heavy events. This bias reflects too dry summer mean conditions in three of the models, while it is partly compensated by too many low-intensity events in the other two models. Similar intermodel differences are found for other European subregions. Interestingly, the model errors are very similar between the two models with the same dynamical core (but different parameterizations) and they differ considerably between the two models with similar parameterizations (but different dynamics). Despite considerable biases, the models reproduce prominent mesoscale features of heavy precipitation, which is a promising result for their use in climate change downscaling over complex topography.

Statistical decadal predictions for sea surface temperatures: a benchmark for dynamical GCM predictions

Accurate decadal climate predictions could be used to inform adaptation actions to a changing climate. The skill of such predictions from initialised dynamical global climate models (GCMs) may be assessed by comparing with predictions from statistical models which are based solely on historical observations. This paper presents two benchmark statistical models for predicting both the radiatively forced trend and internal variability of annual mean sea surface temperatures (SSTs) on a decadal timescale based on the gridded observation data set HadISST. For both statistical models, the trend related to radiative forcing is modelled using a linear regression of SST time series at each grid box on the time series of equivalent global mean atmospheric CO2 concentration. The residual internal variability is then modelled by (1) a first-order autoregressive model (AR1) and (2) a constructed analogue model (CA). From the verification of 46 retrospective forecasts with start years from 1960 to 2005, the correlation coefficient for anomaly forecasts using trend with AR1 is greater than 0.7 over parts of extra-tropical North Atlantic, the Indian Ocean and western Pacific. This is primarily related to the prediction of the forced trend. More importantly, both CA and AR1 give skillful predictions of the internal variability of SSTs in the subpolar gyre region over the far North Atlantic for lead time of 2 to 5 years, with correlation coefficients greater than 0.5. For the subpolar gyre and parts of the South Atlantic, CA is superior to AR1 for lead time of 6 to 9 years. These statistical forecasts are also compared with ensemble mean retrospective forecasts by DePreSys, an initialised GCM. DePreSys is found to outperform the statistical models over large parts of North Atlantic for lead times of 2 to 5 years and 6 to 9 years, however trend with AR1 is generally superior to DePreSys in the North Atlantic Current region, while trend with CA is superior to DePreSys in parts of South Atlantic for lead time of 6 to 9 years. These findings encourage further development of benchmark statistical decadal prediction models, and methods to combine different predictions.

Spectral analysis of diffusions with jump boundary

In this paper we consider one-dimensional diffusions with constant coefficients in a finite interval with jump boundary and a certain deterministic jump distribution. We use coupling methods in order to identify the spectral gap in the case of a large drift and prove that there is a threshold drift above which the bottom of the spectrum no longer depends on the drift. As a corollary to our result we are able to answer two questions concerning elliptic eigenvalue problems with non-local boundary conditions formulated previously by Iddo Ben-Ari and Ross Pinsky.

Assessment of surface winds over the Atlantic, Indian and Pacific Ocean sectors of the Southern Ocean in CMIP5 models: historical bias, forcing response, and state dependence

An assessment of the fifth Coupled Models Intercomparison Project (CMIP5) models’ simulation of the near-surface westerly wind jet position and strength over the Atlantic, Indian and Pacific sectors of the Southern Ocean is presented. Compared with reanalysis climatologies there is an equatorward bias of 3.7° (inter-model standard deviation of ± 2.2°) in the ensemble mean position of the zonal mean jet. The ensemble mean strength is biased slightly too weak, with the largest biases over the Pacific sector (-1.6±1.1 m/s, 27 -22%). An analysis of atmosphere-only (AMIP) experiments indicates that 41% of the zonal mean position bias comes from coupling of the ocean/ice models to the atmosphere. The response to future emissions scenarios (RCP4.5 and RCP8.5) is characterized by two phases: (i) the period of most rapid ozone recovery (2000-2049) during which there is insignificant change in summer; and (ii) the period 2050-2098 during which RCP4.5 simulations show no significant change but RCP8.5 simulations show poleward shifts (0.30, 0.19 and 0.28°/decade over the Atlantic, Indian and Pacific sectors respectively), and increases in strength (0.06, 0.08 and 0.15 m/s/decade respectively). The models with larger equatorward position biases generally show larger poleward shifts (i.e. state dependence). This inter-model relationship is strongest over the Pacific sector (r=-0.89) and insignificant over the Atlantic sector (r=-0.50). However, an assessment of jet structure shows that over the Atlantic sector jet shift is significantly correlated with jet width whereas over the Pacific sector the distance between the sub-polar and sub-tropical westerly jets appears to be more important.

Systematic winter sea-surface temperature biases in the northern Arabian Sea in HiGEM and the CMIP3 models

Analysis of 20th century simulations of the High resolution Global Environment Model (HiGEM) and the Third Coupled Model Intercomparison Project (CMIP3) models shows that most have a cold sea-surface temperature (SST) bias in the northern Arabian Sea during boreal winter. The association between Arabian Sea SST and the South Asian monsoon has been widely studied in observations and models, with winter cold biases known to be detrimental to rainfall simulation during the subsequent monsoon in coupled general circulation models (GCMs). However, the causes of these SST biases are not well understood. Indeed this is one of the first papers to address causes of the cold biases. The models show anomalously strong north-easterly winter monsoon winds and cold air temperatures in north-west India, Pakistan and beyond. This leads to the anomalous advection of cold, dry air over the Arabian Sea. The cold land region is also associated with an anomalously strong meridional surface temperature gradient during winter, contributing to the enhanced low-level convergence and excessive precipitation over the western equatorial Indian Ocean seen in many models.

Fractional order modeling of large three-dimensional RC networks

An incidence matrix analysis is used to model a three-dimensional network consisting of resistive and capacitive elements distributed across several interconnected layers. A systematic methodology for deriving a descriptor representation of the network with random allocation of the resistors and capacitors is proposed. Using a transformation of the descriptor representation into standard state-space form, amplitude and phase admittance responses of three-dimensional random RC networks are obtained. Such networks display an emergent behavior with a characteristic Jonscher-like response over a wide range of frequencies. A model approximation study of these networks is performed to infer the admittance response using integral and fractional order models. It was found that a fractional order model with only seven parameters can accurately describe the responses of networks composed of more than 70 nodes and 200 branches with 100 resistors and 100 capacitors. The proposed analysis can be used to model charge migration in amorphous materials, which may be associated to specific macroscopic or microscopic scale fractal geometrical structures in composites displaying a viscoelastic electromechanical response, as well as to model the collective responses of processes governed by random events described using statistical mechanics.

Interface dynamics in planar neural field models

Neural field models describe the coarse-grained activity of populations of interacting neurons. Because of the laminar structure of real cortical tissue they are often studied in two spatial dimensions, where they are well known to generate rich patterns of spatiotemporal activity. Such patterns have been interpreted in a variety of contexts ranging from the understanding of visual hallucinations to the generation of electroencephalographic signals. Typical patterns include localized solutions in the form of traveling spots, as well as intricate labyrinthine structures. These patterns are naturally defined by the interface between low and high states of neural activity. Here we derive the equations of motion for such interfaces and show, for a Heaviside firing rate, that the normal velocity of an interface is given in terms of a non-local Biot-Savart type interaction over the boundaries of the high activity regions. This exact, but dimensionally reduced, system of equations is solved numerically and shown to be in excellent agreement with the full nonlinear integral equation defining the neural field. We develop a linear stability analysis for the interface dynamics that allows us to understand the mechanisms of pattern formation that arise from instabilities of spots, rings, stripes and fronts. We further show how to analyze neural field models with linear adaptation currents, and determine the conditions for the dynamic instability of spots that can give rise to breathers and traveling waves.

A closer look at chaotic advection in the stratosphere: part II: statistical diagnostics

Statistical diagnostics of mixing and transport are computed for a numerical model of forced shallow-water flow on the sphere and a middle-atmosphere general circulation model. In particular, particle dispersion statistics, transport fluxes, Liapunov exponents (probability density functions and ensemble averages), and tracer concentration statistics are considered. It is shown that the behavior of the diagnostics is in accord with that of kinematic chaotic advection models so long as stochasticity is sufficiently weak. Comparisons with random-strain theory are made.

Evaluation of Earth system models using modern and palaeo-observations: the state-of-the-art

Earth system models are increasing in complexity and incorporating more processes than their predecessors, making them important tools for studying the global carbon cycle. However, their coupled behaviour has only recently been examined in any detail, and has yielded a very wide range of outcomes, with coupled climate-carbon cycle models that represent land-use change simulating total land carbon stores by 2100 that vary by as much as 600 Pg C given the same emissions scenario. This large uncertainty is associated with differences in how key processes are simulated in different models, and illustrates the necessity of determining which models are most realistic using rigorous model evaluation methodologies. Here we assess the state-of-the-art with respect to evaluation of Earth system models, with a particular emphasis on the simulation of the carbon cycle and associated biospheric processes. We examine some of the new advances and remaining uncertainties relating to (i) modern and palaeo data and (ii) metrics for evaluation, and discuss a range of strategies, such as the inclusion of pre-calibration, combined process- and system-level evaluation, and the use of emergent constraints, that can contribute towards the development of more robust evaluation schemes. An increasingly data-rich environment offers more opportunities for model evaluation, but it is also a challenge, as more knowledge about data uncertainties is required in order to determine robust evaluation methodologies that move the field of ESM evaluation from "beauty contest" toward the development of useful constraints on model behaviour.

On the lack of stratospheric dynamical variability in low-top versions of the CMIP5 models

We describe the main differences in simulations of stratospheric climate and variability by models within the fifth Coupled Model Intercomparison Project (CMIP5) that have a model top above the stratopause and relatively fine stratospheric vertical resolution (high-top), and those that have a model top below the stratopause (low-top). Although the simulation of mean stratospheric climate by the two model ensembles is similar, the low-top model ensemble has very weak stratospheric variability on daily and interannual time scales. The frequency of major sudden stratospheric warming events is strongly underestimated by the low-top models with less than half the frequency of events observed in the reanalysis data and high-top models. The lack of stratospheric variability in the low-top models affects their stratosphere-troposphere coupling, resulting in short-lived anomalies in the Northern Annular Mode, which do not produce long-lasting tropospheric impacts, as seen in observations. The lack of stratospheric variability, however, does not appear to have any impact on the ability of the low-top models to reproduce past stratospheric temperature trends. We find little improvement in the simulation of decadal variability for the high-top models compared to the low-top, which is likely related to the fact that neither ensemble produces a realistic dynamical response to volcanic eruptions.

Problems with binary pattern measures for flood model evaluation

As the calibration and evaluation of flood inundation models are a prerequisite for their successful application, there is a clear need to ensure that the performance measures that quantify how well models match the available observations are fit for purpose. This paper evaluates the binary pattern performance measures that are frequently used to compare flood inundation models with observations of flood extent. This evaluation considers whether these measures are able to calibrate and evaluate model predictions in a credible and consistent way, i.e. identifying the underlying model behaviour for a number of different purposes such as comparing models of floods of different magnitudes or on different catchments. Through theoretical examples, it is shown that the binary pattern measures are not consistent for floods of different sizes, such that for the same vertical error in water level, a model of a flood of large magnitude appears to perform better than a model of a smaller magnitude flood. Further, the commonly used Critical Success Index (usually referred to as F<2 >) is biased in favour of overprediction of the flood extent, and is also biased towards correctly predicting areas of the domain with smaller topographic gradients. Consequently, it is recommended that future studies consider carefully the implications of reporting conclusions using these performance measures. Additionally, future research should consider whether a more robust and consistent analysis could be achieved by using elevation comparison methods instead.