Dispersion of a point-source release of a passive scalar through an urban-like array for different wind directions

The dispersion of a point-source release of a passive scalar in a regular array of cubical, urban-like, obstacles is investigated by means of direct numerical simulations. The simulations are conducted under conditions of neutral stability and fully rough turbulent flow, at a roughness Reynolds number of Reτ = 500. The Navier–Stokes and scalar equations are integrated assuming a constant rate release from a point source close to the ground within the array. We focus on short-range dispersion, when most of the material is still within the building canopy. Mean and fluctuating concentrations are computed for three different pressure gradient directions (0◦ , 30◦ , 45◦). The results agree well with available experimental data measured in a water channel for a flow angle of 0◦ . Profiles of mean concentration and the three-dimensional structure of the dispersion pattern are compared for the different forcing angles. A number of processes affecting the plume structure are identified and discussed, including: (i) advection or channelling of scalar down ‘streets’, (ii) lateral dispersion by turbulent fluctuations and topological dispersion induced by dividing streamlines around buildings, (iii) skewing of the plume due to flow turning with height, (iv) detrainment by turbulent dispersion or mean recirculation, (v) entrainment and release of scalar in building wakes, giving rise to ‘secondary sources’, (vi) plume meandering due to unsteady turbulent fluctuations. Finally, results on relative concentration fluctuations are presented and compared with the literature for point source dispersion over flat terrain and urban arrays. Keywords Direct numerical simulation · Dispersion modelling · Urban array

Evidence of dispersion relations for the nonlinear response of the Lorenz 63 system

Along the lines of the nonlinear response theory developed by Ruelle, in a previous paper we have proved under rather general conditions that Kramers-Kronig dispersion relations and sum rules apply for a class of susceptibilities describing at any order of perturbation the response of Axiom A non equilibrium steady state systems to weak monochromatic forcings. We present here the first evidence of the validity of these integral relations for the linear and the second harmonic response for the perturbed Lorenz 63 system, by showing that numerical simulations agree up to high degree of accuracy with the theoretical predictions. Some new theoretical results, showing how to derive asymptotic behaviors and how to obtain recursively harmonic generation susceptibilities for general observables, are also presented. Our findings confirm the conceptual validity of the nonlinear response theory, suggest that the theory can be extended for more general non equilibrium steady state systems, and shed new light on the applicability of very general tools, based only upon the principle of causality, for diagnosing the behavior of perturbed chaotic systems and reconstructing their output signals, in situations where the fluctuation-dissipation relation is not of great help.

Portfolio size and the reduction of dispersion: the case of the United Kingdom commercial real estate market

This paper investigates the potential benefits and limitations of equal and value-weighted diversification using as the example the UK institutional property market. To achieve this it uses the largest sample (392) of actual property returns that is currently available, over the period 1981 to 1996. To evaluate these issues two approaches are adopted; first, an analysis of the correlations within the sectors and regions and secondly simulations of property portfolios of increasing size constructed both naively and with value-weighting. Using these methods it is shown that the extent of possible risk reduction is limited because of the high positive correlations between assets in any portfolio, even when naively diversified. It is also shown that portfolios exhibit high levels of variability around the average risk, suggesting that previous work seriously understates the number of properties needed to achieve a satisfactory level of diversification. The results have implications for the development and maintenance of a property portfolio because they indicate that the achievable level of risk reduction depends upon the availability of assets, the weighting system used and the investor’s risk tolerance.

Data assimilation for state and parameter estimation: application to morphodynamic modelling

Data assimilation is predominantly used for state estimation; combining observational data with model predictions to produce an updated model state that most accurately approximates the true system state whilst keeping the model parameters fixed. This updated model state is then used to initiate the next model forecast. Even with perfect initial data, inaccurate model parameters will lead to the growth of prediction errors. To generate reliable forecasts we need good estimates of both the current system state and the model parameters. This paper presents research into data assimilation methods for morphodynamic model state and parameter estimation. First, we focus on state estimation and describe implementation of a three dimensional variational(3D-Var) data assimilation scheme in a simple 2D morphodynamic model of Morecambe Bay, UK. The assimilation of observations of bathymetry derived from SAR satellite imagery and a ship-borne survey is shown to significantly improve the predictive capability of the model over a 2 year run. Here, the model parameters are set by manual calibration; this is laborious and is found to produce different parameter values depending on the type and coverage of the validation dataset. The second part of this paper considers the problem of model parameter estimation in more detail. We explain how, by employing the technique of state augmentation, it is possible to use data assimilation to estimate uncertain model parameters concurrently with the model state. This approach removes inefficiencies associated with manual calibration and enables more effective use of observational data. We outline the development of a novel hybrid sequential 3D-Var data assimilation algorithm for joint state-parameter estimation and demonstrate its efficacy using an idealised 1D sediment transport model. The results of this study are extremely positive and suggest that there is great potential for the use of data assimilation-based state-parameter estimation in coastal morphodynamic modelling.

Ensemble forecasts of a flood-producing storm: comparison of the influence of model-state perturbations and parameter modifications

High-resolution ensemble simulations (Δx = 1 km) are performed with the Met Office Unified Model for the Boscastle (Cornwall, UK) flash-flooding event of 16 August 2004. Forecast uncertainties arising from imperfections in the forecast model are analysed by comparing the simulation results produced by two types of perturbation strategy. Motivated by the meteorology of the event, one type of perturbation alters relevant physics choices or parameter settings in the model's parametrization schemes. The other type of perturbation is designed to account for representativity error in the boundary-layer parametrization. It makes direct changes to the model state and provides a lower bound against which to judge the spread produced by other uncertainties. The Boscastle has genuine skill at scales of approximately 60 km and an ensemble spread which can be estimated to within ∼ 10% with only eight members. Differences between the model-state perturbation and physics modification strategies are discussed, the former being more important for triggering and the latter for subsequent cell development, including the average internal structure of convective cells. Despite such differences, the spread in rainfall evaluated at skilful scales is shown to be only weakly sensitive to the perturbation strategy. This suggests that relatively simple strategies for treating model uncertainty may be sufficient for practical, convective-scale ensemble forecasting.

European plant phenology and climate as seen in a 20-year AVHRR land-surface parameter dataset

Vegetation distribution and state have been measured since 1981 by the AVHRR (Advanced Very High Resolution Radiometer) instrument through satellite remote sensing. In this study a correction method is applied to the Pathfinder NDVI (Normalized Difference Vegetation Index) data to create a continuous European vegetation phenology dataset of a 10-day temporal and 0.1° spatial resolution; additionally, land surface parameters for use in biosphere–atmosphere modelling are derived. The analysis of time-series from this dataset reveals, for the years 1982–2001, strong seasonal and interannual variability in European land surface vegetation state. Phenological metrics indicate a late and short growing season for the years 1985–1987, in addition to early and prolonged activity in the years 1989, 1990, 1994 and 1995. These variations are in close agreement with findings from phenological measurements at the surface; spring phenology is also shown to correlate particularly well with anomalies in winter temperature and winter North Atlantic Oscillation (NAO) index. Nevertheless, phenological metrics, which display considerable regional differences, could only be determined for vegetation with a seasonal behaviour. Trends in the phenological phases reveal a general shift to earlier (−0.54 days year−1) and prolonged (0.96 days year−1) growing periods which are statistically significant, especially for central Europe.

Bayesian parameter estimation for latent Markov random fields and social networks

Undirected graphical models are widely used in statistics, physics and machine vision. However Bayesian parameter estimation for undirected models is extremely challenging, since evaluation of the posterior typically involves the calculation of an intractable normalising constant. This problem has received much attention, but very little of this has focussed on the important practical case where the data consists of noisy or incomplete observations of the underlying hidden structure. This paper specifically addresses this problem, comparing two alternative methodologies. In the first of these approaches particle Markov chain Monte Carlo (Andrieu et al., 2010) is used to efficiently explore the parameter space, combined with the exchange algorithm (Murray et al., 2006) for avoiding the calculation of the intractable normalising constant (a proof showing that this combination targets the correct distribution in found in a supplementary appendix online). This approach is compared with approximate Bayesian computation (Pritchard et al., 1999). Applications to estimating the parameters of Ising models and exponential random graphs from noisy data are presented. Each algorithm used in the paper targets an approximation to the true posterior due to the use of MCMC to simulate from the latent graphical model, in lieu of being able to do this exactly in general. The supplementary appendix also describes the nature of the resulting approximation.

The importance of friction in mountain wave drag amplification by Scorer parameter resonance

A mechanism for amplification of mountain waves, and their associated drag, by parametric resonance is investigated using linear theory and numerical simulations. This mechanism, which is active when the Scorer parameter oscillates with height, was recently classified by previous authors as intrinsically nonlinear. Here it is shown that, if friction is included in the simplest possible form as a Rayleigh damping, and the solution to the Taylor-Goldstein equation is expanded in a power series of the amplitude of the Scorer parameter oscillation, linear theory can replicate the resonant amplification produced by numerical simulations with some accuracy. The drag is significantly altered by resonance in the vicinity of n/l_0 = 2, where l_0 is the unperturbed value of the Scorer parameter and n is the wave number of its oscillation. Depending on the phase of this oscillation, the drag may be substantially amplified or attenuated relative to its non-resonant value, displaying either single maxima or minima, or double extrema near n/l_0 = 2. Both non-hydrostatic effects and friction tend to reduce the magnitude of the drag extrema. However, in exactly inviscid conditions, the single drag maximum and minimum are suppressed. As in the atmosphere friction is often small but non-zero outside the boundary layer, modelling of the drag amplification mechanism addressed here should be quite sensitive to the type of turbulence closure employed in numerical models, or to computational dissipation in nominally inviscid simulations.

Design of delay-tolerant linear dispersion codes

In cooperative communication networks, owing to the nodes' arbitrary geographical locations and individual oscillators, the system is fundamentally asynchronous. This will damage some of the key properties of the space-time codes and can lead to substantial performance degradation. In this paper, we study the design of linear dispersion codes (LDCs) for such asynchronous cooperative communication networks. Firstly, the concept of conventional LDCs is extended to the delay-tolerant version and new design criteria are discussed. Then we propose a new design method to yield delay-tolerant LDCs that reach the optimal Jensen's upper bound on ergodic capacity as well as minimum average pairwise error probability. The proposed design employs stochastic gradient algorithm to approach a local optimum. Moreover, it is improved by using simulated annealing type optimization to increase the likelihood of the global optimum. The proposed method allows for flexible number of nodes, receive antennas, modulated symbols and flexible length of codewords. Simulation results confirm the performance of the newly-proposed delay-tolerant LDCs.

Chaotic mixing and transport in Rossby-wave critical layers

A simple, dynamically consistent model of mixing and transport in Rossby-wave critical layers is obtained from the well-known Stewartson–Warn–Warn (SWW) solution of Rossby-wave critical-layer theory. The SWW solution is thought to be a useful conceptual model of Rossby-wave breaking in the stratosphere. Chaotic advection in the model is a consequence of the interaction between a stationary and a transient Rossby wave. Mixing and transport are characterized separately with a number of quantitative diagnostics (e.g. mean-square dispersion, lobe dynamics, and spectral moments), and with particular emphasis on the dynamics of the tracer field itself. The parameter dependences of the diagnostics are examined: transport tends to increase monotonically with increasing perturbation amplitude whereas mixing does not. The robustness of the results is investigated by stochastically perturbing the transient-wave phase speed. The two-wave chaotic advection model is contrasted with a stochastic single-wave model. It is shown that the effects of chaotic advection cannot be captured by stochasticity alone.

Input type and parameter resetting: is naturalistic input necessary?

It has been argued that extended exposure to naturalistic input provides L2 learners with more of an opportunity to converge of target morphosyntactic competence as compared to classroom-only environments, given that the former provide more positive evidence of less salient linguistic properties than the latter (e.g., Isabelli 2004). Implicitly, the claim is that such exposure is needed to fully reset parameters. However, such a position conflicts with the notion of parameterization (cf. Rothman and Iverson 2007). In light of two types of competing generative theories of adult L2 acquisition – the No Impairment Hypothesis (e.g., Duffield and White 1999) and so-called Failed Features approaches (e.g., Beck 1998; Franceschina 2001; Hawkins and Chan 1997), we investigate the verifiability of such a claim. Thirty intermediate L2 Spanish learners were tested in regards to properties of the Null-Subject Parameter before and after study-abroad. The data suggest that (i) parameter resetting is possible and (ii) exposure to naturalistic input is not privileged.

Complex dynamics in simple systems with periodic parameter oscillations

We study systems with periodically oscillating parameters that can give way to complex periodic or nonperiodic orbits. Performing the long time limit, we can define ergodic averages such as Lyapunov exponents, where a negative maximal Lyapunov exponent corresponds to a stable periodic orbit. By this, extremely complicated periodic orbits composed of contracting and expanding phases appear in a natural way. Employing the technique of ϵ-uncertain points, we find that values of the control parameters supporting such periodic motion are densely embedded in a set of values for which the motion is chaotic. When a tiny amount of noise is coupled to the system, dynamics with positive and with negative nontrivial Lyapunov exponents are indistinguishable. We discuss two physical systems, an oscillatory flow inside a duct and a dripping faucet with variable water supply, where such a mechanism seems to be responsible for a complicated alternation of laminar and turbulent phases.

Multi-site evaluation of an urban land-surface model: intra-urban heterogeneity, seasonality and parameter complexity requirements

An extensive off-line evaluation of the Noah/Single Layer Urban Canopy Model (Noah/SLUCM) urban land-surface model is presented using data from 15 sites to assess (1) the ability of the scheme to reproduce the surface energy balance observed in a range of urban environments, including seasonal changes, and (2) the impact of increasing complexity of input parameter information. Model performance is found to be most dependent on representation of vegetated surface area cover; refinement of other parameter values leads to smaller improvements. Model biases in net all-wave radiation and trade-offs between turbulent heat fluxes are highlighted using an optimization algorithm. Here we use the Urban Zones to characterize Energy partitioning (UZE) as the basis to assign default SLUCM parameter values. A methodology (FRAISE) to assign sites (or areas) to one of these categories based on surface characteristics is evaluated. Using three urban sites from the Basel Urban Boundary Layer Experiment (BUBBLE) dataset, an independent evaluation of the model performance with the parameter values representative of each class is performed. The scheme copes well with both seasonal changes in the surface characteristics and intra-urban heterogeneities in energy flux partitioning, with RMSE performance comparable to similar state-of-the-art models for all fluxes, sites and seasons. The potential of the methodology for high-resolution atmospheric modelling application using the Weather Research and Forecasting (WRF) model is highlighted. This analysis supports the recommendations that (1) three classes are appropriate to characterize the urban environment, and (2) that the parameter values identified should be adopted as default values in WRF.

Examining reliability of seasonal to decadal sea surface temperature forecasts: the role of ensemble dispersion

Useful probabilistic climate forecasts on decadal timescales should be reliable (i.e. forecast probabilities match the observed relative frequencies) but this is seldom examined. This paper assesses a necessary condition for reliability, that the ratio of ensemble spread to forecast error being close to one, for seasonal to decadal sea surface temperature retrospective forecasts from the Met Office Decadal Prediction System (DePreSys). Factors which may affect reliability are diagnosed by comparing this spread-error ratio for an initial condition ensemble and two perturbed physics ensembles for initialized and uninitialized predictions. At lead times less than 2 years, the initialized ensembles tend to be under-dispersed, and hence produce overconfident and hence unreliable forecasts. For longer lead times, all three ensembles are predominantly over-dispersed. Such over-dispersion is primarily related to excessive inter-annual variability in the climate model. These findings highlight the need to carefully evaluate simulated variability in seasonal and decadal prediction systems.Useful probabilistic climate forecasts on decadal timescales should be reliable (i.e. forecast probabilities match the observed relative frequencies) but this is seldom examined. This paper assesses a necessary condition for reliability, that the ratio of ensemble spread to forecast error being close to one, for seasonal to decadal sea surface temperature retrospective forecasts from the Met Office Decadal Prediction System (DePreSys). Factors which may affect reliability are diagnosed by comparing this spread-error ratio for an initial condition ensemble and two perturbed physics ensembles for initialized and uninitialized predictions. At lead times less than 2 years, the initialized ensembles tend to be under-dispersed, and hence produce overconfident and hence unreliable forecasts. For longer lead times, all three ensembles are predominantly over-dispersed. Such over-dispersion is primarily related to excessive inter-annual variability in the climate model. These findings highlight the need to carefully evaluate simulated variability in seasonal and decadal prediction systems.