Evolving graphs: dynamical models, inverse problems and propagation

Applications such as neuroscience, telecommunication, online social networking, transport and retail trading give rise to connectivity patterns that change over time. In this work, we address the resulting need for network models and computational algorithms that deal with dynamic links. We introduce a new class of evolving range-dependent random graphs that gives a tractable framework for modelling and simulation. We develop a spectral algorithm for calibrating a set of edge ranges from a sequence of network snapshots and give a proof of principle illustration on some neuroscience data. We also show how the model can be used computationally and analytically to investigate the scenario where an evolutionary process, such as an epidemic, takes place on an evolving network. This allows us to study the cumulative effect of two distinct types of dynamics.

Magnetic cloud distortion resulting from propagation through a structured solar wind: Models and observations

Numerical simulations of magnetic clouds (MCs) propagating through a structured solar wind suggest that MC-associated magnetic flux ropes are highly distorted by inhomogeneities in the ambient medium. In particular, a solar wind configuration of fast wind from high latitudes and slow wind at low latitudes, common at periods close to solar minimum, should distort the cross section of magnetic clouds into concave-outward structures. This phenomenon has been reported in observations of shock front orientations, but not in the body of magnetic clouds. In this study an analytical magnetic cloud model based upon a kinematically distorted flux rope is modified to simulate propagation through a structured medium. This new model is then used to identify specific time series signatures of the resulting concave-outward flux ropes. In situ observations of three well studied magnetic clouds are examined with comparison to the model, but the expected concave-outward signatures are not present. Indeed, the observations are better described by the convex-outward flux rope model. This may be due to a sharp latitudinal transition from fast to slow wind, resulting in a globally concave-outward flux rope, but with convex-outward signatures on a local scale.

Ocean acoustic models for low frequency propagation in 2D and 3D environments

In this paper we are mainly concerned with the development of efficient computer models capable of accurately predicting the propagation of low-to-middle frequency sound in the sea, in axially symmetric (2D) and in fully 3D environments. The major physical features of the problem, i.e. a variable bottom topography, elastic properties of the subbottom structure, volume attenuation and other range inhomogeneities are efficiently treated. The computer models presented are based on normal mode solutions of the Helmholtz equation on the one hand, and on various types of numerical schemes for parabolic approximations of the Helmholtz equation on the other. A new coupled mode code is introduced to model sound propagation in range-dependent ocean environments with variable bottom topography, where the effects of an elastic bottom, of volume attenuation, surface and bottom roughness are taken into account. New computer models based on finite difference and finite element techniques for the numerical solution of parabolic approximations are also presented. They include an efficient modeling of the bottom influence via impedance boundary conditions, they cover wide angle propagation, elastic bottom effects, variable bottom topography and reverberation effects. All the models are validated on several benchmark problems and versus experimental data. Results thus obtained were compared with analogous results from standard codes in the literature.

Growth rate and vertical propagation of the initial error in baroclinic models

The present study investigates the growth of error in baroclinic waves. It is found that stable or neutral waves are particularly sensitive to errors in the initial condition. Short stable waves are mainly sensitive to phase errors and the ultra long waves to amplitude errors. Analysis simulation experiments have indicated that the amplitudes of the very long waves become usually too small in the free atmosphere, due to the sparse and very irregular distribution of upper air observations. This also applies to the four-dimensional data assimilation experiments, since the amplitudes of the very long waves are usually underpredicted. The numerical experiments reported here show that if the very long waves have these kinds of amplitude errors in the upper troposphere or lower stratosphere the error is rapidly propagated (within a day or two) to the surface and to the lower troposphere.

Benchmarking 2D hydraulic models for urban flooding

This paper describes benchmark testing of six two-dimensional (2D) hydraulic models (DIVAST, DIVASTTVD, TUFLOW, JFLOW, TRENT and LISFLOOD-FP) in terms of their ability to simulate surface flows in a densely urbanised area. The models are applied to a 1·0 km × 0·4 km urban catchment within the city of Glasgow, Scotland, UK, and are used to simulate a flood event that occurred at this site on 30 July 2002. An identical numerical grid describing the underlying topography is constructed for each model, using a combination of airborne laser altimetry (LiDAR) fused with digital map data, and used to run a benchmark simulation. Two numerical experiments were then conducted to test the response of each model to topographic error and uncertainty over friction parameterisation. While all the models tested produce plausible results, subtle differences between particular groups of codes give considerable insight into both the practice and science of urban hydraulic modelling. In particular, the results show that the terrain data available from modern LiDAR systems are sufficiently accurate and resolved for simulating urban flows, but such data need to be fused with digital map data of building topology and land use to gain maximum benefit from the information contained therein. When such terrain data are available, uncertainty in friction parameters becomes a more dominant factor than topographic error for typical problems. The simulations also show that flows in urban environments are characterised by numerous transitions to supercritical flow and numerical shocks. However, the effects of these are localised and they do not appear to affect overall wave propagation. In contrast, inertia terms are shown to be important in this particular case, but the specific characteristics of the test site may mean that this does not hold more generally.

Convectively coupled equatorial waves in high resolution Hadley centre climate models

Current global atmospheric models fail to simulate well organised tropical phenomena in which convection interacts with dynamics and physics. A new methodology to identify convectively coupled equatorial waves, developed by NCAS-Climate, has been applied to output from the two latest models of the Met Office/Hadley Centre which have fundamental differences in dynamical formulation. Variability, horizontal and vertical structures, and propagation characteristics of tropical convection and equatorial waves, along with their coupled behaviour in the models are examined and evaluated against a previous comprehensive study of observations. It is shown that, in general, the models perform well for equatorial waves coupled with off-equatorial convection. However they perform poorly for waves coupled with equatorial convection. The vertical structure of the simulated wave is not conducive to energy conversion/growth and does not support the correct physical-dynamical coupling that occurs in the real world. The following figure shows an example of the Kelvin wave coupled with equatorial convection. It shows that the models fail to simulate a key feature of convectively coupled Kelvin wave in observations, namely near surface anomalous equatorial zonal winds together with intensified equatorial convection and westerly winds in phase with the convection. The models are also not able to capture the observed vertical tilt structure and the vertical propagation of the Kelvin wave into the lower stratosphere as well as the secondary peak in the mid-troposphere, particularly in HadAM3. These results can be used to provide a test-bed for experimentation to improve the coupling of physics and dynamics in climate and weather models.

Subspace system identification framework for the analysis of multimoded propagation of THz-transient signals

We provide a system identification framework for the analysis of THz-transient data. The subspace identification algorithm for both deterministic and stochastic systems is used to model the time-domain responses of structures under broadband excitation. Structures with additional time delays can be modelled within the state-space framework using additional state variables. We compare the numerical stability of the commonly used least-squares ARX models to that of the subspace N4SID algorithm by using examples of fourth-order and eighth-order systems under pulse and chirp excitation conditions. These models correspond to structures having two and four modes simultaneously propagating respectively. We show that chirp excitation combined with the subspace identification algorithm can provide a better identification of the underlying mode dynamics than the ARX model does as the complexity of the system increases. The use of an identified state-space model for mode demixing, upon transformation to a decoupled realization form is illustrated. Applications of state-space models and the N4SID algorithm to THz transient spectroscopy as well as to optical systems are highlighted.

Modelling the propagation of terahertz radiation through a tissue simulating phantom

Terahertz (THz) frequency radiation, 0.1 THz to 20 THz, is being investigated for biomedical imaging applications following the introduction of pulsed THz sources that produce picosecond pulses and function at room temperature. Owing to the broadband nature of the radiation, spectral and temporal information is available from radiation that has interacted with a sample; this information is exploited in the development of biomedical imaging tools and sensors. In this work, models to aid interpretation of broadband THz spectra were developed and evaluated. THz radiation lies on the boundary between regions best considered using a deterministic electromagnetic approach and those better analysed using a stochastic approach incorporating quantum mechanical effects, so two computational models to simulate the propagation of THz radiation in an absorbing medium were compared. The first was a thin film analysis and the second a stochastic Monte Carlo model. The Cole–Cole model was used to predict the variation with frequency of the physical properties of the sample and scattering was neglected. The two models were compared with measurements from a highly absorbing water-based phantom. The Monte Carlo model gave a prediction closer to experiment over 0.1 to 3 THz. Knowledge of the frequency-dependent physical properties, including the scattering characteristics, of the absorbing media is necessary. The thin film model is computationally simple to implement but is restricted by the geometry of the sample it can describe. The Monte Carlo framework, despite being initially more complex, provides greater flexibility to investigate more complicated sample geometries.

Two methods for modelling the propagation of terahertz radiation in a layered structure

Modelling the interaction of terahertz(THz) radiation with biological tissueposes many interesting problems. THzradiation is neither obviously described byan electric field distribution or anensemble of photons and biological tissueis an inhomogeneous medium with anelectronic permittivity that is bothspatially and frequency dependent making ita complex system to model.A three-layer system of parallel-sidedslabs has been used as the system throughwhich the passage of THz radiation has beensimulated. Two modelling approaches havebeen developed a thin film matrix model anda Monte Carlo model. The source data foreach of these methods, taken at the sametime as the data recorded to experimentallyverify them, was a THz spectrum that hadpassed though air only.Experimental verification of these twomodels was carried out using athree-layered in vitro phantom. Simulatedtransmission spectrum data was compared toexperimental transmission spectrum datafirst to determine and then to compare theaccuracy of the two methods. Goodagreement was found, with typical resultshaving a correlation coefficient of 0.90for the thin film matrix model and 0.78 forthe Monte Carlo model over the full THzspectrum. Further work is underway toimprove the models above 1 THz.

Importance of oceanic resolution and mean state on the extra-tropical response to El Niño in a matrix of coupled models

The extra-tropical response to El Niño in configurations of a coupled model with increased horizontal resolution in the oceanic component is shown to be more realistic than in configurations with a low resolution oceanic component. This general conclusion is independent of the atmospheric resolution. Resolving small-scale processes in the ocean produces a more realistic oceanic mean state, with a reduced cold tongue bias, which in turn allows the atmospheric model component to be forced more realistically. A realistic atmospheric basic state is critical in order to represent Rossby wave propagation in response to El Niño, and hence the extra-tropical response to El Niño. Through the use of high and low resolution configurations of the forced atmospheric-only model component we show that, in isolation, atmospheric resolution does not significantly affect the simulation of the extra-tropical response to El Niño. It is demonstrated, through perturbations to the SST forcing of the atmospheric model component, that biases in the climatological SST field typical of coupled model configurations with low oceanic resolution can account for the erroneous atmospheric basic state seen in these coupled model configurations. These results highlight the importance of resolving small-scale oceanic processes in producing a realistic large-scale mean climate in coupled models, and suggest that it might may be possible to “squeeze out” valuable extra performance from coupled models through increases to oceanic resolution alone.

The effects of explicit versus parameterized convection on the MJO in a large-domain high-resolution tropical case study. Part I: Characterization of large-scale organization and propagation

High-resolution simulations over a large tropical domain (∼20◦S–20◦N and 42◦E–180◦E) using both explicit and parameterized convection are analyzed and compared to observations during a 10-day case study of an active Madden-Julian Oscillation (MJO) event. The parameterized convection model simulations at both 40 km and 12 km grid spacing have a very weak MJO signal and little eastward propagation. A 4 km explicit convection simulation using Smagorinsky subgrid mixing in the vertical and horizontal dimensions exhibits the best MJO strength and propagation speed. 12 km explicit convection simulations also perform much better than the 12 km parameterized convection run, suggesting that the convection scheme, rather than horizontal resolution, is key for these MJO simulations. Interestingly, a 4 km explicit convection simulation using the conventional boundary layer scheme for vertical subgrid mixing (but still using Smagorinsky horizontal mixing) completely loses the large-scale MJO organization, showing that relatively high resolution with explicit convection does not guarantee a good MJO simulation. Models with a good MJO representation have a more realistic relationship between lower-free-tropospheric moisture and precipitation, supporting the idea that moisture-convection feedback is a key process for MJO propagation. There is also increased generation of available potential energy and conversion of that energy into kinetic energy in models with a more realistic MJO, which is related to larger zonal variance in convective heating and vertical velocity, larger zonal temperature variance around 200 hPa, and larger correlations between temperature and ascent (and between temperature and diabatic heating) between 500–400 hPa.

Estimation of optimal gravity wave parameters for climate models using data assimilation

There is a current need to constrain the parameters of gravity wave drag (GWD) schemes in climate models using observational information instead of tuning them subjectively. In this work, an inverse technique is developed using data assimilation principles to estimate gravity wave parameters. Because mostGWDschemes assume instantaneous vertical propagation of gravity waves within a column, observations in a single column can be used to formulate a one-dimensional assimilation problem to estimate the unknown parameters. We define a cost function that measures the differences between the unresolved drag inferred from observations (referred to here as the ‘observed’ GWD) and the GWD calculated with a parametrisation scheme. The geometry of the cost function presents some difficulties, including multiple minima and ill-conditioning because of the non-independence of the gravity wave parameters. To overcome these difficulties we propose a genetic algorithm to minimize the cost function, which provides a robust parameter estimation over a broad range of prescribed ‘true’ parameters. When real experiments using an independent estimate of the ‘observed’ GWD are performed, physically unrealistic values of the parameters can result due to the non-independence of the parameters. However, by constraining one of the parameters to lie within a physically realistic range, this degeneracy is broken and the other parameters are also found to lie within physically realistic ranges. This argues for the essential physical self-consistency of the gravity wave scheme. A much better fit to the observed GWD at high latitudes is obtained when the parameters are allowed to vary with latitude. However, a close fit can be obtained either in the upper or the lower part of the profiles, but not in both at the same time. This result is a consequence of assuming an isotropic launch spectrum. The changes of sign in theGWDfound in the tropical lower stratosphere, which are associated with part of the quasi-biennial oscillation forcing, cannot be captured by the parametrisation with optimal parameters.

Uncertainties and assessments of chemistry-climate models of the stratosphere

In recent years a number of chemistry-climate models have been developed with an emphasis on the stratosphere. Such models cover a wide range of time scales of integration and vary considerably in complexity. The results of specific diagnostics are here analysed to examine the differences amongst individual models and observations, to assess the consistency of model predictions, with a particular focus on polar ozone. For example, many models indicate a significant cold bias in high latitudes, the “cold pole problem”, particularly in the southern hemisphere during winter and spring. This is related to wave propagation from the troposphere which can be improved by improving model horizontal resolution and with the use of non-orographic gravity wave drag. As a result of the widely differing modelled polar temperatures, different amounts of polar stratospheric clouds are simulated which in turn result in varying ozone values in the models. The results are also compared to determine the possible future behaviour of ozone, with an emphasis on the polar regions and mid-latitudes. All models predict eventual ozone recovery, but give a range of results concerning its timing and extent. Differences in the simulation of gravity waves and planetary waves as well as model resolution are likely major sources of uncertainty for this issue. In the Antarctic, the ozone hole has probably reached almost its deepest although the vertical and horizontal extent of depletion may increase slightly further over the next few years. According to the model results, Antarctic ozone recovery could begin any year within the range 2001 to 2008. The limited number of models which have been integrated sufficiently far indicate that full recovery of ozone to 1980 levels may not occur in the Antarctic until about the year 2050. For the Arctic, most models indicate that small ozone losses may continue for a few more years and that recovery could begin any year within the range 2004 to 2019. The start of ozone recovery in the Arctic is therefore expected to appear later than in the Antarctic.

The ability of CMIP5 models to simulate North Atlantic extratropical cyclones

The ability of the climate models participating in phase 5 of the Coupled Model Intercomparison Project (CMIP5) to simulate North Atlantic extratropical cyclones in winter [December–February (DJF)] and summer [June–August (JJA)] is investigated in detail. Cyclones are identified as maxima in T42 vorticity at 850 hPa and their propagation is tracked using an objective feature-tracking algorithm. By comparing the historical CMIP5 simulations (1976–2005) and the ECMWF Interim Re-Analysis (ERA-Interim; 1979–2008), the authors find that systematic biases affect the number and intensity of North Atlantic cyclones in CMIP5 models. In DJF, the North Atlantic storm track tends to be either too zonal or displaced southward, thus leading to too few and weak cyclones over the Norwegian Sea and too many cyclones in central Europe. In JJA, the position of the North Atlantic storm track is generally well captured but some CMIP5 models underestimate the total number of cyclones. The dynamical intensity of cyclones, as measured by either T42 vorticity at 850 hPa or mean sea level pressure, is too weak in both DJF and JJA. The intensity bias has a hemispheric character, and it cannot be simply attributed to the representation of the North Atlantic large- scale atmospheric state. Despite these biases, the representation of Northern Hemisphere (NH) storm tracks has improved since CMIP3 and some CMIP5 models are able of representing well both the number and the intensity of North Atlantic cyclones. In particular, some of the higher-atmospheric-resolution models tend to have a better representation of the tilt of the North Atlantic storm track and of the intensity of cyclones in DJF.

A systematic approach to identify the sources of tropical SST errors in coupled models using the adjustment of initialised experiments

Understanding the sources of systematic errors in climate models is challenging because of coupled feedbacks and errors compensation. The developing seamless approach proposes that the identification and the correction of short term climate model errors have the potential to improve the modeled climate on longer time scales. In previous studies, initialised atmospheric simulations of a few days have been used to compare fast physics processes (convection, cloud processes) among models. The present study explores how initialised seasonal to decadal hindcasts (re-forecasts) relate transient week-to-month errors of the ocean and atmospheric components to the coupled model long-term pervasive SST errors. A protocol is designed to attribute the SST biases to the source processes. It includes five steps: (1) identify and describe biases in a coupled stabilized simulation, (2) determine the time scale of the advent of the bias and its propagation, (3) find the geographical origin of the bias, (4) evaluate the degree of coupling in the development of the bias, (5) find the field responsible for the bias. This strategy has been implemented with a set of experiments based on the initial adjustment of initialised simulations and exploring various degrees of coupling. In particular, hindcasts give the time scale of biases advent, regionally restored experiments show the geographical origin and ocean-only simulations isolate the field responsible for the bias and evaluate the degree of coupling in the bias development. This strategy is applied to four prominent SST biases of the IPSLCM5A-LR coupled model in the tropical Pacific, that are largely shared by other coupled models, including the Southeast Pacific warm bias and the equatorial cold tongue bias. Using the proposed protocol, we demonstrate that the East Pacific warm bias appears in a few months and is caused by a lack of upwelling due to too weak meridional coastal winds off Peru. The cold equatorial bias, which surprisingly takes 30 years to develop, is the result of an equatorward advection of midlatitude cold SST errors. Despite large development efforts, the current generation of coupled models shows only little improvement. The strategy proposed in this study is a further step to move from the current random ad hoc approach, to a bias-targeted, priority setting, systematic model development approach.