An aggregated wind power generation model based on MERRA reanalysis data: MATLAB model and example data for the April 2014 wind farm distribution of Great Britain.

The MATLAB model is contained within the compressed folders (versions are available as .zip and .tgz). This model uses MERRA reanalysis data (>34 years available) to estimate the hourly aggregated wind power generation for a predefined (fixed) distribution of wind farms. A ready made example is included for the wind farm distribution of Great Britain, April 2014 ("CF.dat"). This consists of an hourly time series of GB-total capacity factor spanning the period 1980-2013 inclusive. Given the global nature of reanalysis data, the model can be applied to any specified distribution of wind farms in any region of the world. Users are, however, strongly advised to bear in mind the limitations of reanalysis data when using this model/data. This is discussed in our paper: Cannon, Brayshaw, Methven, Coker, Lenaghan. "Using reanalysis data to quantify extreme wind power generation statistics: a 33 year case study in Great Britain". Submitted to Renewable Energy in March, 2014. Additional information about the model is contained in the model code itself, in the accompanying ReadMe file, and on our website: http://www.met.reading.ac.uk/~energymet/data/Cannon2014/

Mapping power law distributions in digital health social networks: methods, interpretations, and practical implications

BACKGROUND: Social networks are common in digital health. A new stream of research is beginning to investigate the mechanisms of digital health social networks (DHSNs), how they are structured, how they function, and how their growth can be nurtured and managed. DHSNs increase in value when additional content is added, and the structure of networks may resemble the characteristics of power laws. Power laws are contrary to traditional Gaussian averages in that they demonstrate correlated phenomena. OBJECTIVES: The objective of this study is to investigate whether the distribution frequency in four DHSNs can be characterized as following a power law. A second objective is to describe the method used to determine the comparison. METHODS: Data from four DHSNs—Alcohol Help Center (AHC), Depression Center (DC), Panic Center (PC), and Stop Smoking Center (SSC)—were compared to power law distributions. To assist future researchers and managers, the 5-step methodology used to analyze and compare datasets is described. RESULTS: All four DHSNs were found to have right-skewed distributions, indicating the data were not normally distributed. When power trend lines were added to each frequency distribution, R(2) values indicated that, to a very high degree, the variance in post frequencies can be explained by actor rank (AHC .962, DC .975, PC .969, SSC .95). Spearman correlations provided further indication of the strength and statistical significance of the relationship (AHC .987. DC .967, PC .983, SSC .993, P<.001). CONCLUSIONS: This is the first study to investigate power distributions across multiple DHSNs, each addressing a unique condition. Results indicate that despite vast differences in theme, content, and length of existence, DHSNs follow properties of power laws. The structure of DHSNs is important as it gives insight to researchers and managers into the nature and mechanisms of network functionality. The 5-step process undertaken to compare actor contribution patterns can be replicated in networks that are managed by other organizations, and we conjecture that patterns observed in this study could be found in other DHSNs. Future research should analyze network growth over time and examine the characteristics and survival rates of superusers.

A stress relaxation model for the viscoelastic solids based on the steady-state creep equation

Creep and stress relaxation are inherent mechanical behaviors of viscoelastic materials. It is considered that both are different performances of one identical physical phenomenon. The relationship between the decay stress and time during stress relaxation has been derived from the power law equation of the steady-state creep. The model was used to analyse the stress relaxation curves of various different viscoelastic materials (such as pure polycrystalline ice, polymers, foods, bones, metal, animal tissues, etc.). The calculated results using the theoretical model agree with the experimental data very well. Here we show that the new mathematical formula is not only simple but its parameters have the clear physical meanings. It is suitable to materials with a very broad scope and has a strong predictive ability.

Effectiveness of landmark analysis for establishing locality in p2p networks

Locality to other nodes on a peer-to-peer overlay network can be established by means of a set of landmarks shared among the participating nodes. Each node independently collects a set of latency measures to landmark nodes, which are used as a multi-dimensional feature vector. Each peer node uses the feature vector to generate a unique scalar index which is correlated to its topological locality. A popular dimensionality reduction technique is the space filling Hilbert’s curve, as it possesses good locality preserving properties. However, there exists little comparison between Hilbert’s curve and other techniques for dimensionality reduction. This work carries out a quantitative analysis of their properties. Linear and non-linear techniques for scaling the landmark vectors to a single dimension are investigated. Hilbert’s curve, Sammon’s mapping and Principal Component Analysis have been used to generate a 1d space with locality preserving properties. This work provides empirical evidence to support the use of Hilbert’s curve in the context of locality preservation when generating peer identifiers by means of landmark vector analysis. A comparative analysis is carried out with an artificial 2d network model and with a realistic network topology model with a typical power-law distribution of node connectivity in the Internet. Nearest neighbour analysis confirms Hilbert’s curve to be very effective in both artificial and realistic network topologies. Nevertheless, the results in the realistic network model show that there is scope for improvements and better techniques to preserve locality information are required.

On the fast decay of Agulhas rings

The Indian Ocean water that ends up in the Atlantic Ocean detaches from the Agulhas Current retroflection predominantly in the form of Agulhas rings and cyclones. Using numerical Lagrangian float trajectories in a high-resolution numerical ocean model, the fate of coherent structures near the Agulhas Current retroflection is investigated. It is shown that within the Agulhas Current, upstream of the retroflection, the spatial distributions of floats ending in the Atlantic Ocean and floats ending in the Indian Ocean are to a large extent similar. This indicates that Agulhas leakage occurs mostly through the detachment of Agulhas rings. After the floats detach from the Agulhas Current, the ambient water quickly looses its relative vorticity. The Agulhas rings thus seem to decay and loose much of their water in the Cape Basin. A cluster analysis reveals that most water in the Agulhas Current is within clusters of 180 km in diameter. Halfway in the Cape Basin there is an increase in the number of larger clusters with low relative vorticity, which carry the bulk of the Agulhas leakage transport through the Cape Basin. This upward cascade with respect to the length scales of the leakage, in combination with a power law decay of the magnitude of relative vorticity, might be an indication that the decay of Agulhas rings is somewhat comparable to the decay of two-dimensional turbulence.

Assembly rules for protein networks derived from phylogenetic-statistical analysis of whole genomes

Background: We report an analysis of a protein network of functionally linked proteins, identified from a phylogenetic statistical analysis of complete eukaryotic genomes. Phylogenetic methods identify pairs of proteins that co-evolve on a phylogenetic tree, and have been shown to have a high probability of correctly identifying known functional links. Results: The eukaryotic correlated evolution network we derive displays the familiar power law scaling of connectivity. We introduce the use of explicit phylogenetic methods to reconstruct the ancestral presence or absence of proteins at the interior nodes of a phylogeny of eukaryote species. We find that the connectivity distribution of proteins at the point they arise on the tree and join the network follows a power law, as does the connectivity distribution of proteins at the time they are lost from the network. Proteins resident in the network acquire connections over time, but we find no evidence that 'preferential attachment' - the phenomenon of newly acquired connections in the network being more likely to be made to proteins with large numbers of connections - influences the network structure. We derive a 'variable rate of attachment' model in which proteins vary in their propensity to form network interactions independently of how many connections they have or of the total number of connections in the network, and show how this model can produce apparent power-law scaling without preferential attachment. Conclusion: A few simple rules can explain the topological structure and evolutionary changes to protein-interaction networks: most change is concentrated in satellite proteins of low connectivity and small phenotypic effect, and proteins differ in their propensity to form attachments. Given these rules of assembly, power law scaled networks naturally emerge from simple principles of selection, yielding protein interaction networks that retain a high-degree of robustness on short time scales and evolvability on longer evolutionary time scales.

Assembling spatially explicit landscape models of pollen and spore dispersal by wind for risk assessment

Models of windblown pollen or spore movement are required to predict gene flow from genetically modified (GM) crops and the spread of fungal diseases. We suggest a simple form for a function describing the distance moved by a pollen grain or fungal spore, for use in generic models of dispersal. The function has power-law behaviour over sub-continental distances. We show that air-borne dispersal of rapeseed pollen in two experiments was inconsistent with an exponential model, but was fitted by power-law models, implying a large contribution from distant fields to the catches observed. After allowance for this 'background' by applying Fourier transforms to deconvolve the mixture of distant and local sources, the data were best fit by power-laws with exponents between 1.5 and 2. We also demonstrate that for a simple model of area sources, the median dispersal distance is a function of field radius and that measurement from the source edge can be misleading. Using an inverse-square dispersal distribution deduced from the experimental data and the distribution of rapeseed fields deduced by remote sensing, we successfully predict observed rapeseed pollen density in the city centres of Derby and Leicester (UK).

Segmental dynamics in entangled linear polymer melts

We present molecular dynamics (MD) and slip-springs model simulations of the chain segmental dynamics in entangled linear polymer melts. The time-dependent behavior of the segmental orientation autocorrelation functions and mean-square segmental displacements are analyzed for both flexible and semiflexible chains, with particular attention paid to the scaling relations among these dynamic quantities. Effective combination of the two simulation methods at different coarse-graining levels allows us to explore the chain dynamics for chain lengths ranging from Z ≈ 2 to 90 entanglements. For a given chain length of Z ≈ 15, the time scales accessed span for more than 10 decades, covering all of the interesting relaxation regimes. The obtained time dependence of the monomer mean square displacements, g1(t), is in good agreement with the tube theory predictions. Results on the first- and second-order segmental orientation autocorrelation functions, C1(t) and C2(t), demonstrate a clear power law relationship of C2(t) C1(t)m with m = 3, 2, and 1 in the initial, free Rouse, and entangled (constrained Rouse) regimes, respectively. The return-to-origin hypothesis, which leads to inverse proportionality between the segmental orientation autocorrelation functions and g1(t) in the entangled regime, is convincingly verified by the simulation result of C1(t) g1(t)−1 t–1/4 in the constrained Rouse regime, where for well-entangled chains both C1(t) and g1(t) are rather insensitive to the constraint release effects. However, the second-order correlation function, C2(t), shows much stronger sensitivity to the constraint release effects and experiences a protracted crossover from the free Rouse to entangled regime. This crossover region extends for at least one decade in time longer than that of C1(t). The predicted time scaling behavior of C2(t) t–1/4 is observed in slip-springs simulations only at chain length of 90 entanglements, whereas shorter chains show higher scaling exponents. The reported simulation work can be applied to understand the observations of the NMR experiments.

A study into the accuracy of using meteorological wind data to estimate turbine generation output

Meteorological (met) station data is used as the basis for a number of influential studies into the impacts of the variability of renewable resources. Real turbine output data is not often easy to acquire, whereas meteorological wind data, supplied at a standardised height of 10 m, is widely available. This data can be extrapolated to a standard turbine height using the wind profile power law and used to simulate the hypothetical power output of a turbine. Utilising a number of met sites in such a manner can develop a model of future wind generation output. However, the accuracy of this extrapolation is strongly dependent on the choice of the wind shear exponent alpha. This paper investigates the accuracy of the simulated generation output compared to reality using a wind farm in North Rhins, Scotland and a nearby met station in West Freugh. The results show that while a single annual average value for alpha may be selected to accurately represent the long term energy generation from a simulated wind farm, there are significant differences between simulation and reality on an hourly power generation basis, with implications for understanding the impact of variability of renewables on short timescales, particularly system balancing and the way that conventional generation may be asked to respond to a high level of variable renewable generation on the grid in the future.

On the statistical modeling of persistence in total ozone anomalies

Geophysical time series sometimes exhibit serial correlations that are stronger than can be captured by the commonly used first‐order autoregressive model. In this study we demonstrate that a power law statistical model serves as a useful upper bound for the persistence of total ozone anomalies on monthly to interannual timescales. Such a model is usually characterized by the Hurst exponent. We show that the estimation of the Hurst exponent in time series of total ozone is sensitive to various choices made in the statistical analysis, especially whether and how the deterministic (including periodic) signals are filtered from the time series, and the frequency range over which the estimation is made. In particular, care must be taken to ensure that the estimate of the Hurst exponent accurately represents the low‐frequency limit of the spectrum, which is the part that is relevant to long‐term correlations and the uncertainty of estimated trends. Otherwise, spurious results can be obtained. Based on this analysis, and using an updated equivalent effective stratospheric chlorine (EESC) function, we predict that an increase in total ozone attributable to EESC should be detectable at the 95% confidence level by 2015 at the latest in southern midlatitudes, and by 2020–2025 at the latest over 30°–45°N, with the time to detection increasing rapidly with latitude north of this range.

Impact of long-range correlations on trend detection in total ozone

Total ozone trends are typically studied using linear regression models that assume a first-order autoregression of the residuals [so-called AR(1) models]. We consider total ozone time series over 60°S–60°N from 1979 to 2005 and show that most latitude bands exhibit long-range correlated (LRC) behavior, meaning that ozone autocorrelation functions decay by a power law rather than exponentially as in AR(1). At such latitudes the uncertainties of total ozone trends are greater than those obtained from AR(1) models and the expected time required to detect ozone recovery correspondingly longer. We find no evidence of LRC behavior in southern middle-and high-subpolar latitudes (45°–60°S), where the long-term ozone decline attributable to anthropogenic chlorine is the greatest. We thus confirm an earlier prediction based on an AR(1) analysis that this region (especially the highest latitudes, and especially the South Atlantic) is the optimal location for the detection of ozone recovery, with a statistically significant ozone increase attributable to chlorine likely to be detectable by the end of the next decade. In northern middle and high latitudes, on the other hand, there is clear evidence of LRC behavior. This increases the uncertainties on the long-term trend attributable to anthropogenic chlorine by about a factor of 1.5 and lengthens the expected time to detect ozone recovery by a similar amount (from ∼2030 to ∼2045). If the long-term changes in ozone are instead fit by a piecewise-linear trend rather than by stratospheric chlorine loading, then the strong decrease of northern middle- and high-latitude ozone during the first half of the 1990s and its subsequent increase in the second half of the 1990s projects more strongly on the trend and makes a smaller contribution to the noise. This both increases the trend and weakens the LRC behavior at these latitudes, to the extent that ozone recovery (according to this model, and in the sense of a statistically significant ozone increase) is already on the verge of being detected. The implications of this rather controversial interpretation are discussed.

On the nature of ULF wave power during nightside auroral activations and substorms: 2. temporal evolution

We present a statistical analysis of the time evolution of ground magnetic fluctuations in three (12–48 s, 24–96 s and 48–192 s) period bands during nightside auroral activations. We use an independently derived auroral activation list composed of both substorms and pseudo-breakups to provide an estimate of the activation times of nightside aurora during periods with comprehensive ground magnetometer coverage. One hundred eighty-one events in total are studied to demonstrate the statistical nature of the time evolution of magnetic wave power during the ∼30 min surrounding auroral activations. We find that the magnetic wave power is approximately constant before an auroral activation, starts to grow up to 90 s prior to the optical onset time, maximizes a few minutes after the auroral activation, then decays slightly to a new, and higher, constant level. Importantly, magnetic ULF wave power always remains elevated after an auroral activation, whether it is a substorm or a pseudo-breakup. We subsequently divide the auroral activation list into events that formed part of ongoing auroral activity and events that had little preceding geomagnetic activity. We find that the evolution of wave power in the ∼10–200 s period band essentially behaves in the same manner through auroral onset, regardless of event type. The absolute power across ULF wave bands, however, displays a power law-like dependency throughout a 30 min period centered on auroral onset time. We also find evidence of a secondary maximum in wave power at high latitudes ∼10 min following isolated substorm activations. Most significantly, we demonstrate that magnetic wave power levels persist after auroral activations for ∼10 min, which is consistent with recent findings of wave-driven auroral precipitation during substorms. This suggests that magnetic wave power and auroral particle precipitation are intimately linked and key components of the substorm onset process.

Aerosol impacts on drizzle properties in warm clouds from ARM Mobile Facility maritime and continental deployments

We have extensively evaluated the response of cloud-base drizzle rate (Rcb; mm day–1) in warm clouds to liquid water path (LWP; g m–2) and to cloud condensation nuclei (CCN) number concentration (NCCN; cm–3), an aerosol proxy. This evaluation is based on a 19-month long dataset of Doppler radar, lidar, microwave radiometers and aerosol observing systems from the Atmospheric Radiation Measurement (ARM) Mobile Facility deployments at the Azores and in Germany. Assuming 0.55% supersaturation to calculate NCCN, we found a power law , indicating that Rcb decreases by a factor of 2–3 as NCCN increases from 200 to 1000 cm–3 for fixed LWP. Additionally, the precipitation susceptibility to NCCN ranges between 0.5 and 0.9, in agreement with values from simulations and aircraft measurements. Surprisingly, the susceptibility of the probability of precipitation from our analysis is much higher than that from CloudSat estimates, but agrees well with simulations from a multi-scale high-resolution aerosol-climate model. Although scale issues are not completely resolved in the intercomparisons, our results are encouraging, suggesting that it is possible for multi-scale models to accurately simulate the response of LWP to aerosol perturbations.

Instantaneous gelation in Smoluchowski’s coagulation equation revisited

We study the solutions of the Smoluchowski coagulation equation with a regularization term which removes clusters from the system when their mass exceeds a specified cutoff size, M. We focus primarily on collision kernels which would exhibit an instantaneous gelation transition in the absence of any regularization. Numerical simulations demonstrate that for such kernels with monodisperse initial data, the regularized gelation time decreasesas M increases, consistent with the expectation that the gelation time is zero in the unregularized system. This decrease appears to be a logarithmically slow function of M, indicating that instantaneously gelling kernels may still be justifiable as physical models despite the fact that they are highly singular in the absence of a cutoff. We also study the case when a source of monomers is introduced in the regularized system. In this case a stationary state is reached. We present a complete analytic description of this regularized stationary state for the model kernel, K(m1,m2)=max{m1,m2}ν, which gels instantaneously when M→∞ if ν>1. The stationary cluster size distribution decays as a stretched exponential for small cluster sizes and crosses over to a power law decay with exponent ν for large cluster sizes. The total particle density in the stationary state slowly vanishes as [(ν−1)logM]−1/2 when M→∞. The approach to the stationary state is nontrivial: Oscillations about the stationary state emerge from the interplay between the monomer injection and the cutoff, M, which decay very slowly when M is large. A quantitative analysis of these oscillations is provided for the addition model which describes the situation in which clusters can only grow by absorbing monomers.

The dynamics of Baroclinic Zonal jets

Multiple alternating zonal jets are a ubiquitous feature of planetary atmospheres and oceans. However, most studies to date have focused on the special case of barotropic jets. Here, the dynamics of freely evolving baroclinic jets are investigated using a two-layer quasigeostrophic annulus model with sloping topography. In a suite of 15 numerical simulations, the baroclinic Rossby radius and baroclinic Rhines scale are sampled by varying the stratification and root-mean-square eddy velocity, respectively. Small-scale eddies in the initial state evolve through geostrophic turbulence and accelerate zonally as they grow in horizontal scale, first isotropically and then anisotropically. This process leads ultimately to the formation of jets, which take about 2500 rotation periods to equilibrate. The kinetic energy spectrum of the equilibrated baroclinic zonal flow steepens from a −3 power law at small scales to a −5 power law near the jet scale. The conditions most favorable for producing multiple alternating baroclinic jets are large baroclinic Rossby radius (i.e., strong stratification) and small baroclinic Rhines scale (i.e., weak root-mean-square eddy velocity). The baroclinic jet width is diagnosed objectively and found to be 2.2–2.8 times larger than the baroclinic Rhines scale, with a best estimate of 2.5 times larger. This finding suggests that Rossby wave motions must be moving at speeds of approximately 6 times the turbulent eddy velocity in order to be capable of arresting the isotropic inverse energy cascade.