Ensemble prediction for nowcasting with a convection-permitting model - II: forecast error statistics

A 24-member ensemble of 1-h high-resolution forecasts over the Southern United Kingdom is used to study short-range forecast error statistics. The initial conditions are found from perturbations from an ensemble transform Kalman filter. Forecasts from this system are assumed to lie within the bounds of forecast error of an operational forecast system. Although noisy, this system is capable of producing physically reasonable statistics which are analysed and compared to statistics implied from a variational assimilation system. The variances for temperature errors for instance show structures that reflect convective activity. Some variables, notably potential temperature and specific humidity perturbations, have autocorrelation functions that deviate from 3-D isotropy at the convective-scale (horizontal scales less than 10 km). Other variables, notably the velocity potential for horizontal divergence perturbations, maintain 3-D isotropy at all scales. Geostrophic and hydrostatic balances are studied by examining correlations between terms in the divergence and vertical momentum equations respectively. Both balances are found to decay as the horizontal scale decreases. It is estimated that geostrophic balance becomes less important at scales smaller than 75 km, and hydrostatic balance becomes less important at scales smaller than 35 km, although more work is required to validate these findings. The implications of these results for high-resolution data assimilation are discussed.

Evidence for the chaotic origin of Northern Annular Mode variability

Exponential spectra are found to characterize variability of the Northern Annular Mode (NAM) for periods less than 36 days. This corresponds to the observed rounding of the autocorrelation function at lags of a few days. The characteristic persistence timescales during winter and summer is found to be ∼5 days for these high frequencies. Beyond periods of 36 days the characteristic decorrelation timescale is ∼20 days during winter and ∼6 days in summer. We conclude that the NAM cannot be described by autoregressive models for high frequencies; the spectra are more consistent with low-order chaos. We also propose that the NAM exhibits regime behaviour, however the nature of this has yet to be identified.

The correlation structure of spatial autoregressions

This paper investigates how the correlations implied by a first-order simultaneous autoregressive (SAR(1)) process are affected by the weights matrix and the autocorrelation parameter. A graph theoretic representation of the covariances in terms of walks connecting the spatial units helps to clarify a number of correlation properties of the processes. In particular, we study some implications of row-standardizing the weights matrix, the dependence of the correlations on graph distance, and the behavior of the correlations at the extremes of the parameter space. Throughout the analysis differences between directed and undirected networks are emphasized. The graph theoretic representation also clarifies why it is difficult to relate properties ofW to correlation properties of SAR(1) models defined on irregular lattices.

The persistence of solar activity indicators and the descent of the sun into Maunder Minimum conditions

The recent low and prolonged minimum of the solar cycle, along with the slow growth in activity of the new cycle, has led to suggestions that the Sun is entering a Grand Solar Minimum (GSMi), potentially as deep as the Maunder Minimum (MM). This raises questions about the persistence and predictability of solar activity. We study the autocorrelation functions and predictability R^2_L(t) of solar indices, particularly group sunspot number R_G and heliospheric modulation potential phi for which we have data during the descent into the MM. For R_G and phi, R^2_L (t) > 0.5 for times into the future of t = 4 and 3 solar cycles, respectively: sufficient to allow prediction of a GSMi onset. The lower predictability of sunspot number R_Z is discussed. The current declines in peak and mean R_G are the largest since the onset of the MM and exceed those around 1800 which failed to initiate a GSMi.

Features for detection of Parkinson's disease tremor from local field potentials of the subthalamic nucleus

Deep Brain Stimulation (DBS) is a treatment routinely used to alleviate the symptoms of Parkinson's disease (PD). In this type of treatment, electrical pulses are applied through electrodes implanted into the basal ganglia of the patient. As the symptoms are not permanent in most patients, it is desirable to develop an on-demand stimulator, applying pulses only when onset of the symptoms is detected. This study evaluates a feature set created for the detection of tremor - a cardinal symptom of PD. The designed feature set was based on standard signal features and researched properties of the electrical signals recorded from subthalamic nucleus (STN) within the basal ganglia, which together included temporal, spectral, statistical, autocorrelation and fractal properties. The most characterized tremor related features were selected using statistical testing and backward algorithms then used for classification on unseen patient signals. The spectral features were among the most efficient at detecting tremor, notably spectral bands 3.5-5.5 Hz and 0-1 Hz proved to be highly significant. The classification results for determination of tremor achieved 94% sensitivity with specificity equaling one.

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.

Automatic near real-time selection of flood water levels from high resolution Synthetic Aperture Radar images for assimilation into hydraulic models: a case study

Flood extents caused by fluvial floods in urban and rural areas may be predicted by hydraulic models. Assimilation may be used to correct the model state and improve the estimates of the model parameters or external forcing. One common observation assimilated is the water level at various points along the modelled reach. Distributed water levels may be estimated indirectly along the flood extents in Synthetic Aperture Radar (SAR) images by intersecting the extents with the floodplain topography. It is necessary to select a subset of levels for assimilation because adjacent levels along the flood extent will be strongly correlated. A method for selecting such a subset automatically and in near real-time is described, which would allow the SAR water levels to be used in a forecasting model. The method first selects candidate waterline points in flooded rural areas having low slope. The waterline levels and positions are corrected for the effects of double reflections between the water surface and emergent vegetation at the flood edge. Waterline points are also selected in flooded urban areas away from radar shadow and layover caused by buildings, with levels similar to those in adjacent rural areas. The resulting points are thinned to reduce spatial autocorrelation using a top-down clustering approach. The method was developed using a TerraSAR-X image from a particular case study involving urban and rural flooding. The waterline points extracted proved to be spatially uncorrelated, with levels reasonably similar to those determined manually from aerial photographs, and in good agreement with those of nearby gauges.

Endogenous business cycles with frictional labour markets

We present a neoclassical model of capital accumulation with frictional labour markets. Under standard parameter values the equilibrium of the model is indeterminate and consequently displays expectations-driven business cycles – so-called endogenous business cycles. We study the properties of such cycles, and find that the model predicts the high autocorrelation in output growth and the hump-shaped impulse response of output found in US data – important features that existing endogenous real business cycle models fail to explain. The indeterminacy of the equilibrium stems from job search externalities and does not rely on increasing returns to scale as in most models.

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.

Climatology and predictability of the late summer stratospheric zonal wind turnaround over Vanscoy, Saskatchewan

A climatology of the late summer stratospheric zonal wind turnaround phenomenon is presented, with a particular focus on the behaviour over the Meteorological Service of Canada’s balloon-launching site at Vanscoy, Saskatchewan (52°N, 107°W). Turnaround refers to the change in sign of the zonal wind velocity and occurs twice each year at stratospheric mid-latitudes, in early spring and in late summer. The late summer turnaround is of particular interest to the high-altitude ballooning community because it offers the ideal conditions for launch, but it is also an interesting dynamical phenomenon in its own right. It is studied here using both the National Centers for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) reanalysis and the United Kingdom Meteorological Office (MetO) analysis products as well as climate simulation data from the Canadian Middle Atmosphere Model (CMAM). The phenomenon and its interannual variability are documented. The predictability of the late summer turnaround over Vanscoy is investigated using both statistical averages and autocorrelation analysis. From the statistical averages, it is found that during every year since 1993, the period from 26 August to 5 September has contained appropriate launch dates. From the autocorrelation analysis, it is found that stratospheric zonal wind anomalies can persist for a month or more during most of the summer, but there is a predictability horizon at the end of the summer — just before turnaround

Time and the price impact of a trade

We use Hasbrouck's (1991) vector autoregressive model for prices and trades to empirically test and assess the role played by the waiting time between consecutive transactions in the process of price formation. We find that as the time duration between transactions decreases, the price impact of trades, the speed of price adjustment to trade‐related information, and the positive autocorrelation of signed trades all increase. This suggests that times when markets are most active are times when there is an increased presence of informed traders; we interpret such markets as having reduced liquidity.

Improving the evaluation of hydrological multi-model forecast performance in the Upper Danube Catchment

Medium range flood forecasting activities, driven by various meteorological forecasts ranging from high resolution deterministic forecasts to low spatial resolution ensemble prediction systems, share a major challenge in the appropriateness and design of performance measures. In this paper possible limitations of some traditional hydrological and meteorological prediction quality and verification measures are identified. Some simple modifications are applied in order to circumvent the problem of the autocorrelation dominating river discharge time-series and in order to create a benchmark model enabling the decision makers to evaluate the forecast quality and the model quality. Although the performance period is quite short the advantage of a simple cost-loss function as a measure of forecast quality can be demonstrated.

Agriculture and the life histories of Mauritius kestrels

Habitat modification for agriculture is one of the greatest current threats to global biodiversity. Studies show large-scale population declines and short-term demographic impacts, but knowledge of the long-term effects of agriculture on individuals remains poor. This thesis examines the short- and long-term impact of agriculture on a reintroduced population of the Mauritius kestrel Falco punctatus, a tropical forest-dwelling raptor endemic to the island of Mauritius, that also utilises agricultural habitats. This population is a particularly appropriate model system, because complete life history data exists for individuals over a 22-year period, alongside detailed habitat and climate data. Agriculture has a short-term detrimental effect on Mauritius kestrel breeding success by exacerbating the seasonal decline in fledgling production. This is partly driven by the habitat-specific composition of the prey community that kestrels exploit to feed their chicks. The fledglings from agricultural territories tend to recruit in agricultural territories. This is largely due to poor natal dispersal and fine-scale spatial autocorrelation in the habitat matrix. Breeders do not respond to agriculture in the breeding territory by dispersing, unless the pair bond is broken. Therefore, individuals originating in agricultural territories tend to recruit, and remain in, agricultural territories throughout their lives. In addition to this, females from agricultural natal territories have shorter lifespans, schedule their peak reproductive output earlier in life, and exhibit more rapid senescence than non-agricultural females. The combination of this long-term effect and the adult experience of agriculture imposed by life history and environmental constraints, leads to a lower mean lifetime reproductive rate compared to females originating in non-agricultural habitats. These results demonstrate that agriculture experienced in early life has a lifelong effect on individuals. The effects can persist in time and space, with potentially delayed effects on population dynamics. These findings are important for understanding species’ responses to agricultural expansion.

Novel single trial movement classification based on temporal dynamics of EEG

Various complex oscillatory processes are involved in the generation of the motor command. The temporal dynamics of these processes were studied for movement detection from single trial electroencephalogram (EEG). Autocorrelation analysis was performed on the EEG signals to find robust markers of movement detection. The evolution of the autocorrelation function was characterised via the relaxation time of the autocorrelation by exponential curve fitting. It was observed that the decay constant of the exponential curve increased during movement, indicating that the autocorrelation function decays slowly during motor execution. Significant differences were observed between movement and no moment tasks. Additionally, a linear discriminant analysis (LDA) classifier was used to identify movement trials with a peak accuracy of 74%.

Field-perpendicular and field-aligned plasma flows observed by EISCAT during a prolonged period of northward IMF

The effect of a prolonged period of strongly northward Interplanetary Magnetic Field (IMF) on the high-latitude F-region is studied using data from the EISCAT Common Programme Zero mode of operation on 11–12 August 1982. The analysis of the raw autocorrelation functions is kept to the directly derived parameters Ne, Te, Ti and velocity, and limits are defined for the errors introduced by assumptions about ion composition and by changes in the transmitted power and system constant. Simple data-cleaning criteria are employed to eliminate problems due to coherent signals and large background noise levels. The observed variations in plasma densities, temperatures and velocities are interpreted in terms of supporting data from ISEE-3 and local riometers and magnetometers. Both field-aligned and field-perpendicular plasma flows at Tromsø showed effects of the northward IMF: convection was slow and irregular and field-aligned flow profiles were characteristic of steady-state polar wind outflow with flux of order 1012 m−2 s−1. This period followed a strongly southward IMF which had triggered a substorm. The substorm gave enhanced convection, with a swing to equatorward flow and large (5 × 1012 m−2 s−1), steady-state field-aligned fluxes, leading to the possibility of O+ escape into the magnetosphere. The apparent influence of the IMF over both field-perpendicular and field-aligned flows is explained in terms of the cross-cap potential difference and the location of the auroral oval.