131,447 research outputs found
A Bayesian framework for verification and recalibration of ensemble forecasts: How uncertain is NAO predictability?
Predictability estimates of ensemble prediction systems are uncertain due to
limited numbers of past forecasts and observations. To account for such
uncertainty, this paper proposes a Bayesian inferential framework that provides
a simple 6-parameter representation of ensemble forecasting systems and the
corresponding observations. The framework is probabilistic, and thus allows for
quantifying uncertainty in predictability measures such as correlation skill
and signal-to-noise ratios. It also provides a natural way to produce
recalibrated probabilistic predictions from uncalibrated ensembles forecasts.
The framework is used to address important questions concerning the skill of
winter hindcasts of the North Atlantic Oscillation for 1992-2011 issued by the
Met Office GloSea5 climate prediction system. Although there is much
uncertainty in the correlation between ensemble mean and observations, there is
strong evidence of skill: the 95% credible interval of the correlation
coefficient of [0.19,0.68] does not overlap zero. There is also strong evidence
that the forecasts are not exchangeable with the observations: With over 99%
certainty, the signal-to-noise ratio of the forecasts is smaller than the
signal-to-noise ratio of the observations, which suggests that raw forecasts
should not be taken as representative scenarios of the observations. Forecast
recalibration is thus required, which can be coherently addressed within the
proposed framework.Comment: 36 pages, 10 figure
Scale invariant Green-Kubo relation for time averaged diffusivity
In recent years it was shown both theoretically and experimentally that in
certain systems exhibiting anomalous diffusion the time and ensemble average
mean squared displacement are remarkably different. The ensemble average
diffusivity is obtained from a scaling Green-Kubo relation, which connects the
scale invariant non-stationary velocity correlation function with the transport
coefficient. Here we obtain the relation between time averaged diffusivity,
usually recorded in single particle tracking experiments, and the underlying
scale invariant velocity correlation function. The time averaged mean squared
displacement is given by where is the total measurement time and
the lag time. Here is the anomalous diffusion exponent
obtained from ensemble averaged measurements
while marks the growth or decline of the kinetic energy . Thus we establish a connection between exponents
which can be read off the asymptotic properties of the velocity correlation
function and similarly for the transport constant . We demonstrate our
results with non-stationary scale invariant stochastic and deterministic
models, thereby highlighting that systems with equivalent behavior in the
ensemble average can differ strongly in their time average. This is the case,
for example, if averaged kinetic energy is finite, i.e. , where
Force correlations in molecular and stochastic dynamics
A molecular gas system in three dimensions is numerically studied by the
energy conserving molecular dynamics (MD). The autocorrelation functions for
the velocity and the force are computed and the friction coefficient is
estimated. From the comparison with the stochastic dynamics (SD) of a Brownian
particle, it is shown that the force correlation function in MD is different
from the delta-function force correlation in SD in short time scale. However,
as the measurement time scale is increased further, the ensemble equivalence
between the microcanonical MD and the canonical SD is restored. We also discuss
the practical implication of the result.Comment: 9 pages, 4 figures and Computer Physics Communcations (in press
Nonlinear forced change and nonergodicity: The case of ENSO-Indian monsoon and global precipitation teleconnections
We study the forced response of the teleconnection between the El
Nino-Southern Oscillation (ENSO) and global precipitation in general and the
Indian summer monsoon (IM) in particular in the Max Planck Institute Grand
Ensemble. The forced response of the teleconnection is defined as the
time-dependence of a correlation coefficient evaluated over the ensemble. The
ensemble-wise variability is taken either wrt. spatial averages or dominant
spatial modes in the sense of Maximal Covariance Analysis or Canonical
Correlation Analysis or EOF analysis. We find that the strengthening of the
ENSO-IM teleconnection is robustly or consistently featured in view of all four
teleconnection representations, whether sea surface temperature (SST) or sea
level pressure (SLP) is used to characterise ENSO, and both in the historical
period and under the RCP8.5 forcing scenario. The main contributor to this
strengthening in terms of a linear regression model is the regression
coefficient, which can outcompete even a declining ENSO variability in view of
using the SLP. We also find that the forced change of the teleconnection is
typically nonlinear by (1) formally rejecting the hypothesis that ergodicity
holds, i.e., that expected values of temporal correlation coefficients with
respect to the ensemble equal the ensemble-wise correlation coefficient itself,
and also showing that (2) the trivial contributions of the forced changes of
e.g. the mean SST and/or precipitation to temporal correlations are
insignificant here. We also provide, in terms of the test statistics, global
maps of the degree of nonlinearity/nonergodicity of the forced change of the
teleconnection between local precipitation and ENSO
Laser transit anemometer software development program
Algorithms were developed for the extraction of two components of mean velocity, standard deviation, and the associated correlation coefficient from laser transit anemometry (LTA) data ensembles. The solution method is based on an assumed two-dimensional Gaussian probability density function (PDF) model of the flow field under investigation. The procedure consists of transforming the data ensembles from the data acquisition domain (consisting of time and angle information) to the velocity space domain (consisting of velocity component information). The mean velocity results are obtained from the data ensemble centroid. Through a least squares fitting of the transformed data to an ellipse representing the intersection of a plane with the PDF, the standard deviations and correlation coefficient are obtained. A data set simulation method is presented to test the data reduction process. Results of using the simulation system with a limited test matrix of input values is also given
Analysis of a growing dynamic length scale in a glass-forming binary hard-sphere mixture
We examine a length scale that characterizes the spatial extent of
heterogeneous dynamics in a glass-forming binary hard-sphere mixture up to the
mode-coupling volume fraction phi_c. First, we characterize the system's
dynamics. Then, we utilize a new method [Phys. Rev. Lett. 105, 217801 (2010)]
to extract and analyze the ensemble independent dynamic susceptibility chi_4(t)
and the dynamic correlation length xi(t) for a range of times between the beta
and alpha relaxation times. We find that in this time range the dynamic
correlation length follows a volume fraction independent curve xi(t) ~ ln(t).
For longer times, xi(t) departs from this curve and remains constant up to the
largest time at which we can determine the length accurately. In addition to
the previously established correlation tau_alpha ~ exp[xi(tau_alpha)] between
the alpha relaxation time, tau_alpha, and the dynamic correlation length at
this time, xi(tau_alpha), we also find a similar correlation for the diffusion
coefficient D ~ exp[xi(tau_alpha)^theta] with theta approximately 0.6. We
discuss the relevance of these findings for different theories of the glass
transition
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