NG31C-01 INVITED 08:05h
Complexity in Magnetospheric Dynamics: from Modeling to forecasting
The solar wind-magnetosphere coupling exhibits complex behavior involving both global coherent and multi-scale dynamical features. Early attempts to explain its complexity in terms of low-dimensional dynamical chaos failed to reproduce its multi-scale constituent. More recent cellular automata models effectively reproduce the observed power-law spectra lacking the description of coherent dynamical features. The input-output analysis of various magnetospheric time series suggests a new data-derived description of the system. Based on the combination of nonlinear dynamical methods and statistical physics approach it reveals both global coherent and multi-scale features of solar wind - magnetosphere coupling. This data-derived approach yields an efficient forecasting model of magnetospheric dynamics during storms and substorms. It provides deterministic predictions of global component of magnetospheric dynamics and probabilistic predictions of its multi-scale features.
NG31C-02 08:20h
Robustness and scaling: Key Observables in the Complex Dynamic Magnetosphere
Plasma transport and energy dissipation in the driven dynamic magnetosphere are intermittent (bursty), and occur on a range of spatiotemporal scales. System observables such as geomagnetic indices, and auroral images, show evidence of scaling in the statistics of these events. Taken together these are hallmarks of a complex system. Here we compare two simple models- that of a system in an SOC state, and the Edwards Wilkinson (EW) model for interface growth, to underline the importance of robustness in these statistical signatures with respect to variability in the drive, and of bursty transport as opposed to intermittent structures, as key signatures of nonlinear complex avalanching systems. Power law statistics of bursty events do not necessarily require an underlying nonlinearity.
NG31C-03 08:35h
Self-generation of phase coherence in multiply-coupled triplet system
We have demonstrated in previous presentations that large amplitude MHD waves observed in the solar wind are not completely phase random (as assumed in quasi-linear theories), but are almost always phase correlated to a certain degree. This presumably is a consequence of nonlinear interaction among the MHD waves. Recently we have developed a method to quantitatively evaluate the phase coherence among waves from a given turbulence time series, via comparison of structure functions of the original data as well as its phase shuffled and phase coherent surrogates (Hada et al., 2003; Koga and Hada, 2003). From a statistical study using Geotail magnetic field data, it is concluded that the phase correlation is almost always non-zero, is enhanced when the turbulence energy is high (nonlinear interaction is strong), and that the waves only within a finite frequency range are responsible for the generation of the phase coherence. In order to understand the physical mechanism of the phase coherence generation, we have constructed a simple model of weak turbulence by coupling multiple triplets, which are the minimum units of nonlinear interaction among the modes (nonlinear interaction of three waves in resonance). According to our numerical simulations, long time statistical behavior of the coupled system critically depends on how the triplets are connected: if the connection is given in such a 'physical' way that the frequency of each mode can be uniquely determined, the system approaches the SOC state as time elapses; otherwise, the system does not evolve to any statistically interesting state. Furthermore, adjacent modes often tend to phase synchronize, as the modes exchange energy (quanta) between them. Implications of the results to the phase coherence detected in the solar wind data will be discussed.
NG31C-04 INVITED 08:50h
Assimilation of Lagrangian Data for Estimation and Forecast of Coherent Structures and Transport in Geophysical Flows
Various manifestations of Lagrangian dynamics exist in the geophysical systems and their signatures may arise in distinct forms at a wide range of spatial scales. Capturing these Lagrangian signatures helps us enhance our predictive capability using the Eulerian model. In the macroscopic form, the Lagrangian signatures may be visible as coherent structures in the sequence of Eulerian synoptic fields. They are dynamically active and often identified as the regions of conserved properties with sharp gradients along the boundaries. These boundaries may be dynamically less active but are important because they govern the mixing process between the interior and exterior. In the microscopic form, the Lagrangian signature is manifest in the trajectory of a traceable marker which can be an observation instrument. The primary attributes of Lagrangian information obtained by the instruments are the ability to trace large-scale coherent structures on one hand and display small-scale mixing process on the other hand, while satisfying the conservation laws for many observed properties the along the trajectory. Lagrangian information thus offers unique perspectives of the circulation. We develop a comprehensive data assimilation platform with a focus on estimation of coherent structures in the Eulerian model through assimilation of Lagrangian data. Recent developments in the use of dynamical systems theory have brought a new aspect of Lagrangian analysis to the geophysical flow dynamics. It offers an algorithm to detect the unseen boundaries of the coherent structures as a non-local material curves originating from the relevant hyperbolic trajectories. Our data assimilation platform takes advantage of the dynamical systems theory. Targeting these hyperbolic trajectories naturally leads to an adaptive observing system.
NG31C-05 INVITED 09:10h
Global Temperature Fluctuations Regulate El Nino Frequency
A theory has been proposed recently to explain the relation between global temperature and the El Niño/Southern Oscillation (ENSO). Accordingly1, the frequency of El Niño and La Niña events depends strongly on global temperature tendency. When global temperatures are rising (falling), the onset of an El Niño (La Niña) is much more likely. Moreover the theory asserts that despite an initial warming resulting from El Niño, the regional climate event subsequently acts to reverse the global temperature tendency making ENSO a `safety valve' against a runaway climate system. Here we show how observed and model data lend support to this theory. The analysis shows that temperature increases (decreases) tend to lead El Niño (La Niña). Coherency in the correlation peaks at a significant level at approximately three years (roughly the period of the ENSO "oscillation,") and three months. The latter peak gives a possible interpretation for an El Niño trigger in that it approximates a basin-crossing time for a Kelvin wave. The analyses from SOI, Nino 3 index and GCM's are all comparable.
NG31C-06 INVITED 09:25h
Integrating biogeochemistry and atmospheric chemistry into Earth system models: Where are the non-linearities?
The biogeochemical cycles are key regulators of the Earth System, linking terrestrial, marine, photochemical, and industrial processes. The carbon, nitroge, and sulfur cycles are integral to and affected by the climate and chemical systems. Important non-linearities are emerging as we move toward integrated Earth System models. I will show our strategy and progress toward a more fully integrated Earth System model. Explicit representation of biogeochemistry and atmospheric chemistry is an important step toward better understanding of climate-earth system interactions. Building on the existing community land model that represents leaf level exchange of energy, water and carbon dioxide, we have integrated "process-based models" of biogenic volatile organic carbon emissions, carbon and nitrogen cycling, and dry deposition of reactive C, N, , S and ozone. This provides the framework for integration of a fully coupled biogeochemical cycles, and land use change together with atmospheric chemistry. Each of the sub-models developed is undergoing careful evaluation by comparison with existing measurements taking advantage of a growing number of flux measurements throughout the globe, as well as regional biogeochemical and atmospheric chemistry studies. The credibility of the effort and the need for their utilization in assessment requires evaluation of both the sub-models and their coupled simulations. Our long-term overall goal is to examine the complex interactions of biology, climate, atmospheric chemistry and human society by including the interactions between the global reactive carbon and nitrogen cycles.
NG31C-07 09:45h
Generalized Laplace Motion: A Multifractal That May Unite Turbulence, Subsurface Heterogeneity and Other Irregular Phenomena.
Stochastic fractals arise naturally from the theory of non-stationary stochastic processes with stationary increments. Examples of such processes that occur in nature include velocity distributions "V(x)" in inertial-range turbulence, tracer distributions "C(x)" in turbulent flow and log(hydraulic conductivity) distributions "ln(K(x))" in heterogeneous sediments. However, the increments (fluctuations over a distance "h") of such quantities ($\Delta$$_{h}$V = V(x + h) - V(x), $\Delta$$_{h}$C = C(x + h) - C(x), and $\Delta$$_{h}$ln(K) = ln(K(x + h)) - ln(K(x)) appear to be stationary (stochastic properties independent of position), and for some time this has served as a basis for study. Stationary increment distributions for a fixed h (lag) may be fitted empirically with probability density functions (PDFs), and if the selected PDF is a member of an infinitely divisible family, then some type of orderly scaling structure is built into the increments of the non-stationary process. A commonly observed scaling property is the occurrence of a power-law variogram [$<$($\Delta$$_{h}$V)$^{2}$$>$; $<$ $>$ = expected value], also called a second order structure function. Well-known PDFs that are infinitely divisible include the Gaussian and Levy distributions. If these PDFs are fitted to increment distributions, the resulting stochastic processes are known as fractional Brownian motion (fBm) and fractional Levy motion (fLm), respectively. However, studies over the past decade have shown that neither PDF is an ideal model for increment distributions. Such distributions are not always Gaussian or Levy, a requirement of fBm and fLm, and the infinite variance feature of the Levy PDF makes this distribution unrealistic physically. What has been observed for both $\Delta$$_{h}$V and $\Delta$$_{h}$ln(K) measurements, is a change from the so-called stretched Laplace PDF (tail decay slower than exponential) - through pure Laplace (double exponential PDF) - to Gaussian behavior as h changes from smaller values to larger values. It is not widely known that the Laplace PDF is infinitely divisible, and therefore can serve as the basis for a stochastic fractal (Meerschaert et al., GRL, 31, L08501, 2004). In order to derive the infinitely divisible family, one must develop the concept of a generalized Laplace PDF (Kotz et al., The Laplace Distributions and Generalizations, Birkhauser, Boston, 2001), hence the name generalized Laplace motion (gLam), having increments called generalized Laplace noise (gLan). In general, gLam is a multifractal (displays a nonlinear dependence of the structure function exponent on lag), but behaves as a monofractal in what might be called the scaling ranges of h. The most general form of the model allows for both positive and negative correlation of the increments, as well as skewed increment distributions. For small h, gLan exhibits highly intermittent behavior, a phenomenon that has been observed in turbulent flow. All of these various properties are presented, and we conclude that through the geometric central limit theorem that applies to the Laplace PDF, the generalized Laplace stochastic process may capture fundamental aspects of a variety of heterogeneous phenomena.