M. P. Freeman

Revisiting Levy flight search patterns of wandering albatrosses, bumblebees and deer

The study of animal foraging behaviour is of practical ecological importance, and exemplifies the wider scientific problem of optimizing search strategies. Lévy flights are random walks, the step lengths of which come from probability distributions with heavy power-law tails, such that clusters of short steps are connected by rare long steps. Lévy flights display fractal properties, have no typical scale, and occur in physical and chemical systems. An attempt to demonstrate their existence in a natural biological system presented evidence that wandering albatrosses perform Lévy flights when searching for prey on the ocean surface. This well known finding was followed by similar inferences about the search strategies of deer and bumblebees. These pioneering studies have triggered much theoretical work in physics (for example, refs 11, 12), as well as empirical ecological analyses regarding reindeer, microzooplankton, grey seals, spider monkeys and fishing boats. Here we analyse a new, high-resolution data set of wandering albatross flights, and find no evidence for Lévy flight behaviour. Instead we find that flight times are gamma distributed, with an exponential decay for the longest flights. We re-analyse the original albatross data using additional information, and conclude that the extremely long flights, essential for demonstrating Lévy flight behaviour, were spurious. Furthermore, we propose a widely applicable method to test for power-law distributions using likelihood and Akaike weights. We apply this to the four original deer and bumblebee data sets, finding that none exhibits evidence of Lévy flights, and that the original graphical approach is insufficient. Such a graphical approach has been adopted to conclude Lévy flight movement for other organisms, and to propose Lévy flight analysis as a potential real-time ecosystem monitoring tool. Our results question the strength of the empirical evidence for biological Lévy flights.

A study of an expanding interplanetary magnetic cloud and its interaction with the Earth's magnetosphere: The interplanetary aspect

In a series of three interlinked papers we present a study of an interplanetary magnetic cloud and its interaction with the Earths magnetosphere on January 14/15, 1988. This first paper is divided into three parts describing the principal results concerning the magnetic cloud. First, by applying the cylindrically symmetric, magnetic flux rope model to the high time resolution magnetic field and plasma data obtained by the IMP-8 spacecraft, we show that the axis of the magnetic cloud in question is approximately in the ecliptic and orthogonal to the Earth-Sun line. We note the presence of pulsations of ∼5-hour period in the bulk flow speed which are superimposed on an otherwise monotonically falling bulk speed profile. Second, we apply ideal MHD to model the self-similar, radial expansion of a magnetic cloud of cylindrical geometry. As initial condition for the magnetic field we choose a constant-α, force-free magnetic configuration. We demonstrate that the theoretical velocity profile for the free expansion of a magnetic cloud is consistent with observations made during the January 14/15, 1988, magnetic cloud encounter. Comparing model with data, we infer that prior to the start of observations at 1 AU the magnetic cloud had been expanding for 65.4 hours; the radius of the magnetic cloud at the time it arrived at Earth was 0.18 AU; and its expansion speed at 1 AU was ∼114 km/s. Third, we discuss energetic (∼1 MeV) ion data, also from instrumentation on IMP-8. We highlight the appearance of a sharp enhancement in the intensity of ∼0.5-MeV ions while IMP-8 was inside the cloud. These ions travel as a collimated, field-aligned beam from the west of the Sun. This is an “impulsive” solar event in which particles accelerated at a magnetically well-connected solar flare arrive promptly at the spacecraft. The observation of solar flare particles inside the cloud suggests that field lines within the magnetic cloud remained connected to the Sun. The observation is, however, inconsistent with the supposition that the cloud is formed of closed magnetic field loops disconnected from the Sun.

PRESSURE-DRIVEN MAGNETOPAUSE MOTIONS AND ATTENDANT RESPONSE ON THE GROUND

The terrestrial magnetopause suffered considerable sudden changes in its location on 9–10 September 1978. These magnetopause motions were accompanied by disturbances of the geomagnetic field on the ground. We present a study of the magnetopause motions and the ground magnetic signatures using, for the latter, 10 s averaged data from 14 high latitude ground magnetometer stations. Observations in the solar wind (from IMP 8) are employed and the motions of the magnetopause are monitored directly by the spacecraft ISEE 1 and 2. With these coordinated observations we are able to show that it is the sudden changes in the solar wind dynamic pressure that are responsible for the disturbances seen on the ground. At some ground stations we see evidence of a “ringing” of the magnetospheric cavity, while at others only the initial impulse is evident. We note that at some stations field perturbations closely match the hypothesized ground signatures of flux transfer events. In accordance with more recent work in the area (e.g. Potemra et al., 1989, J. geophys. Res., in press), we argue that causes other than impulsive reeonnection may produce the twin ionospheric flow vortex originally proposed as a flux transfer even signature.

Evidence for a solar wind origin of the power law burst lifetime distribution of the AE indices

In this paper we examine the claim that the power law distribution of burst lifetimes in the AE index is evidence that the magnetosphere is a Self-Organized Critical (SOC) system. To do this we compare the burst lifetime distributions of the AU and |AL| indices with those of the υBs and e solar wind input functions. We show for the first time that both the υBs and e burst lifetime distributions are of power law form with an exponential cut-off, consistent with the solar wind being an SOC system. Furthermore, the power law of the e burst lifetime distribution is not significantly different to that of the AU and |AL| indices, indicating that this scale-free property of the AE indices could arise from the solar wind input and may not be an intrinsic property of the magnetospheric system. We discuss the implications of this result for SOC theories of the magnetosphere.

The Earth's magnetosphere under continued forcing: Substorm activity during the passage of an interplanetary magnetic cloud

In this third paper on magnetic clouds and their interaction with the terrestrial magnetosphere we focus on substorm activity attending the 30-hour-long passage of the magnetic cloud seen at 1 AU on January 14/15, 1988. Our main aim is to describe high resolution field and plasma data from six spacecraft at geostationary orbit and beyond (up to 9 RE), supplemented by ground magnetograms, in order to estimate the number of substorm onsets that occurred during this passage. This analysis, attempted here for the first time over such an extended data interval, enables us to obtain a comprehensive view of the magnetospheric behavior. We then relate the interplanetary field and plasma input to the magnetospheric and ionospheric output. The paper is a case study of the response of the nightside magnetosphere to particularly well-behaved interplanetary conditions: the variations with time of the field and plasma parameters in the magnetic cloud are simple; and the north-south (Bz) and east-west (By) components of the magnetic field range slowly over ∼20 nT on both sides of zero. From a synopsis of the substorm observations we find that during the earlier 11-h interval when Bz was continuously positive, the magnetosphere was quiescent, whereas in the later 18-h interval, when Bz was uninterruptedly negative, a large magnetic storm was set off. In this latter interval the substorm onsets recur on average every 50 min. Their average recurrence frequency remains relatively undiminished even when the magnetic cloud Bz and other measures of the interplanetary energy input have decreased considerably. We find these results to concur with the current models of magnetospheric substorms based on deterministic nonlinear dynamics. Using ancillary information from HF radar observations of ionospheric convection, we investigate the magnetospheric conditions preceding the first substorm onset in the long substorm sequence. We find that it occurred when the clouds magnetic field had a persistent northward component but was predominantly westward pointing.

Dayside ionospheric convection changes in response to long-period interplanetary magnetic field oscillations - Determination of the ionospheric phase velocity

Ground magnetic field perturbations recorded by the CANOPUS magnetometer network in the 7 to 13 MLT sector are used to examine how reconfigurations of the dayside polar ionospheric flow take place in response to north-south changes of the IMF. During the 6-hour interval in question IMF Bz oscillates between ±7 nT with about a 1-hour period. Corresponding variations in the ground magnetic disturbance are observed which we infer are due to changes in ionospheric flow. Cross correlation of the data obtained from two ground stations at 73.5° magnetic latitude, but separated by ∼2 hours in MLT, shows that changes in the flow are initiated in the prenoon sector (∼10 MLT) and then spread outward toward dawn and dusk with a phase speed of ∼5 km s−1 over the longitude range ∼8 to 12 MLT, slowing to ∼2 km s−1 outside this range. Cross correlating the data from these ground stations with IMP 8 IMF Bz records produces a MLT variation in the ground response delay relative to the IMF which is compatible with these deduced phase speeds. We interpret these observations in terms of the ionospheric response to the onset, expansion and decay of magnetic reconnection at the dayside magnetopause.

The interaction of a magnetic cloud with the Earth - Ionospheric convection in the Northern and Southern Hemispheres for a wide range of quasi-steady interplanetary magnetic field conditions

This is the second of three papers which study a large interplanetary magnetic cloud, and its interaction with the earths magnetosphere. Here the authors study flows within the ionosphere during the passage of the magnetic cloud on Jan 13-15, 1988. This is the first study of ionospheric convections during prolonged periods of stable and different IMF orientations, which result from the stable, but spatially varying field structure within the magnetic cloud. Data from IMP-8 and DMSP-F8 are analyzed for this work. This observation gave information on ionospheric responses to greater than 10 hour period of northward and southward IMF, with a gradual change from one to the other. Issues studied included strengths of peak flows for north and south IMF; changes in cross polar cap potential with IMF B[sub z]; types and variations of convective patterns vs IMF; variations in size of the polar cap; etc.

A minimal substorm model that explains the observed statistical distribution of times between substorms

A minimal model for the evolution of the global dynamical state of the magnetotail during the substorm has been developed, involving only three simple rules and one free parameter D-the period between substorms under constant solar wind driving. The model is driven with a power input derived from solar wind observations from the Wind spacecraft between 1995 and 1998, to derive a sequence of simulated substorm onsets. For values of D between 2.6 h and 2.9 h, the probability distribution of waiting times between successive simulated substorm onsets is not significantly different to an empirical distribution derived from energetic particle observations at geostationary orbit in 1982-3. Similar results are obtained using solar wind data from the ACE spacecraft between 1998 and 2002. Thus, we argue that the minimal substorm model provides a useful statistical and physical description of the timing of substorm onsets and possibly other substorm properties.

Saturn's dynamic magnetotail: A comprehensive magnetic field and plasma survey of plasmoids and traveling compression regions and their role in global magnetospheric dynamics

We present a comprehensive study of the magnetic field and plasma signatures of reconnection events observed with the Cassini spacecraft during the tail orbits of 2006. We examine their “local” properties in terms of magnetic field reconfiguration and changing plasma flows. We also describe the “global” impact of reconnection in terms of the contribution to mass loss, flux closure, and large-scale tail structure. The signatures of 69 plasmoids, 17 traveling compression regions (TCRs), and 13 planetward moving structures have been found. The direction of motion is inferred from the sign of the change in the Bθ component of the magnetic field in the first instance and confirmed through plasma flow data where available. The plasmoids are interpreted as detached structures, observed by the spacecraft tailward of the reconnection site, and the TCRs are interpreted as the effects of the draping and compression of lobe magnetic field lines around passing plasmoids. We focus on the analysis and interpretation of the tailward moving (south-to-north field change) plasmoids and TCRs in this work, considering the planetward moving signatures only from the point of view of understanding the reconnection x-line position and recurrence rates. We discuss the location spread of the observations, showing that where spacecraft coverage is symmetric about midnight, reconnection signatures are observed more frequently on the dawn flank than on the dusk flank. We show an example of a chain of two plasmoids and two TCRs over 3 hours and suggest that such a scenario is associated with a single-reconnection event, ejecting multiple successive plasmoids. Plasma data reveal that one of these plasmoids contains H+ at lower energy and W+ at higher energy, consistent with an inner magnetospheric source, and the total flow speed inside the plasmoid is estimated with an upper limit of 170 km/s. We probe the interior structure of plasmoids and find that the vast majority of examples at Saturn show a localized decrease in field magnitude as the spacecraft passes through the structure. We take the trajectory of Cassini into account, as, during 2006, the spacecrafts largely equatorial position beneath the hinged current sheet meant that it rarely traversed the center of plasmoids. We present an innovative method of optimizing the window size for minimum variance analysis (MVA) and apply this MVA across several plasmoids to explore their interior morphology in more detail, finding that Saturns tail contains both loop-like and flux rope-like plasmoids. We estimate the mass lost downtail through reconnection and suggest that the apparent imbalance between mass input and observed plasmoid ejection may mean that alternative mass loss methods contribute to balancing Saturns mass budget. We also estimate the rate of magnetic flux closure in the tail and find that when open field line closure is active, it plays a very significant role in flux cycling at Saturn.

A comparison of midlatitude Pi 2 pulsations and geostationary orbit particle injections as substorm indicators

Both the injection of energetic particles at geostationary orbit and ground magnetic observations of Pi 2 wave activity are characteristic indicators of the onset of the substorm expansion phase. Occurrence statistics for the appearance of electron and proton particle injection at three geostationary spacecraft and for the detection of midlatitude magnetic Pi 2 pulsations in a 3-hour local time sector have been compiled from 240 hours of data. Throughout this interval a signature was detected on one or more of the instruments on average every 65 min. It is demonstrated that the detection of geostationary orbit particle injections and the detection of ground-based Pi 2 pulsations are correlated at a very high significance level, and that both appear to be effective substorm indicators. However, a small percentage of events (∼10% in each case) may be identified as a Pi 2 event but not as an injection event or viceversa, without any obvious explanation, such as the local time of the observing instrumentation. A number of possible explanations for the discrepancies between the two data sets are discussed.