Determining Stationary Periods across Multiple Sensors: An Application to Observed Canopy Turbulence Response to Atmospheric Stability

A recently proposed multisensor stationarity analysis technique (MSATv1) is improved to eliminate the initial interrogation of time-averaged wind directions, a redundant and potentially biasing procedure for a technique capable of detecting changes in mean wind directions. The new technique, MSATv2, satisfies two basic expectations that are not guaranteed in MSATv1: 1) a nonstationary event should not belong to any stationary interval identified with a given stringency, and 2) nonstationary events identified with an arbitrary stringency should continue to be identified as nonstationary with increasing stringency. These expectations are confirmed by applying MSATv2 to two long periods, during the defoliated phase of the Canopy Horizontal Array Turbulence Study (CHATS), whose durations are determined solely by data availability. MSATv2 successfully determines visually trivial and nontrivial nonstationary transitions, uncovering details of the time evolution of dynamic processes. MSATv2 yields ensemble-average estimates of mean wind speeds and directions with well-controlled and quantifiable uncertainties for atmospheric stability conditions ranging from near neutral to free convection. These results enable interrogation of the observed canopy turbulence response to atmospheric stability in isolation from contamination by spatial variation with position relative to canopy elements. MSATv2 results also reveal the connection between the presence of organized convective structures and variability in mean shear, showing the role of organized convective structures in the observed relationship between the bulk drag coefficient and atmospheric instability.

Long-range dependent point processes and their Palm-Khinchin distributions

For a stationary long-range dependent point process N(.) with Palm distribution P0, the Hurst index H ≡ sup{h : lim sup t→∞t-2h var N(0,t] = ∞} is related to the moment index κ ≡ sup{k : E0(Tk) < ∞} of a generic stationary interval T between points (E0 denotes expectation with respect to P0) by 2H + κ ≥ 3, it being known that equality holds for a stationary renewal process. Thus, a stationary point process for which κ < 2 is necessarily long-range dependent with Hurst index greater than ½. An extended example of a Wold process shows that a stationary point process can be both long-range count dependent and long-range interval dependent and have finite mean square interval length, i.e., E0(T2) < ∞.

Kinematic analysis of tongue movements during chemosensory behaviour in the European green lizard, Lacerta viridis (Reptilia: Lacertidae)

High-speed cinematography (100 frames/s) was used to allow quantitative analysis of the kinematic profiles of tongue and jaw displacements during chemosensory activities in the scleroglossan lizard Lacerta viridis. The types of tongue flicking were simple downward extensions (SDE), single oscillations (SOC), and submultiple oscillations (SMOC) of the tongue out of the mouth. The SMOC type involves a downward or upward movement of the tongue performed before a typical oscillation and it is therefore suggested that this is an intermediate category of flick between the typical SOC and MOC of lizards. Closing and opening of the mouth in SDE, SOC, and SMOC cycles may or may not be separated by a stationary stage during which the jaws are held open at a constant gape. The duration of this stationary interval increases from SDE to SMOC. Gape cycles do not show any division into slow and fast stages. The gape is produced largely by depression of the lower jaw; the upper jaw is slightly elevated by protrusion of the tongue. Patterns of correlation of kinematic variables depicting jaw and tongue movements differed between SDE, SOC, and SMOC. A principal component analysis shows that the three flick types overlap in a multivariate space constructed from the kinematic variables depicting jaw and tongue displacements. Overlap between SOC and SMOC categories is greater than that between SOC, SMOC, and SDE categories. The kinematic patterns of tongue displacement during SMOC in Lacerta viridis show similarities with those of MOC in other lizards and in snakes. Kinematically, the pattern of jaw and tongue displacements of Lacerta viridis during chemosensory activities shows similarities with those that occur during drinking and prey capture.

The steady-state behaviour of multistate monotone systems

In this paper the steady-state behaviour of multistate monotone systems of multistate components is considered by applying the theory for stationary and synchronous processes with an embedded point process. After reviewing some general results on stationary availability, stationary interval availability and stationary mean interval performance probabilities, we concentrate on systems with independently working and separately maintained components. For this case an explicit formula is given for the mean time which the system in steady state sojourns in states not below a fixed critical level.

The steady-state behaviour of multistate monotone systems

In this paper the steady-state behaviour of multistate monotone systems of multistate components is considered by applying the theory for stationary and synchronous processes with an embedded point process. After reviewing some general results on stationary availability, stationary interval availability and stationary mean interval performance probabilities, we concentrate on systems with independently working and separately maintained components. For this case an explicit formula is given for the mean time which the system in steady state sojourns in states not below a fixed critical level.