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The Kalman filter in question, which was implemented in the time scale algorithm TA(NIST), produces time scales with poor short-term stability. A simple modification of the error covariance matrix allows the filter to produce time scales with good stability at all averaging times, as verified by simulations of clock ensembles.
Previous statistical observations have shown that the recovery time scales of substorms occurring in the winter and near equinox (when the nighttime auroral zone was in darkness) are roughly twice as long as the recovery time scales for substorms occurring in the summer (when the nighttime auroral region was sunlit). This suggests that auroral substorms in the northern and southern hemispheres develop asymmetrically during solstice conditions with substorms lasting longer in the winter (dark) hemisphere than in the summer (sunlit) hemisphere. Additionally, this implies that more energy is deposited by electron precipitation in the winter hemisphere than in the summer one during substorms. This result, coupled with previous observations that have shown that auroral activity is more common when the ionosphere is in darkness and is suppressed when the ionosphere is in daylight, strongly suggests that the ionospheric conductivity plays an important role governing how magnetospheric energy is transferred to the ionosphere during substorms. Therefore, the ionosphere itself may dictate how much energy it will accept from the magnetosphere during substorms rather than this being an externally imposed quantity. Here, we extend our earlier work by statistically analyzing the recovery time scales for a large number of substorms observed in the conjugate hemispheres simultaneously by two orbiting global auroral imagers: Polar UVI and IMAGE FUV. Our current results are consistent with previous observations. The recovery time scales are observed to be longer in the winter (dark) hemisphere while the auroral activity has a shorter duration in the summer (sunlit) hemisphere. This leads to an asymmetric energy input from the magnetosphere to the ionosphere with more energy being deposited in the winter hemisphere than in the summer hemisphere.
A study is conducted of feedback design for systems with multiple time-scale structure uncovering an intrinsic time-scale structure for a state feedback system with full state output. From this a multiple time-scale asymptotic observer and a system with state feedback via a two time-scale asymptotic observer is considered. Finally more general results for a restricted class of systems are obtained.
The KPW (Kalman plus weights) time scale algorithm uses a Kalman filter to provide frequency and drift information to a basic time scale equation. This paper extends the algorithm to three-state clocks nd gives results for a simulated eight-clock ensemble.
Time scales in turbulent and transitional flow provide a link between experimental data and modeling, both in terms of physical content and for quantitative assessment. The problem of interest here is the definition of time scales in an unsteady flow. Using representative samples of data from GEAE low pressure turbine experiment in low speed research turbine facility with wake-induced transition, we document several methods to extract dominant frequencies, and compare the results. We show that conventional methods of time scale evaluation (based on autocorrelation functions and on Fourier spectra) and wavelet-based methods provide similar information when applied to stationary signals. We also show the greater flexibility of the wavelet-based methods when dealing with intermittent or strongly modulated data, as are encountered in transitioning boundary layers and in flows with unsteady forcing associated with wake passing. We define phase-averaged dominant frequencies that characterize the turbulence associated with freestream conditions and with the passing wakes downstream of a rotor. The relevance of these results for modeling is discussed in the paper.
Drought occurs on a wide range of time scales, and within a variety of different types of regional climates. It is driven foremost by an extended period of reduced precipitation, but it is the impacts on such quantities as soil moisture, streamflow and crop yields that are often most important from a users perspective. While recognizing that different users have different needs for drought information, it is nevertheless important to understand that progress in predicting drought and satisfying such user needs, largely hinges on our ability to improve predictions of precipitation. This talk reviews our current understanding of the physical mechanisms that drive precipitation variations on subseasonal to decadal time scales, and the implications for predictability and prediction skill. Examples are given highlighting the phenomena and mechanisms controlling precipitation on monthly (e.g., stationary Rossby waves, soil moisture), seasonal (ENSO) and decadal time scales (PD~ and AMO).
Two methods for analyzing the time-scale properties of aircraft trajectory optimization problems are presented. Time-scale properties must be identified before solutions can be obtained by using singular perturbation methods. Both methods only require a knowledge of the state equations, the aircraft characteristics, and the bounds on the state and control variables. Although these methods give only rough estimates of time-scale separation, they do not require that an 'exact' optimal trajectory be known, as do the more rigorous methods, and they are an improvement on the ad hoc methods currently in use. The two methods are applied to an example problem for a high performance aircraft.
On decadal to multi-decadal time scales, thermal expansion of sea waters and land ice loss are the main contributors to sea level variations. However, modification of the terrestrial water cycle due to climate variability and direct anthropogenic forcing may also affect sea level. For the past decades, variations in land water storage and corresponding effects on sea level cannot be directly estimated from observations because these are almost non-existent at global continental scale. However, global hydrological models developed for atmospheric and climatic studies can be used for estimating total water storage. For the recent years (since mid-2002), terrestrial water storage change can be directly estimated from observations of the GRACE space gravimetry mission. In this study, we analyse the interannual variability of total land water storage, and investigate its contribution to mean sea level variability at interannual time scale. We consider three different periods that, each, depend on data availability: (1) GRACE era (2003-2009), (2) 1993-2003 and (3) 1955-1995. For the GRACE era (period 1), change in land water storage is estimated using different GRACE products over the 33 largest river basins worldwide. For periods 2 and 3, we use outputs from the ISBA-TRIP (Interactions between Soil, Biosphere, and Atmosphere-Total Runoff Integrating Pathways) global hydrological model. For each time span, we compare change in land water storage (expressed in sea level equivalent) to observed mean sea level, either from satellite altimetry (periods 1 and 2) or tide gauge records (period 3). For each data set and each time span, a trend has been removed as we focus on the interannual variability. We show that whatever the period considered, interannual variability of the mean sea level is essentially explained by interannual fluctuations in land water storage, with the largest contributions arising from tropical river basins.
Quasi-global precipitation analyses at fine time scales (3-hr) are described. TRMM observations (radar and passive microwave) are used to calibrate polar-orbit microwave observations from SSM/I (and other satellites instruments, including AMSR and AMSU) and geosynchronous IR observations. The individual data sets are then merged using a priority order based on quality to form the TRMM Multi-satellite Precipitation Analysis (MPA). Raingauge information is used to help constrain the satellite-based estimates over land. The TRMM standard research product (Version 6 3B-42 of the TRMM products) will be available for the entire TRMM period (January 1998-present) by the end of 2004. The real-time version of this merged product has been produced over the past two years and is available on the U.S. TRMM web site (trmm.gsfc.nasa.gov) at 0.25" latitude-longitude resolution over the latitude range from 5O0N-50"S. Validation of daily totals indicates good results, with limitations noted in mid-latitude winter over land and regions of shallow, orographic precipitation. Various applications of these estimates are described, includmg: 1) detecting potential floods in near real-time; 2) analyzing Indian Ocean precipitation variations related to the initiation of El Nino; 3) determining characteristics of the African monsoon; and 4) analysis of diurnal variations.
Issues pertaining to the well-posedness of a two time scale approach to the output feedback regulator design problem are examined. An approximate quadratic performance index which reflects a two time scale decomposition of the system dynamics is developed. It is shown that, under mild assumptions, minimization of this cost leads to feedback gains providing a second-order approximation of optimal full system performance. A simplified approach to two time scale feedback design is also developed, in which gains are separately calculated to stabilize the slow and fast subsystem models. By exploiting the notion of combined control and observation spillover suppression, conditions are derived assuring that these gains will stabilize the full-order system. A sequential numerical algorithm is described which obtains output feedback gains minimizing a broad class of performance indices, including the standard LQ case. It is shown that the algorithm converges to a local minimum under nonrestrictive assumptions. This procedure is adapted to and demonstrated for the two time scale design formulations.
A relative time scale for ordering channel and chaos forming events was constructed for areas within the Margaritifer Sinus region of Mars. Transection and superposition relationships of channels, chaotic terrain, and the surfaces surrounding them were used to create the relative time scale; crater density studies were not used. Channels and chaos in contact with one another were treated as systems. These systems were in turn treated both separately (in order to understand internal relationships) and as members of the suite of Martian erosional forms (in order to produce a combined, master time scale). Channeling events associated with chaotic terrain development occurred over an extended geomorphic period. The channels can be divided into three convenient groups: those that pre-date intercrater plains development post-plains, pre-chasma systems; and those associated with the development of the Vallis Marineris chasmata. No correlations with cyclic climatic changes, major geologic events in other regions on Mars, or triggering phenomena (for example, specific impact events) were found.
ABSTRACT The stochastic photometric variability of quasars is known to follow a random-walk phenomenology on emission time-scales of months to years. Some high-cadence rest-frame optical monitoring in the past has hinted at a suppression of variability amplitudes on shorter time-scales of a few days or weeks, opening the question of what drives the suppression and how it might scale with quasar properties. Here, we study a few thousand of the highest luminosity quasars in the sky, mostly in the luminosity range of $L_{\rm bol}$$=[46.4, 47.3]$ and redshift range of $z=[0.7, 2.4]$. We use a data set from the NASA/Asteroid Terrestrial-impact Last Alert System facility with nightly cadence, weather permitting, which has been used before to quantify strong regularity in longer term rest-frame-UV variability. As we focus on a careful treatment of short time-scales across the sample, we find that a linear function is sufficient to describe the UV variability structure function. Although the result can not rule out the existence of breaks in some groups completely, a simpler model is usually favoured under this circumstance. In conclusion, the data are consistent with a single-slope random walk across rest-frame time-scales of $\Delta t=[10, 250]$ d.
A new turbulence model, based upon dynamic and thermal turbulent time scale transport equations, is developed and applied to homogeneous shear flows with constant velocity and temperature gradients. The new model comprises transport equations for k, the turbulent kinetic energy; tau, the dynamic time scale; k(sub theta), the fluctuating temperature variance; and tau(sub theta), the thermal time scale. It offers conceptually parallel modeling of the dynamic and thermal turbulence at the two equation level, and eliminates the customary prescription of an empirical turbulent Prandtl number, Pr(sub t), thus permitting a more generalized prediction capability for turbulent heat transfer in complex flows and geometries. The new model also incorporates constitutive relations, based upon invariant theory, that allow the effects of nonequilibrium to modify the primary coefficients for the turbulent shear stress and heat flux. Predictions of the new model, along with those from two other similar models, are compared with experimental data for decaying homogeneous dynamic and thermal turbulence, homogeneous turbulence with constant temperature gradient, and homogeneous turbulence with constant temperature gradient and constant velocity gradient. The new model offers improvement in agreement with the data for most cases considered in this work, although it was no better than the other models for several cases where all the models performed poorly.
Pressure-sensitive paint (PSP) is an optical pressure sensor that utilizes the oxygen quenching of luminescence. PSP measurements in unsteady aerodynamic flows require fast time response of the paint. There are two characteristic time-scales that are related to the time response of PSP. One is the luminescent lifetime representing an intrinsic physical limit for the achievable temporal resolution of PSP. Another is the time-scale of oxygen diffusion across the PSP layer. When the time-scale of oxygen diffusion is much larger than the luminescent lifetime, the time response of PSP is controlled by oxygen diffusion. In a thin homogenous polymer layer where diffusion is Fickian, the oxygen concentration 1021 can be described by the diffusion equation in one-dimension.
The paper reports progress in developing a closure employing two or more independently calculated time scales with which to characterize the rates of progress of different turbulent interactions. The approach contrasts with that used by earlier single-point models which adopt just a single time scale, proportional to the turbulence energy turnover time. The present treatment divides the energy containing part of the spectrum into two regions which respond at different rates and in different ways to changes in the environment. Computational results are reported for several thin shear flows which show striking improvement in the level of agreement with experiment over that obtained with models employing only one time scale.
Recent developments in the theory of singular perturbations and time scales (SPaTS) in discrete control systems are reviewed. Sources of discrete models and the effect of the discretizing interval on the model are examined. The analysis of two-time scale systems is presented to bring out typical characteristic features of SPaTS. In the control of the two-time scale systems, the important issue of multirate sampling is addressed.
We report a series of experiments to explore clima~ responses to two types of solar spectral forcing on decadal and centennial time scales - one based on prior reconstructions, and another implied by recent observations from the SORCE (Solar Radiation and Climate Experiment) SIM (Spectral 1rradiance Monitor). We apply these forcings to the Goddard Institute for Space Studies (GISS) Global/Middle Atmosphere Model (GCMAM). that couples atmosphere with ocean, and has a model top near the mesopause, allowing us to examine the full response to the two solar forcing scenarios. We show different climate responses to the two solar forCing scenarios on decadal time scales and also trends on centennial time scales. Differences between solar maximum and solar minimum conditions are highlighted, including impacts of the time lagged reSponse of the lower atmosphere and ocean. This contrasts with studies that assume separate equilibrium conditions at solar maximum and minimum. We discuss model feedback mechanisms involved in the solar forced climate variations.
A two-time-scale autopilot is proposed for the Aircraft Controls Design Challenge problem. This control law uses a nonlinear aircraft model constructed from the given vehicle simulation. The vehicle model is partitioned into slow translational dynamics and fast rotational dynamics. Feedback linearization is then employed to synthesize control laws for these two-time scales. Due to the nature of the synthesis, the control law is suitable for automatic trajectory following, and also for pilot control.