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NASA NTRS1973

Lp-stability (1 less than or equal to p less than or equal to infinity) of multivariable nonlinear time-varying feedback systems that are open-loop unstable

A class of multivariable, nonlinear time-varying feedback systems with an unstable convolution subsystem as feedforward and a time-varying nonlinear gain as feedback was considered. The impulse response of the convolution subsystem is the sum of a finite number of increasing exponentials multiplied by nonnegative powers of the time t, a term that is absolutely integrable and an infinite series of delayed impulses. The main result is a theorem. It essentially states that if the unstable convolution subsystem can be stabilized by a constant feedback gain F and if incremental gain of the difference between the nonlinear gain function and F is sufficiently small, then the nonlinear system is L(p)-stable for any p between one and infinity. Furthermore, the solutions of the nonlinear system depend continuously on the inputs in any L(p)-norm. The fixed point theorem is crucial in deriving the above theorem.

Callier, F. M.↗

NASA NTRSDate not supplied

Toward The Development of Hailstorm Climatologies Derived From Reanalyses and Infared/Passive Microwave Satellite Imagers

Geostationary satellite imagers, such as those of the Geostationary Operational Environmental Satellite (GOES) and Meteosat series, provide both historical and near-real-time observations of cloud top patterns that are commonly associated with severe convection. Environmental conditions favorable for severe weather are thought to be represented well by reanalyses. Predicting exactly where convection and costly storm hazards like hail will occur using models or satellite imagery alone, however, is extremely challenging. The multivariate combination of satellite-observed cloud patterns with reanalysis environmental parameters, linked to United States Next Generation Weather Radar- (NEXRAD-) estimated Maximum Expected Size of Hail (MESH) using a deep neural network (DNN), enables estimation of potentially severe hail likelihood for any observed storm cell. These estimates are specifically designed to make hail likelihood distinctions based on satellite-indicated points of deep convection within environments favorable for storm development. We seek an approach that can be used to estimate climatological hailstorm frequency and risk throughout the historical satellite data record. This presentation demonstrates that statistical distributions of convective parameters from satellite and reanalysis show separation between non-severe/severe hailstorm classes for predictors including overshooting cloud top temperature and area characteristics, convective available potential energy, vertical wind shear, 500 hPa temperature, mid-level lapse rate, precipitable water, and convective inhibition. These complex, multivariate predictor relationships are exploited within a DNN to produce a hail likelihood metric with a critical success index of 0.504 and Heidke skill score of 0.403, which is exceptional among recent analogous hail studies. Furthermore, applications of the DNN to select case studies demonstrate good qualitative agreement between hail likelihood and MESH. These hail classifications are aggregated across an 11-year GOES-12/13 image database to derive a hail frequency and severity climatology, which denotes the Central Plains, the Midwest, and northwestern Mexico as being the most hail-prone regions within the domain studied. Opportunities for training and applying DNN-based hailstorm predictions to recently developed GOES-8/10/12/13/16 and Meteosat Second Generation convective storm detection and characterization climatologies over South America and South Africa, respectively, will also be presented.

Kristopher Bedka↗

NASA NTRS2011

El Nino-Southern Oscillation Correlated Aerosol Angstrom Exponent Anomaly Over the Tropical Pacific Discovered in Satellite Measurements

El Nino.Southern Oscillation (ENSO) is the dominant mode of interannual variability in the tropical atmosphere. ENSO could potentially impact local and global aerosol properties through atmospheric circulation anomalies and teleconnections. By analyzing aerosol properties, including aerosol optical depth (AOD) and Angstrom exponent (AE; often used as a qualitative indicator of aerosol particle size) from the Moderate Resolution Imaging Spectrometer, the Multiangle Imaging Spectroradiometer and the Sea ]viewing Wide Field ]of ]view Sensor for the period 2000.2011, we find a strong correlation between the AE data and the multivariate ENSO index (MEI) over the tropical Pacific. Over the western tropical Pacific (WTP), AE increases during El Nino events and decreases during La Nina events, while the opposite is true over the eastern tropical Pacific (ETP). The difference between AE anomalies in the WTP and ETP has a higher correlation coefficient (>0.7) with the MEI than the individual time series and could be considered another type of ENSO index. As no significant ENSO correlation is found in AOD over the same region, the change in AE (and hence aerosol size) is likely to be associated with aerosol composition changes due to anomalous meteorological conditions induced by the ENSO. Several physical parameters or mechanisms that might be responsible for the correlation are discussed. Preliminary analysis indicates surface wind anomaly might be the major contributor, as it reduces sea ]salt production and aerosol transport during El Nino events. Precipitation and cloud fraction are also found to be correlated with tropical Pacific AE. Possible mechanisms, including wet removal and cloud shielding effects, are considered. Variations in relative humidity, tropospheric ozone concentration, and ocean color during El Nino have been ruled out. Further investigation is needed to fully understand this AE ]ENSO covariability and the underlying physical processes responsible for it.

Li, Jing↗

NASA NTRS2015

Assessing Wetland Hydroperiod and Soil Moisture With Remote Sensing: A Demonstration for the NASA Plum Brook Station Year 2

Primary Goal: Assist with the evaluation and measuring of wetlands hydroperiod at the PlumBrook Station using multi-source remote sensing data as part of a larger effort on projecting climate change-related impacts on the station's wetland ecosystems. MTRI expanded on the multi-source remote sensing capabilities to help estimate and measure hydroperiod and the relative soil moisture of wetlands at NASA's Plum Brook Station. Multi-source remote sensing capabilities are useful in estimating and measuring hydroperiod and relative soil moisture of wetlands. This is important as a changing regional climate has several potential risks for wetland ecosystem function. The year two analysis built on the first year of the project by acquiring and analyzing remote sensing data for additional dates and types of imagery, combined with focused field work. Five deliverables were planned and completed: 1) Show the relative length of hydroperiod using available remote sensing datasets 2) Date linked table of wetlands extent over time for all feasible non-forested wetlands 3) Utilize LIDAR data to measure topographic height above sea level of all wetlands, wetland to catchment area radio, slope of wetlands, and other useful variables 4) A demonstration of how analyzed results from multiple remote sensing data sources can help with wetlands vulnerability assessment 5) A MTRI style report summarizing year 2 results. This report serves as a descriptive summary of our completion of these our deliverables. Additionally, two formal meetings were held with Larry Liou and Amanda Sprinzl to provide project updates and receive direction on outputs. These were held on 2/26/15 and 9/17/15 at the Plum Brook Station. Principal Component Analysis (PCA) is a multivariate statistical technique used to identify dominant spatial and temporal backscatter signatures. PCA reduces the information contained in the temporal dataset to the first few new Principal Component (PC) images. Some advantages of PCA include the ability to filter out temporal autocorrelation and reduce speckle to the higher order PC images. A PCA was performed using ERDAS Imagine on a time series of PALSAR dates. Hydroperiod maps were created by separating the PALSAR dates into two date ranges, 2006-2008 and 2010, and performing an unsupervised classification on the PCAs.

Brooks, Colin↗

NASA NTRS1992

A reliable algorithm for optimal control synthesis

In recent years, powerful design tools for linear time-invariant multivariable control systems have been developed based on direct parameter optimization. In this report, an algorithm for reliable optimal control synthesis using parameter optimization is presented. Specifically, a robust numerical algorithm is developed for the evaluation of the H(sup 2)-like cost functional and its gradients with respect to the controller design parameters. The method is specifically designed to handle defective degenerate systems and is based on the well-known Pade series approximation of the matrix exponential. Numerical test problems in control synthesis for simple mechanical systems and for a flexible structure with densely packed modes illustrate positively the reliability of this method when compared to a method based on diagonalization. Several types of cost functions have been considered: a cost function for robust control consisting of a linear combination of quadratic objectives for deterministic and random disturbances, and one representing an upper bound on the quadratic objective for worst case initial conditions. Finally, a framework for multivariable control synthesis has been developed combining the concept of closed-loop transfer recovery with numerical parameter optimization. The procedure enables designers to synthesize not only observer-based controllers but also controllers of arbitrary order and structure. Numerical design solutions rely heavily on the robust algorithm due to the high order of the synthesis model and the presence of near-overlapping modes. The design approach is successfully applied to the design of a high-bandwidth control system for a rotorcraft.

Vansteenwyk, Brett↗

NASA NTRS2017

Interactive Visualization of High-Dimensional Petascale Ocean Data

We describe an application for interactive visualization of 5 petabytes of time-varying multivariate data from a high-resolution global ocean circulation model. The input data are 10311 hourly (ocean time) time steps of various 2D and 3D fields from a 22-billion point 1/48- degree “lat-lon cap” configuration of the MIT General Circulation Model (MITgcm). We map the global horizontal model domain onto our 128-screen (8x16) tiled display wall to produce a canonical tiling with approximately one MITgcm grid point per display pixel, and using this tiling we encode the entire time series for multiple native and computed scalar quantities at a collection of ocean depths. We reduce disk bandwidth requirements by converting the model’s floating point data to 16-bit fixed point values, and compressing those values with a lossless video encoder, which together allow synchronized playback at 24 time steps per second across all 128 displays. The application allows dynamic assignment of any two encoded tiles to any display, and has multiple interfaces for quickly specifying various orderly arrangements of tiles. All subsequent rendering is done on the fly, with run time control of colormaps, transfer functions, histogram equalization, and labeling. The two data streams on each screen can be rendered independently and combined in various ways, including blending, differencing, horizontal/ vertical wipes, and checkerboarding. The two data streams on any screen can optionally be displayed as a scatterplot in their joint attribute space. All scatterplots and map-view plots from the same x/y location and depth are linked so they all show the current brushable selection. Ocean scientists have used the system, and have found previously unidentified features in the data.

Interactive↗

NASA NTRS2003

Predictability of Malaria Transmission Intensity in the Mpumalanga Province, South Africa, Using Land Surface Climatology and Autoregressive Analysis

There has been increasing effort in recent years to employ satellite remotely sensed data to identify and map vector habitat and malaria transmission risk in data sparse environments. In the current investigation, available satellite and other land surface climatology data products are employed in short-term forecasting of infection rates in the Mpumalanga Province of South Africa, using a multivariate autoregressive approach. The climatology variables include precipitation, air temperature and other land surface states computed by the Off-line Land-Surface Global Assimilation System (OLGA) including soil moisture and surface evaporation. Satellite data products include the Normalized Difference Vegetation Index (NDVI) and other forcing data used in the Goddard Earth Observing System (GEOS-1) model. Predictions are compared to long- term monthly records of clinical and microscopic diagnoses. The approach addresses the high degree of short-term autocorrelation in the disease and weather time series. The resulting model is able to predict 11 of the 13 months that were classified as high risk during the validation period, indicating the utility of applying antecedent climatic variables to the prediction of malaria incidence for the Mpumalanga Province.

Grass, David↗

NASA NTRS2001

A stochastic differential equation model of diurnal cortisol patterns

Circadian modulation of episodic bursts is recognized as the normal physiological pattern of diurnal variation in plasma cortisol levels. The primary physiological factors underlying these diurnal patterns are the ultradian timing of secretory events, circadian modulation of the amplitude of secretory events, infusion of the hormone from the adrenal gland into the plasma, and clearance of the hormone from the plasma by the liver. Each measured plasma cortisol level has an error arising from the cortisol immunoassay. We demonstrate that all of these three physiological principles can be succinctly summarized in a single stochastic differential equation plus measurement error model and show that physiologically consistent ranges of the model parameters can be determined from published reports. We summarize the model parameters in terms of the multivariate Gaussian probability density and establish the plausibility of the model with a series of simulation studies. Our framework makes possible a sensitivity analysis in which all model parameters are allowed to vary simultaneously. The model offers an approach for simultaneously representing cortisol's ultradian, circadian, and kinetic properties. Our modeling paradigm provides a framework for simulation studies and data analysis that should be readily adaptable to the analysis of other endocrine hormone systems.

NASA Discipline Space Human Factors↗

NASA NTRS2011

Lessons Learned from Assimilating Altimeter Data into a Coupled General Circulation Model with the GMAO Augmented Ensemble Kalman Filter

Satellite altimetry measurements have provided global, evenly distributed observations of the ocean surface since 1993. However, the difficulties introduced by the presence of model biases and the requirement that data assimilation systems extrapolate the sea surface height (SSH) information to the subsurface in order to estimate the temperature, salinity and currents make it difficult to optimally exploit these measurements. This talk investigates the potential of the altimetry data assimilation once the biases are accounted for with an ad hoc bias estimation scheme. Either steady-state or state-dependent multivariate background-error covariances from an ensemble of model integrations are used to address the problem of extrapolating the information to the sub-surface. The GMAO ocean data assimilation system applied to an ensemble of coupled model instances using the GEOS-5 AGCM coupled to MOM4 is used in the investigation. To model the background error covariances, the system relies on a hybrid ensemble approach in which a small number of dynamically evolved model trajectories is augmented on the one hand with past instances of the state vector along each trajectory and, on the other, with a steady state ensemble of error estimates from a time series of short-term model forecasts. A state-dependent adaptive error-covariance localization and inflation algorithm controls how the SSH information is extrapolated to the sub-surface. A two-step predictor corrector approach is used to assimilate future information. Independent (not-assimilated) temperature and salinity observations from Argo floats are used to validate the assimilation. A two-step projection method in which the system first calculates a SSH increment and then projects this increment vertically onto the temperature, salt and current fields is found to be most effective in reconstructing the sub-surface information. The performance of the system in reconstructing the sub-surface fields is particularly impressive for temperature, but not as satisfactory for salt.

Keppenne, Christian↗

NASA NTRS2014

Tropospheric Ozone Increases over the Southern Africa Region: Bellwether for Rapid Growth in Southern Hemisphere Pollution?

Increases in free-tropospheric (FT) ozone based on ozonesonde records from the early 1990s through 2008 over two subtropical stations, Irene (near Pretoria, South Africa) and Réunion (21 deg. S, 55 deg. E; approx. 2800 km NE of Irene in the Indian Ocean), have been reported. Over Irene a large increase in the urban-influenced boundary layer (BL, 1.5-4 km) was also observed during the 18-year period, equivalent to 30%decade−1. Here we show that the Irene BL trend is at least partly due to a gradual change in the sonde launch times from early morning to the midday period. The FT ozone profiles over Irene in 1990-2007 are re-examined, filling in a 1995-1999 gap with ozone profiles taken during the Measurements of Ozone by Airbus In-service Aircraft (MOZAIC) project over nearby Johannesburg. A multivariate regression model that accounts for the annual ozone cycle, El Niño-Southern Oscillation (ENSO) and possible tropopause changes was applied to monthly averaged Irene data from 4 to 11 km and to 1992-2011 Réunion sonde data from 4 to 15 km. Statistically significant trends appear predominantly in the middle and upper troposphere (UT; 4-11 km over Irene, 4-15 km over Réunion) in winter (June-August), with increases 1 ppbv yr(exp. −1) over Irene and approx. 2 ppbv yr(exp. −1) over Réunion. These changes are equivalent to approx. 25 and 35-45%decade( exp. −1), respectively. Both stations also display smaller positive trends in summer, with a 45%decade(exp. −1) ozone increase near the tropopause over Réunion in December. To explain the ozone increases, we investigated a time series of dynamical markers, e.g., potential vorticity (PV) at 330-350 K. PV affects UT ozone over Irene in November-December but displays little relationship with ozone over Réunion. A more likely reason for wintertime FT ozone increases over Irene and Réunion appears to be long-range transport of growing pollution in the Southern Hemisphere. The ozone increases are consistent with trajectory origins of air parcels sampled by the sondes and with recent NOx emissions trends estimated for Africa, South America and Madagascar. For Réunion trajectories also point to sources from the eastern Indian Ocean and Asia.

Trends↗

NASA NTRS1984

Prediction of the space adaptation syndrome

The univariate and multivariate relationships of provocative measures used to produce motion sickness symptoms were described. Normative subjects were used to develop and cross-validate sets of linear equations that optimally predict motion sickness in parabolic flights. The possibility of reducing the number of measurements required for prediction was assessed. After describing the variables verbally and statistically for 159 subjects, a factor analysis of 27 variables was completed to improve understanding of the relationships between variables and to reduce the number of measures for prediction purposes. The results of this analysis show that none of variables are significantly related to the responses to parabolic flights. A set of variables was selected to predict responses to KC-135 flights. A series of discriminant analyses were completed. Results indicate that low, moderate, or severe susceptibility could be correctly predicted 64 percent and 53 percent of the time on original and cross-validation samples, respectively. Both the factor analysis and the discriminant analysis provided no basis for reducing the number of tests.

Reschke, M. F.↗

NASA NTRS2020

The role of blocking circulation and emerging open water feedbacks on Greenland cold‐season air temperature variability over the last century

Substantial marine, terrestrial, and atmospheric changes have occurred over the Greenland region during the last century. Several studies have documented record‐levels of Greenland Ice Sheet (GrIS) summer melt extent during the 2000s and 2010s, but relatively little work has been carried out to assess regional climatic changes in other seasons. Here, we focus on the less studied cold‐season (i.e., autumn and winter) climate, tracing the long‐term (1873–2013) variability of Greenland's air temperatures through analyses of coastal observations and model‐derived outlet glacier series and their linkages with North Atlantic sea ice, sea surface temperature (SST), and atmospheric circulation indices. Through a statistical framework, large amounts of west and south Greenland temperature variance (up to r^2~50%) can be explained by the seasonally‐contemporaneous combination of the Greenland Blocking Index (GBI) and the North Atlantic Oscillation (NAO; hereafter the combination of GBI and NAO is termed GBI). Lagged and concomitant regional sea‐ice concentration (SIC) and the Atlantic Multidecadal Oscillation (AMO) seasonal indices account for small amounts of residual air temperature variance (r^2<~10%) relative to the GBI. The correlations between GBI and cold‐season temperatures are predominantly positive and statistically‐significant through time, while regional SIC conditions emerge as a significant covariate from the mid‐20th century through the conclusion of the study period. The inclusion of the cold‐season Pacific Decadal Oscillation (PDO) in multivariate analyses bolsters the air temperature variance explained by the North Atlantic regional predictors, suggesting the remote, background climate state is important to long‐term Greenland temperature variability. These findings imply that large‐scale tropospheric circulation has a strong control on surface temperature over Greenland through dynamic and thermodynamic impacts and stress the importance of understanding the evolving two‐way linkages between the North Atlantic marine and atmospheric environment in order to more accurately predict Greenland seasonal climate variability and change through the 21st century.

air temperatures↗

NASA NTRS1988

A methodology for the synthesis of robust feedback systems

A new methodology is developed for the synthesis of linear, time-variant (LTI) controllers for multivariable LTI systems. The resulting closed-loop system is nominally stable and exhibits a known level of performance. In addition, robustness of the feedback system is guaranteed, i.e., stability and performance are retained in the presence of multiple unstructured uncertainty blocks located at various points in the feedback loop. The design technique is referred to as the Causality Recovery Methodology (CRM). The CRM relies on the Youla parameterization of all stabilizing compensators to ensure nominal stability of the feedback system. A frequency-domain inequality in terms of the structured singular value mu defines the robustness specification. The optimal compensator, with respect to the mu condition, is shown to be noncausal in general. The aim of the CRM is to find a stable, causal transfer function matrix that approximates the robustness characteristics of the optimal solution. The CRM, via a series of infinite-dimensional convex programs, produces a closed-loop system whose performance robustness is at least as good as that of any initial design. The algorithm is approximated by a finite dimensional process for the purposes of implementation. Two numerical examples confirm the potential viability of the CRM concept; however, the robustness improvement comes at the expense of increased computational burden and compensator complexity.

Milich, David Albert↗

NASA NTRS1970

Discrete control of linear distributed systems with application to the deformable primary mirror of a large orbiting telescope

One of the more significant technological problems associated with the orbital operation of large astronomical telescope's is the fabrication and maintenance of the primary mirror surface to the tolerance required for diffraction-limited performance. An interesting approach to the solution of this problem involves continuously measuring and automatically correcting the optical surface of a thin deformable mirror by means of discrete actuators located on its rear surface: The realization of diffraction-limited performance from a telescope in space by this method rests on the ability of the designer to achieve extremely accurate control of a highly complex, interacting, multivariable system. This paper presents the results of a detailed study of the discrete control of linear distributed systems with specific application to the design of a practical controller for a plant representative of a telescope primary mirror for an orbiting astronomical observatory. The problem of controlling the distributed plant is treated by employing modal techniques to represent variations in the optical figure. Distortion of the mirror surface, which arises primarily from thermal gradients, is countered by actuators working against a backing structure to apply a corrective force distribution to the controlled surface. Each displacement actuator is in series with a spring attached to the mirror by means of a pad intentionally introduced to restrict the excitation of high-order modes. Control is then exerted over a finite number (equal.to the number of actuators) of the most significant modes. Through the application of the modal expansion technique the mirror equation of motion is transformed tb a set of uncoupled, linear, time-invariant, ordinary differential equations. The desired dynamic response and static accuracy may then be achieved by the application of classical single-variable design techniques. The formulation of a quadratic performance index which incorporates a measure of image quality permits determination of the trade-off between the-number of actuators and optical purity. A criterion for defining actuator placement and pad size is presented which minimizes the tendency of the controller to excite the unmonitored modes.

Jeremiah F Creedon↗