Results for “ORTHOGONAL FUNCTION” — Page 8

NASA NTRS2011

Experiments in Reconstructing Twentieth-Century Sea Levels

One approach to reconstructing historical sea level from the relatively sparse tide-gauge network is to employ Empirical Orthogonal Functions (EOFs) as interpolatory spatial basis functions. The EOFs are determined from independent global data, generally sea-surface heights from either satellite altimetry or a numerical ocean model. The problem is revisited here for sea level since 1900. A new approach to handling the tide-gauge datum problem by direct solution offers possible advantages over the method of integrating sea-level differences, with the potential of eventually adjusting datums into the global terrestrial reference frame. The resulting time series of global mean sea levels appears fairly insensitive to the adopted set of EOFs. In contrast, charts of regional sea level anomalies and trends are very sensitive to the adopted set of EOFs, especially for the sparser network of gauges in the early 20th century. The reconstructions appear especially suspect before 1950 in the tropical Pacific. While this limits some applications of the sea-level reconstructions, the sensitivity does appear adequately captured by formal uncertainties. All our solutions show regional trends over the past five decades to be fairly uniform throughout the global ocean, in contrast to trends observed over the shorter altimeter era. Consistent with several previous estimates, the global sea-level rise since 1900 is 1.70 +/- 0.26 mm/yr. The global trend since 1995 exceeds 3 mm/yr which is consistent with altimeter measurements, but this large trend was possibly also reached between 1935 and 1950.

Ray, Richard D.↗

NASA NTRS2011

Method of performing computational aeroelastic analyses

Computational aeroelastic analyses typically use a mathematical model for the structural modes of a flexible structure and a nonlinear aerodynamic model that can generate a plurality of unsteady aerodynamic responses based on the structural modes for conditions defining an aerodynamic condition of the flexible structure. In the present invention, a linear state-space model is generated using a single execution of the nonlinear aerodynamic model for all of the structural modes where a family of orthogonal functions is used as the inputs. Then, static and dynamic aeroelastic solutions are generated using computational interaction between the mathematical model and the linear state-space model for a plurality of periodic points in time.

Silva, Walter A.↗

NASA NTRS2005

Observed Land Impacts on Clouds, Water Vapor, and Rainfall at Continental Scales

How do the continents affect large-scale hydrological cycles? How important can one continent be to the climate system? To address these questions, five years of National Aeronautics and Space Administration (NASA) Terra Moderate Resolution Imaging Spectroradiometer (MODIS) observations, Tropical Rainfall Measuring Mission (TRMM) observations, and the Global Precipitation Climatology Project (GPCP) global precipitation analysis, were used to assess the land impacts on clouds, ~ainfall, and water vapor at continental scales. At these scales, Empirical Orthogonal Function (EOF) and continentally averaged analyses illustrate that continents as integrated regions enhance the seasonality of atmospheric and surface hydrological parameters. Specifically, the continents of Eurasia and North America enhance the seasonality of cloud optical thickness, cirrus fraction, rainfall, and water vapor. Over land, both liquid water and ice cloud effective radii are smaller than over oceans, primarily because land has more aerosol particles. In addition, different continents have similar impacts on hydrological variables in terms of seasonality, but differ in magnitude. For example, in winter, North America and Eurasia increase cloud optical thickness to 17.5 and 16, respectively, while in summer, Eurasia has much smaller cloud optical thicknesses than North An1erica. Such different land impacts are determined by each continent's geographical condition, land cover, and land use. These new understandings help further address the land-ocean contrasts on global climate, help validate global climate model simulated land-atmosphere interactions, and shed light on interpreting climate change over land.

Jin, Menglin↗

NASA NTRS2012

A Technique Using Principal Component Analysis to Compare Seasonal Cycles of Earth Radiation from CERES and Model Computations

A method for quantitatively comparing the seasonal cycles of two global data sets is presented. The seasonal cycles of absorbed solar radiation (ASR) and outgoing longwave radiation (OLR) have been computed from an eight-year data set from the Clouds and Earth's Radiant Energy System (CERES) scanning radiometers and from a model data set produced by the NASA Goddard Space Flight Center Global Modeling and Assimilation Office. To compare the seasonal cycles from these two data sets, principal component (PC) analysis is used, where the PCs express the time variations and the corresponding empirical orthogonal functions (EOFs) describe the geographic variations. Ocean has a long thermal response time compared to land, so land and ocean are separated for the analysis. The root-mean square values for the seasonal cycles of ASR and OLR are extremely close for the two data sets. The first three PCs are quite close, showing that the time responses and magnitudes over the globe are very similar. The agreement between the two sets of PCs is quantified by computing the matrix of inner products of the two sets. For ASR over land, the first PCs of CERES and the model agree to better than 99.9%. The EOF maps are similar for most of the globe, but differ in a few places, and the agreement of the EOF maps is likewise quantified. Maps of differences between the annual cycles show regions of agreement and disagreement.

Smith, G. Louis↗

NASA NTRS2013

Application of Spectral Analysis Techniques in the Intercomparison of Aerosol Data: 1. an EOF Approach to the Spatial-Temporal Variability of Aerosol Optical Depth Using Multiple Remote Sensing Data Sets

Many remote sensing techniques and passive sensors have been developed to measure global aerosol properties. While instantaneous comparisons between pixel-level data often reveal quantitative differences, here we use Empirical Orthogonal Function (EOF) analysis, also known as Principal Component Analysis, to demonstrate that satellite-derived aerosol optical depth (AOD) data sets exhibit essentially the same spatial and temporal variability and are thus suitable for large-scale studies. Analysis results show that the first four EOF modes of AOD account for the bulk of the variance and agree well across the four data sets used in this study (i.e., Aqua MODIS, Terra MODIS, MISR, and SeaWiFS). Only SeaWiFS data over land have slightly different EOF patterns. Globally, the first two EOF modes show annual cycles and are mainly related to Sahara dust in the northern hemisphere and biomass burning in the southern hemisphere, respectively. After removing the mean seasonal cycle from the data, major aerosol sources, including biomass burning in South America and dust in West Africa, are revealed in the dominant modes due to the different interannual variability of aerosol emissions. The enhancement of biomass burning associated with El Niño over Indonesia and central South America is also captured with the EOF technique.

variability↗

NASA NTRS2013

Northern North Atlantic Sea Surface Height and Ocean Heat Content Variability

The evolution of nearly 20 years of altimetric sea surface height (SSH) is investigated to understand its association with decadal to multidecadal variability of the North Atlantic heat content. Altimetric SSH is dominated by an increase of about 14 cm in the Labrador and Irminger seas from 1993 to 2011, while the opposite has occurred over the Gulf Stream region over the same time period. During the altimeter period the observed 0-700 m ocean heat content (OHC) in the subpolar gyre mirrors the increased SSH by its dominantly positive trend. Over a longer period, 1955-2011, fluctuations in the subpolar OHC reflect Atlantic multidecadal variability (AMV) and can be attributed to advection driven by the wind stress ''gyre mode'' bringing more subtropical waters into the subpolar gyre. The extended subpolar warming evident in SSH and OHC during the altimeter period represents transition of the AMV from cold to warm phase. In addition to the dominant trend, the first empirical orthogonal function SSH time series shows an abrupt change 2009-2010 reaching a new minimum in 2010. The change coincides with the change in the meridional overturning circulation at 26.5N as observed by the RAPID (Rapid Climate Change) project, and with extreme behavior of the wind stress gyre mode and of atmospheric blocking. While the general relationship between northern warming and Atlantic meridional overturning circulation (AMOC) volume transport remains undetermined, the meridional heat and salt transport carried by AMOC's arteries are rich with decade-to-century timescale variability.

Sea-surface↗

NASA NTRS2014

Statistical Mechanics of Turbulent Dynamos

Incompressible magnetohydrodynamic (MHD) turbulence and magnetic dynamos, which occur in magnetofluids with large fluid and magnetic Reynolds numbers, will be discussed. When Reynolds numbers are large and energy decays slowly, the distribution of energy with respect to length scale becomes quasi-stationary and MHD turbulence can be described statistically. In the limit of infinite Reynolds numbers, viscosity and resistivity become zero and if these values are used in the MHD equations ab initio, a model system called ideal MHD turbulence results. This model system is typically confined in simple geometries with some form of homogeneous boundary conditions, allowing for velocity and magnetic field to be represented by orthogonal function expansions. One advantage to this is that the coefficients of the expansions form a set of nonlinearly interacting variables whose behavior can be described by equilibrium statistical mechanics, i.e., by a canonical ensemble theory based on the global invariants (energy, cross helicity and magnetic helicity) of ideal MHD turbulence. Another advantage is that truncated expansions provide a finite dynamical system whose time evolution can be numerically simulated to test the predictions of the associated statistical mechanics. If ensemble predictions are the same as time averages, then the system is said to be ergodic; if not, the system is nonergodic. Although it had been implicitly assumed in the early days of ideal MHD statistical theory development that these finite dynamical systems were ergodic, numerical simulations provided sufficient evidence that they were, in fact, nonergodic. Specifically, while canonical ensemble theory predicted that expansion coefficients would be (i) zero-mean random variables with (ii) energy that decreased with length scale, it was found that although (ii) was correct, (i) was not and the expected ergodicity was broken. The exact cause of this broken ergodicity was explained, after much investigation, by greatly extending the statistical theory of ideal MHD turbulence. The mathematical details of broken ergodicity, in fact, give a quantitative explanation of how coherent structure, dynamic alignment and force-free states appear in turbulent magnetofluids. The relevance of these ideal results to real MHD turbulence occurs because broken ergodicity is most manifest in the ideal case at the largest length scales and it is in these largest scales that a real magnetofluid has the least dissipation, i.e., most closely approaches the behavior of an ideal magnetofluid. Furthermore, the effects grow stronger when cross and magnetic helicities grow large with respect to energy, and this is exactly what occurs with time in a real magnetofluid, where it is called selective decay. The relevance of these results found in ideal MHD turbulence theory to the real world is that they provide at least a qualitative explanation of why confined turbulent magnetofluids, such as the liquid iron that fills the Earth's outer core, produce stationary, large-scale magnetic fields, i.e., the geomagnetic field. These results should also apply to other planets as well as to plasma confinement devices on Earth and in space, and the effects should be manifest if Reynolds numbers are high enough and there is enough time for stationarity to occur, at least approximately. In the presentation, details will be given for both theoretical and numerical results, and references will be provided.

Shebalin, John V.↗

NASA NTRS2014

A Generic Nonlinear Aerodynamic Model for Aircraft

A generic model of the aerodynamic coefficients was developed using wind tunnel databases for eight different aircraft and multivariate orthogonal functions. For each database and each coefficient, models were determined using polynomials expanded about the state and control variables, and an othgonalization procedure. A predicted squared-error criterion was used to automatically select the model terms. Modeling terms picked in at least half of the analyses, which totalled 45 terms, were retained to form the generic nonlinear aerodynamic (GNA) model. Least squares was then used to estimate the model parameters and associated uncertainty that best fit the GNA model to each database. Nonlinear flight simulations were used to demonstrate that the GNA model produces accurate trim solutions, local behavior (modal frequencies and damping ratios), and global dynamic behavior (91% accurate state histories and 80% accurate aerodynamic coefficient histories) under large-amplitude excitation. This compact aerodynamics model can be used to decrease on-board memory storage requirements, quickly change conceptual aircraft models, provide smooth analytical functions for control and optimization applications, and facilitate real-time parametric system identification.

Grauer, Jared A.↗

NASA NTRS2014

The East Atlantic - West Russia Teleconnection in the North Atlantic: Climate Impact and Relation to Rossby Wave Propagation

Large-scale winter teleconnection of the East Atlantic - West Russia (EA-WR) over the Atlantic and surrounding regions is examined in order to quantify its impacts on temperature and precipitation and identify the physical mechanisms responsible for its existence. A rotated empirical orthogonal function (REOF) analysis of the upper-tropospheric monthly height field captures successfully the EA-WR pattern and its interannual variation, with the North Atlantic Oscillation as the first mode. EA-WRs climate impact extends from eastern North America to Eurasia. The positive (negative) EA-WR produces positive (negative) temperature anomalies over the eastern US, western Europe and Russia east of Caspian Sea, with negative (positive) anomalies over eastern Canada, eastern Europe including Ural Mountains and the Middle East. These anomalies are largely explained by lower-tropospheric temperature advections. Positive (negative) precipitation anomalies are found over the mid-latitude Atlantic and central Russia around 60E, where lower-level cyclonic (anticyclonic) circulation anomaly is dominant. The eastern Canada and the western Europe are characterized by negative (positive) precipitation anomalies.The EA-WR is found to be closely associated with Rossby wave propagation. Wave activity fluxes show that it is strongly tied to large-scale stationary waves. Furthermore, a stationary wave model (SWM) forced with vorticity transients in the mid-latitude Atlantic (approximately 40N) or diabatic heat source over the subtropical Atlantic near the Caribbean Sea produces well-organized EA-WR-like wave patterns, respectively. Sensitivity tests with the SWM indicate improvement in the simulation of the EA-WR when the mean state is modified to have a positive NAO component that enhances upper-level westerlies between 40-60N.

EA/WR↗

NASA NTRS2014

MHD Turbulence and Magnetic Dynamos

Incompressible magnetohydrodynamic (MHD) turbulence and magnetic dynamos, which occur in magnetofluids with large fluid and magnetic Reynolds numbers, will be discussed. When Reynolds numbers are large and energy decays slowly, the distribution of energy with respect to length scale becomes quasi-stationary and MHD turbulence can be described statistically. In the limit of infinite Reynolds numbers, viscosity and resistivity become zero and if these values are used in the MHD equations ab initio, a model system called ideal MHD turbulence results. This model system is typically confined in simple geometries with some form of homogeneous boundary conditions, allowing for velocity and magnetic field to be represented by orthogonal function expansions. One advantage to this is that the coefficients of the expansions form a set of nonlinearly interacting variables whose behavior can be described by equilibrium statistical mechanics, i.e., by a canonical ensemble theory based on the global invariants (energy, cross helicity and magnetic helicity) of ideal MHD turbulence. Another advantage is that truncated expansions provide a finite dynamical system whose time evolution can be numerically simulated to test the predictions of the associated statistical mechanics. If ensemble predictions are the same as time averages, then the system is said to be ergodic; if not, the system is nonergodic. Although it had been implicitly assumed in the early days of ideal MHD statistical theory development that these finite dynamical systems were ergodic, numerical simulations provided sufficient evidence that they were, in fact, nonergodic. Specifically, while canonical ensemble theory predicted that expansion coefficients would be (i) zero-mean random variables with (ii) energy that decreased with length scale, it was found that although (ii) was correct, (i) was not and the expected ergodicity was broken. The exact cause of this broken ergodicity was explained, after much investigation, by greatly extending the statistical theory of ideal MHD turbulence. The mathematical details of broken ergodicity, in fact, give a quantitative explanation of how coherent structure, dynamic alignment and force-free states appear in turbulent magnetofluids. The relevance of these ideal results to real MHD turbulence occurs because broken ergodicity is most manifest in the ideal case at the largest length scales and it is in these largest scales that a real magnetofluid has the least dissipation, i.e., most closely approaches the behavior of an ideal magnetofluid. Furthermore, the effects grow stronger when cross and magnetic helicities grow large with respect to energy, and this is exactly what occurs with time in a real magnetofluid, where it is called selective decay. The relevance of these results found in ideal MHD turbulence theory to the real world is that they provide at least a qualitative explanation of why confined turbulent magnetofluids, such as the liquid iron that fills the Earth's outer core, produce stationary, large-scale magnetic fields, i.e., the geomagnetic field. These results should also apply to other planets as well as to plasma confinement devices on Earth and in space, and the effects should be manifest if Reynolds numbers are high enough and there is enough time for stationarity to occur, at least approximately. In the presentation, details will be given for both theoretical and numerical results, and references will be provided.

Shebalin, John V↗

NASA NTRS2013

North Pacific Decadal Variability in the GEOS-5 Atmosphere-Ocean Model

This study examines the mechanisms of the Pacific decadal oscillation (PDO) in the GEOS-5 general circulation model. The model simulates a realistic PDO pattern that is resolved as the first empirical orthogonal function (EOF) of winter sea surface temperature (SST). The simulated PDO is primarily forced by Aleutian low through Ekman transport and surface fluxes, and shows a red spectrum without any preferred periodicity. This differs from the observations, which indicate a greater role of El Nino-Southern Oscillation (ENSO) forcing, and likely reflects the too short time scale of the simulated ENSO. The geostrophic transport in response to the Aleutian low is limited to the Kuroshio-Oyashio Extension, and is unlikely the main controlling factor in this model, although it reinforces the Ekman-induced SST anomalies. The delay between the Aleutian low and the PDO is relatively short (1 year) suggesting that the fast Ekman response (rather than Rossby wave propagation) sets the SST pattern immediately following an Aleutian low fluctuation. The atmospheric feedback (response to the SST) is only about 25 of the forcing and never evolves into an Aleutian low completely, instead projecting onto the North Pacific Oscillation (NPO), a meridional dipole in sea level pressure (SLP). The lack of preferred periodicity and weak atmospheric response bothindicate a coupled oscillation is an unlikely mechanism for the PDO in this model. In agreement with recent studies, the NPO is correlated with the North Pacific Gyre Oscillation (NPGO), which is another leading EOF of the North Pacific SST. A possible connection between the PDO and the NPGO is discussed.

Pacific Decadal Variability↗

NASA NTRS2013

Trends and Variations of Ocean Surface Latent Heat Flux: Results from GSSTF2c Data Set

Trends and variations of Goddard Satellite-based Surface Turbulent Fluxes (GSSTF) version 2c (GSSTF2c) latent heat flux (LHF) are examined. This version of LHF takes account of the correction in Earth incidence angle. The trend of global mean LHF for GSSTF2c is much reduced relative to GSSTF version 2b Set 1 and Set 2 for the same period 1988-2008. Temporal increase of GSSTF2c LHF in the two decades is 11.0%, in which 3.1%, 5.8%, and 2.1% are attributed to the increase in wind, the increase in sea surface saturated air humidity, and the decrease in near-surface air humidity, respectively. The first empirical orthogonal function of LHF is a conventional El Nino Southern Oscillation (ENSO) mode. However, the trends in LHF are independent of conventional ENSO phenomena. After removing ENSO signal, the pattern of LHF trends is primarily determined by the pattern of air-sea humidity difference trends.

global mean↗

NASA NTRS2014

Real-Time Onboard Global Nonlinear Aerodynamic Modeling from Flight Data

Flight test and modeling techniques were developed to accurately identify global nonlinear aerodynamic models onboard an aircraft. The techniques were developed and demonstrated during piloted flight testing of an Aermacchi MB-326M Impala jet aircraft. Advanced piloting techniques and nonlinear modeling techniques based on fuzzy logic and multivariate orthogonal function methods were implemented with efficient onboard calculations and flight operations to achieve real-time maneuver monitoring and analysis, and near-real-time global nonlinear aerodynamic modeling and prediction validation testing in flight. Results demonstrated that global nonlinear aerodynamic models for a large portion of the flight envelope were identified rapidly and accurately using piloted flight test maneuvers during a single flight, with the final identified and validated models available before the aircraft landed.

Brandon, Jay M.↗

NASA NTRS2016

North Pacific Decadal Variability: Insights from a Biennial ENSO Environment

This study examines the mechanisms of the Pacific decadal oscillation (PDO) in the NASA GEOS-5 general circulation model (GCM). Similar to several other state-of-the-art GCMs, the El Niño-Southern Oscillation (ENSO) simulated by the GEOS-5 has a strong biennial periodicity. Since this is a model bias that precludes a strong role of ENSO, it provides a unique environment to assess the other leading mechanisms of North Pacific decadal variability. Despite the biennial ENSO periodicity, the model simulates a realistic PDO pattern in the North Pacific that is resolved as the first empirical orthogonal function (EOF) of winter mean sea surface temperature (SST). The spectrum of the PDO indicates no preferred periodicity. The SST anomalies associated with the PDO, particularly its basin wide structure, are primarily forced by the Aleutian low through Ekman transport. The slow geostrophic transport in association with the meridional adjustment of the subtropical gyre is limited to a narrow region in the Kuroshio-Oyashio extension, north of 40degN. The atmosphere's response to the PDO, while weak, projects onto the North Pacific Oscillation (NPO), a meridional dipole in sea level pressure. Both the lack of preferred periodicity and the weak atmospheric response indicate an air-sea coupled oscillation is an unlikely mechanism in this model. In agreement with recent studies, the NPO is correlated with the North Pacific Gyre Oscillation, which is another leading EOF of North Pacific SST variability. The results emphasize the role of atmospheric variability in the North Pacific SST modes, thereby bringing into question the potential for their predictability.

GCM↗

NASA NTRS2017

Efficient Testing Combining Design of Experiment and Learn-to-Fly Strategies

Rapid modeling and efficient testing methods are important in a number of aerospace applications. In this study efficient testing strategies were evaluated in a wind tunnel test environment and combined to suggest a promising approach for both ground-based and flight-based experiments. Benefits of using Design of Experiment techniques, well established in scientific, military, and manufacturing applications are evaluated in combination with newly developing methods for global nonlinear modeling. The nonlinear modeling methods, referred to as Learn-to-Fly methods, utilize fuzzy logic and multivariate orthogonal function techniques that have been successfully demonstrated in flight test. The blended approach presented has a focus on experiment design and identifies a sequential testing process with clearly defined completion metrics that produce increased testing efficiency.

Murphy, Patrick C.↗

NASA NTRS2017

Climate Controls on Tree Growth in the Western Mediterranean

The first large-scale network of tree-ring chronologies from the western Mediterranean (WM; 32 deg N-43 deg N, 10 deg W-17 deg E) is described and analyzed to identify the seasonal climatic signal in indices of annual ring width. Correlation and rotated empirical orthogonal function analyses are applied to 85 tree-ring series and corresponding gridded climate data to assess the climate signal embedded in the network. Chronologies range in length from 80 to 1129 years. Monthly correlations and partial correlations show overall positive associations for Pinus halepensis (PIHA) and Cedrus atlantica (CDAT) with winter (December-February) and spring (March-May) precipitation across this network. In both seasons, the precipitation correlation with PIHA is stronger, while CDAT chronologies tend to be longer. A combination of positive correlations between growth and winter-summer precipitation and negative partial correlations with growing season temperatures suggests that chronologies in at least part of the network reflect soil moisture and the integrated effects of precipitation and evapotranspiration signal. The range of climate response observed across this network reflects a combination of both species and geographic influences. Western Moroccan chronologies have the strongest association with the North Atlantic Oscillation.

chronology development↗

NASA NTRS2016

Degree of Ice Particle Surface Roughness Inferred from Polarimetric Observations

The degree of surface roughness of ice particles within thick, cold ice clouds is inferred from multidirectional, multi-spectral satellite polarimetric observations over oceans, assuming a column-aggregate particle habit. An improved roughness inference scheme is employed that provides a more noise-resilient roughness estimate than the conventional best-fit approach. The improvements include the introduction of a quantitative roughness parameter based on empirical orthogonal function analysis and proper treatment of polarization due to atmospheric scattering above clouds. A global 1-month data sample supports the use of a severely roughened ice habit to simulate the polarized reflectivity associated with ice clouds over ocean. The density distribution of the roughness parameter inferred from the global 1- month data sample and further analyses of a few case studies demonstrate the significant variability of ice cloud single-scattering properties. However, the present theoretical results do not agree with observations in the tropics. In the extra-tropics, the roughness parameter is inferred but 74% of the sample is out of the expected parameter range. Potential improvements are discussed to enhance the depiction of the natural variability on a global scale.

surface↗

NASA NTRS2017

An Investigation of Dust Storms Observed with the Mars Color Imager

Daily global imaging by the Mars Color Imager (MARCI) continues the record of the Mars Orbiter Camera (MOC) and has allowed creation of a long-duration record of Martian dust storms. We observe dust storms over the first two Mars years of the MARCI record, including tracking individual storms over multiple sols, as well as tracking the growth and recession of the seasonal polar caps. Using the combined 6 Mars year record of textured dust storms (storms with visible textures on the observed dust cloud tops), we study the relationship between textured dust storm activity and meteorology (as simulated by the MarsWRF general circulation model) and surface properties. We find that textured dust storms preferentially occur in places and seasons with above average surface wind stress. Textured dust storm occurrence also has a modest linear anti-correlation with surface albedo (0.43) and topography (0.40). Lastly, we perform an empirical orthogonal function (EOF) analysis on the distribution of occurrence of textured dust storms and find that over 50 of the variance in textured dust storm activity can be explained by two EOF modes. We associate the first EOF mode with cap-edge storms just before Ls = 180deg and the second EOF mode with flushing dust storms that occur from Ls = 180-210deg and again near Ls = 320deg.

Guzewich, Scott D.↗