Search NASA⌕ Search

SEARCH · Search NASA

Results for “ORTHOGONAL FUNCTION”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
NASA NTRS1988

An efficient approach for statistical calculations with globally gridded filtered time series

The formulas for performing several statistical calculations based on Fourier coefficients are presented for use in atmospheric observational studies. The calculations discussed include a method for estimating the degree of temporal freedoms of two correlated time series and a method for performing seasonal analyses using a half-year summer/winter projection operator in the frequency domain. A modified lag-correlation calculation is proposed for obtaining lag correlations in the frequency domain. Also, a spectral approach for Empirical Orthogonal Function (EOF) and Extended EOF analysis is given which reduces the size of the matrix to be solved in the eigenproblem.

Gao, X. H.↗
NASA NTRS1989

A normal-mode approach to Jovian atmospheric dynamic

A nonlinear, quasi-geostrophic, baroclinic model of Jovian atmospheric dynamics is proposed, in which vertical variations of velocity are represented by a truncated sum over a complete set of orthogonal functions obtained by a separation of variables of the linearized quasi-geostrophic potential vorticity equation. A set of equations for the time variation of the mode amplitudes in the nonlinear case is then derived. It is shown that, for a planet with a neutrally stable, fluid interior instead of a solid lower boundary, the barotropic mode represents motions in the interior, and is not affected by the baroclinic modes. One consequence of this is that a normal-mode model with one baroclinic mode is dynamically equivalent to a one-layer model with solid lower topography. It is also shown that, for motions in Jupiter's cloudy lower troposphere, the stratosphere behaves nearly as a rigid lid, so that the normal-mode is applicable to Jupiter. The accuracy of the normal-mode model for Jupiter is tested using the following simple problems: (1) forced, vertically propagating Rossby waves, using two and three baroclinic modes, and (2) baroclinic instability, using two baroclinic modes. It is found that the normal-mode model provides qualitatively correct results, even with only a very limited number of vertical degrees of freedom.

Achterberg, Richard K.↗
NASA NTRS1989

Annual and interannual variations of Earth-emitted radiation based on a 10-year data set

The method of empirical orthogonal functions (EOF) was applied to a 10-year data set of outgoing longwave radiation. Spherical harmonic functions are used as a basis set for producing equal area map results. The following findings are noted. The first EOF accounts for 66 percent of the variance. After that, each EOF accounts for only a small variance, forming a slowly converging series. The first two EOF's describe mainly the annual cycle. The third EOF is primarily the semiannual cycle although many other EOF's also contain significant semiannual parts. These results reaffirm those based on a shorter data set. In addition, a much stronger spring/fall mode was found in the central equatorial Pacific Ocean for the second EOF than was found earlier. This difference is attributed to the use of broadband radiometer data which were available for the present study. The earlier study used data from a window channel instrument which is not as sensitive to water vapor variations. The fourth EOF describes much of the 1976 to 1977 and 1982 to 1983 ENSO phenomena. There is typically a gap in the spectrum between a semiannual peak and the annual cycle for all but the first EOF. A semiannual OLR dipole straddles the Asian-Australian monsoon track.

Bess, T. Dale↗
NASA NTRS1990

Annual and interannual variations of absorbed solar radiation based on a 10-year data set

Annual and interannual variations of absorbed solar radiation (ASR) are studied using the 10-year earth radiation budget data set from the Nimbus-6 and Nimbus-7 earth radiation budget instruments in the form of monthly averaged maps of ASR. Empirical orthogonal functions (EOFs) are computed for the global distribution of ASR. Six EOFs are found which have physical significance and which account for 97.8 percent of the spatial variance of the data set. The first EOF describes the annual cycle and is primarily a latitudinal variation which is driven by the incident solar radiation. The second and fourth EOFs are semiannual cycles. EOFs 3 through 6 are strongly longitudinally dependent. EOF 3 describes the spring/fall part of the annual cycle, and EOF 4 describes the part of the semiannual cycle which is out of phase with EOF 2. EOF 5 is the response of the ASR to El Nino. The annual cycle and its harmonics account for 97.6 percent of the variance with time. When the data set is deseasonalized, the first two EOFs of the resulting set are found to correspond closely to EOFs 5 and 6 of the data set with season included. As with outgoing longwave radiation, most of the interannual variation is found over the tropical oceans.

Smith, G. Louis↗
NASA NTRS1991

Potential vorticity index

Based on the European Center For Medium Range Weather Forecasting (ECMWF) First Global Atmospheric Research Program Global Experiment (FGGE) IIIb data set in the 1978 to 1979 winter, a potential vorticity (PV) index was defined as a measure of the zonally averaged, mid-latitude PV gradient on the 300 K isentropic surface in the Northern Hemisphere. The evolution of that index and its relation to teleconnection patterns of 500 mb geopotential height anomaly are studied. The results of the temporal and spatial variation of blocking and cyclogenesis in the 1978 to 1979 winter and its relation to global and local PV gradients were obtained. Complex empirical orthogonal function (EOF) analyses were performed, using the same FGGE data set for the 1978 to 1979 winter, for a representative high latitude band and mid latitude band geopotential height anomalies at 500 mb, phi sub h, phi sub m, and PV gradient at 300 K, delta(Q), at each longitude for the three month period. The focus of current research is the following: (1) to perform Fourier analyses for the first three EOF's of phi sub h, phi sub m, and delta(Q) at given latitude bands, and to find the dominant wavenumbers and frequencies which are responsible for these EOF's; (2) to compare the results from EOF and Fourier analyses which will be used to explore the relations of blocking and cyclogensis with local and global PV gradients; and (3) to study the time dependence of the local PV gradients and relate it to the PV index vacillation cycles observed in the PV index cycle.

Barcilon, Albert↗
NASA NTRS1991

Research highlights: June 1990 - May 1991

Linear instability calculations at MSFC have suggested that the Geophysical Fluid Flow Cell (GFFC) should exhibit classic baroclinic instability at accessible parameter settings. Interest was in the mechanisms of transition to temporal chaos and the evolution of spatio-temporal chaos. In order to understand more about such transitions, high resolution numerical experiments for the physically simplest model of two layer baroclinic instability were conducted. This model has the advantage that the numerical code is exponentially convergent and can be efficiently run for very long times, enabling the study of chaotic attractors without the often devastating effects of low-order trunction found in many previous studies. Numerical algorithms for implementing an empirical orthogonal function (EOF) analysis of the high resolution numerical results were completed. Under conditions of rapid rotation and relatively low differential heating, convection in a spherical shell takes place as columnar banana cells wrapped around the annular gap, but with axes oriented along the axis of rotation; these were clearly evident in the GFFC experiments. The results of recent numerical simulations of columnar convection and future research plans are presented.

Source record↗
NASA NTRS1991

Intraseasonal oscillations in the global atmosphere. I - Northern Hemisphere and tropics

Oscillatory modes in the Northern Hemisphere and in the tropics were examined systematically. The 700 mb heights were used to analyze extratropical oscillations, and the outgoing longwave radiation to study tropical oscillations in convection. All datasets were band-pass filtered to focus on the intraseasonal (IS) band of 10-120 days. Leading spatial patterns of variability were obtained by applying empirical orthogonal function analysis to these IS data. The leading principal components were subjected to singular spectrum analysis. In the Northern Hemisphere, there are two important modes of oscillation with periods near 48 and 23 days, respectively. The 48-day mode is the most important of the two. It has both traveling and standing components, and is dominated by a zonal wavenumber two. The 23-day mode has the spatial structure and propagation properties described by Branstator and by Kushnir (1987). In the tropics, the 40-50 day oscillation documented by Madden and Julian (1972), Weickmann (1983), Lau, and their colleagues, dominates the Indian and Pacific oceans from 60 deg E to the date line. From 170 deg W to 90 deg W, however, a 24-28 day oscillation is equally strong. The extratropical modes are often independent of, and sometimes lead, the tropical modes.

Ghil, Michael↗
NASA NTRS1991

Intraseasonal oscillations in the global atmosphere. II - Southern Hemisphere

A systematic examination of oscillatory modes in the global atmosphere is completed by studying 12 years of 500 mb geopotential heights in the Southern Hemisphere. The data were band-pass filtered to focus on intraseasonal (IS) phenomena, and spatial empirical orthogonal functions (EOFs) were obtained. The leading principal components were subjected to singular spectrum analysis in order to identify nonlinear IS oscillations with high statistical confidence. In the Southern Hemisphere, the dominant mode has a period of 23 days, with spatial patterns carried by the second and third winter EOF of the IS band. It has a zonal wavenumber-four structure. The 40-day mode is second, and is dominated by wavenumbers three and four, while a 16-day mode is too weak to separate its spatial behavior from the previous two. The IS dynamics in the Southern Hemisphere is more complex and dominated by shorter wavenumbers than the Northern Hemisphere. No statistically significant correlations between the Southern Hemisphere and the tropics or the Northern Hemisphere are apparent in the IS band.

Ghil, Michael↗
NASA NTRS1991

Phytoplankton pigment patterns and wind forcing off central California

Mesoscale variability in phytoplankton pigment distributions of central California during the spring-summer upwelling season are studied via a 4-yr time series of high-resolution coastal zone color scanner imagery. Empirical orthogonal functions are used to decompose the time series of spatial images into its dominant modes of variability. The coupling between wind forcing of the upper ocean and phytoplankton distribution on mesoscales is investigated. Wind forcing, in particular the curl of the wind stress, was found to play an important role in the distribution of phytoplankton pigment in the California Current. The spring transition varies in timing and intensity from year to year but appears to be a recurrent feature associated with the rapid onset of the upwelling-favorable winds. Although the underlying dynamics may be dominated by processes other than forcing by wind stress curl, it appears that curl may force the variability of the filaments and hence the pigment patterns.

Abbott, Mark R.↗
NASA NTRS1991

Tidal and atmospheric forcing of the upper ocean in the Gulf of California. I - Sea surface temperature variability

SST variability in the northern Gulf of California is examined on the basis of findings of two years of satellite infrared imagery (1984-1986). Empirical orthogonal functions of the temporal and spatial SST variance for 20 monthly mean images show that the dominant SST patterns are generated by spatially varying tidal mixing in the presence of seasonal heating and cooling. Atmospheric forcing of the northern gulf appears to occur over large spatial scales. Area-averaged SSTs for the Guaymas Basin, island region, and northern basin exhibit significant fluctuations which are highly correlated. These fluctuations in SST correspond to similar fluctuations in the air temperature which are related to synoptic weather events over the gulf. A regression analysis of the SST relative to the fortnightly tidal range shows that tidal mixing occurs over the sills in the island region as well as on the shallow northern shelf. Mixing over the sills occurs as a result of large breaking internal waves of internal hydraulic jumps which mix over water in the upper 300-500 m.

Paden, Cynthia A.↗
NASA NTRS1991

Adaptive filtering and maximum entropy spectra with application to changes in atmospheric angular momentum

The spectral resolution and statistical significance of a harmonic analysis obtained by low-order MEM can be improved by subjecting the data to an adaptive filter. This adaptive filter consists of projecting the data onto the leading temporal empirical orthogonal functions obtained from singular spectrum analysis (SSA). The combined SSA-MEM method is applied both to a synthetic time series and a time series of AAM data. The procedure is very effective when the background noise is white and less so when the background noise is red. The latter case obtains in the AAM data. Nevertheless, reliable evidence for intraseasonal and interannual oscillations in AAM is detected. The interannual periods include a quasi-biennial one and an LF one, of 5 years, both related to the El Nino/Southern Oscillation. In the intraseasonal band, separate oscillations of about 48.5 and 51 days are ascertained.

Penland, Cecile↗
NASA NTRS1992

Large-scale ocean-atmosphere interactions in a simplified coupled model of the midlatitude wintertime circulation

Midlatitude ocean-atmosphere interactions are studied in simulations from a simplified coupled model that includes synoptic-scale atmospheric variability, ocean current advection of SST, and air-sea heat exchange. Although theoretical dynamical ('identical twin') predictions using this model have shown that the SST anomalies in this model indeed influence the atmosphere, it is found here that standard cross correlation and empirical orthogonal function analyses of monthly mean model output yield the standard result, familiar from observational studies, that the atmosphere forces the ocean with little or no feedback. Therefore, these analyses are inconclusive and leave open the question of whether anomalous SST is influencing the atmosphere. In contrast, it is found that compositing strong warm events of model SST is a useful indicator of ocean forcing the atmosphere. Additional evidence is presented for oceanic influence on the atmosphere, namely, that ocean current advection appears to enhance the persistence of model SST anomalies through a feedback effect that is absent when only heat flux is allowed to influence SST anomaly evolution.

Miller, Arthur J.↗
NASA NTRS1992

Transport of the Norwegian Atlantic current as determined from satellite altimetry

Relatively warm and salty North Atlantic surface waters flow through the Faeroe-Shetland Channel into the higher latitudes of the Nordic Seas, preserving an ice-free winter environment for much of the exterior coast of northern Europe. This flow was monitored along the Norwegian coast using Geosat altimetry on two ascending arcs during the Exact Repeat Mission in 1987-1989. Concurrent undertrack CTD surveys were used to fix a reference surface for the altimeter-derived SSH anomalies, in effect creating time series of alongtrack surface dynamic height topographies. Climatologic CTD casts were then used, with empirical orthogonal function (EOF) analysis, to derive relationships between historical surface dynamic heights and vertical temperature and salinity profiles. Applying these EOF relationships to the altimeter signals, mean transports of volume, heat, and salt were calculated at approximately 2.9 Sverdrups, 8.1 x 10 exp 11 KCal/s and 1.0 x 10 exp 8 Kg/s, respectively. Maximum transports occurred in February/March and minimum in July/August.

Pistek, Pavel↗
NASA NTRS1992

Annual and interannual variations of earth-emitted radiation based on a 10-year data set

The method of empirical orthogonal functions (EOFs) was applied to a 10-yr data set of outgoing longwave radiation. Spherical harmonic functions are used as a basis set for producing equal area map results. The first EOF accounts for 66 percent of the variance. After that, each EOF accounts for only a small variance, forming a slowly converging series. The first two EOFs describe mainly the annual cycle. The third EOF is primarily the semiannual cycle although many other EOFs also contain significant semiannual parts. These results reaffirm those based on a shorter data set. In addition, a much stronger spring/fall mode was found in the central equatorial Pacific Ocean for the second EOF than was found earlier. The fourth EOF describes much of the 1976 to 1977 and 1982 to 1983 ENSO phenomena. There is typically a gap in the spectrum between a semiannual peak and the annual cycle for all but the first EOF. A semiannual OLR dipole straddles the Asian-Australian monsoon track.

Bess, T. D.↗
NASA NTRS1992

Lower stratosphere waves during 1986-1989 southern springs

Global NMC height analyses and Nimbus 7 TOMS Grid-T Version 6 data are used to investigate the horizontal structure of ozone and 50-mb height waves for the 1986-1989 springs of the Southern Hemisphere. Empirical orthogonal functions (EOFs) are obtained for the ozone and height data independently to identify the meridional structure of observed long waves as well as their propagation characteristics. The leading EOFs for both the ozone and 50-mb height waves exhibit wavenumber 1 and 2 patterns. The correlation coefficients between ozone and 50-mb height principal components are high. They indicate high/low ozone values associated with high/low values of 50-mb heights. This distribution is consistent with the advection of ozone by planetary waves south of the ozone maximum, as shown by a simple linear wave model. The observed total ozone amplitudes for waves 1 and 2 for most years are consistent with the total ozone predictions by the wave model.

Nogues-Paegle, Julia↗
NASA NTRS1992

The influence of the Alaskan Gyre on the coastal circulation in the Gulf of Alaska

The circulation of the northeast Pacific Ocean and the Gulf of Alaska is simulated by means of a reduced-gravity wind-driven model to study seasonal and interannual flow variability. The circulation in the NE Pacific is discussed emphasizing its ramifications for the physical domain, equations, and boundary conditions of the numerical model. The pseudostress fields used to drive the model are based on 20 years of data from the Comprehensive Ocean-Atmosphere Data Set and are analyzed with empirical orthogonal function analysis. The monthly stresses from 1986-89 are used to drive the model, and regional oceanographic features are reproduced including the Alaskan Gyre, Coastal Current, the Sitka eddy, and a severe cyclonic eddy. Comparisons with experimental data show that the high-resolution baroclinic model is valid and demonstrates the applicability of reduced-gravity models.

Heim, Paul K., II↗
NASA NTRS1992

Observation of mesoscale ocean features in the northeast Pacific using Geosat radar altimetry data

Mesoscale circulation in the Gulf of Alaska is studied by means of processed Geosat radar altimetry results with comparisons to observations of mesoscale eddies and surface circulation. The first set of Geosat data is treated by sea-surface height (SSH) binning in 1-deg latitude x 2-deg longitude boxes and analyzed by complex empirical orthogonal functions and 2D spectral analysis. The second set is taken from ascending Geosat tracks and analyzed as a time series. The Geosat data are compared to observational data including mesoscale eddies and fluctuations in mean surface circulation as well as sea-surface signals generated by numerical models. The data demonstrate the feasibility of a westward propagation of sea-level anomalies, and the Geosat SSH data are found to agree well with model solutions of seasonal variations in sea level in the northeast Pacific.

Matthews, Paul E.↗
NASA NTRS1992

Annual sea level variations in the southern tropical Indian Ocean from Geosat and shallow-water simulations

Sea level variations in the Indian Ocean north of 20 deg S are analyzed from Geosat satellite altimeter data in 1987-1988. These observed variations are compared with numerical simulations from a reduced-gravity model forced by observed winds over the same period. The first complex empirical orthogonal function of observed and simulated variations is an annual signal. For this signal, observations and simulations are highly correlated in both time and space. Off-equatorial sea level variations propagate westward and poleward as Rossby waves. The strongest annual variations occur in the southeastern tropical Indian Ocean. The maximum amplitude (about 12 cm) is located at about 90 deg E, 12 deg S, although the wind stress curl is weak there and east of it. The signal propagates from the eastern boundary to the southwest across almost all the basin.

Perigaud, Claire↗