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NASA NTRS1986

The 1984 solar oscillation program of the Mt. Wilson 60-foot tower

The instrumentation, data, and preliminary results from the summer, 1984, solar oscillation observing program which was carried out using the 60-foot tower telescope of the Mt. Wilson Observatory are described. This program was carried out with a dedicated solar oscillation observing system and obtained full-disk Dopplergrams every 40 seconds for up to 11 hours per day. Between June and September, 1984, observations were obtained with a Na magneto-optical filter on 90 different days. The data analysis has progressed to the point that spherical harmonic filter functions were employed to generate a few one-dimensional power spectra from a single day's observations.

Rhodes, Edward J., Jr.↗
NASA NTRS1986

Vertical structure of the wind field during the Special Observing Period I of the Global Weather Experiment

The vertical structure of the global atmosphere is analyzed for selected periods of the Special Observing Period I (SOP-I) for the Global Weather Experiment (GWE). The analysis consists of projection of the stream-function and velocity potential at 200 and 850 mb on spherical harmonics and of the wind and height fields on the normal modes of a linearized form of the primitive equations for a basic state at rest. The kinematic vertical structure is discussed in terms of correlation coefficients of the 200 mb and 850 mb winds and analysis of the internal and external normal modes of the primitive equations. The reliability of the results is checked by applying the same analysis methods to data sets obtained from three different institutions: Geophysical Fluid Dynamics Laboratory (GFDL), European Center for Medium Range Weather Forecasting (ECMWF), and Goddard Laboratory for the Atmospheres (GLA). It is found that, on a global basis, vertically reversing circulations are as important as the equivalent barotropic structures. For the verticaly reversing components, the gravity and mixed Rossby-gravity modes have contributions of the same order of magnitude as those of the Rossby modes in tropical latitudes.

Paegle, J. N.↗
NASA NTRS1987

Nimbus 7 earth radiation budget wide field of view climate data set improvement. I - The earth albedo from deconvolution of shortwave measurements

A deconvolution method for extracting the top of the atmosphere (TOA) mean, daily albedo field from a set of wide-FOV (WFOV) shortwave radiometer measurements is proposed. The method is based on constructing a synthetic measurement for each satellite observation. The albedo field is represented as a truncated series of spherical harmonic functions, and these linear equations are presented. Simulation studies were conducted to determine the sensitivity of the method. It is observed that a maximum of about 289 pieces of data can be extracted from a set of Nimbus 7 WFOV satellite measurements. The albedos derived using the deconvolution method are compared with albedos derived using the WFOV archival method; the developed albedo field achieved a 20 percent reduction in the global rms regional reflected flux density errors. The deconvolution method is applied to estimate the mean, daily average TOA albedo field for January 1983. A strong and extensive albedo maximum (0.42), which corresponds to the El Nino/Southern Oscillation event of 1982-1983, is detected over the south central Pacific Ocean.

Hucek, Richard R.↗
NASA NTRS1987

Solar oscillations - A method for deriving nonlinear effects

The frequencies of solar oscillations are so closely spaced that nonlinear interactions among modes are probable. The rate of interaction is proportional to an integral involving the eigenfunctions of the interacting modes, which usually are known only numerically. An approximation in which the eigenfunctions are strictly sinusoidal functions of a suitably defined radial variable, and the numerical details of stellar structure are banished to a coefficient in the integrand, are here explored. The physical assumptions are the same as in the asymptotic approximation of p- or g-modes. This method should allow a general investigation as to likely nonlinear interactions and which modes may participate in such interactions. The coupling of two p-modes by possible large-scale internal magnetic fields is introduced as an anisotropic pressure response to a displacement. Pairs of modes differing in frequency by less than the fraction magnetic/thermal pressure are strongly coupled, and energy appears to oscillate slowly between the two associated spherical harmonics. Potentially, upper limits may be derived for internal magnetic fields.

Wentzel, Donat G.↗
NASA NTRS1987

Atlas of wide-field-of-view outgoing longwave radiation derived from Nimbus 7 Earth radiation budget data set - November 1978 to October 1985

An atlas of monthly mean outgoing longwave radiation global contour maps and associated spherical harmonic coefficients is presented. The atlas contains 84 months of continuous data from November 1978 to October 1985. The data were derived from the second Earth radiation budget experiment, which was flown on the Nimbus 7 Sun-synchronous satellite in 1978. This data set is a companion set and extension to a similar report of the Nimbus 6 satellite. Together these two reports give a data set covering a 10 year time period and will be very valuable in studying different aspects of our changing climate over monthly, annual, and interannual scales in the time domain and over regional, zonal, and global scales in the spatial domain.

Bess, T. Dale↗
NASA NTRS1987

Photochemical ozone overburden correction

One-half of the total ozone column is predominantly under photochemical control under all conditions except polar winter. The other half is dynamically controlled. Since the photochemical forcing is phased with the solar declination and modulated by air temperature variation in the upper stratosphere and the dynamic forcing is tied to wave activity in the upper troposphere, the total ozone column is a mixture of the two drivers. If the total ozone is used to infer a property of the dynamic field, namely the tropopause height, it is necessary to correct for the photochemical variations. It should be possible to remove the photochemical component of the total ozone by using SBUV profile information along the orbital track as long as the spatial variations are low frequency. The column integral above the Umkehr levels in the lower stratosphere are examined to determine the level where the spatial variability decreases to the expected photochemical range to find an approximate dividing line between photochemical and dynamic control. Given this a spherical harmonic function will be fitted to the ozone field and subtracted from the TOMS total ozone field. This residual field will then be correlated with tropopause height to determine whether an improvement is obtained over the total ozone correlation.

Stefanick, Michael↗
NASA NTRS1988

Comparisons of global topographic/isostatic models to the Earth's observed gravity field

The Earth's gravitational potential, as described by a spherical harmonic expansion to degree 180, was compared to the potential implied by the topography and its isostatic compensation using five different hypothesis. Initially, series expressions for the Airy/Heiskanen topographic isostatic model were developed to the third order in terms of (h/R), where h is equivalent rock topography and R is a mean Earth radius. Using actual topographic developments for the Earth, it was found that the second and third terms of the expansion contributed 30 and 3 percents, of the first of the expansion. With these new equations it is possible to compute depths (D) of compensation, by degree, using 3 different criteria. The results show that the average depth implied by criterion I is 60 km while it is about 33 km for criteria 2 and 3 with smaller compensation depths at the higher degrees. Another model examined was related to the Vening-Meinesz regional hypothesis implemented in the spectral domain. Finally, oceanic and continental response functions were derived for the global data sets and comparisons made to locally determined values.

Rummel, Reiner↗
NASA NTRS1988

Non-Newtonian gravity or gravity anomalies?

Geophysical measurements of G differ from laboratory values, indicating that gravity may be non-Newtonian. A spherical harmonic formulation is presented for the variation of (Newtonian) gravity inside the Earth. Using the GEM-10B Earth Gravitational Field Model, it is shown that long-wavelength gravity anomalies, if not corrected, may masquerade as non-Newtonian gravity by providing significant influences on experimental observation of delta g/delta r and G. An apparent contradiction in other studies is also resolved: i.e., local densities appear in equations when average densities of layers seem to be called for.

Rubincam, David P.↗
NASA NTRS1987

Simultaneous stochastic inversion for geomagnetic main field and secular variation. I - A large-scale inverse problem

The method of stochastic inversion is extended to the simultaneous inversion of both main field and secular variation. In the present method, the time dependency is represented by an expansion in Legendre polynomials, resulting in a simple diagonal form for the a priori covariance matrix. The efficient preconditioned Broyden-Fletcher-Goldfarb-Shanno algorithm is used to solve the large system of equations resulting from expansion of the field spatially to spherical harmonic degree 14 and temporally to degree 8. Application of the method to observatory data spanning the 1900-1980 period results in a data fit of better than 30 nT, while providing temporally and spatially smoothly varying models of the magnetic field at the core-mantle boundary.

Bloxham, Jeremy↗
NASA NTRS1987

Error growth and predictability in operational ECMWF forecasts

The forecast error growth in the 100-day ECMWF data set of 10-day forecasts previously utilized by Lorenz (1982) is studied, separating the square of the error into systematic and random components. The nature of the errors is analyzed in the spherical harmonics wavenumber domain, and a new parametrization and its application to global errors are presented. The wavenumber dependence of the error growth is studied.

Dalcher, Amnon↗
NASA NTRS1987

Equipotential transformation of multipole systems to dipole systems

The vector sum of fields produced by a set of magnetic dipoles with different magnetic moments that are both tilted from the planetary spin axis and offset from the planetary center by different amounts can be used to completely represent a planetary magnetic field in the conventional form of spherical harmonic expansion. The scalar equipotential transformation analytically results in 24 equations that may subsequently be solved for the 24 adjustable parameters in dipole systems with the predetermined main dipole. Attention is given to this method's application to the Jovian magnetic field.

Wang, W. X.↗
NASA NTRS1987

A computer model of global thermospheric winds and temperatures

Output data from the NCAR Thermospheric GCM and a vector-spherical-harmonic (VSH) representation of the wind field are used in constructing a computer model of time-dependent global horizontal vector neutral wind and temperature fields at altitude 130-300 km. The formulation of the VSH model is explained in detail, and some typical results obtained with a preliminary version (applicable to December solstice at solar maximum) are presented graphically. Good agreement with DE-2 satellite measurements is demonstrated.

Killeen, T. L.↗
NASA NTRS1988

The quasi-rigid rotation of coronal magnetic fields

Spherical harmonic analysis and numerical simulations are used to study the rotational properties of the coronal magnetic field under the assumption that it can be approximated by a current-free extension of the photospheric field. It is found that the rotation rate in the outer corona is determined, principally, by coronal filtering, the global averages of the photospheric rotation rate, and ongoing source eruptions. The present model is able to account for observationally inferred rotational properties. It is suggested that the coronal rotation rate accelerates gradually due to the equatorward migration of sunspots, and that the 27-day equatorial period is approached toward sunspot minimum as the decaying photospheric flux becomes localized near the equator.

Wang, Y.-M.↗
NASA NTRS1987

A full simulation of a vortex ring

A three-dimensional spectral method is developed for the solution to the incompressible Navier-Stokes equations in an unbounded domain. The spectral method relies on divergence-free basis functions as proposed by Leonard (1981). The basis functions are formed using vector spherical harmonics and Jacobi polynomials together with a mapping in the radial direction. An axisymmetric code was written and is verified using an exact solution of the Stokes equations. Preliminary results for the evolution of a vortex ring according to the Navier-Stokes equations are presented.

Stanaway, S. K.↗
NASA NTRS1988

Frequencies of low-degree solar acoustic oscillations and the phase of the solar cycle

A study of the solar total irradiance data of the Active Cavity Radiometer Irradiance Monitor on the SMM satellite shows a small but formally significant shift in the frequencies of solar acoustic (p-mode) oscillations between the epochs of maximum and minimum solar activity. Specifically, the mean frequency of the strongest p-mode resonances of low spherical-harmonic degree (l = 0-2) is approximately 1.3 parts in 10,000 higher in 1980, near the time of sunspot maximum, than at around 1985, near sunspot minimum. The observed frequency shift may be an 11-yr effect but the precise mechanism is not clear.

Woodard, Martin F.↗
NASA NTRS1988

A new gravitational model for the earth from satellite tracking data - GEM-T1

A computation of a terrestrial gravitational field model called the Goddard Earth Model GEM-T1 is discussed and compared to previous models, including the GEM-L2. The software tools were redesigned for the model, allowing for the optimization of the technique of relative data weighting and model estimation used in GEM solutions. The GEM-T1 model provides a simultaneous solution for a gravity model in spherical harmonics complete to degree and order 36, a subset of 66 ocean tidal coefficients for the long-wavelength components of 12 major tides, and 5-day averaged earth rotation and polar motion parameters for the 1980 period on. GEM-T1 was derived from satellite tracking data acquired on 17 different satellites whose inclinations ranged from 15 degrees to polar. A simulation of the TOPEX/POSEIDON orbit using the covariances of the GEM-T1 model was made. Estimated radial error for the simulation was reduced to less than 30 cm rms.

Marsh, J. G.↗
NASA NTRS1988

Observed tidal braking in the earth/moon/sun system

The low degree and order terms in the spherical harmonic model of the tidal potential were observed through the perturbations which are induced on near-earth satellite orbital motions. Evaluations of tracking observations from 17 satellites and a GEM-T1 geopotential model were used in the tidal recovery which was made in the presence of over 600 long-wavelength coefficients from 32 major and minor tides. Wahr's earth tidal model was used as a basis for the recovery of the ocean tidal terms. Using this tidal model, the secular change in the moon's mean motion due to tidal dissipation was found to be -25.27 + or - 0.61 arcsec/century-squared. The estimation of lunar acceleration agreed with that observed from lunar laser ranging techniques (-24.9 + or - 1.0 arcsec/century-squared), with the corresponding tidal braking of earth's rotation being -5.98 + or - 0.22 X 10 to the -22 rad/second-squared. If the nontidal braking of the earth due to the observed secular change in the earth's second zonal harmonic is considered, satellite techniques yield a total value of the secular change in the earth's rotation rate of -4.69 + or - 0.36 X 10 to the -22 rad/second-squared.

Christodoulidis, D. C.↗
NASA NTRS1988

Dynamically supported geoid highs over hotspots - Observation and theory

Hotspots are associated with long wavelength geoid highs, an association that is even stronger when the geoid highs associated with subduction zones are removed. These associations are quantified by expanding the hotspot distribution in spherical harmonics and calculating correlation coefficients as a function of harmonic degree. The hotspot distribution spectrum is essentially white, with peaks at degrees 2 and 6. It is correlated positively with the slab residual geoid for degrees 2 to 6, with low seismic velocity in the lower mantle at degree 2, and with low seismic velocity in the upper mantle at degree 6. A variety of fluid mechanical models were tested for hotspots, including lithospheric delamination and hot plumes, by calculating their predicted dynamic geoid responses and comparing them to the observations. These models include the effects of temperature dependent rheology. The preferred hotspot model, based on observations of the geoid and seismic tomography, has plumes preferentially occurring in regions of large scale background temperature highs in a mantle with substantial viscosity increase with depth, although other models are possible.

Richards, Mark A.↗