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All sourcesNASA NTRSDOE OSTI
NASA NTRS1994

Preferred latitudes of the intertropical convergence zone

The latitude preference of the intertropical convergence zone (ITCZ) is examined on the basis of observations, theory, and a modeling analysis. Observations show that convection is enhanced at latitudes of about 4 deg to 10 deg relative to the equator, even in regions where the sea surface temperature (SST) is maximum on the equator. Both linear shallow-water theory and a moist primitive equation model suggest a new explanation for the off-equatorial latitude preference of the ITCZ that requires neither the existence of zonally propagating disturbances nor an off-equatorial maximum in SST. The shallow-water theory indicates that a finite-width, zonally oriented, midtropospheric heat source (i.e., an ITCZ) produces the greatest local low-level convergence when placed a finite distance away from the equator. This result suggests that an ITCZ is most likely to be supported via low-level convergence of moist energy when located at these "preferred" latitudes away from the equator. For a plausible range of heating widths and damping parameters, the theoretically predicted latitude is approximately equal to the observed position (s) of the ITCZ (s). Analysis with an axially symmetric, moist, primitive equation model indicates that when the latent heating field is allowed to be determined internally, a positive feedback develops between the midtropospheric latent heating and the low-level convergence, with the effect of enhancing the organization of convection at latitudes of about 4 deg to 12 deg. Numerical experiments show that (1) two peaks in convective precipitation develop straddling the equator when the SST maximum is located on the equator; (2) steady ITCZ-like structures form only when the SST maximum is located away from the equator; and (3) peaks in convection can develop away from the maximum in SST, with a particular preference for latitudes of about 4 deg to 12 deg, even in the ('cold') hemisphere without the SST maximum. The relationship between this mechanism and earlier theories is discussed, as are implications for the coupled ocean-atmosphere system and the roles played by midlevel latent heating and SST gradients in forcing the low-level atmospheric circulation in the tropics.

Waliser, Duane E.↗
NASA NTRS1991

Diagnostic evaluation of numerical model simulations using the tendency equation

A procedure is proposed to expand the diagnostic capabilities of the pressure tendency equation of a primitive equation NWP model by computing the pressure tendency in physical coordinates. The advantages of isolating the density advection as a diagnostic tool to understand pressure changes is shown. By simple thermodynamic arguments it is demonstrated that in areas of synoptic-scale cyclonic development, the vertically integrated density advection is more than sufficient to explain the depletion of mass over a growing depression. Consequently, the joint contribution of the net divergence and vertical motion opposes the pressure fall. This is illustrated for a case of rapid cyclogenesis in southern South America.

Jusem, Juan C.↗
NASA NTRS1987

An analysis of the vertical structure equation for arbitrary thermal profiles

The vertical structure equation is a singular Sturm-Liouville problem whose eigenfunctions describe the vertical dependence of the normal modes of the primitive equations linearized about a given thermal profile. The eigenvalues give the equivalent depths of the modes. The spectrum of the vertical structure equation and the appropriateness of various upper boundary conditions, both for arbitrary thermal profiles were studied. The results depend critically upon whether or not the thermal profile is such that the basic state atmosphere is bounded. In the case of a bounded atmosphere it is shown that the spectrum is always totally discrete, regardless of details of the thermal profile. For the barotropic equivalent depth, which corresponds to the lowest eigen value, upper and lower bounds which depend only on the surface temperature and the atmosphere height were obtained. All eigenfunctions are bounded, but always have unbounded first derivatives. It was proved that the commonly invoked upper boundary condition that vertical velocity must vanish as pressure tends to zero, as well as a number of alternative conditions, is well posed. It was concluded that the vertical structure equation always has a totally discrete spectrum under the assumptions implicit in the primitive equations.

Cohn, Stephen E.↗
NASA NTRS1989

An analysis of the vertical structure equation for arbitrary thermal profiles

The vertical structure equation is a singular Sturm-Liouville problem whose eigenfunctions describe the vertical dependence of the normal modes of the primitive equations linearized about a given thermal profile. The eigenvalues give the equivalent depths of the modes. The spectrum of the vertical structure equation and the appropriateness of various upper boundary conditions, both for arbitrary thermal profiles were studied. The results depend critically upon whether or not the thermal profile is such that the basic state atmosphere is bounded. In the case of a bounded atmosphere it is shown that the spectrum is always totally discrete, regardless of details of the thermal profile. For the barotropic equivalent depth, which corresponds to the lowest eigen value, upper and lower bounds which depend only on the surface temperature and the atmosphere height were obtained. All eigenfunctions are bounded, but always have unbounded first derivatives. It was proved that the commonly invoked upper boundary condition that vertical velocity must vanish as pressure tends to zero, as well as a number of alternative conditions, is well posed. It was concluded that the vertical structure equation always has a totally discrete spectrum under the assumptions implicit in the primitive equations.

Cohn, Stephen E.↗
NASA NTRS1993

Analyzing Martian winds and tracer concentrations using Mars Observer data

During the courses of a day, the Mars Observer spacecraft will acquire globally distributed profiles of the martian atmosphere. It is highly desirable that this data be assembled into synoptic weather maps (complete specifications of the atmospheric pressure, temperature, and winds at a given time), which can in turn be used as starting points in the study of many meteorological phenomena. Unfortunately, the special nature of the Mars Observer data presents several challenges above and beyond the usual difficult problem of data initialization. Mars Observer atmospheric data will consist almost exclusively of asynoptic vertical profiles of temperatures (or radiances) and pressures, whereas winds are generally in balance with horizontal gradients of these quantities (which will not be observed). It will therefore be necessary to resort to dynamical models to analyze the wind fields. As a rule, data assimilation into atmospheric models can result in the generation of spurious gravity waves, so special steps must be taken to suppress these. In addition, the asynoptic nature of the data will require a four-dimensional (space and time) data assimilation scheme. The problem is to find a full set of meteorological fields (winds and temperatures) such that, when marched forward in time in the model, they achieve a best fit (in the weighted least-squares sense) to the data. The proposed solution is to develop a model especially for the Mars Observer data assimilation problem. Gravity waves are filtered from the model by eliminating all divergence terms from the prognostic divergence equation. This leaves a diagnostic gradient wind relation between the rotational wind and the temperature field. The divergent wind is diagnosed as the wind required to maintain the gradient wind balance in the presence of the diabatic heating. The primitive equations of atmospheric dynamics (with three principal dependent variables) are thus reduced to a simpler system with a single prognostic equation for temperature - the variable that will be best observed. (This balance system was apparently first derived by Charney as a first-order Rossby number expansion of the equations of motion). Experience with a full primitive equation model of the martian atmosphere indicates that a further simplification is possible: at least for short-term integrations, the model can be linearized about the zonally symmetric basic state.

Houben, Howard C.↗
NASA NTRS1984

Research Relative to High Spatial Resolution Passive Microwave Sounding Systems

Methods to obtain high resolution passive microwave weather observations, and understanding of their probable impact on numerical weather prediction accuracy were investigated. The development of synthetic aperture concepts for geosynchronous passive microwave sounders were studied. The effects of clouds, precipitation, surface phenomena, and atmospheric thermal fine structure on a scale of several kilometers were examined. High resolution passive microwave sounders (e.g., AMSU) with an increased number of channels will produce initialization data for numerical weather prediction (NWP) models with both increased spatial resolution and coverage. The development of statistical models for error growth in high resolution primitive equation NWP models which permit the consequences of various observing system alternatives, including sensors and assimilation times and procedures is discussed. A high resolution three dimensional primitive equation NWP model to determine parameters in an error growth model similar to that formulated by Lorenz, but with more degrees of freedom is utilized.

Staelin, D. H.↗
NASA NTRS1988

Balanced and unbalanced upper-level frontogenesis

The impacts of vertical shear in the cross-front component of the geostrophic wind, and of its implied along-front temperature gradient, on frontogenesis at upper levels were investigated using a hierarchy of three dynamical models based on the Keyser and Pecnick (1985) primitive-equation model. The three models are (in order of decreasing sophistication) the anelastic (AN), the geostrophic momentum (GM), and the quasi-geostsrophic (QG) approximations to the primitive equations. Intercomparison of the broad-scale structure of the upper-level jet-fronts as described by the AN and GM models showed close agreement. In contrast, the QG model exhibited marked differences with its AN counterpart, which became more pronounced with increased geostrophic wind.

Reeder, Michael J.↗
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 NTRS1983

A linear analysis of the transition curve for the baroclinic annulus

A primitive equation linear model is shown to be capable of quantitatively predicting the neutral curve for a baroclinic annulus. Flows unstable to small nonaxisymmetric perturbations are assumed to lie on the nonaxisymmetric side of a transition curve, while the stable flows are on the axisymmetric side. The stability in the presence of perturbations is tested with linearized hydrostatic primitive equations. Attention is given to the fastest growing eigenmodes, demonstrating that the linear and nonlinear wave have similar structures at a particular point in the nonaxisymmetric regime. All the waves are similar to the Eddy wave except at the extreme to the transition curve, where the waves maintain little structure with height. The eddy kinetic energy is baroclinic with a potential energy suppresed by the large static stability of the basic state. Eddy dissipation is noted to be significant near all boundaries.

Miller, T. L.↗
NASA NTRS2003

Collaborative Research: Atlantic Ocean Tropical/Subtropical Processes from Seasonal to Decadal Time Scales: Model/Data, Model/Model Comparison and Model/Data Synthesis Through Assimilation

The effort of this first year of research has been focused on the assimilation of TOPEX/Poseidon altimetric data into a primitive equation model of the Atlantic tropical/subtropical circulation. A reduced-rank, stationary Kalman filter has been constructed to assimilate the altimetric sea surface height anomaly (SHA) into the model. The goal is to assess how the inter-hemispheric transports between the Atlantic subtropics and tropics are affected by the assimilation and how the subsurface thermocline structure , and its variability ,is dynamically constrained by the SHA. The model is a reduced-gravity primitive equation GCM of the upper Atlantic Ocean between 30 S and 30 N. The assimilation scheme is an approximation to the extended Kalman filter in which the error covariances of the state estimates are calculated only in a reduced- dimension subspace. The subspace is defined by the leading empirical orthogonal functions calculated from an unconstrained model calculation. Both an identical twin experiment using simulated SHA observations and assimilation of the real TOPEX data were performed. Results from the twin experiments demonstrate the ability of the method to constrain the ocean circulation and the subsurface temperature structure. The impact on the subsurface temperature structure of TOPEX assimilation was assessed using data from expandable bathythermographs. This showed a substantial improvement in the estimated temperature variability only within 13 degrees in latitude around the equator. The impact of TOPEX SHA assimilation on zonally integrated meridional transport across different latitudes was also estimated. Again within 13 degrees from the equator both the mean amplitude and interannual variability of the surface and subsurface transports were significantly enhanced, while the transports were insensitive to the assimilation in the subtropics.

Malannotte-Rizzoli, Paola↗
NASA NTRS1998

EOS Interdisciplinary Investigation: Observational and Modeling Studies of Radiative, Chemical, and Dynamical Interactions in the Earth's Atmosphere

A 3-dimensional model of atmospheric dynamics and photochemistry has been developed from the primitive equations in isentropic coordinates. The model extends from the upper troposphere through the middle atmosphere and is driven by observed dynamical and chemical structure in the troposphere. The model's formulation is entirely spectral: Horizontal structure is represented in terms of vector Hough functions, which explicitly partition the motion into its rotational and divergent components. This formulation enables the model's computational performance to be increased dramatically by filtering high-frequency gravity waves, which do not affect PV conservation. Vertical structure is represented in terms of eigenfunctions that follow from the primitive equations in isentropic coordinates. The model's fully spectral formulation enables scale-selective dissipation, necessary for numerical stability, to be applied at 6th order-in all 3 coordinate directions. This feature leaves all but the shortest vertical scales undamped and, consequently, allows potential vorticity and chemical tracers to be conserved quite accurately, distinctly better than in the model's layered counterpart. These dynamical features are complemented by a basic but fairly complete treatment of gas phase photochemistry, which accounts for some 48 chemical species, diurnally-varying SW absorption by O2 and O3, and LW cooling calculated via a detailed band calculation of radiative transfer. Driven by observed tropospheric structure, the 3D model reproduces observed structure in the middle atmosphere, inclusive of transport by the Brewer-Dobson circulation and accompanying chemical variations. Calculated residual motion is consistent with diabatic cooling rates, poleward transport, and descent in the polar night derived from satellite measurements of chemical tracers made from LIMS, SAGE, and UARS. The model also reproduces the observed structure of chemical species like O3, HNO3, and ClO. At the same time, it provides a respectable 3D simulation of the wintertime increase of midlatitude total ozone, as well as its geographical structure observed by Nimbus-7 TOMS. The 3D model has been used to explore the origin of diabatic upwelling in the tropical lower stratosphere, which has been related to planetary wave absorption in the winter- time stratosphere, as well as to influences from tropospheric convection at the tropical tropopause.

Salby, Murry L.↗
NASA NTRS1993

Multi-grid domain decomposition approach for solution of Navier-Stokes equations in primitive variable form

The new multigrid (or adaptive) pseudospectral element method was carried out for the solution of incompressible flow in terms of primitive variable formulation. The desired features of the proposed method include the following: (1) the ability to treat complex geometry; (2) high resolution adapted in the interesting areas; (3) requires minimal working space; and (4) effective in a multiprocessing environment. The approach for flow problems, complex geometry or not, is to first divide the computational domain into a number of fine-grid and coarse-grid subdomains with the inter-overlapping area. Next, it is necessary to implement the Schwarz alternating procedure (SAP) to exchange the data among subdomains, where the coarse-grid correction is used to remove the high frequency error that occurs when the data interpolation from the fine-grid subdomain to the coarse-grid subdomain is conducted. The strategy behind the coarse-grid correction is to adopt the operator of the divergence of the velocity field, which intrinsically links the pressure equation, into this process. The solution of each subdomain can be efficiently solved by the direct (or iterative) eigenfunction expansion technique with the least storage requirement, i.e. O(N(exp 3)) in 3-D and O(N(exp 2)) in 2-D. Numerical results of both driven cavity and jet flow will be presented in the paper to account for the versatility of the proposed method.

Ku, Hwar-Ching↗
DOE OSTI2023

A Perturbative Solution for Nonlinear Stratified Upwelling over a Frictional Slope

Abstract A perturbative solution of simplified primitive equations for nonlinear weakly stratified upwelling over a frictional slope is found that resolves the vertical structure of velocity fields and can satisfy Ertel’s potential vorticity conservation in the stratified inviscid interior. The solution uses assumptions consistent with the model proposed by Lentz and Chapman, including a steady-state, constant cross-shore density gradient, no alongshore gradients, laterally inviscid, and consideration of cross-shore advection of alongshore momentum. The solution resolves the vertical structure of velocity fields (including subsurface maxima of compensational flow, not resolved by Lentz and Chapman) and can satisfy Ertel’s potential vorticity conservation in the stratified inviscid interior. The dynamics are similar to Lentz and Chapman; bottom stress balances alongshore wind stress in a homogeneous density ocean and is replaced by nonlinear cross-shore transport of alongshore momentum as the Burger number (S=αN/f, whereα,N, andfare the bottom slope, buoyancy frequency, Coriolis frequency, respectively) increases. When the solution uses the empirical relation between cross-shore and vertical density gradients proposed by Lentz and Chapman, vorticity conservation is not satisfied and the nonlinear momentum transport estimated by the solution linearly increases withS, asymptotically matching Lentz and Chapman forS< 1. When the solution conserves interior potential vorticity, the momentum transport is proportional toS 2 forS< 1 and is in better agreement with numerical simulations.

Oceanography↗
NASA NTRS1981

An explicit mixed numerical method for mesoscale model

A mixed numerical method has been developed for mesoscale models. The technique consists of a forward difference scheme for time tendency terms, an upstream scheme for advective terms, and a central scheme for the other terms in a physical system. It is shown that the mixed method is conditionally stable and highly accurate for approximating the system of either shallow-water equations in one dimension or primitive equations in three dimensions. Since the technique is explicit and two time level, it conserves computer and programming resources.

Hsu, H.-M.↗
NASA NTRS1985

Marching iterative methods for the parabolized and thin layer Navier-Stokes equations

Downstream marching iterative schemes for the solution of the Parabolized or Thin Layer (PNS or TL) Navier-Stokes equations are described. Modifications of the primitive equation global relaxation sweep procedure result in efficient second-order marching schemes. These schemes take full account of the reduced order of the approximate equations as they behave like the SLOR for a single elliptic equation. The improved smoothing properties permit the introduction of Multi-Grid acceleration. The proposed algorithm is essentially Reynolds number independent and therefore can be applied to the solution of the subsonic Euler equations. The convergence rates are similar to those obtained by the Multi-Grid solution of a single elliptic equation; the storage is also comparable as only the pressure has to be stored on all levels. Extensions to three-dimensional and compressible subsonic flows are discussed. Numerical results are presented.

Israeli, M.↗
NASA NTRS1985

Marching iterative methods for the Parabolized and Thin Layer Navier-Stokes equations

Downstream marching iterative schemes for the solution of the Parabolized or Thin Layer (PNS or TL) Navier-Stokes equations are described. Modifications of the primitive equation global relaxation sweep procedure result in efficient second-order marching schemes. These schemes take full account of the reduced order of the approximate equations as they behave like the SLOR for a single elliptic equation. The improved smoothing properties permit the introduction of Multi-Grid acceleration. The proposed algorithm is essentially Reynolds number independent and therefore can be applied to the solution of the subsonic Euler equations. The convergence rates are similar to those obtained by the Multi-Grid solution of a single elliptic equation; the storage is also comparable as only the pressure has to be stored on all levels. Extensions to three-dimensional and compressible subsonic flows are discussed. Numerical results are presented.

Israeli, M.↗
NASA NTRS1985

A numerical study of global axisymmetric states and their stability to quasi-geostrophic disturbances

A steady, axisymmetric model of the general circulation is developed as a basis for climate stability studies. The model includes the effects of heating, rotation, and internal friction, but neglects topography. It is assumed that the axisymmetric flow may be modeled by making the Boussinesq and deep convection approximations. The hydrostatic assumption is not made, thus permitting the advective terms to be included in the vertical equation of motion. The initial set of five primitive equations is reduced to three equations in terms of the zonal velocity, meridional streamfunction, and the potential temperature perturbation. The application of the Boussinesq, deep convection, and quasi-geostrophic assumptions limits the ranges of the heating and rotation rates. For values not too far from typical atmospheric values, the model produces a stability boundary separating Hadley from Rossby flow. The boundary is characterized by a particular value of vertical wind shear, which suggests that baroclinic instability is the primary mechanism for the loss of stability. The initial growth rates are largest for longitudinal waves 4-7, also in agreement with studies of baroclinic instability.

Henderson, H. W.↗
DOE OSTI2024

Topological Signature of Stratospheric Poincaré-Gravity Waves

The rotation of Earth breaks time-reversal and reflection symmetries in an opposite sense north and south of the equator, leading to a topological origin for certain atmospheric and oceanic equatorial waves. Away from the equator, the rotating shallow-water and stably stratified primitive equations exhibit Poincaré inertia–gravity waves that have nontrivial topology as evidenced by their strict superinertial time scale and a phase singularity in frequency–wavevector space. This nontrivial topology then predicts, via the principle of bulk-interface correspondence, the existence of two equatorial waves along the equatorial interface, the Kelvin and Yanai waves. To directly test the nontrivial topology of Poincaré-gravity waves in observations, we examine ERA5 data and study cross correlations between the wind velocity and geopotential height of the midlatitude stratosphere at the 50 hPa height. We find the predicted vortex and antivortex in the relative phase of the geopotential height and velocity at the high frequencies of the waves. By contrast, lower-frequency planetary waves are found to have trivial topology also as expected from theory. These results demonstrate a new way to understand stratospheric waves and provide a new qualitative tool to investigate waves in other components of the climate system.

54 ENVIRONMENTAL SCIENCES↗