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NASA NTRS1975

A numerical investigation of severe thunderstorm gust fronts

A numerical model was developed to simulate the evolution and structure of severe thunderstorm gust fronts. The model is a non-hydrostatic, fine resolution, cross-sectional primitive equation model. Two-dimensional horizontal and vertical equations of motion, the continuity equation, and the thermodynamic energy equation were utilized. It was shown that two dominant factors influencing gust front configuration are surface friction and the solenoidal field coincident with the front. It is suggested that solenoidal accelerations oppose the deceleration of surface friction. After a downdraft is initiated in the model, these opposing tendencies soon reach a balance and the gust front achieves a quasi-steady configuration. Thus, the experiments indicate that surface friction does not induce a cycle of front formation and collapse. In addition, the effect of evaporative cooling in producing a vigorous downdraft was parameterized by a local cooling function. Greater cooling in the downdraft results in a more intense gust front that exhibits stronger wind maximums and greater shears. The ambient air stability was shown to be an important factor influencing the depth of the cold outflow.

Mitchell, K. E.↗
NASA NTRS1976

Calculation of wind-driven surface currents in the North Atlantic Ocean

Calculations to simulate the wind driven near surface currents of the North Atlantic Ocean are described. The primitive equations were integrated on a finite difference grid with a horizontal resolution of 2.5 deg in longitude and latitude. The model ocean was homogeneous with a uniform depth of 100 m and with five levels in the vertical direction. A form of the rigid-lid approximation was applied. Generally, the computed surface current patterns agreed with observed currents. The development of a subsurface equatorial countercurrent was observed.

Rees, T. H.↗
NASA NTRS1976

Atmospheric analysis and prediction model development, volume 1

A set of hemispheric atmospheric analysis and prediction models was designed and tested. All programs were executed on either a 63 x 63 or 187 x 187 polar stereographic grid of the Northern Hemisphere. Parameters for objective analysis included sea surface temperature, sea level pressure, and twelve levels (from 1,000 to 100 millibars) of temperatures, heights, and winds. Stratospheric extensions (up to 10 millibars) were also provided. Four versions of a complex atmospheric prediction model, based on primitive equations, were programmed and tested. These models were executed on either the 63 x 63 or 187 x 187 grid, using either five or ten computational layers. The coarse-mesh (63 x 63) models were tested using real data for the period 21-23 April 1976. The fine-mesh (187 x 187) models were debugged, but insufficient computer resources precluded production tests. Preliminary test results for the 63 x 63 models are provided. Problem areas and proposed solutions are discussed.

Kesel, P. G.↗
NASA NTRS1976

Meteorological analysis models, volume 2

As part of the SEASAT program, two sets of analysis programs were developed. One set of programs produce 63 x 63 horizontal mesh analyses on a polar stereographic grid. The other set produces 187 x 187 third mesh analyses. The parameters analyzed include sea surface temperature, sea level pressure and twelve levels of upper air temperature, height and wind analyses. Both sets use operational data provided by a weather bureau. The analysis output is used to initialize the primitive equation forecast models also included.

Langland, R. A.↗
NASA NTRS1976

Prediction of convective activity using a system of parasitic-nested numerical models

A limited area, three dimensional, moist, primitive equation (PE) model is developed to test the sensitivity of quantitative precipitation forecasts to the initial relative humidity distribution. Special emphasis is placed on the squall-line region. To accomplish the desired goal, time dependent lateral boundaries and a general convective parameterization scheme suitable for mid-latitude systems were developed. The sequential plume convective parameterization scheme presented is designed to have the versatility necessary in mid-latitudes and to be applicable for short-range forecasts. The results indicate that the scheme is able to function in the frontally forced squallline region, in the gently rising altostratus region ahead of the approaching low center, and in the over-riding region ahead of the warm front. Three experiments are discussed.

Perkey, D. J.↗
NASA NTRS1976

A numerical study of the radiative-dynamic interaction in the stratosphere by a time-dependent zonal mean circulation model

The response of a zonal mean circulation model was compared to different heating functions used to simulate the interannual climate cycle. Two heating functions were used: A simple Newtonian heating function and a sophisticated heating function (Ramanathan, 1976). The emphasis was on the coupling between radiative transfer and the circulation in the stratosphere. The model was formulated in terms of primitive equations with 10 deg latitudinal resolution and 18 levels in pressure. Eddy transport of heat in the stratosphere was treated by the Reed and German (1965) formulation, while Stone's (1973) formulation is used in the troposphere. Momentum eddy fluxes are specified by climate statistics after Harwood and Pyle (1975). The model dynamics resulting from the two runs are compared to demonstrate the benefits of using detailed heating functions.

Turner, R. E.↗
NASA NTRS1977

Numerical simulation of the Gulf Stream and Mid-Ocean eddies

Oceanographic field measurements have revealed intense, transient mesoscale motions in many parts of the world ocean. The circulation of the western North Atlantic, considered in the present study as a rectangular basin, is simulated with a primitive equation model that has five levels and a horizontal grid size of 37 km. The model ocean is driven by a 2.5 gyre pattern of steady zonal wind stress and by a Newtonian-type surface heating. Two cases are considered: the first uses a Laplacian formulation for the subgrid-scale lateral diffusions of heat and momentum; the second uses a highly scale-selective biharmonic formulation for these diffusions. An analysis of the heat transport, in the biharmonic experiment, shows that the horizontal transport of heat by eddies is much larger than the subgrid-scale horizontal heat diffusion. In the Gulf Stream region, the eddy heat transport is comparable to the effect of a lateral diffusion coefficient of 10 to the 7th sq cm/s.

Semtner, A. J., Jr.↗
NASA NTRS1977

Updating prediction models by dynamical relaxation - An examination of the technique

A dynamical relaxation technique for updating prediction models is analyzed with the help of the linear and nonlinear barotropic primitive equations. It is assumed that a complete four-dimensional time history of some prescribed subset of the meteorological variables is known. The rate of adaptation of the flow variables toward the true state is determined for a linearized f-model, and for mid-latitude and equatorial beta-plane models. The results of the analysis are corroborated by numerical experiments with the nonlinear shallow-water equations.

Davies, H. C.↗
NASA NTRS1977

Atmospheric model development in support of SEASAT. Volume 2: Analysis models

As part of the SEASAT program of NASA, two sets of analysis programs were developed for the Jet Propulsion Laboratory. One set of programs produce 63 x 63 horizontal mesh analyses on a polar stereographic grid. The other set produces 187 x 187 third mesh analyses. The parameters analyzed include sea surface temperature, sea level pressure and twelve levels of upper air temperature, height and wind analyses. The analysis output is used to initialize the primitive equation forecast models.

Langland, R. A.↗
NASA NTRS1976

Atmospheric prediction model survey

As part of the SEASAT Satellite program of NASA, a survey of representative primitive equation atmospheric prediction models that exist in the world today was written for the Jet Propulsion Laboratory. Seventeen models developed by eleven different operational and research centers throughout the world are included in the survey. The surveys are tutorial in nature describing the features of the various models in a systematic manner.

Wellck, R. E.↗
NASA NTRS1978

Large eddy simulation of incompressible turbulent channel flow

The three-dimensional, time-dependent primitive equations of motion were numerically integrated for the case of turbulent channel flow. A partially implicit numerical method was developed. An important feature of this scheme is that the equation of continuity is solved directly. The residual field motions were simulated through an eddy viscosity model, while the large-scale field was obtained directly from the solution of the governing equations. An important portion of the initial velocity field was obtained from the solution of the linearized Navier-Stokes equations. The pseudospectral method was used for numerical differentiation in the horizontal directions, and second-order finite-difference schemes were used in the direction normal to the walls. The large eddy simulation technique is capable of reproducing some of the important features of wall-bounded turbulent flows. The resolvable portions of the root-mean square wall pressure fluctuations, pressure velocity-gradient correlations, and velocity pressure-gradient correlations are documented.

Moin, P.↗
NASA NTRS1978

Numerical solutions and laser-Doppler measurements of spin-up

The spin-up flow in a cylinder of homogeneous fluid has been examined both experimentally and numerically. A series of laser-Doppler measurements was made of the zonal flow over a range of Ekman numbers and Rossby numbers at various locations in the interior of the flow. These measurements exceed previous ones in accuracy. The weak inertial modes excited by the impulsive start are detectable. The numerical simulations used the primitive equations in axisymmetric form and employed finite-difference techniques on both constant and variable grids. The number of grid points necessary to resolve the Ekman layers was determined. A thorough comparison of the simulations and the experimental measurements is made which includes the details of the amplitude and frequency of the inertial modes. Agreement to within the experimental tolerance is achieved. Analytical results for conditions identical to those in the experiments are not available but some similar linear and nonlinear theories are also compared with the experiments.

Warn-Varnas, A.↗
NASA NTRS1977

Severe weather prediction studies

A numerical forecast model is described which uses three-dimensional primitive equations to predict the evolution of the wind, temperature and moisture fields along with the subsynoptic-scale convective activity. There are 15 vertical levels set on a longitude-latitude horizontal grid. In this study, the horizontal grid distance is 70 km (0.625 deg latitude and 0.816 deg longitude at 40 deg N) and the time step is 90 sec. Orography is included and terrain coordinates are adopted. The forecast model is used to test two tornado-producing storms with very different synoptic structures. A 12 hr forecast is carried out for both cases. The rms errors of the forecast indicate much smaller errors in the middle troposphere than in the lower troposphere. The results demonstrate that a rather fine-mesh limited-area numerical model is capable of providing a valuable short-range forecast of the circulation and the mesoscale precipitation features.

Chang, C.-B.↗
NASA NTRS1979

Middle atmosphere project. A semi-spectral numerical model for the large-scale stratospheric circulation

The complete model is a semispectral model in which the longitudinal dependence is represented by expansion in zonal harmonics while the latitude and height dependencies are represented by a finite difference grid. The model is based on the primitive equations in the log pressure coordinate system. The lower boundary of the model domain is set at the 100 mb level (i.e., near the tropopause) and the effects of tropospheric forcing are included in the lower boundary condition. The upper boundary is at approximately 96 km, and the latitudinal extent is either global or hemispheric. The basic differential equations and boundary conditions are outlined. The finite difference equations are described. The initial conditions are discussed and a sample calculation is presented. The FORTRAN code is given in the appendix.

Holton, J. R.↗
NASA NTRS1979

An isentropic and sigma coordinate hybrid numerical model - Model development and some initial tests

A solution is presented for matching boundary conditions across the interface of an isentropic and sigma coordinate hybrid model. A hybrid model based on the flux form of the primitive equations is developed which allows direct vertical exchange between the model domains, satisfies conservation principles with respect to transport processes, and maintains a smooth transition across the interface without need for artificial adjustment or parameterization schemes. The initial hybrid model simulations of a jet streak propagating in a zonal channel are used to test the feasibility of the hybrid model approach. High efficiency of the hybrid model is demonstrated.

Uccellini, L. W.↗
NASA NTRS1979

The response of an equatorial ocean to simple wind stress patterns. I - Model formulation and analytic results. II - Numerical results

A time-dependent, primitive equation, beta plane model that is two-dimensional in the horizontal has been developed to model wind-driven equatorial ocean circulation. A simple vertical structure consisting of two layers above the thermocline with the same constant density permits a steady-state undercurrent in the model. An analytical study of the linear dynamics of the model suggests that the addition of inertial effects is needed to simulate the undercurrent properly. Also, both linear and nonlinear dynamics of the model are investigated numerically. Such nonlinear response to wind stress as a strong eastward equatorial undercurrent and an intense eastward 'countercurrent' at three deg N are noted in the numerical results.

Cane, M. A.↗
NASA NTRS1979

Equatorial wave-mean flow interaction - A numerical study of the role of latitudinal shear

A time-dependent primitive equation model for an equatorial channel is used to assess the interaction of equatorial Kelvin and mixed Rossby-gravity waves with the mean flow. The proposed model involves a semiimplicit time-differencing scheme and a finite-difference grid in the meridional plane. It is shown that forced equatorial waves interact with mean flow to produce equatorial jets characterized by downward-moving westerly (Kelvin wave forcing) and easterly (mixed Rossby-gravity wave forcing) shear zones, respectively. For parameters characteristic of the observed waves in the equatorial stratosphere, the wave-mean flow interaction process always reduces the amplitude of any initial cross-equatorial mean wind shear. The mean flow profile tends to become symmetric about the equator as the interaction process continues.

Holton, J. R.↗
NASA NTRS1979

Geos 3 wave height measurements - An assessment during high sea state conditions in the North Atlantic

The sea state in the North Atlantic Ocean has been monitored in February, 1977 to obtain data for verification of Geos 3 radio altimeter wave form data. The altimeter sea state data were found to be in good agreement with in situ sea state measurements and with aircraft remote sensing measurements of wave height. The average difference between the supporting data and Geos 3 was 0.34 m, and the standard deviation 0.61 m. Contour maps of sea state constructed for large regions of the earth's oceans on the basis of Geos 3 altimeter measurements exhibited systematic differences from operationally available computerized maps. It is thought that the underestimation of significant wave height maxima in the operational maps and the underestimation of the speed of movement of oceanic cyclones may be due to basic errors in the output of atmospheric primitive-equation models. Because of the narrow swath width of the Geos-3 sensor, data from several satellite orbits must be combined to construct contour maps, leading to low values of significant wave heights.

Parsons, C. L.↗