Model Grid Points Research Articles

Experimental study of transalpine transport of trace effluents: a comparison with synoptic trajectories of airflow

It is aim of this work to acquire information useful to understand the trasborder transport of atmospheric trace elements passing through the Alps. To this end it is necessary to know with a good accuracy the atmospheric movements and their thermodynamic structure at the synoptic scale. With these objects in view, from the one hand a measuring campaign on the Western Alps (Sestrieres Pass) has been performed, during which the concentration of some gaseous constituents of the atmosphere (O3, NO x , SO2) and thermodynamic structure of the air masses which carried them have been measured; on the other hand, synoptic air trajectoris (based on the Reading ECMWF data) passing through that measuring station have been computed. Such calculations have been carried out by two algorithms: the first one computes the 3D air mass trajectory on the ground of the three wind velocity components only (which are known on the Reading model grid points). The second one behaves as the first one as far as the horizontal movement is concerned, but compels the atmosphere to move along surfaces of equal pseudopotential temperature (isentropic surface) in the vertical plane.

Valley Winds and the Diurnal Circulation over Plateaus

Abstract The role of valley winds in the diurnal circulation of large-scale mountain massifs like the Tibetan Plateau is investigated. We consider a circular plateau with radial valleys leading to the surrounding lowlands. A low-resolution grid point model is used to compute the diurnal circulation above the plateau and in the valleys. The circulation is driven by the diurnal variation of the surface temperature. The model produces valley winds and a diurnal circulation above the plateau in qualitative agreement with observations. The inflow towards the plateau in the valleys is strongest in the afternoon. There is nocturnal outflow. During the day, a low pressure system with a corresponding cyclonic circulation around the massif resides at the plateau and we find high pressure well above it. At night it is the reverse. It is demonstrated that the valley winds contribute significantly to the fluxes of mass and moisture in the plateau's diurnal circulation. Linear calculations for a neutrally stratified at...

The Use and Interpretation of Numerical Weather Prediction Model Output in Identifying Synoptic-Scale Environments Associated with Development of Mesoscale Convective Systems

Abstract An experiment is reported in which derived diagnostic parameters computed from Limited-area Fine-Mesh (LFM) model gridpoint data were examined to determine subjectively whether their availability in real time would assist the forecaster in interpreting and understanding the model's forecast of the weather. Specifically, model products thought to relate to the development of mesoscale convective weather systems (MCSs) were combined into a composite forecast and compared with the standard ensemble of LFM products for 25 episodes of significant convective activity. An objective verification of the LFM forecasts themselves was not attempted. Both 12 and 24 h forecasts from the 1200 UTC run were considered. In a majority of cases, it was evident that derived diagnostic gridpoint data added information about parameter patterns and values important to MCS development that was not obvious from viewing the conventional model products alone. Two case studies demonstrate how information about 850 mb moistur...

Semi-Lagrangian Advection on a Gaussian Grid

The treatment of advection is related to the stability, accuracy and efficiency of models used in numerical weather prediction. In order to remain stable, conventional Eulerian advection schemes must respect a Courant-Friedrichs-Lewy (CFL) criterion, which limits the size of the time step that can be used in conjunction with a given spatial resolution. In recent years, tests with gridpoint models have shown that semi-Lagrangian schemes permit the use of large time steps (roughly three to six times those permitted by the CFL criterion for the corresponding Eulerian models), without reducing the accuracy of the forecasts. This leads to improved model efficiency, since fewer steps are needed to complete the forecast. Can similar results be achieved in spectral models? This paper examines the semi-Lagrangian treatment of advection on the Gaussian grid used in spectral models. Interpolating and noninterpolating versions of the semi-Lagrangian scheme are applied to the problem of solid body rotation on the globe, and their performance is compared with that of an Eulerian spectral treatment. It is shown that the semi-Lagrangian models produce stable, accurate integrations using time steps that far exceed the CFL limit for the Eulerian spectral model.

The effect of vertical and slantwise convection on the simulation of polar lows

Two polar low cases during February 1984 are simulated with a mesoscale limited area grid point model. The role of released latent heat on different scales as a driving mechanism for polar lows is investigated by studying a series of prognoses with condensation schemes for the large-, meso-, and cloud-scales. For the mesoscales, a parameterization method for slantwise convection is developed and applied. The simulations show that release of latent heat from condensation is crucial in order to obtain sufficiently strong developments. When working alone, large-scale condensation leads to unstable lapse rates and to fast developments. Convection shifts the area of maximum heating upwards and stabilizes the atmosphere, while slantwise convection in addition spreads the heating horizontally away from the surface disturbance. The large-scale response to parameterized slantwise convection is to stabilize the model atmosphere with respect to symmetric instability, to shift areas of ascending motion towards sloping absolute momentum surfaces and to enhance low-level winds. DOI: 10.1111/j.1600-0870.1987.tb00313.x

Simple models of the valley-plain circulation Part II: Flow resolving model

In extension of the work presented in the first part of this paper a simple two-level grid point model for valley-plain flow is described where basic horizontal flow structures can be resolved. Except for the increased horizontal resolution this flow resolving model (FR-model) bears strong resemblance to the MR-model discussed in the first part.

Elimination of the Helmholtz Equation Associated with the Semi-Implicit Scheme in a Grid Point Model of the Shallow Water Equations

Abstract A modification is introduced in a semi-implicit version of a grid point model of the shallow water equations. The new model is simpler, runs one-third, and after 5 days of integration, the forecasts differ by less than 1 m.

時間的に変化する境界を持つ局地スペクトルモデルとその多層プリミティブモデルへの応用

A spectral limited-area primitive-equation model with a time-dependent lateral boundary condition is described.The model is nested in one way to a low resolution model.A spectral representation of the horizontal fields of prognostic variables is performed by introducing a modified double Fourier series.This series is composed of the usual orthogonal double Fourier series, that is suitable for prediction in the limited-area with a free-slip wall boundary condition, and a few additional bases by which the boundary condition which does not belong to the wall condition will be satisfied.Fluxes of mass, momentum, energy, etc.across the boundary can be specified using the additional bases.The proposed spectral method prescribes the amplitude of the additional bases, using the historical data from a coarse-mesh model forecast.The model predicts the amplitude of only the orthogonal bases that satisfy the wall boundary condition.A boundary relaxation technique is incorporated in order to reduce the amplitude of a spurious solution near the boundary due to ill-posed lateral boundary condition.A one-dimensional, linear advection equation is integrated by the present spectral method and by a grid-point method.The comparison of these two methods reveals that the spectral method give far better results than those of the grid point method.This is mainly due to the improved accuracy in estimating horizontal derivatives in the spectral method i.e., the computational dispersion and the systematic phase error that are unavoidable in the grid-point method are completely excluded in the spectral method.The spectral formulation of a limited-area model is applied to the Japan Meteorological Agency (JMA) operational grid-point 12-level fine-mesh limited-area model (12L-FLM; March, 1983 -) and the forecasts of the two 12L-FLMs are compared.The spectral 12L-FLM almost perfectly duplicates the forecast of the grid-point 12L-FLM for relatively large-scale disturbances, within the resolution limit of the latter.However, the forecast of the spectral 12L-FLM is superior to the grid-point model for relatively small-scale disturbances.The compared case includes a well-organized intense typhoon in the initial field.The horizontal scale of the typhoon is almost marginal to be resolved by the grid-point 12L-FLM.The predicted typhoon by the spectral model is more realistically intense and symmetric than that by the grid-point model.The amount of computation required by the spectral 12L-FLM, whose transform grid is the same as that of the grid-point model, is 20∼30 per cent larger than the amount required by the grid-point 12L-FLM.We conclude from this that the computational economy of the spectral 12L-FLM is practically superior to the grid-point 12L-FLM, since the effective resolution of the spectral model is about 1.5times better than the grid-point model.We plan to apply the spectral method to the next operational limited-area model in JMA.

Numerical experiments on the genesis of vortices over the Qinghai-Tibet plateau

The formation of a vortex and shear line over the Qinghai-Tibet Plateau (QTP) was investigated with numerical experiments using the ECMWF grid point model. The case chosen occurred between 24 and 26 July, 1982, when the south-west monsoon invaded the QTP and a vortex developed. The correct simulation of the vortex in the model shows that it is possible to predict the atmospheric circulation over the QTP and the consequent weather over China. When the simulation was rerun with a dry model (i.e., without the release of latent heat), it was found that only a weak vortex formed. This shows that the release of latent heat is an extremely important factor in the development of the vortex over the QTP, and confirms earlier diagnostic and synoptic studies. The surface sensible heat fluxes, large near the northern and southern flanks of the QTP, appear to have a damping effect on the formation of the vortex; i.e., the vortex was greatly intensified in their absence. It was also found that the intensity of the vortex was dependent upon the height of the QTP: when the mountain height was reduced, the westerly trough invaded the QTP and no vortex formed at 500 mb; when it was increased, the south-west monsoon travelled along the southern boundary of the QTP and intensified the low-level jet south of the vortex area. The results of a 48-h integration with a fine-mesh model (resolution 0.5° of latitude and longitude) showed an improvement in forecasting the location of the vortex with respect to the coarse-mesh model (1.875° of latitude and longitude). However, when compared with the coarse-mesh analysis, the intensity of the vortex was overpredicted. This may be due to mesoscale orographic forcing and exaggerated latent heating. DOI: 10.1111/j.1600-0870.1986.tb00468.x

Transilient Turbulence Theory. Part III: Bulk Dispersion Rate and Numerical Stability

Abstract Even though a continuum of mixing parameters γ(t, z, ζ) is used in transilient turbulence theory to describe the effects of many superimposed eddy sizes (ζ) on the mean field at height z, the overall bulk dispersive rate at any height can be measured by one number, N2(z). By utilizing second moment measures of dispersion, it is shown theoretically, for various special cases that the variance of tract position, σs2, is given by σz2(z, t = N2(z)t, where N2(z) = ∫ ζ2γ(z, ζ)dζ. An analogous expression for N2(z) is derived for the discrete version of transilient theory, as can be used for grid point models. These bulk dispersive rates can easily be compared to eddy diffusivity, K(z), because the variance of tracer position for K theory is known to be σs2(z, t) = 2K(z)t. The discrete version of transilient turbulence theory is shown to be absolutely numerically stable, regardless of the timestep size or the grid point spacing. In addition, it is shown how the values of the discrete transilient coeffici...

A primitive equation spectral model for study of planetary-scale atmospheric flow

The developments in numercial modelling for the atmosphere in recent years have shown that the spectral models are well suited for general circulation studies of the planetary-scale atmosphere. The use of transform method developed during last decade has made the spectral models comparable in computational speed with the grid point models.
 A global primitive equation model using spectral formulation is under development in the India Meteorological Department. The spectral representation is in terms of a truncated series of surface spherical harmonic functions. The computational facllitiesavaila1Jle at present do not perlt1it the development of a high-resolution model. The horizontal resolution, therefore, is limited to six Fourier waves in the zonal direction, and six zeros of Legendre functions in the meridional direction. In the vertical, the model has three layers in sigma coordinate.
 The model is in Its early stage of development. The model formulation, the results of some experiments performed with It and the future development plans are discussed in this paper.

Prediction of a typhoon using a fine-mesh NWP model

The ECMWF operational grid point model (with a resolution of 1.875° of latitude and longitude) and its limited area version (with a resolution of !0.47° of latitude and longitude) with boundary values from the global model have been used to study the simulation of the typhoon Tip. The fine-mesh model was capable of simulating the main structural features of the typhoon and predicting a fall in central pressure of 60 mb in 3 days. The structure of the forecast typhoon, with a warm core (maximum potential temperature anomaly 17 K). intense swirling wind (maximum 55 m s -1 at 850 mb) and spiralling precipitation patterns is characteristic of a tropical cyclone. Comparison with the lower resolution forecast shows that the horizontal resolution is a determining factor in predicting not only the structure and intensity but even the movement of these vortices. However, an accurate and refined initial analysis is considered to be a prerequisite for a correct forecast of this phenomenon. DOI: 10.1111/j.1600-0870.1985.tb00273.x

Systematic errors in the behaviour of cyclones in the ECMWF operational models

Systematic errors in the forecasts (up to 10 days) of cyclones over the north Atlantic and Europe by the ECMWF operational grid point model (N48) for the 1981–82 winter seasons are described, and some corresponding results for the ECMWF operational spectral model (T63) for the 1983–84 winter season are shown. Statistics for the cyclone tracks, central pressure, deepening rates, etc., are given. The forecasts from the grid point model tend to displace the cyclone tracks towards the south, especially after day 4, except near Newfoundland where a northward displacement is found. The corresponding errors are reduced in the spectral model. A systematic phase error is evident in the grid point model with the waves being too slow, usually in the developing stages of cyclones. This error is also apparent for the fast moving cyclones in the spectral model. For the grid point model, the forecast deepening and filling rates are less than those observed. However, the deepening rate is more realistic in the spectral model, though the filling rate is still underestimated. For both models the horizontal scale of the cyclones is too small during the first 2 or 3 days, especially in the forecasts started from several days prior to the day on which the cyclone was generated; during the later stages of cyclone development, the scale is too large. In comparing these errors to similar errors documented for other numerical models, some hypotheses are discussed about their likely causes. DOI: 10.1111/j.1600-0870.1985.tb00429.x

A three-dimensional numerical study of turbulence in homogeneous fluids

Results are reported from computations of homogeneous, nearly isotropic turbulence using a low resolution three-dimensional numerical model with subgrid-scale closure. Both the nonlinear eddy viscosity closure of Smagorinsky and a modified second-order closure involving solution of a prognostic equation for the subgrid-scale kinetic energy are tested in a 20 3 grid-point model. A higher resolution 32 3 model is exercised to examine the effects of changes in model constants and in grid-point resolution. It is shown, based on comparisons of the turbulence energy spectra, that calculations using the nonlinear eddy viscosity formulation are extremely sensitive to variations in the constant. It is also concluded that little is to be gained from the use of second-order closure in problems where stratification is unimportant. This is not inconsistent with results from a previous study by the authors of thermal convection in the planetary boundary layer. From that study it was concluded that some form of second-order closure is essential in stratified turbulence calculations.

Prediction of a typhoon using a fine-mesh NWP model

The ECMWF operational grid point model (with a resolution of 1.875° of latitude and longitude) and its limited area version (with a resolution of !0.47° of latitude and longitude) with boundary values from the global model have been used to study the simulation of the typhoon Tip. The fine-mesh model was capable of simulating the main structural features of the typhoon and predicting a fall in central pressure of 60 mb in 3 days. The structure of the forecast typhoon, with a warm core (maximum potential temperature anomaly 17 K). intense swirling wind (maximum 55 m s -1 at 850 mb) and spiralling precipitation patterns is characteristic of a tropical cyclone. Comparison with the lower resolution forecast shows that the horizontal resolution is a determining factor in predicting not only the structure and intensity but even the movement of these vortices. However, an accurate and refined initial analysis is considered to be a prerequisite for a correct forecast of this phenomenon. DOI: 10.1111/j.1600-0870.1985.tb00273.x

Variational Normal Mode Initialization for a Multilevel Model

The application of variational normal mode initialization to the ECMWF multilevel grid-point model is described. The technique involves minimizing a variational integral of the changes made by the initialization to the analyzed mass and wind fields, suitably weighted with a view to exerting some control over the relative magnitudes of the adjustments to these fields. We show how to construct an appropriate three-dimensional integral, and describe an efficient procedure for solving the minimization problem in the simple case where the weights depend only on latitude. Experimental results are presented to demonstrate that, in comparison with unconstrained initialization, the changes made to the analyzed mass field can be considerably reduced without undue damage to the wind field, and without compromising the benefits of initialization in providing a forecast free of high-frequency oscillations. In the case studied here, the use of constrained normal mode initialization has no significant impact on the results of a subsequent 5-day forecast.

Numerical experiments on the seasonal transition of general circulation over asia—part ii

The onset of the 1979 summer monsoon is investigated using the ECMWF grid-point model. The role of the Tibetan Plateau in this process is investigated by means of parallel model integrations with different orographies. Similarly, the relative roles of land-sea thermal contrast, latent heat release and Southern Hemisphere influence are studied. The influence of the African Highland on the onset of the Somali jet is also explored. A generally satisfactory performance of the model in representing the onset of the monsoon is documented and various contributions to this from different model components are discussed. In Part I of this paper the impact from the Southern Hemisphere is presented.

An Air Mass Transformation Model for Short-Range Weather Forecasting

Abstract A model has been constructed for the purpose of forecasting at specific places the potential temperature, the specific humidity and the depth of the boundary layer. The model, an Air Mass Transformation model (AMT model), consists of a trajectory model and a one-dimensional boundary layer model. The horizontal and vertical advection of air masses is described by trajectories. The trajectories are computed from the analyzed geostrophic wind fields of a large-scale grid-point model. The lowest trajectory advects the air in the boundary layer. The air-mass transformations in the boundary layer are described by a simple boundary layer model. During unstable conditions, a slab model is used; during stable conditions, linear potential temperature profiles and humidity profiles are assumed. Along the lowest trajectory, the surface fluxes of heat and water vapor are computed from a simple parameterization scheme. The initial conditions for the state of the boundary layer are obtained from an analysis sch...

Medium Range Prediction by a GFDL Global Spectral Model: Results for Three Winter Cases and Sensitivity to Dissipation

Abstract A preliminary evaluation is made of the medium range predictive capability of a GFDL global spectral model of the atmosphere, based upon three winter blocking cases. Analogous forecasts by a GFDL global grid point model provide a background standard of comparison. The spectral model is rhomboidally truncated at wavenumber 30, has 9 sigma levels, incorporates sub-grid scale physical processes commonly associated with general circulation models and employs semi-implicit time differencing. The grid point model has somewhat finer horizontal resolution and fairly similar sub-grid scale physical processes, and employs explicit time differencing. The spectral model is up to 6 times more economical. The level of forecast skill for the 5 to 15 day range is generally less than practically useful and is more case-dependent than spectral versus grid point model-dependent. In the most successful case, i.e., 16 January 1979, an observed Atlantic blocking ridge is simulated quite well, especially by the spectra...

Total and Planetary-Scale Systematic Errors in Recent NMC Operational Model Forecasts

The total and systematic errors in the 500 mb geopotential height forecasts from the NMC grid-point and spectral operational models are compared and contrasted for two recent winters. The spectral model is shown to be an improvement in the forecasts through a more skillful prediction of the planetary-scale (zonal wavenumbers 1-2) quasi-stationary wave amplitudes, and through the elimination of the grid-point model's large systematic error at low latitudes. In agreement with estimates from related studies, the systematic error in the NMC spectral model accounts for 15-20% of the total error variance. Approximately one-half of the total systematic error resides in the planetary scales.