The latitude-longitude grid is used for the global domain, and rotated latitude-longitude coordinate is employed for regional applications. With the Equator of the rotated system running through the middle of the integration domain, more uniform grid distances are obtained. A general, pressure-based terrain following vertical coordinate is applied. The forward-backward time-differencing scheme is used for horizontally propagating fast waves, and an implicit scheme is applied for vertically propagating sound waves. Stabilized Adams-Bashforth scheme is employed for non-split horizontal advection of the basic dynamical variables and the Coriolis force. In order to eliminate stability problems due to thin vertical layers, the Crank-Nicholson scheme is used to compute the contributions of vertical advection.
The model is fully compressible. The nonhydrostatic component of the model is designed in such a way as to avoid overspecification. As a consequence, the number of prognostic equations is reduced by one. The nonhydrostatic dynamics is implemented as an add–on module that can be turned on or off depending on resolution.
“Isotropic” quadratic conservative finite-volume horizontal differencing employed in the model conserves a variety of basic and derived dynamical and quadratic quantities and preserves some important properties of differential operators. Among these, the conservation of energy and enstrophy improves the accuracy of the nonlinear dynamics of the model on all scales. Conservative “across the pole” polar boundary conditions are specified in the global limit. The polar filter selectively slows down the wave components of the basic dynamical variables that would otherwise propagate faster in the zonal direction than the fastest wave propagating in the meridional direction. As a compromise between requirements for affordability and accuracy, a fast Eulerian conservative and positive definite scheme has been developed for model tracers. Conservative monotonization is applied in order to control over-steepening by the tracer advection scheme. The results of the tests have been encouraging concerning the tracer mass conservation and shape preservation, as well as computational efficiency. A variety of NCEP's and WRF physical parameterizations developed for global and regional scales have been coupled to the model.
In very high-resolution tests the model successfully reproduced the classical two-dimensional nonhydrostatic solutions. In regional short range runs, the model dynamics demonstrated the ability to develop the observed –3 and –5/3 spectral slopes with realistic transition between the two spectral ranges. These properties of the spectra are not induced by computational noise and maintained by numerical filters. The necessary condition for the development of the –5/3 spectrum was presence of strong forcing on synoptic and meso scales. In a decaying turbulence case on convective cloud scales, the model dynamics developed the –5/3 spectrum consistent with the 3D turbulence theory.
As a possible model upgrade, starting from three advanced Eulerian second order nonlinear advection schemes for semi staggered grids B/E, advection schemes of fourth order of formal accuracy were developed. All three second order advection schemes control the nonlinear energy cascade in case of nondivergent flow by conserving quadratic quantities, and linearization of all three schemes leads to the same second order linear advection scheme. The second order term of the truncation error of the linear advection scheme has a special form so that it can be eliminated by modifying the advected quantity while still preserving consistency. Demanding long-term and low-resolution nonlinear tests were carried out in order to investigate how well the fourth order schemes control the nonlinear energy cascade. All three schemes were able to maintain meaningful solutions throughout the test, and the impact of the best performing scheme with enhanced formal accuracy was examined on a sizable sample of global medium range forecasts. The 500 hPa anomaly correlation coefficient obtained using the fourth order scheme did not show an improvement compared to the tests using its second order counterpart. In other words, the enhanced formal accuracy of a well behaved quadratic conservative nonlinear advection scheme did not add measurable value to extended global forecasts.
A global forecasting system based on the NMMB has been run for more than two years in order to test and tune the model, and in particular, to examine its potential for medium range weather forecasting. The system was initialized and verified using the spectral analyses of NCEP's Global Forecasting System (GFS). Note that the spectral model data cannot be perfectly converted into grid point model data due to differences between the two modeling approaches. Nevertheless, the skill of the medium range forecasts produced by the NMMB was comparable to that of other major medium range forecasting systems. Interestingly, even though the NMMB and GFS were starting from very similar initial conditions, the skill of the two individual medium range forecasts was often disparate. When one model produced a bad forecast, the forecast from the other model could be quite good. Such behavior appears potentially advantageous for application of the model for multi-model ensemble forecasting.
On the meso scales, the NMMB is planned to replace the WRF NMM in operations at NCEP as the North American Model (NAM) and in a number of nested high resolution runs. Within efforts to upgrade the physical package on the meso scales, the problem of application of deep moist convection parameterization with single digit resolutions has been addressed using the Betts-Miller-Janjic (BMJ) scheme. Being an adjustment scheme with proper asymptotic behavior, the application of the BMJ scheme at very high, single digit resolutions is not in conflict with the basic parameterization assumptions. The proposed approach reduces excessive precipitation bias, shows no detrimental effect on timing of precipitation, and at the same time preserves realistic spatial structure of precipitation forecasts. Most near-surface and upper-air skill scores are improved.
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