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| Titel |
Multi-scale Eulerian model within the new National Environmental Modeling System |
| VerfasserIn |
Zavisa Janjic, Tijana Janjic, Ratko Vasic |
| Konferenz |
EGU General Assembly 2010
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 12 (2010) |
| Datensatznummer |
250037758
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| Zusammenfassung |
| The unified Non-hydrostatic Multi-scale Model on the Arakawa B grid (NMMB) is being
developed at NCEP within the National Environmental Modeling System (NEMS). The
finite-volume horizontal differencing employed in the model preserves important properties
of differential operators and conserves a variety of basic and derived dynamical and quadratic
quantities. Among these, conservation of energy and enstrophy improves the accuracy of
nonlinear dynamics of the model.
Within further model development, advection schemes of fourth order of formal accuracy
have been developed. It is argued that higher order advection schemes should not be used in
the thermodynamic equation in order to preserve consistency with the second order scheme
used for computation of the pressure gradient force. Thus, the fourth order scheme is applied
only to momentum advection.
Three sophisticated second order schemes were considered for upgrade. Two of them,
proposed in Janjic(1984), conserve energy and enstrophy, but with enstrophy calculated
differently. One of them conserves enstrophy as computed by the most accurate second order
Laplacian operating on stream function. The other scheme conserves enstrophy as computed
from the B grid velocity. The third scheme (Arakawa 1972) is arithmetic mean of the former
two. It does not conserve enstrophy strictly, but it conserves other quadratic quantities that
control the nonlinear energy cascade.
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 simply preconditioning the advected quantity.
Tests with linear advection of a cone confirm the advantage of the fourth order scheme.
However, if a localized, large amplitude and high wave-number pattern is present in initial
conditions, the clear advantage of the fourth order scheme disappears. In real data runs,
problems with noisy data may appear due to mountains. Thus, accuracy and formal accuracy
may not be synonymous.
The nonlinear fourth order schemes are quadratic conservative and reduce to the Arakawa
Jacobian in case of non-divergent flow. In case of general flow the conservation properties of
the new momentum advection schemes impose stricter constraint on the nonlinear cascade
than the original second order schemes. However, for non-divergent flow, the conservation
properties of the fourth order schemes cannot be proven in the same way as those of the
original second order schemes. Therefore, nonlinear tests were carried out in order to check
how well the fourth order schemes control the nonlinear energy cascade. In the tests
nonlinear shallow water equations are solved in a rotating rectangular domain (Janjic,
1984). The domain is covered with only 17 x 17 grid points. A diagnostic quantity is
used to monitor qualitative changes in the spectrum over 116 days of simulated
time.
All schemes maintained meaningful solutions throughout the test. Among the second
order schemes, the best result was obtained with the scheme that conserved enstrophy as
computed by the second order Laplacian of the stream function. It was closely followed by
the Arakawa (1972) scheme, while the remaining scheme was distant third. The fourth order
schemes ranked in the same order, and were competitive throughout the experiments
with their second order counterparts in preventing accumulation of energy at small
scales.
Finally, the impact was examined of the fourth order momentum advection on global
medium range forecasts. The 500 mb anomaly correlation coefficient is used as a measure of
success of the forecasts.
Arakawa, A., 1972: Design of the UCLA general circulation model. Tech. Report
No. 7, Department of Meteorology, University of California, Los Angeles, 116
pp.
Janjic, Z. I., 1984: Non-linear advection schemes and energy cascade on semi-staggered
grids. Monthly Weather Review, 112, 1234-1245. |
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