a non-interpolating semi-lagrangian scheme for the continuity equation of the ecmwf forecast model
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A non-interpolating semi-Lagrangian scheme for the continuity equation of the ECMWF forecast
model.
Project 4: Formation in technical used in the dynamics of the numerical weather models.
Tomás Morales MorínMariano Hortal Reymundo
Area of Modelization
Spanish Meteorological Agency (AEMET)
Outline
• Conclusions of previous works.
• A non-interpolating semi-Lagrangian scheme for the continuity equation (NI-SLCE).
• Implementation of NI-SLCE in semi-Lagrangian semi-implicit (SLSI) scheme of the ECMWF Forecast Model.
• New conclusions.
IFS
Spectral Spacial
Correction
SL Interpolation Correction
HARMONIE
2-D and 3-D interpolation
scheme
Non-Interpolating
semi-Lagrangian scheme
Conservation in Continuity equation
Conservation of NOx, Ozone, Humidity equation without sink and source terms
GMSLSI scheme for h y d r o s t a t i c p r i m i t i v e equations
LAMSLSI scheme for non-hydrostat ic p r i m i t i v e equations
Why should we use a NI-SLCE scheme to calculate the value of the fields at the departure point of the semi-Lagrangian trajectory?
Conclusions of previous works
SL scheme
NI-SL scheme
dX
dt= RHS XA,+ = XD,0 +RHSD,0
XA,+ =
⇢X � d
�X
�x
�⇤,0+RHS⇤,0
�X
�t+ (v
0+ v⇤)
�X
�x= RHS
D⇤X
Dt+ v
0 �X
�x= RHS
• •• •dd
0
d⇤v = v
0+ v⇤
NI-SLCE
A non-interpolating SL scheme for the continuity equation
Temporal discretizationNon-interpolating semi-Lagrangian semi-implicit time integration scheme (only for the continuity equation).
Spacial discretizationSpectral in the horizontal (spherical harmonics).
Pseudo-spectral (finite-element) vertical representation (cubic B-spline).
LnpA,+sup = {Lnpsup � d⇥Lnpsup}⇤,0 + {N.L.+ L.}⇤,0 + {L.}A,+
LnpA,+sup + {L.}A,+ = {Lnpsup � d⇥Lnpsup}⇤,0 + {N.L.+ L.}⇤,0
A B C
21
NI-SLCE
Stepo.F90 / scan2h.F90 / scan2mdm.F90
gp_model.F90
3. Dynamics 4. ECMWF Radiation 5. SL Interpolation
cpg.F90
cpg_dyn.F90
lacdyn.F90
3. Computation o f t he w ind c o m p o n e n t s necessary for SL trajectory
4. Computations of the 3-D eq. RHS terms
5. Computations of the 2-D eq. RHS terms
lavent.F90 lattex.F90 lattes.F90
call_sl.F90
3. SL trajectory research weight and interpolation grid calculation
5. Interpolations
lapinea.F90
larmes.F90
.
..
.
lapineb.F90
larcinb.F90
OpenMP
laiddi.F90 laitli.F90
binislce.F90 trinislce.F90
Bi-dimensional 1 2 - p o i n t interpolations (in horizontal)
T r i l i n e a r interpolations for one variable
/module/ptrslb1.F90 /setup/suslb.F90Implementation of NI-SLCE
Results
40
50
60
70
80
90
100
%
0 1 2 3 4 5 6 7 8 9 10
Forecast Day
es oper 12UTC | Mean method: fairDate: 20091015 12UTC to 20091015 12UTCNHem Extratropics (lat 20.0 to 90.0, lon -180.0 to 180.0)
Anomaly correlation500hPa geopotential
NISLCE
MR
Results
Results
New conclusions
Conclusions
• The NI-SLCE in the horizontal scheme does not improve the conservation of the mass in the continuity equation.
• It is better to continue using interpolation methods to calculate the value of the field at the departure point of the semi-Lagrangian trajectory.
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