Davies Coupling in a Shallow-Water Model
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Department of Meteorology & Climatolog Department of Meteorology & Climatolog FMFI UK Bratislava FMFI UK Bratislava Davies Coupling Davies Coupling in a in a Shallow-Water Shallow-Water Model Model Mat Mat úš M úš M ART ART ÍNI ÍNI
description
Department of Meteorology & Climatology FMFI UK Bratislava. Davies Coupling in a Shallow-Water Model. Mat úš M ART ÍNI. Arakawa , A., 1984. Boundary conditions in limited-area model. Dep. of Atmospheric Sciences. University of California, Los Angeles: 28pp. - PowerPoint PPT Presentation
Transcript of Davies Coupling in a Shallow-Water Model
Department of Meteorology & ClimatologyDepartment of Meteorology & ClimatologyFMFI UK BratislavaFMFI UK Bratislava
Davies CouplingDavies Couplingin a in a Shallow-WaterShallow-Water Model Model
MatMatúš Múš MARTARTÍNIÍNI
ArakawaArakawa, A., 1984. Boundary conditions in limited-area model. Dep. of , A., 1984. Boundary conditions in limited-area model. Dep. of Atmospheric Sciences. University of California, Los Angeles: 28pp.Atmospheric Sciences. University of California, Los Angeles: 28pp.
DaviesDavies, H.C., 1976. A lateral boundary formulation for multi-level , H.C., 1976. A lateral boundary formulation for multi-level prediction models. Q. J. Roy. Met. Soc., Vol. 102, 405-418.prediction models. Q. J. Roy. Met. Soc., Vol. 102, 405-418.
McDonaldMcDonald, A., 1997. Lateral boundary conditions for operational regional , A., 1997. Lateral boundary conditions for operational regional forecast models; a review. Irish Meteorogical Service, Dublin: 25 pp.forecast models; a review. Irish Meteorogical Service, Dublin: 25 pp.
MesingerMesinger, F., Arakawa A., 1976. Numerical Methods Used in , F., Arakawa A., 1976. Numerical Methods Used in Atmospherical Models. Vol. 1, WMO/ICSU Joint Organizing Committee, Atmospherical Models. Vol. 1, WMO/ICSU Joint Organizing Committee, GARP Publication Series No. 17, 53-54.GARP Publication Series No. 17, 53-54.
PhillipsPhillips, N. A., 1990. Dispersion processes in large-scale weather , N. A., 1990. Dispersion processes in large-scale weather prediction. WMO - No. 700, Sixth IMO Lecture: 1-23.prediction. WMO - No. 700, Sixth IMO Lecture: 1-23.
TermoniaTermonia, P., 2002. The specific LAM coupling problem seen as a filter. , P., 2002. The specific LAM coupling problem seen as a filter. Kransjka Gora: 25 pp.Kransjka Gora: 25 pp.
MotivationMotivation
global model with variable resolutionglobal model with variable resolution ARPEGE ARPEGE 22 – 270 km22 – 270 km
low resolution driving model low resolution driving model with nested high resolution LAMwith nested high resolution LAM DWD/GME DWD/LM 60 km 7 kmDWD/GME DWD/LM 60 km 7 km
combination of both methodscombination of both methods ARPEGE ALADIN/LACE ALADIN/SLOKARPEGE ALADIN/LACE ALADIN/SLOK
25 km25 km 12 km 12 km 7 km7 km
High resolution NWP techniques:High resolution NWP techniques:
WHY WHY NESTEDNESTED MODELS MODELS IMPROVE IMPROVE WEATHER - FORECASTWEATHER - FORECAST
the surface is more accurately characterized the surface is more accurately characterized (orography, roughness, type of soil, (orography, roughness, type of soil, vegetation, albedo …)vegetation, albedo …)
more realistic parametrizations might be more realistic parametrizations might be used, eventually some of the physical used, eventually some of the physical processes can be fully resolved in LAMprocesses can be fully resolved in LAM
own assimilation system own assimilation system better initial better initial conditions (early phases of integration)conditions (early phases of integration)
Shallow-water Shallow-water equationsequations
x
uH
t
h
,x
hg
t
u
• 1D system (Coriolis acceleration not considered)1D system (Coriolis acceleration not considered)• linearization around resting backgroundlinearization around resting background
const)H(g,
• forward-backward schemeforward-backward scheme• centered finite differencescentered finite differences
DISCRETIZATION}
Davies relaxation schemeDavies relaxation scheme
),hK(x)(h DM
continuous formulationcontinuous formulation in in shallow-water systemshallow-water system
x
uH
t
hx
hg
t
u
discretediscrete formulation formulation - general formalism: - general formalism:
DMXβXβ)(1X
LAM
h
uX
),uK(x)(u DM
0K(x)
PROPERTIES OF PROPERTIES OF DAVIES RELAXATION SCHEMEDAVIES RELAXATION SCHEME
0
0.2
0.4
0.6
0.8
1
0 20 40 60 80
Input of the wave from the driving modelInput of the wave from the driving model
u
j
Difference betweenDifference between numerical and analytical solutionnumerical and analytical solution
(no relaxation)(no relaxation) 8-point relaxation zone8-point relaxation zone
-0.1
-0.05
0
0.05
0.1
0 20 40 60 80
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-0.05
0
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0.1
0 20 40 60 80
Outcome of the wave, which is Outcome of the wave, which is not represented in driving modelnot represented in driving model
-1
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0
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1
0 20 40 60 80
-1
-0.5
0
0.5
1
0 20 40 60 80
-1
-0.5
0
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1
0 20 40 60 80
-1
-0.5
0
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1
0 20 40 60 80
-1
-0.5
0
0.5
1
0 20 40 60 80
-1
-0.5
0
0.5
1
0 20 40 60 80
t15t 0t t20t
t25t t30t t50t
8-point relaxation zone 8-point relaxation zone
-0.1
0.2
0.5
0.8
1.1
0 20 40 60 80
-0.1
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0.5
0.8
1.1
0 20 40 60 80
-0.1
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0.5
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1.1
0 20 40 60 80
-0.1
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0.5
0.8
1.1
0 20 40 60 80
88 72
8
8
8 72 72
72
t20t t20t t25t
t30t t40t
analytical solution
Minimalization of the reflectionMinimalization of the reflection
• weight functionweight function• width of the relaxation zonewidth of the relaxation zone
the velocity of the wave the velocity of the wave (4 different (4 different velocities satisfying CFL stability criterion)velocities satisfying CFL stability criterion)
(simulation of dispersive system)(simulation of dispersive system) wave-length wave-length x}40x,20x,{10
Choosing the weight functionChoosing the weight function
20
25
30
35
40
3 4 5 6 7 8 9 10
15
20
25
30
35
40
3 4 5 6 7 8 9 10
r [%] r [%]
convex-concave (ALADIN)
cosine
quadratic
quarticquartic
tan hyperbolictan hyperbolic
linearlinear
number of points in relaxation zonenumber of points in relaxation zone
testing criterion - critical reflection coefficient testing criterion - critical reflection coefficient rr
(more accurate representation of surface) (more accurate representation of surface)
-0.5
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1
0 10 20 30 40
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0 10 20 30 40
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0 20 40
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0 20 40
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0 20 40
DM
8 8 8 323232
LAM
H0.81H LAM DM
)c0.9(c LAM DM
DM-driving modelDM-driving model LAM-limited area modelLAM-limited area model
