numex – numerical experiments for the gme fachhochschule bonn-rhein-sieg wolfgang joppich pftool -...
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NUMEX – Numerical experiments for the GME
Fachhochschule Bonn-Rhein-Sieg
Wolfgang Joppich
PFTOOL - Precipitation forecast toolboxSemi-Lagrangian Mass-Integrating Transport Algorithm using the GME Gridwithin
Sabine Pott
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Fachhochschule Bonn-Rhein-Sieg
OutlineOutline
• Motivation• Algorithm• Experiments • Results• Future Work
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Fachhochschule Bonn-Rhein-Sieg
improve the semi-Lagrangian scheme withregard to
-- conservation properties-- preservation of shape
-- reduction of error -- reduction of non-physical oscillations
MotivationMotivation
For the complete chain of precipitation forecast at DWD holds: what you have lost globally (GME-GME2LM)
remains lost locally (LM)
therefore
DWD has reported that there is an obvious defect of mass in the GME , indication to insufficient accuracy
specific humidity, specific cloud liquid water content, specific cloud ice content, ozone mixing ratio
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Fachhochschule Bonn-Rhein-Sieg
AlgorithmAlgorithm
A Semi-Lagrangian integrated-mass transport algorithm based on the integro-differential form of the continuity equation has been developed for the icosahedral grid
)(
)(
,
,0
),(),(
0),(
ttt
st
dMxthdMxtth
dMxthdt
dU
t
Hermitian interpolation of mass on each triangular cell, satisfying1. conservation of mass2. Invariance of variation of mass at two edges3. Interpolation of transported quantity to the 3 corner points
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Fachhochschule Bonn-Rhein-Sieg
AlgorithmAlgorithm
on each triangle the transported quantity is represented as a second order polynomial in the local isothermal coordinates:
254
23210),( aaaaaap
equations for the coefficients are solved by LU decomposition
Key steps: 1. approximation of departure points (previous time
level)2. intersection of icosahedral mesh and departure
mesh3. integrate mass, variation of mass (previous time
level) on polygons of intersection or departure edges respectively
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Fachhochschule Bonn-Rhein-Sieg
Experiments/ResultsExperiments/Results
Several different constant wind fields
Rotation of reversed cosine-bell, different rotation angles, loop across pole and equator
Advection of cosine-bell in a meridional wind-field with div != 0
Both test cases are similar to Williamson‘s test case 1
Tests for ni = 12, 16, 24, 32, 48, 64, 96
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Fachhochschule Bonn-Rhein-Sieg
Experiments/ResultsExperiments/Results
advection of reversed cosine-bell, div = 0, pole-loop
Initial state reached again after 12 days, ni = 48, dt = 540s, global error after 30 days
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Fachhochschule Bonn-Rhein-Sieg
Experiments/ResultsExperiments/Results
advection of reversed cosine-bell, div = 0, pole-loop, ni = 48, 30 days
Relative error in maximumnorm, old(yellow) vs. new(black) scheme
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Fachhochschule Bonn-Rhein-Sieg
Experiments/ResultsExperiments/Results
advection of reversed cosine-bell, div = 0, pole-loop, ni = 48, 30 days
Relative massdefect, old(yellow) vs. new(black) scheme
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Fachhochschule Bonn-Rhein-Sieg
Experiments/ResultsExperiments/Results
advection of reversed cosine-bell, div = 0, pole-loop, ni = 48, 30 days
Relative error in extremum, old(yellow) vs. new(black) scheme
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Fachhochschule Bonn-Rhein-Sieg
Experiments/ResultsExperiments/Results
advection of reversed cosine-bell, div = 0, pole-loop, ni = 48, 30 days
Nonphysical oscillations, old(yellow) vs. new(black) scheme
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Currently doing Currently doing
- implementation of the new scheme, developed within sequential SWE code using the GME mesh, into parallel GME 2.10 (almost production code)
- systematic comparison by means of realistic test cases(benefit vs. numerical cost)
GME
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Future work Future work
- implementation of new scheme into GME- systematic comparison (benefit vs. numerical cost)
- develop conservative interpolation for transfer GME2LM
- adapt scheme for the LM (implementation, evaluation, …)
what you have lost globally (GME-GME2LM) remains lost locally (LM)
then the complete chain has improved conservation properties whichalso hold for low resolutions, especially for the climate verion of GME
GME
GME2LM
LM