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Modern numerical methods in climate analysis and modelling

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Modern numerical methods in climate analysis and modelling Andreas Hense and colleagues (to be announced) Universit t Bonn – PowerPoint PPT presentation

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Title: Modern numerical methods in climate analysis and modelling


1
Modern numerical methods in climate analysis and
modelling
  • Andreas Hense and colleagues
  • (to be announced)
  • Universität Bonn

2
Overview
  • Introduction
  • The water budget of the Arctic from radiosonde
    data
  • method
  • results
  • Solution of the shallow water equations on the
    sphere
  • method
  • results
  • Conclusion

3
The arctic water budget problem
with Martin Göber (Met Office), Reinhard
Hagenbrock , Felix Amendt
4
The arctic water budget problem
  • Arctic Evaporation E and precipitation P almost
    completely unknown
  • Atmospheric moisture flux vq from
  • Reanalyses ERA15 and NCEP
  • Radiosonde (Serezze)
  • Discrepancy between Reanalyses and Radiosonde

5
The arctic water budget problem
6
Reasons of discrepancies
  • Reanalysis budget are not closed
  • Moisture cycle spin-up
  • Spatial sampling problems for radiosondes
  • Measurement errors
  • mass inconsistent wind fields from radiosondes

7
A mass consistent windfield
8
A mass consistent wind field
9
A mass consistent wind field
  • Standard procedure
  • interpolation of observations to a grid
  • Differentiation and minimization on the grid
  • Our solution
  • Discretization of the Minimization integral
  • three dimensional finite elements
  • on an irregular triangular grid

10
The grid (horizontal)
11
The Grid (vertical)
e.g. 500 hPa
e.g.700 hPa
12
Result for the Arctic moisture balance
Effect of mass modification on Radiosonde and
ERA15 (subsampled) 1979-94
13
Result for the Arctic moisture balance
Effects of doubled resolution in subsampled ERA15
doubled
Radiosonde network
14
A semi-Lagrangian semi-implicit finite element
model for the shallow water equations on the
sphere
  • with Thomas Heinze Technical University Munich
  • Develope the dynamic code of a global
    atmospheric model suitable for MPP machines
  • and local refinement capability
  • Unstructured triangular grid
  • finite element or finite volume technique

15
The equations - coordinate free version
16
Discretization in time
  • Integration along backward trajectories
  • coupled equations for the new geopotential
    heights and velocities at the endpoints of the
    trajectories
  • reduce to a elliptic equation for the new
    geopotential height

17
The elliptic equation
Discretization with finite elements on a
triangular mesh leads to the linear equation
18
The algorithm
  • Compute backward trajectories from a given flow
  • evaluate the right hand side through
    interpolation
  • solve the linear equation for the new
    geopotential
  • obtain the new flow field

19
The algorithm
20
How to distribute the triangles on the sphere?
  • Choose a macrotriangulation
  • divide each triangle side in equal parts
  • connect the midpoints
  • one triangle four new
    triangles

21
The macrotriangulation
C
or Soccerball
60
22
Results
Initial field and topography
23
Results
After 10 days
24
Mass- and Energy conservation?
(Mass)
(Energy)
25
Numerical stability?
Grid size ca. 150 km
26
Summary
  • Finite element formulation is a very elegant
    method for least squares problems
  • Difference between Radiosonde and Reanalysis
    related water balance resolvable at twice the
    radiosonde network resolution
  • Finite element formulation is a very efficient
    method for the shallow equations
  • MPP and local refinement possible
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