WS Test program inverse test results for streamfunction

Ross Bannister, September 2004
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4.1 The results (WS)

Experiment E: Inverse tests found from the WS scheme, 4 bands (optimal) top-hat T-transform, triangular U-transform'


Fig E.3a (top left): Field (real part) after acting with TU on a delta function at wavenumber 0.35 units and level 21.
Fig E.3b (top right): Imaginary part of field.
Fig E.3c (bottom left): Field after acting with UT on a delta function at latitude 45 degrees and level 21.


Fig. E.4a (below left): Real part of sub-matrix of TU operator (input and output space is wavenumber, at fixed level 21).
Fig. E.4b (below centre left): Imaginary part.
Fig. E.4c (below centre right): Real part of sub-matrix of TU operator (input and output space is level, at a fixed wavenumber).
Fig. E.4d (below right): Imaginary part.


Fig. E.5a (below left): Sub-matrix of UT operator (input and output space is latitude, at fixed level 21).
Fig. E.5a (below right): Sub-matrix of UT operator (input and output space is level, at fixed latitude 45 degrees).

Experiment G: Inverse tests found from the WS scheme, 4 bands (optimal) top-hat T-transform, top-hat U-transform'


Fig G.3a (top left): Field (real part) after acting with TU on a delta function at wavenumber 0.35 units and level 21.
Fig G.3b (top right): Imaginary part of field.
Fig G.3c (bottom left): Field after acting with UT on a delta function at latitude 45 degrees and level 21.


Fig. G.4a (below left): Real part of sub-matrix of TU operator (input and output space is wavenumber, at fixed level 21).
Fig. G.4b (below centre left): Imaginary part.
Fig. G.4c (below centre right): Real part of sub-matrix of TU operator (input and output space is level, at a fixed wavenumber).
Fig. G.4d (below right): Imaginary part.


Fig. G.5a (below left): Sub-matrix of UT operator (input and output space is latitude, at fixed level 21).
Fig. G.5a (below right): Sub-matrix of UT operator (input and output space is level, at fixed latitude 45 degrees).

Experiment I: Inverse tests found from the WS scheme, 4 bands (optimal) triangular T-transform, triangular U-transform'


Fig I.3a (top left): Field (real part) after acting with TU on a delta function at wavenumber 0.35 units and level 21.
Fig I.3b (top right): Imaginary part of field.
Fig I.3c (bottom left): Field after acting with UT on a delta function at latitude 45 degrees and level 21.


Fig. I.4a (below left): Real part of sub-matrix of TU operator (input and output space is wavenumber, at fixed level 21).
Fig. I.4b (below centre left): Imaginary part.
Fig. I.4c (below centre right): Real part of sub-matrix of TU operator (input and output space is level, at a fixed wavenumber).
Fig. I.4d (below right): Imaginary part.


Fig. I.5a (below left): Sub-matrix of UT operator (input and output space is latitude, at fixed level 21).
Fig. I.5a (below right): Sub-matrix of UT operator (input and output space is level, at fixed latitude 45 degrees).

Experiment K: Inverse tests found from the WS scheme, 1 band (optimal) top-hat T-transform, triangular U-transform'


Fig K.3a (top left): Field (real part) after acting with TU on a delta function at wavenumber 0.35 units and level 21.
Fig K.3b (top right): Imaginary part of field.
Fig K.3c (bottom left): Field after acting with UT on a delta function at latitude 45 degrees and level 21.


Fig. K.4a (below left): Real part of sub-matrix of TU operator (input and output space is wavenumber, at fixed level 21).
Fig. K.4b (below centre left): Imaginary part.
Fig. K.4c (below centre right): Real part of sub-matrix of TU operator (input and output space is level, at a fixed wavenumber).
Fig. K.4d (below right): Imaginary part.


Fig. K.5a (below left): Sub-matrix of UT operator (input and output space is latitude, at fixed level 21).
Fig. K.5a (below right): Sub-matrix of UT operator (input and output space is level, at fixed latitude 45 degrees).

Experiment M: Inverse tests found from the WS scheme, 10 bands (optimal) top-hat T-transform, triangular U-transform'


Fig M.3a (top left): Field (real part) after acting with TU on a delta function at wavenumber 0.35 units and level 21.
Fig M.3b (top right): Imaginary part of field.
Fig M.3c (bottom left): Field after acting with UT on a delta function at latitude 45 degrees and level 21.


Fig. M.4a (below left): Real part of sub-matrix of TU operator (input and output space is wavenumber, at fixed level 21).
Fig. M.4b (below centre left): Imaginary part.
Fig. M.4c (below centre right): Real part of sub-matrix of TU operator (input and output space is level, at a fixed wavenumber).
Fig. M.4d (below right): Imaginary part.


Fig. M.5a (below left): Sub-matrix of UT operator (input and output space is latitude, at fixed level 21).
Fig. M.5a (below right): Sub-matrix of UT operator (input and output space is level, at fixed latitude 45 degrees).




Return to results explanation page, main waveband page, or data assimiation page