4.1 The results (WS)
Experiment Cp: Inverse tests found from the WS scheme, 4 bands (optimal) top-hat T-transform, triangular U-transform'
Fig Cp.3a (top left): Field (real part) after acting with TU on a delta function at wavenumber 0.35 units and level 21.
Fig Cp.3b (top right): Imaginary part of field.
Fig Cp.3c (bottom left): Field after acting with UT on a delta function at latitude 45 degrees and level 21.
Fig. Cp.4a (below left): Real part of sub-matrix of TU operator (input and output space is wavenumber, at fixed level 21).
Fig. Cp.4b (below centre left): Imaginary part.
Fig. Cp.4c (below centre right): Real part of sub-matrix of TU operator (input and output space is level, at a fixed wavenumber).
Fig. Cp.4d (below right): Imaginary part.
Fig. Cp.5a (below left): Sub-matrix of UT operator (input and output space is latitude, at fixed level 21).
Fig. Cp.5a (below right): Sub-matrix of UT operator (input and output space is level, at fixed latitude 45 degrees).
Experiment Dp: Inverse tests found from the WS scheme, 4 bands (optimal) top-hat T-transform, top-hat U-transform'
Fig Dp.3a (top left): Field (real part) after acting with TU on a delta function at wavenumber 0.35 units and level 21.
Fig Dp.3b (top right): Imaginary part of field.
Fig Dp.3c (bottom left): Field after acting with UT on a delta function at latitude 45 degrees and level 21.
Fig. Dp.4a (below left): Real part of sub-matrix of TU operator (input and output space is wavenumber, at fixed level 21).
Fig. Dp.4b (below centre left): Imaginary part.
Fig. Dp.4c (below centre right): Real part of sub-matrix of TU operator (input and output space is level, at a fixed wavenumber).
Fig. Dp.4d (below right): Imaginary part.
Fig. Dp.5a (below left): Sub-matrix of UT operator (input and output space is latitude, at fixed level 21).
Fig. Dp.5a (below right): Sub-matrix of UT operator (input and output space is level, at fixed latitude 45 degrees).
Experiment Ep: Inverse tests found from the WS scheme, 4 bands (optimal) triangular T-transform, triangular U-transform'
Fig Ep.3a (top left): Field (real part) after acting with TU on a delta function at wavenumber 0.35 units and level 21.
Fig Ep.3b (top right): Imaginary part of field.
Fig Ep.3c (bottom left): Field after acting with UT on a delta function at latitude 45 degrees and level 21.
Fig. Ep.4a (below left): Real part of sub-matrix of TU operator (input and output space is wavenumber, at fixed level 21).
Fig. Ep.4b (below centre left): Imaginary part.
Fig. Ep.4c (below centre right): Real part of sub-matrix of TU operator (input and output space is level, at a fixed wavenumber).
Fig. Ep.4d (below right): Imaginary part.
Fig. Ep.5a (below left): Sub-matrix of UT operator (input and output space is latitude, at fixed level 21).
Fig. Ep.5a (below right): Sub-matrix of UT operator (input and output space is level, at fixed latitude 45 degrees).
Experiment Fp: Inverse tests found from the WS scheme, 1 band (optimal) top-hat T-transform, triangular U-transform'
Fig Fp.3a (top left): Field (real part) after acting with TU on a delta function at wavenumber 0.35 units and level 21.
Fig Fp.3b (top right): Imaginary part of field.
Fig Fp.3c (bottom left): Field after acting with UT on a delta function at latitude 45 degrees and level 21.
Fig. Fp.4a (below left): Real part of sub-matrix of TU operator (input and output space is wavenumber, at fixed level 21).
Fig. Fp.4b (below centre left): Imaginary part.
Fig. Fp.4c (below centre right): Real part of sub-matrix of TU operator (input and output space is level, at a fixed wavenumber).
Fig. Fp.4d (below right): Imaginary part.
Fig. Fp.5a (below left): Sub-matrix of UT operator (input and output space is latitude, at fixed level 21).
Fig. Fp.5a (below right): Sub-matrix of UT operator (input and output space is level, at fixed latitude 45 degrees).
Experiment Ip: Inverse tests found from the WS scheme, 10 bands (optimal) top-hat T-transform, triangular U-transform'
Fig Ip.3a (top left): Field (real part) after acting with TU on a delta function at wavenumber 0.35 units and level 21.
Fig Ip.3b (top right): Imaginary part of field.
Fig Ip.3c (bottom left): Field after acting with UT on a delta function at latitude 45 degrees and level 21.
Fig. Ip.4a (below left): Real part of sub-matrix of TU operator (input and output space is wavenumber, at fixed level 21).
Fig. Ip.4b (below centre left): Imaginary part.
Fig. Ip.4c (below centre right): Real part of sub-matrix of TU operator (input and output space is level, at a fixed wavenumber).
Fig. Ip.4d (below right): Imaginary part.
Fig. Ip.5a (below left): Sub-matrix of UT operator (input and output space is latitude, at fixed level 21).
Fig. Ip.5a (below right): Sub-matrix of UT operator (input and output space is level, at fixed latitude 45 degrees).
