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