InternalModesTransform

Apply vertical modal transforms and compute vertical modal spectra.

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Declaration

classdef InternalModesTransform < CAAnnotatedClass

Overview

InternalModesTransform stores forward and inverse vertical operators for one InternalModesBasis. It works only on vertical scalar fields or modal coefficients; full wave-vortex state projectors remain outside this package.

For modal coefficients \(p_j\) and \(q_j\), the vertical cross-spectrum is

\[S[p,q]_j = m\,s_j\,\Re\{p_j q_j^*\},\]

where \(s_j\) is the component spectral weight and \(m\) is an optional horizontal multiplicity supplied by the caller.

coefficients = transform.projectVertical(profile,component="G");
spectrum = transform.spectrum(coefficients,component="G");

Topics

• Inspect transform properties
  • D Water-column depth used by the barotropic F spectral weight.
  • N2 Buoyancy frequency squared sampled at z.
  • componentRoleF F component role label.
  • componentRoleG G component role label.
  • conditionNumberF Condition-number diagnostic for the F forward operator.
  • conditionNumberG Condition-number diagnostic for the G forward operator.
  • f0 Coriolis parameter used by the source mode solve.
  • forwardF Forward F projection matrix from samples to modal coefficients.
  • forwardG Forward G projection matrix from samples to modal coefficients.
  • forwardProjectionAvailableF True when a canonical F projection exists for this basis.
  • forwardProjectionAvailableG True when a canonical G projection exists for this basis.
  • g Gravitational acceleration used by the source mode solve.
  • gramErrorF Relative round-trip error for the retained F modes.
  • gramErrorG Relative round-trip error for the retained G modes.
  • hF Equivalent depths for retained F modes.
  • hG Equivalent depths for retained G modes.
  • inverseF Inverse F reconstruction matrix from coefficients to samples.
  • inverseG Inverse G reconstruction matrix from coefficients to samples.
  • kappa Horizontal wavenumber metadata.
  • nonlinearAliasLimit Number of modes allowed by the nonlinear aliasing policy.
  • omega Frequency metadata.
  • problemType Text label identifying the source vertical eigenvalue problem.
  • projectionResolvedModes Number of modes accepted by the projection-quality diagnostic.
  • rejectedModesF Rejected F mode numbers.
  • rejectedModesG Rejected G mode numbers.
  • retainedModesF Retained F mode numbers.
  • retainedModesG Retained G mode numbers.
  • selectionReason Prefix-selection reason for model-style transforms.
  • sourceDescription Text label identifying the source solver or factory path.
  • transformStatusF F transform construction status.
  • transformStatusG G transform construction status.
  • weightsF Quadrature weights used to build F numerical projections.
  • weightsG Quadrature weights used to build G numerical projections.
  • z Depth grid for vertical fields acted on by this transform.
• Apply vertical transforms
  • crossTransformTo Map coefficients from a target transform into this transform.
  • forward Return a forward vertical projection matrix.
  • inverse Return an inverse vertical reconstruction matrix.
  • projectVertical Project vertical samples onto modal coefficients.
  • reconstructVertical Reconstruct vertical samples from modal coefficients.
• Analyze vertical spectra
  • crossSpectrum Compute a vertical modal cross-spectrum.
  • spectralWeightsF Parseval weights used for F modal spectra.
  • spectralWeightsG Parseval weights used for G modal spectra.
  • spectrum Compute a vertical modal auto-spectrum.
• Persist vertical transforms
  • InternalModesTransform Create a vertical transform from canonical persisted state.
• Other
  • classRequiredPropertyNames

Developer Topics

These items document internal implementation details and are not part of the primary public API.

• Developer topics
  • modeF F-mode coordinate used by annotated NetCDF persistence.
  • modeG G-mode coordinate used by annotated NetCDF persistence.
  • withDiagnostics Return a copy with updated selection diagnostics.
  • zIndex Row coordinate used by annotated NetCDF persistence.

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