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Diagnostic output products

In addition to radiances and transmittances, JURASSIC can produce a variety of diagnostic output products that are primarily relevant for sensitivity analysis, retrieval development, and scientific interpretation. These diagnostics are most commonly generated by the kernel and retrieval applications.

This page provides an overview of the available diagnostic outputs and their interpretation.

Overview of diagnostic products

Depending on the application and configuration, JURASSIC can output:

  • Jacobians / kernels (sensitivities of radiances to state variables)
  • Averaging kernels (retrieval sensitivity and resolution)
  • Error covariance matrices
  • Cost-function diagnostics
  • Auxiliary forward-model quantities (e.g. contribution functions)

Most of these products are written to dedicated output files or to matrix-formatted diagnostic files controlled by runtime options.

Jacobians (kernels)

Definition

Jacobians (also called weighting functions or kernels) describe the sensitivity of the simulated radiances to changes in the atmospheric state vector.

Mathematically, the Jacobian matrix \(\mathbf{K}\) is defined as:

\[ K_{ij} = \frac{\partial y_i}{\partial x_j} \]

where:

  • \(y_i\) is the radiance in detector channel i,
  • \(x_j\) is the j-th element of the state vector.

Physical interpretation

Jacobians quantify:

  • which altitude regions contribute most strongly to a given channel,
  • how sensitive a channel is to temperature or trace gas variations,
  • potential parameter correlations in retrievals.

Large Jacobian magnitudes indicate strong sensitivity.

Output format

Jacobians are typically written as:

  • one file per state-vector component, or
  • matrix-style output if WRITE_MATRIX = 1 is enabled.

The exact layout depends on the application (e.g. kernel, retrieval) and the selected output options.

Averaging kernels

Definition

The averaging kernel matrix \(\mathbf{A}\) describes the sensitivity of the retrieved state to the true atmospheric state:

\[ \mathbf{A} = \frac{\partial \hat{\mathbf{x}}}{\partial \mathbf{x}} \]

Averaging kernels are a central diagnostic in optimal estimation retrieval theory.

Interpretation

Averaging kernels provide information on:

  • vertical resolution of the retrieval,
  • sensitivity to true atmospheric variations,
  • influence of the a priori constraints.

Rows of \(\mathbf{A}\) close to unity indicate good sensitivity, while broader rows indicate vertical smoothing.

Output

Averaging kernels are written by retrieval applications when matrix output is enabled. They are typically stored alongside Jacobians and error covariance matrices.

Retrieval error covariance

Definition

The retrieval error covariance matrix \(\mathbf{S}_x\) quantifies the expected uncertainty of the retrieved atmospheric state:

\[ \mathbf{S}_x = (\mathbf{K}^T \mathbf{S}_\epsilon^{-1} \mathbf{K} + \mathbf{S}_a^{-1})^{-1} \]

Interpretation

Diagonal elements represent variances (squared uncertainties) of the retrieved parameters, while off-diagonal elements describe error correlations.

Error covariance diagnostics are essential for:

  • uncertainty quantification,
  • data assimilation,
  • scientific interpretation of retrieval results.

Cost function and convergence diagnostics

During iterative retrievals, JURASSIC evaluates the optimal-estimation cost function at each iteration.

Typical diagnostic quantities include:

  • total cost function value,
  • measurement contribution,
  • a priori contribution,
  • iteration count and convergence flags.

These diagnostics are usually written to log files or standard output and can be used to assess retrieval stability and convergence behavior.

Contribution functions

Some applications compute contribution functions, which describe the fractional contribution of atmospheric layers to the measured radiance.

Contribution functions are closely related to Jacobians but emphasize radiative transfer rather than retrieval sensitivity.

They are useful for:

  • qualitative interpretation of radiance formation,
  • validation of ray-path and absorption behavior.

Matrix output control

Many diagnostic products are written only when matrix output is explicitly enabled via the control parameter:

  • WRITE_MATRIX

When enabled:

  • Jacobians, averaging kernels, and error covariance matrices are written in a structured, machine-readable format,
  • output files can be large and are intended for post-processing with external tools (e.g. Python, MATLAB).

Practical considerations

  • Diagnostic output can be large; enable it selectively.
  • Always verify that Jacobians are consistent with forward-model behavior when developing new configurations.
  • Compare averaging kernels and error estimates across test cases to ensure retrieval robustness.

Summary

Diagnostic output products in JURASSIC provide essential insight into radiative transfer sensitivities, retrieval performance, and uncertainty characteristics.

These diagnostics are indispensable for advanced users developing new retrieval setups, validating configurations, or interpreting scientific results.