typhon.oem

Collection of functions concerning the Optimal Estimation Method (OEM).

typhon.oem.averaging_kernel_matrix(K, S_a, S_y)[source]

Calculate the averaging kernel matrix.

Parameters:
  • K (np.array) – Simulated Jacobians.
  • S_a (np.array) – A priori error covariance matrix.
  • S_y (np.array) – Measurement covariance matrix.
Returns:

Averaging kernel matrix.

Return type:

np.array

typhon.oem.error_covariance_matrix(K, S_a, S_y)[source]

Calculate the error covariance matrix.

Parameters:
  • K (np.array) – Simulated Jacobians.
  • S_a (np.array) – A priori error covariance matrix.
  • S_y (np.array) – Measurement covariance matrix.
Returns:

Measurement error covariance matrix.

Return type:

np.array

typhon.oem.retrieval_gain_matrix(K, S_a, S_y)[source]

Calculate the averaging kernel matrix.

Parameters:
  • K (np.array) – Simulated Jacobians.
  • S_a (np.array) – A priori error covariance matrix.
  • S_y (np.array) – Measurement covariance matrix.
Returns:

Retrieval gain matrix.

Return type:

np.array

typhon.oem.retrieval_noise(K, S_a, S_y, e_y)[source]

Return the retrieval noise.

Parameters:
  • K (np.array) – Simulated Jacobians.
  • S_a (np.array) – A priori error covariance matrix.
  • S_y (np.array) – Measurement covariance matrix.
  • e_y (ndarray) – Total measurement error.
Returns:

Retrieval noise.

Return type:

ndarray

typhon.oem.smoothing_error(x, x_a, A)[source]

Return the smoothing error through the averaging kernel.

Parameters:
  • x (ndarray) – Atmospherice profile.
  • x_a (ndarray) – A priori profile.
  • A (ndarray) – Averaging kernel matrix.
Returns:

Smoothing error due to correlation between layers.

Return type:

ndarray