rednoisefit

rednoisefit(dt, a, /, nlag=None, nlag_fit=None, axis=0)[source]

Return the \(e\)-folding autocorrelation timescale for the input autocorrelation spectra along an arbitrary axis. Depending on the length of axis, the timescale is obtained with either of the following two approaches:

  1. Find the \(e\)-folding timescale(s) for the pure red noise autocorrelation spectra \(\exp(-x\Delta t / \tau)\) with the least-squares best fit to the provided spectra.

  2. Assume the process is pure red noise and invert the red noise autocorrelation spectrum at lag 1 to solve for \(\tau = \Delta t / \log a_1\).

Approach 2 is used if the length of the data along axis axis is 1, or the data is scalar. In these cases, the data is assumed to represent just the lag-1 autocorrelation(s).

Parameters

  • dt (float, optional) – The timestep. This is used to scale timescales into physical units.

  • a (array-like) – The autocorrelation spectra.

  • nlag (int, optional) – The number of lag timesteps to include in the curve fitting. Default is all the available lags.

  • nlag_fit (int, optional) – The number of lag timesteps to include in the reconstructed pure red noise autocorrelation spectrum. Default is 50 timesteps.

  • axis (int, optional) – The “lag” dimension. Each slice along this axis should represent an autocorrelation spectrum generated with corr. If the length is 1, the data are assumed to be lag-1 autocorrelations and the timescale is computed from the red noise equation. Otherwise, the timescale is estimated from a least-squares curve fit to a red noise spectrum.

Returns

  • tau (array-like) – The autocorrelation timescales. The shape is the same as data but with axis reduced to length 1.

  • sigma (array-like) – The standard errors. If the timescale was inferred using the lag-1 equation, this is an array of zeros. The shape is the same as tau.

  • bestfit (array-like) – The best fit autocorrelation curves. The shape is the same as data but with axis of length nlag.

Example

>>> import climopy as climo
    auto = climo.autocorr(data, axis=0)
    taus, sigmas = climo.rednoise_fit(auto, axis=0)

See also

corr(), rednoise(), rednoise_spectrum()