Weather Regimes¶

The concepts behind earthkit.meteo.regimes.

Computing a Regime Index¶

The computation of a regime index by projection onto a regime pattern follows the approach of Michel and Rivière (2011).

Step 1: Compute Anomaly¶

Regime patterns are typically defined as patterns of anomalies, e.g., anomalies of 500 hPa geopotential height or surface pressure. The field from which a regime index is computed by projection must therefore also contain anomalies:

\[X' = X - \overline{X},\]

where \(\overline{X}\) is a climatological reference field for field \(X\) and the subtraction operation is carried out gridpoint-wise.

The climatological reference field is not necessarily a constant. Its values can vary in time to accomodate seasonality. A gridpoint-wise temporal low-pass filter is often additionally applied to the anomaly fields after computation and before projection.

Step 2: Project onto Pattern¶

The projection of \(X'\) onto a regime pattern \(R\) is a weighted sum of their gridpoint-wise product over the domain \(D\) of the regime pattern:

\[P_r = \frac{ \sum_{i \in D} X'_i \cdot R_i \cdot w_i }{ \sum_{i \in D} w_i },\]

where \(w\) is a field of weights. For fields given on a regular latitude-longitude grid, the weights are typically defined as \(w_i = cos(\phi_i)\), where \(\phi\) is latitude.

The regime pattern \(R\) for a regime \(r\) is not necessarily constant. Patterns may vary in time, e.g., to account for changes in anomaly amplitude over the coarse of the year. Regime patterns are therefore implemented as pattern generators in earthkit-meteo.

Step 3: Standardise Projection¶

The standardised regime index for a regime \(r\) is

\[I_r = \frac{ P_r - \overline{\mu_r} }{ \sigma_r },\]

where \(\mu_r\) is the mean and \(\sigma_r\) the standard deviation of the regime index over a reference period.